Foundations of Computing
Course Materials
Course Outline
The Foundations of Computing provides students with an historical perspective on information technology, introducing the ideas and developments that have been significant in shaping modern technological society, describing and defining computing and computer technology, and looking at the impact of this technology on the contemporary world. The aim is to gain an informed critical perspective from which to assess both the positive and negative aspects of current and future applications of information technology.
The course content provides a general introduction to computing and computer technology by first tracing the historical development of modern technological society and then looking in more detail at information technology and its impact on the modern world. Here we will examine the principles behind modern computer architectures and languages, concentrating on the broader significance of computing in the intellectual, social and economic development of the modern world. Topics covered include:
- Historical roots of technological society
- The nature of scientific investigation
- History of computing
- Theoretical and technical basis of computing
- The impact of information technology on the individual and society
- Computation and intelligence
Topic List
Topic One: A University Education
Lecture Outline:
This introductory lecture asks “What is a university education?” It is intended to challenge the expectation that getting an IT degree is all about acquiring technical expertise in order to get a better job. We look at both Neil Postman’s critique of modern education in Technopoly and Robert Pirsig’s notion of the university as a Church of Reason in his book Zen and the Art of Motorcycle Maintenance (see the attached readings). And, of course, the lecture also provides an overview of the rest of the course.
Foundations Introduction Overheads
Foundations Postman Reading One
Foundations Postman Reading Two
A Framework for Education
From: Postman, Neil. (1992/1993). Technopoly:The Surrender of Culture to Technology. Vintage, London. pp186-195.
[p186] Modern secular education is failing not because it doesn’t teach who Ginger Rogers, Norman Mailer, and a thousand other people are but because it has no moral, social, or intellectual center. There is no set of ideas or attitudes that permeates all parts of the curriculum. The curriculum is not, in fact, a “course of study” at all but a meaningless hodgepodge of subjects. It does not even put forward a clear vision of what constitutes an educated person, unless it is a person who possesses “skills.” In other words, a technocrat’s ideal ‑ a person with no commitment and no point of view but with plenty of marketable skills.
Of course, we must not overestimate the capability of schools to provide coherence in the face of a culture in which almost all coherence seems to have disappeared. In our technicalized, present‑centered information environment, it is not easy to locate a rationale for education, let alone impart one convincingly. It is obvious, for example, that the schools cannot restore religion to the center of the life of learning. With the exception of a few people, perhaps, no one would take seriously the idea that learning is for the greater glory of God. It is equally obvious that the knowledge explosion has blown apart the feasibility of such limited but coordinated curriculums as, for example, a Great Books program. Some people would have us stress love of country as a unifying principle in education. Experience has shown, however, that this invariably translates into love of government, and in practice becomes indistinguishable from what still is at the center of Soviet or Chinese education.
[…] [p187] One obviously treads on shaky ground in suggesting a plausible theme for a diverse, secularized population. Nonetheless, with all due apprehension, I would propose as a possibility the theme that animates Jacob Bronowski’s The Ascent of Man. It is a book, and a philosophy, filled with optimism and suffused with the transcendent belief that humanity’s destiny is the discovery of knowledge. Moreover, although Bronowski’s emphasis is on science, he finds ample warrant to include the arts and humanities as part of our unending quest to gain a unified understanding of nature and our place in it.
Thus, to chart the ascent of man, which I will here call “the ascent of humanity,” we must join art and science. But we must also join the past and the present, for the ascent of humanity is above all a continuous story. It is, in fact, a story of creation, although not quite the one that the fundamentalists fight so fiercely to defend. It is the story of humanity’s creativeness in trying to conquer loneliness, ignorance, and disorder. And it certainly includes the development of various religious systems as a means of giving order and meaning to existence. In this context, it is inspiring to note that the Biblical version of creation, to the astonishment of everyone except possibly the fundamentalists, has turned out to be a near‑perfect blend of artistic imagination and scientific intuition: the Big Bang theory of the creation of the universe, now widely accepted by cosmologists, confirms in essential details what the Bible proposes as having been the case “in the beginning.”
[p188] In any event, the virtues of adopting the ascent of humanity as a scaffolding on which to build a curriculum are many and various, especially in our present situation. For one thing, with a few exceptions which I shall note, it does not require that we invent new subjects or discard old ones. The structure of the subject‑matter curriculum that exists in most schools at present is entirely usable. For another, it is a theme that can begin in the earliest grades and extend through college in ever‑deepening and ‑widening dimensions. Better still, it provides students with a point of view from which to understand the meaning of subjects, for each subject can be seen as a battleground of sorts. an arena in which fierce intellectual struggle has taken place and continues to take place. Each idea within a subject marks the place where someone fell and someone rose. Thus, the ascent of humanity is an optimistic story, not without its miseries but dominated by astonishing and repeated victories. From this point of view, the curriculum itself may be seen as a celebration of human intelligence and creativity, not a meaningless collection of diploma or college requirements.
Best of all, the theme of the ascent of humanity gives us a nontechnical, noncommercial definition of education. It is a definition drawn from an honorable humanistic tradition and reflects a concept of the purposes of academic life that goes counter to the biases of the technocrats. I am referring to the idea that to become educated means to become aware of the origins and growth of knowledge and knowledge systems; to be familiar with the intellectual and creative processes by which the best that has been thought and said has been produced; to learn how to participate, even if as a listener, in what Robert Maynard Hutchins once called The Great Conversation, which is merely a different metaphor for what is meant by the ascent of humanity. You will note that such a definition is not child-centered, not training‑centered, not skill‑centered, not even problem‑centered. It is idea‑centered and coherence‑centered. It [p189] is also otherworldly, inasmuch as it does not assume that what one learns in school must be directly and urgently related to a problem of today. In other words, it is an education that stresses history, the scientific mode of thinking, the disciplined use of language, a wide‑ranging knowledge of the arts and religion, and the continuity of human enterprise. It is education as an excellent corrective to the antihistorical, information‑saturated, technology‑loving character of Technopoly.
Let us consider history first, for it is in some ways the central discipline in all this. It is hardly necessary for me to argue here that, as Cicero put it, “To remain ignorant of things that happened before you were born is to remain a child.” It is enough to say that history is our most potent intellectual means of achieving a “raised consciousness.” But there are some points about history and its teaching that require stressing, since they are usually ignored by our schools. The first is that history is not merely one subject among many that may be taught; every subject has a history, including biology, physics, mathematics, literature, music, and art. I would propose here that every teacher must be a history teacher. To teach, for example, what we know about biology today without also teaching what we once knew, or thought we knew, is to reduce knowledge to a mere consumer product. It is to deprive students of a sense of the meaning of what we know, and of how we know. To teach about the atom without Democritus, to teach about electricity without Faraday, to teach about political science without Aristotle or Machiavelli, to teach about music without Haydn, is to refuse our students access to The Great Conversation. It is to deny them knowledge of their roots, about which no other social institution is at present concerned. For to know about your roots is not merely to know where your grandfather came from and what he had to endure. It is also to know where your ideas come from and why you happen to believe them; to know where your moral and aesthetic sensibilities come from. It is to [p190] know where your world, not just your family, comes from. To complete the presentation of Cicero’s thought, begun above: “What is a human life worth unless it is incorporated into the lives of one’s ancestors and set in an historical context?” By “ancestors” Cicero did not mean your mother’s aunt.
Thus, I would recommend that every subject be taught as history. In this way, children, even in the earliest grades, can begin to understand, as they now do not, that knowledge is not a fixed thing but a stage in human development, with a past and a future. To return for a moment to theories of creation, we want to be able to show how an idea conceived almost four thousand years ago has traveled not only in time but in meaning, from science to religious metaphor to science again. What a lovely and profound coherence there is in the connection between the wondrous speculations in an ancient Hebrew desert tent and the equally wondrous speculations in a modem MIT classroom! What I am trying to say is that the history of subjects teaches connections; it teaches that the world is not created anew each day, that everyone stands on someone else’s shoulders.
I am well aware that this approach to subjects would be difficult to use. There are, at present, few texts that would help very much, and teachers have not, in any case, been prepared to know about knowledge in this way. Moreover, there is the added difficulty of our learning how to do this for children of different ages. But that it needs to be done is, in my opinion, beyond question.
The teaching of subjects as studies in historical continuities is not intended to make history as a special subject irrelevant. If every subject is taught with a historical dimension, the history teacher will be free to teach what histories are: hypotheses and theories about why change occurs. In one sense, there is no such thing as “history,” for every historian from Thucydides to Toynbee has known that his stories must be told from a special [p191] point of view that will reflect his particular theory of social development. And historians also know that they write histories for some particular purpose more often than not, either to glorify or to condemn the present. There is no definitive history of anything; there are only histories, human inventions which do not give us the answer, but give us only those answers called forth by the questions that have been asked.
Historians know all of this ‑ it is a commonplace idea among them. Yet it is kept a secret from our youth. Their ignorance of it prevents them from understanding how “history” can change and why the Russians, Chinese, American Indians, and virtually everyone else see historical events differently than the authors of history schoolbooks. The task of the history teacher, then, is to become a “histories teacher.” This does not mean that some particular version of the American, European, or Asian past should remain untold. A student who does not know at least one history is in no position to evaluate others. But it does mean that a histories teacher will be concerned, at all times, to show how histories are themselves products of culture; how any history is a mirror of the conceits and even metaphysical biases of the culture that produced it; how the religion, politics, geography, and economy of a people lead them to re‑create their past along certain lines. The histories teacher must clarify for students the meaning of “objectivity” and “events,” must show what a “point of view” and a “theory” are, must provide some sense of how histories may be evaluated. […]
[p192] Whatever events may be included in the study of the past, the worst thing we can do is to present them devoid of the coherence that a theory or theories can provide that is to say, as meaningless. This, we can be sure, Technopoly does daily. The histories teacher must go far beyond the “event” level into the realm of concepts, theories, hypotheses, comparisons, deductions, evaluations. The idea is to raise the level of abstraction at which “history” is taught. This idea would apply to all subjects, including science.
From the point of view of the ascent of humanity, the scientific enterprise is one of our most glorious achievements. On humanity’s Judgment Day we can be expected to speak almost at once of our science. I have already stressed the importance of teaching the history of science in every science course, but this is no more important than teaching its “philosophy.” I mention this with some sense of despair. More than half the high schools in the United States do not even offer one course in physics. And at a rough guess, I would estimate that in 90 percent of the schools chemistry is still taught as if students were being trained to be druggists. To suggest, therefore, that science is an exercise in human imagination, that it is something quite different from technology, that there are “philosophies” of science, and that all of this ought to form part of a scientific [p193] education, is to step out of the mainstream. But I believe it nonetheless.
Would it be an exaggeration to say that not one student in fifty knows what “induction” means? Or knows what a scientific theory is? Or a scientific model? Or knows what are the optimum conditions of a valid scientific experiment? Or has ever considered the question of what scientific truth is? In The Identity of Man Bronowski says the following: “This is the paradox of imagination in science, that it has for its aim the impoverishment of imagination. By that outrageous phrase, I mean that the highest flight of scientific imagination is to weed out the proliferation of new ideas. In science, the grand view is a miserly view, and a rich model of the universe is one which is as poor as possible in hypotheses.”
Is there one student in a hundred who can make any sense out of this statement? Though the phrase “impoverishment of imagination” may be outrageous, there is nothing startling or even unusual about the idea contained in this quotation. Every practicing scientist understands what Bronowski is saying. Yet it is kept a secret from our students. It should be revealed. In addition to having each science course include a serious histories dimension, I would propose that every school – elementary through college – offer and require a course in the philosophy of science. Such a course should consider the language of science, the nature of scientific proof, the source of scientific hypotheses, the role of imagination, the conditions of experimentation, and especially the value of error and disproof. If I am not mistaken, many people still believe that what makes a statement scientific is that it can be verified. In fact, exactly the opposite is the case: What separates scientific statements from nonscientific statements is that the former can be subjected to the test of falsifiability. What makes science possible is not our ability to recognize “truth” but our ability to recognize falsehood.
[p194] What such a course would try to get at is the notion that science is not pharmacy or technology or magic tricks but a special way of employing human intelligence. It would be important for students to learn that one becomes scientific not by donning a white coat (which is what television teaches) but by practicing a set of canons of thought, many of which have to do with the disciplined use of language. Science involves a method of employing language that is accessible to everyone. The ascent of humanity has rested largely on that.
On the subject of the disciplined use of language, I should like to propose that, in addition to courses in the philosophy of science, every school ‑ again, from elementary school through college – offer a course in semantics ‑ in the processes by which people make meaning. In this connection I must note the gloomy fact that English teachers have been consistently obtuse in their approach to this subject ‑ which is to say, they have largely ignored it. This has always been difficult for me to understand, since English teachers claim to be concerned with teaching reading and writing. But if they do not teach anything about the relationship of language to reality ‑ which is what semantics studies ‑ I cannot imagine how they expect reading and writing to improve.
Every teacher ought to be a semantics teacher, since it is not possible to separate language from what we call knowledge. Like history, semantics is an interdisciplinary subject: it is necessary to know something about it in order to understand any subject. But it would be extremely useful to the growth of their intelligence if our youth had available a special course in which fundamental principles of language were identified and explained. Such a course would deal not only with the various uses of language but with the relationship between things and words, symbols and signs, factual statements and judgments, and grammar and thought. Especially for young students, the course ought to emphasize the kinds of semantic errors that are [p195] common to all of us, and that are avoidable through awareness and discipline – the use of either‑or categories, misunderstanding of levels of abstraction, confusion of words with things, sloganeering, and self‑reflexiveness.
Of all the disciplines that might be included in the curriculum, semantics is certainly among the most “basic.” Because it deals with the processes by which we make and interpret meaning, it has great potential to affect the deepest levels of student intelligence. And yet semantics is rarely mentioned when “back to the basics” is proposed. Why? My guess is that it cuts too deep. To adapt George Orwell, many subjects are basic but some are more basic than others. Such subjects have the capability of generating critical thought and of giving students access to questions that get to the heart of the matter. This is not what “back to the basics” advocates usually have in mind. They want language technicians: people who can follow instructions, write reports clearly, spell correctly. There is certainly ample evidence that the study of semantics will improve the writing and reading of students. But it invariably does more. It helps students to reflect on the sense and truth of what they are writing and of what they are asked to read. It teaches them to discover the underlying assumptions of what they are told. It emphasizes the manifold ways in which language can distort reality. It assists students in becoming what Charles Weingartner and I once called “crap‑detectors.” Students who have a firm grounding in semantics are therefore apt to find it difficult to take reading tests. A reading test does not invite one to ask whether or not what is written is true. Or, if it is true, what it has to do with anything. The study of semantics insists upon these questions. But “back to the basics” advocates don’t require education to be that basic. Which is why they usually do not include literature, music, and art as part of their agenda either. But of course, in using the ascent of humanity as a theme, we would of necessity elevate these subjects to prominence.
Foundations Pirsig Reading One
The Church of Reason
From: Pirsig, Robert M. (1974/1991). Zen and the Art of Motorcycle Maintenance: An Inquiry into Values. Vintage, London. pp150-155.
[p150] The school was what could euphemistically be called a ‘teaching college.’ At a teaching college you teach and you teach and you teach with no time for research, no time for contemplation, no time for participation in outside affairs. Just teach and teach and teach until your mind grows dull and your creativity vanishes and you become an automaton saying the same dull things over and over to endless waves of innocent students who cannot understand why you are so dull, lose respect and fan this disrespect out into the community. The reason you teach and you teach and you teach is that this is a very clever way of running a college on the cheap while giving a false appearance of genuine education.
Yet despite this he called the school by a name that didn’t make much sense, in fact sounded a little ludicrous in view of its actual nature. But the name had great meaning to him, and he stuck to it and he felt, before he left, that he had rammed it into a few minds sufficiently hard to make it stick. He called it a ‘Church of Reason,’ and much of the puzzlement people had about him could have ended if they’d understood what he meant by this.
The state of Montana at this time was undergoing an outbreak of ultra‑right‑wing politics like that which occurred in Dallas, Texas, just prior to President Kennedy’s assassination. A nationally known professor from the University of Montana at Missoula was prohibited from speaking on campus on the grounds that it would ‘stir up trouble.’ Professors were told that all public statements must be cleared through the college public‑relations office before they could be made.
Academic standards were demolished. The legislature had previously prohibited the school from refusing entry to any [p151] student over twenty‑one whether he had a high‑school diploma or not. Now the legislature had passed a law fining the college eight thousand dollars for every student who failed, virtually an order to pass every student.
The newly elected governor was trying to fire the college president for both personal and political reasons. The college president was not only a personal enemy, he was a Democrat, and the governor was no ordinary Republican. His campaign manager doubled as state coordinator for the John Birch Society. This was the same governor who supplied the list of fifty subversives we heard about a few days ago.
Now, as part of this vendetta, funds to the college were being cut. The college president had passed on an unusually large part of the cut to the English department, of which Phaedrus was a member, and whose members had been quite vocal on issues of academic freedom.
Phaedrus had given up, was exchanging letters with the Northwest Regional Accrediting Association to see if they could help prevent these violations of accreditation requirements. In addition to this private correspondence he had publicly called for an investigation of the entire school situation.
At this point some students in one of his classes had asked Phaedrus, bitterly, if his efforts to stop accreditation meant he was trying to prevent them from getting an education.
Phaedrus said no.
Then one student, apparently a partisan of the governor, said angrily that the legislature would prevent the school from losing its accreditation.
Phaedrus asked how.
The student said they would post police to prevent it.
Phaedrus pondered this for a while, then realized the enormity of the student’s misconception of what accreditation was all about.
That night, for the next day’s lecture, he wrote out his defense of what he was doing. This was the Church of Reason lecture, which, in contrast to his usual sketchy lecture notes, was very long and very carefully elaborated.
It began with reference to a newspaper article about a [p152] country church building with an electric beer sign hanging right over the front entrance. The building had been sold and was being used as a bar. One can guess that some classroom laughter started at this point. The college was well‑known for drunken partying and the image vaguely fitted. The article said a number of people had complained to the church officials about it. It had been a Catholic church, and the priest who had been delegated to respond to the criticism had sounded quite irritated about the whole thing. To him it had revealed an incredible ignorance of what a church really was. Did they think that bricks and boards and glass constituted a church? Or the shape of the roof? Here, posing as piety was an example of the very materialism the church opposed. The building in question was not holy ground. It had been desanctified. That was the end of it. The beer sign resided over a bar, not a church, and those who couldn’t tell the difference were simply revealing something about themselves.
Phaedrus said the same confusion existed about the University and that was why loss of accreditation was hard to understand. The real University is not a material object. It is not a group of buildings that can be defended by police. He explained that when a college lost its accreditation, nobody came and shut down the school. There were no legal penalties, no fines, no jail sentences. Classes did not stop. Everything went on just as before. Students got the same education they would if the school didn’t lose its accreditation. All that would happen, Phaedrus said, would simply be an official recognition of a condition that already existed. It would be similar to excommunication. What would happen is that the real University, which no legislature can dictate to and which can never be identified by any location of bricks or boards or glass, would simply declare that this place was no longer ‘holy ground.’ The real University would vanish from it, and all that would be left was the bricks and the books and the material manifestation.
It must have been a strange concept to all of the students, and I can imagine him waiting for a long time for it to sink in, and perhaps then waiting for the question, What do you think the real University is?
[p153] His notes, in response to this question, state the following: The real University, he said, has no specific location. It owns no property, pays no salaries and receives no material dues. The real University is a state of mind. It is that great heritage of rational thought that has been brought down to us through the centuries and which does not exist at any specific location. It’s a state of mind which is regenerated throughout the centuries by a body of people who traditionally carry the title of professor, but even that title is not part of the real University. The real University is nothing less than the continuing body of reason itself.
In addition to this state of mind, ‘reason,’ there’s a legal entity which is unfortunately called by the same name but which is quite another thing. This is a nonprofit corporation, a branch of the state with a specific address. It owns property, is capable of paying salaries, of receiving money and of responding to legislative pressures in the process.
But this second university, the legal corporation, cannot teach, does not generate new knowledge or evaluate ideas. It is not the real University at all. It is just a church building, the setting, the location at which conditions have been made favorable for the real church to exist.
Confusion continually occurs in people who fail to see this difference, he said, and think that control of the church buildings implies control of the church. They see professors as employees of the second university who should abandon reason when told to and take orders with no backtalk, the same way employees do in other corporations.
They see the second university, but fall to see the first.
I remember reading this for the first time and remarking about the analytic craftsmanship displayed. He avoided splitting the University into fields or departments and dealing with the results of that analysis. He also avoided the traditional split into students, faculty and administration. When you split it either of those ways you get a lot of dull stuff that doesn’t really tell you much you can’t get out of the official school bulletin. But Phaedrus split it between ‘the church’ and ‘the location,’ and once this cleavage is made the same rather dull and imponderable institution seen in the bulletin suddenly is [p154] seen with a degree of clarity that wasn’t previously available. On the basis of this cleavage he provided explanations for a number of puzzling but normal aspects of University life.
After these explanations he returned to the analogy of the religious church. The citizens who build such a church and pay for it probably have in mind that they’re doing this for the community. A good sermon can put the parishioners in a right frame of mind for the coming week. Sunday school will help the children grow up right. The minister who delivers the sermon and directs the Sunday school understands these goals and normally goes along with them, but he also knows that his primary goals are not to serve the community. His primary goal is always to serve God. Normally there’s no conflict but occasionally one creeps in when trustees oppose the minister’s sermons and threaten reduction of funds. That happens.
A true minister, in such situations, must act as though he’d never heard the threats. His primary goal isn’t to serve the members of the community, but always God.
The primary goal of the Church of Reason, Phaedrus said, is always Socrates’s old goal of truth, in its ever‑changing forms, as it’s revealed by the process of rationality. Everything else is subordinate to that. Normally this goal is in no conflict with the location goal of improving the citizenry, but on occasion some conflict arises, as in the case of Socrates himself. It arises when trustees and legislators who’ve contributed large amounts of time and money to the location take points of view in opposition to the professors’ lectures or public statements. They can then lean on the administration by threatening to cut off funds if the professors don’t say what they want to hear. That happens too.
True churchmen in such situations must act as though they had never heard these threats. Their primary goal never is to serve the community ahead of everything else. Their primary goal is to serve, through reason, the goal of truth.
That was what he meant by the Church of Reason. There was no question but that it was a concept that was deeply felt by him. He was regarded as something of a troublemaker but was never censured for it in any proportion to the amount [p155] of trouble he made. What saved him from the wrath of everyone around him was partly an unwillingness to give any support to the enemies of the college, but also partly a begrudging understanding that all of his troublemaking was ultimately motivated by a mandate they were never free from themselves: the mandate to speak the rational truth.
Foundations Pirsig Reading Two
University and Education
From: Pirsig, Robert M. (1974/1991). Zen and the Art of Motorcycle Maintenance: An Inquiry into Values. Vintage, London. pp194-203.
[p194] He’d been having trouble with students who had nothing to say. At first he thought it was laziness but later it became apparent that it wasn’t. They just couldn’t think of anything to say.
One of them, a girl with strong‑lensed glasses, wanted to write a five‑hundred‑word essay about the United States. He was used to the sinking feeling that comes from statements like this, and suggested without disparagement that she narrow it down to just Bozeman.
When the paper came due she didn’t have it and was quite upset. She had tried and tried but she just couldn’t think of anything to say.
He had already discussed her with her previous instructor and they’d confirmed his impressions of her. She was very serious, disciplined and hardworking, but extremely dull. Not a spark of creativity in her anywhere. Her eyes, behind the [p195] thick‑lensed glasses, were the eyes of a drudge. She wasn’t bluffing him, she really couldn’t think of anything to say, and was upset by her inability to do as she was told.
It just stumped him. Now he couldn’t think of anything to say. A silence occurred, and then a peculiar answer: ‘Narrow it down to the main street of Bozeman.’ It was a stroke of insight.
She nodded dutifully and went out. But just before her next class she came back in real distress, tears this time, distress that had obviously been there for a long time. She still couldn’t think of anything to say, and couldn’t understand why, if she couldn’t think of anything about all of Bozeman, she should be able to think of something about just one street.
He was furious. ‘You’re not looking!’ he said. A memory came back of his own dismissal from the University for having too much to say. For every fact there is an infinity of hypotheses. The more you look the more you see. She really wasn’t looking and yet somehow she didn’t understand this.
He told her angrily, ‘Narrow it down to the front of one building on the main street of Bozeman. The Opera House. Start with the upper left‑hand brick.’
Her eyes, behind the thick‑lensed glasses, opened wide.
She came in the next class with a puzzled look and handed him a five‑thousand‑word essay on the front of the Opera House on the main street of Bozeman, Montana. ‘I sat in the hamburger stand across the street,’ she said, ‘and started writing about the first brick, and the second brick, and then by the third brick it all started to come and I couldn’t stop. They thought I was crazy, and they kept kidding me, but here it all is. I don’t understand it.’
Neither did he, but on long walks through the streets of town he thought about it and concluded she was evidently stopped with the same kind of blockage that had paralyzed him on his first day of teaching. She was blocked because she was trying to repeat, in her writing, things she had already heard, just as on the first day he had tried to repeat things he had already decided to say. She couldn’t think of anything to write about Bozeman because she couldn’t recall [p196] anything she had heard worth repeating. She was strangely unaware that she could look and see freshly for herself, as she wrote, without primary regard for what had been said before. The narrowing down to one brick destroyed the blockage because it was so obvious she had to do some original and direct seeing.
He experimented further. In one class he had everyone write all hour about the back of his thumb. Everyone gave him funny looks at the beginning of the hour, but everyone did it, and there wasn’t a single complaint about ‘nothing to say.’
In another class he changed the subject from the thumb to a coin, and got a full hour’s writing from every student. In other classes it was the same. Some asked, ‘Do you have to write about both sides?’ Once they got into the idea of seeing directly for themselves they also saw there was no limit to the amount they could say. It was a confidence‑building assignment too, because what they wrote, even though seemingly trivial, was nevertheless their own thing, not a mimicking of someone else’s. Classes where he used that coin exercise were always less balky and more interested.
As a result of his experiments he concluded that imitation was a real evil that had to be broken before real rhetoric teaching could begin. This imitation seemed to be an external compulsion. Little children didn’t have it. It seemed to come later on, possibly as a result of school itself.
That sounded right, and the more he thought about it the more right it sounded. Schools teach you to imitate. If you don’t imitate what the teacher wants you get a bad grade. Here, in college, it was more sophisticated, of course; you were supposed to imitate the teacher in such a way as to convince the teacher you were not imitating, but taking the essence of the instruction and going ahead with it on your own. That got you A’s. Originality on the other hand could get you anything from A to F. The whole grading system cautioned against it.
He discussed this with a professor of psychology who lived next door to him, an extremely imaginative teacher, who said, [p197] ‘Right. Eliminate the whole degree‑and‑grading system and then you’ll get real education.’
Phaedrus thought about this, and when weeks later a very bright student couldn’t think of a subject for a term paper, it was still on his mind, so he gave it to her as a topic. She didn’t like the topic at first, but agreed to take it anyway.
Within a week she was talking about it to everyone, and within two weeks had worked up a superb paper. The class she delivered it to didn’t have the advantage of two weeks to think about the subject, however, and was quite hostile to the whole idea of eliminating grades and degrees. This didn’t slow her down at all. Her tone took on an old‑time religious fervor. She begged the other students to listen, to understand this was really right. ‘I’m not saying this for him,’ she said and glanced at Phaedrus. ‘It’s for you.’
Her pleading tone, her religious fervor, greatly impressed him, along with the fact that her college entrance examinations had placed her in the upper one percent of the class. During the next quarter, when teaching ‘persuasive writing,’ he chose this topic as a ‘demonstrator,’ a piece of persuasive writing he worked up by himself, day by day, in front of and with the help of the class.
He used the demonstrator to avoid talking in terms of principles of composition, all of which he had deep doubts about. He felt that by exposing classes to his own sentences as he made them, with all the misgivings and hang‑ups and erasures, he would give a more honest picture of what writing was like than by spending class time picking nits in completed student work or holding up the completed work of masters for emulation. This time he developed the argument that the whole grading system and degree should be eliminated, and to make it something that truly involved the students in what they were hearing, he withheld all grades during the quarter.
[…] [p198] Phaedrus’s argument for the abolition of the degree‑and‑grading system produced a nonplussed or negative reaction in all but a few students at first, since it seemed, on first judgement, to destroy the whole University system. One student laid it wide open when she said with complete candor, ‘Of course you can’t eliminate the degree and grading system. After all, that’s what we’re here for.’
She spoke the complete truth. The idea that the majority of students attend a university for an education independent of the degree and grades is a little hypocrisy everyone is happier not to expose. Occasionally some students do arrive for an education but rote and the mechanical nature [p199] of the institution soon converts them to a less idealistic attitude.
The demonstrator was an argument that elimination of grades and degrees would destroy this hypocrisy. Rather than deal with generalities it dealt with the specific career of an imaginary student who more or less typified what was found in the classroom, a student completely conditioned to work for a grade rather than for the knowledge the grade was supposed to represent.
Such a student, the demonstrator hypothesized, would go to his first class, get his first assignment and probably do it out of habit. He might go to his second and third as well. But eventually the novelty of the course would wear off and, because his academic life was not his only life, the pressure of other obligations or desires would create circumstances where he just would not be able to get an assignment in.
Since there was no degree or grading system he would incur no penalty for this. Subsequent lectures which presumed he’d completed the assignment might be a little more difficult to understand, however, and this difficulty, in turn, might weaken his interest to a point where the next assignment, which he would find quite hard, would also be dropped. Again no penalty.
In time his weaker and weaker understanding of what the lectures were about would make it more and more difficult for him to pay attention in class. Eventually he would see he wasn’t learning much; and facing the continual pressure of outside obligations, he would stop studying, feel guilty about this and stop attending class. Again, no penalty would be attached.
But what had happened? The student, with no hard feelings on anybody’s part, would have flunked himself out. Good! This is what should have happened. He wasn’t there for a real education in the first place and had no real business there at all. A large amount of money and effort had been saved and there would be no stigma of failure and ruin to haunt the rest of his life. No bridges had been burned.
The student’s biggest problem was a slave mentality which had been built into by years of carrot‑and‑whip grading, a [p200] mule mentality which said, ‘If you don’t whip me, I won’t work.’ He didn’t get whipped. He didn’t work. And the cart of civilization, which he supposedly was being trained to pull, was just going to have to creak along a little slower without him.
This is a tragedy, however, only if you presume that the cart of civilization, ‘the system,’ is pulled by mules. This is a common, vocational, ‘location’ point of view, but it’s not the Church attitude.
The Church attitude is that civilization, or ‘the system’ or ‘society’ or whatever you want to call it, is best served not by mules but by free men. The purpose of abolishing grades and degrees is not to punish mules or to get rid of them but to provide an environment in which that mule can turn into a free man.
The hypothetical student, still a mule, would drift around for a while. He would get another kind of education quite as valuable as the one he’d abandoned, in what used to be called the ‘school of hard knocks.’ Instead of wasting money and time as a high‑status mule, he would now have to get a job as a low‑status mule, maybe as a mechanic. Actually his real status would go up. He would be making a contribution for a change. Maybe that’s what he would do for the rest of his life. Maybe he’d found his level. But don’t count on it.
In time ‑ six months; five years, perhaps ‑ a change could easily begin to take place. He would become less and less satisfied with a kind of dumb, day‑to‑day shopwork. His creative intelligence, stifled by too much theory and too many grades in college, would now become reawakened by the boredom of the shop. Thousands of hours of frustrating mechanical problems would have made him more interested in machine design. He would like to design machinery himself. He’d think he could do a better job. He would try modifying a few engines, meet with success, look for more success, but feel blocked because he didn’t have the theoretical information. He would discover that when before he felt stupid because of his lack of interest in theoretical information, he’d now find a brand of theoretical information which he’d have a lot of respect for, namely, mechanical engineering.
[p201] So he would come back to our degreeless and gradeless school, but with a difference. He’d no longer be a grade-motivated person. He’d be a knowledge‑motivated person. He would need no external pushing to learn. His push would come from inside. He’d be a free man. He wouldn’t need a lot of discipline to shape him up. In fact, if the instructors assigned him were slacking on the job he would be likely to shape them up by asking rude questions. He’d be there to learn something, would be paying to learn something and they’d better come up with it.
Motivation of this sort, once it catches hold, is a ferocious force, and in the gradeless, degreeless institution where our student would find himself, he wouldn’t stop with rote engineering information. Physics and mathematics were going to come within his sphere of interest because he’d see he needed them. Metallurgy and electrical engineering would come up for attention. And, in the process of intellectual maturing that these abstract studies gave him, he would be likely to branch out into other theoretical areas that weren’t directly related to machines but had become a part of a newer larger goal. This larger goal wouldn’t be the imitation of education in Universities today, glossed over and concealed by grades and degrees that give the appearance of something happening when, in fact, almost nothing is going on. It would be the real thing.
Such was Phaedrus’s demonstrator, his unpopular argument, and he worked on it all quarter long, building it up and modifying it, arguing for it, defending it. All quarter long papers would go back to the students with comments but no grades, although the grades were entered in a book.
As I said before, at first almost everyone was sort of nonplussed. The majority probably figured they were stuck with some idealist who thought removal of grades would make them happier and thus work harder, when it was obvious that without grades everyone would just loaf. Many of the students with A records in previous quarters were contemptuous and angry at first, but because of their acquired self‑discipline went ahead and did the work anyway. The B students and high‑C students missed some of the early [p202] assignments or turned in sloppy work. Many of the low‑C and D students didn’t even show up for class. At this time another teacher asked him what he was going to do about this lack of response.
‘Outwait them,’ he said.
His lack of harshness puzzled the students at first, then made them suspicious. Some began to ask sarcastic questions. These received soft answers and the lectures and speeches proceeded as usual, except with no grades.
Then a hoped‑for phenomenon began. During the third or fourth week some of the A students began to get nervous and started to turn in superb work and hang around after class with questions that fished for some indication as to how they were doing. The B and high‑C students began to notice this and work a little and bring up the quality of their papers to a more usual level. The low C, D and future F’s began to show up for class just to see what was going on.
After midquarter an even more hoped‑for phenomenon took place. The A‑rated students lost their nervousness and became active participants in everything that went on with a friendliness that was uncommon in a grade‑getting class. At this point the B and C students were in a panic, and turned in stuff that looked as though they’d spent hours of painstaking work on it. The D’s and F’s turned in satisfactory assignments.
In the final weeks of the quarter, a time when normally everyone knows what his grade will be and just sits back half asleep, Phaedrus was getting a kind of class participation that made other teachers take notice. The B’s and C’s had joined the A’s in friendly free‑for‑all discussion that made the class seem like a successful party. Only the D’s and F’s sat frozen in their chairs, in a complete internal panic.
The phenomenon of relaxation and friendliness was explained later by a couple of students who told him, ‘A lot of us got together outside of class to try to figure out how to beat this system. Everyone decided the best way was just to figure you were going to fail and then go ahead and do what you could anyway. Then you start to relax. Otherwise you go out of your mind!’
[p203] The students added that once you got used to it it wasn’t so bad, you were more interested in the subject matter, but repeated that it wasn’t easy to get used to.
At the end of the quarter the students were asked to write an essay evaluating the system. None of them knew at the time of writing what his or her grade would be. Fifty‑four percent opposed it. Thirty‑seven percent ‑ favored it. Nine percent were neutral.
On the basis of one man, one vote, the system was very unpopular. The majority of students definitely wanted their grades as they went along. But when Phaedrus broke down the returns according to the grades that were in his book ‑ and the grades were not out of line with grades predicted by previous classes and entrance evaluations ‑ another story was told. The A students were 2 to I in favor of the system. The B and C students were evenly divided. And the D’s and F’s were unanimously opposed!
This surprising result supported a hunch he had had for a long time: that the brighter, more serious students were the least desirous of grades, possibly because they were more interested in the subject matter of the course, whereas the dull or lazy students were the most desirous of grades, possibly because grades told them if they were getting by.
Topic Two: Early Mathematical Foundations
Lecture Objective:
To gain an understanding of the idea of a number, a state, a number system and a mathematical proof procedure, and to gain an overview of the foundational contributions of Greek civilisation in the development of the modern world.
Overview of Topics:
- The Idea of a State
- The Origins of Number
- Egyptian and Babylonian Number Systems
- The Greeks
- Mathematical Proof
- The Classical Legacy
The lecture is based on Chapter 1 of The Foundations of Computing and the Information Technology Age.
Foundations Topic 2 Overheads
Foundations Book Chapter 1
Foundations Topic 2 Tutorial
Foundations Koestler Reading One
Foundations Koestler Reading Two
Topic Three: The Birth of the Modern Era
Lecture Objective:
To gain a basic understanding of the evolution of science, computation and mathematics from the fall of Rome in 476 CE to the scientific revolution of the 17th and 18th centuries.
Overview of Topics:
- The Hindu-Arabic Number System
- The Renaissance
- The Science of Aristotle
- The Scientific Revolution
- Pre-Mechanised Computation
- Mathematical Breakthroughs
The lecture is based on Chapter 2 of The Foundations of Computing and the Information Technology Age.
Foundations Topic 3 Overheads
Foundations Book Chapter 2
Foundations Topic 3 Tutorial
Foundations Ifrah Reading One
The Beginnings of Automatic Calculation
From: Ifrah, Georges. (2001). The Universal History of Computing: From the Abacus to the Quantum Computer. John Wiley and Sons, Inc: New York. pp108-121.
[p108]
THE GREAT SYNTHESIS FROM WHICH EMERGED THE COMPUTER
Clearly, therefore, the development of computers was a revolution in the history of our civilisation. However, it did not come about at the wave of a magic wand, nor did it result from the solitary work of some inventor of genius. Nor, in historical reality, does it make sense to talk of “the invention of the computer” as the common phrase would have it. Instead, the computer came about as the result of the confluence of a multitude of streams whose sources are ancient and widely separated, and from a long and concentrated succession of reflections and responses to needs (see Fig. 5.2).
First and foremost, this revolution is the fruit of everlasting contributions by a multitude of scholars, philosophers, visionaries, inventors, engineers, mathematicians, physicists, and technicians from every corner of the world and from every period of history. The movement principally began to take on form during the Industrial Revolution of the nineteenth century. Subsequently, it became philosophically and intellectually [p109] plausible with the spread of machines and automation. Then it became seen as theoretically possible as a result of more recent advances in symbolic logic and the science of mathematics, and it became technically achievable through the technological revolution of the twentieth century.
Finally, it became a concrete reality owing to the emergence and expansion of industrialised societies which were stimulated by vision, by need, by experience, by competence and by competition, under pressures from many directions ‑ social, economic, commercial, scientific, even and crucially the political and military urgency during the Second World War to oppose Nazism.
In short, computers emerged as the materialisation of multitudinous dreams and desires, through a gigantic synthesis which gathered up a cascade of inventions and innovations at the moment when a long slow evolution had come to term, whose beginnings date back to the dawn of time.
In the history that follows in this chapter, do not suppose that the important ideas here set out were originally expressed as precisely as you will see them written. They indeed became clearly established over the generations, but in a diffuse, uncoordinated way. As Bertrand Gille emphasises: “The historian is always somewhat at a loss in speaking of his own times. He lacks the possibility to stand back from events, and often fears that he will misunderstand them, weigh up the phenomena incorrectly, and misjudge the signs to be found in the world around us now.”
So I have, over many years, hesitated long and often before publishing the account which follows. I have held back for so long as the ideas which I expressed were still no better structured than the accounts in sundry ”static” histories, mere accumulations of fact but not co‑ordinated on the historical scale, great though their contribution has been in terms of information and documentation. To paraphrase Henri Poincare’s words on science: it is true that history is built up of facts, as a house is built of stones; but an accumulation of facts is no more a history than a heap of stones is a house (cf. La science et l’hypothese4).
In mitigation of this charge against traditional histories of information science, which often set out their facts neither structured nor classified, it must be acknowledged that at the times of their writing they could not but reflect the current state of a discipline which was still unsynthesised and disorganised.
In fact, if it is possible now to bring out a coherent account of matters (which would certainly have been impossible two or three decades ago), it
4 Translated as Science and Hypothesis (Walter Scott Publishing Company, 1905), and republished in 1952 ‑, Dover Publications Inc. (see p. 141). [Transl.]
[p110] is because at the present time we are passing through a phase where we can indeed stand back from events, and in which the maturation and synthesis of the many concepts involved now begin to let “information science” be perceived as a discipline worthy to be called a science.
2. Pre‑Renaissance Obstacles to Mechanical Calculation and the Beginnings of the Breakthrough
THE BEGINNINGS OF ARTIFICIAL CALCULATION
The origins of the computer can be found in the European Renaissance, when astronomers and mathematicians encountered the need to carry out calculations which, as a result of developments in mathematics, science and technology, had become much longer, more complicated, and more difficult than before.
At the same time, then, as the Indian number‑system and the Indian methods of arithmetic had, in the sixteenth century, finally supplanted the old numerals and counter‑boards which dated back to Roman times, European scholars found themselves obliged to seek yet further efficacy in calculation. If they could not altogether avoid manual methods, at least they sought ways of making calculation less heavy, more rapid, and more reliable.
The Indian methods, for all their ingenuity and despite the great simplification which they had brought about, were nevertheless quite inadequate for these purposes. In long or complex procedures, these methods ‑ as they are commonly employed to our own day ‑ are relatively slow, and demand continual conscious attention to detail: they are therefore tedious, they soon become monotonous, and they allow much opportunity for error. In calculation, every operation executed by a human can lead to an error of mental arithmetic, to an error in reading a number, to an error in copying numbers from one row of a table of calculations to another, or from one column to another. Since these errors may pass unnoticed at the moment they are made, and may subsequently hide unseen in the mass of working, they can only be corrected by repeating the whole calculation, perhaps using a different method, until the same answer has been obtained sufficiently often to give confidence that it is right. [p111]
THE EARLIEST ARTIFICIAL AIDS TO HUMAN CALCULATION
There are various arithmetical instruments which can be found amongst the very earliest material tools intended to lend support to human calculation. Devised to lighten the work of simple arithmetic, they worked directly with digital representations of numbers, and could give their results after a few simple manipulative operations. We point out, in passing, that in contrast to the ancient types of calculating apparatus such as the abacus ‑ which had been devised to compensate for the inadequacy of ancient written number‑systems which were not directly adapted to arithmetical operations ‑ the devices we are about to discuss were created to compensate for the inadequacies of human beings, engaged in calculations, who nevertheless were already using the modern number system ‑ nine digits and a zero ‑ created by the Indians.
One of the most famous examples from this early period was the invention of “Napier’s bones” (or “rods”), as they were called, in 1617, by the Scottish mathematician John Napier (1550‑1617) of Merchiston (near Edinburgh). A set of Napier’s bones consisted of ten wooden rods, of square cross‑section. Each of the four sides of each rod corresponded to one of the digits from 0 to 9, and marked down its length, in nine divisions, were the multiples of the corresponding digit (with, for two‑digit multiples, the two digits separated by a diagonal line). It was therefore a kind of multiplication table for the digits and, when the rods corresponding to the digits of a number were placed side by side, the result of the multiplication of that number by a digit could be read off horizontally. Multiplication of one number by another could therefore be achieved by using the rods to read off the partial products corresponding to the digits of the second number. Economical, exact and reliable in use, this method of easing the labour of multiplication had a great success in Europe which endured even to the start of the twentieth century.
Napier’s bones were not, of course, the only example of such devices. Since Napier’s time a great variety have been devised and constructed, ranging from the simple slide rule to much more elaborate mechanisms which facilitated not only multiplication and division, but even the extraction of square roots. We may mention the adding machines of Caze (1720), of Perrault (1666) and of Kummer (1847); the arithmographs of Troncet (beginning of twentieth century) and of Clabor (1906); Samuel Morland’s multiplicator (1666); Michel Roos’s instrument (1869) which consisted of an ingenious combination of a Chinese abacus with a cylindrical form of Napier’s bones; the arithmetical rods of Lucas and Genaille [p112] (beginning of twentieth century); General Sebert’s adder‑multiplier (1918); Leon Bollee’s ingenious multiplying and dividing machine (1893); etc.
THE REAL PROBLEM OF MECHANISING ARITHMETIC
Devices like those mentioned above were not true calculating machines. They certainly made arithmetic easier, but they did not “mechanise” it in the true sense of the word. While in many cases they were genuine machines in that they had cogs and gears and cams and so forth, they nevertheless demanded continual manual intervention by the operator as well as constant attention and thought on his part on the path from entering the data to reading the result. So they were simply extensions adjuncts or prostheses ‑ of the human mind and hand in their arithmetical operations on the digits of the numbers. They did not, so to speak, take the calculation away and come back with the answer.
The real problem of mechanising arithmetical calculation lies in finding a way to reduce human intervention to the absolute minimum, in finding a means which will be rapid, simple, reliable and exact to carry out calculations solely by the purely mechanical and automatic movements of a mechanism. The search for solutions to this problem led to the invention and development of simple numerical calculating machines.
WHY DID MECHANICAL CALCULATION NOT BEGIN EARLIER?
The concept of a mechanical calculator seems obvious and banal to us today, but four hundred years ago the very notion was bold and daring, not only from the difficulty of conceiving but even more so from the difficulty of constructing such a machine.
The mechanisation of arithmetic was the culmination of a long fine of evolution which began with the very earliest developments of mechanical technique and, therefore, with the most ancient civilisations known to history.
However, the story truly begins only in the period between the sixth century BCE and the third century CE. It was during this time that a certain school of Greek mechanicians flourished, who developed such fundamental mechanical elements as cogs, gears, levers. etc., and of whom, amongst the many, we may particularly mention Archytas of Tarentum, Archimedes, Ctesibius, Philo of Byzantium, and Hero of Alexandria. In this story pride of place must go to Aristotle (384‑322 BCE), who was the first to embark on a theoretical study of mechanics, and above all to Archimedes (287‑212 BCE). Archimedes was the true founder of mechanical science, [p113] and to him are due the concept of centre of gravity, the principles of the lever and of the inclined plane, the principle which governs the buoyancy of floating bodies (still known as “Archimedes’s principle”),5 and also several mechanical inventions such as the “screw of Archimedes” (a screw‑like spiral encased in a tube which, turning on its axis, can be used to raise water), the endless screw (or worm gear), the pulley and the pulley‑block, and various engines of war.
The mathematician Pappus of Alexandria (third‑fourth centuries CE) continued the work of Archimedes, but his was the final flicker of the flame of a civilisation already extinguished.
The Greek tradition did not die, however. The Byzantine Greeks carried on the work and, to a degree, were the vehicle of communication between the Greeks of Alexandria and those of mediaeval Europe. But the Greek tradition was passed on by, above all, the efforts of mechanicians of the Arab world. Here too, the Arabs absorbed the heritage they received, subjected it to synthesis, made important improvements to the techniques they inherited, and even made innovations of their own.
The Arabian school of mechaniciansl which began to be formed in the ninth century, played an important role in transmitting the ideas and techniques of the school of Alexandria to the engineers and mechanicians of the mediaeval era and of the European Renaissance. Amongst the latter we may particularly mention Villard de Honnecourt, Giovanni de Dondi, Konrad Keyser, Jean Errard de Bar‑le‑Duc, Leonardo da Vinci, Francesco di Giorgio Martini, Giuliano da Sangallo, Giovanni Fontana, Jean Fernel, Oreste Vanocci; these made spectacular advances which brought essential contributions to the domains of mechanics, clockwork, and precision engineering [see Feldman and Fold (1979); Gille (1978); Singer (1955‑1957)]. We well know how the European world, awakening to these ideas, strove to develop new techniques and to manufacture ever better clocks and other mechanisms ‑ to the point where the fourteenth‑century chronicler Jean Froissart was moved to compose a long poem in praise of the clock.
The oldest known purely mechanical clocks in Europe are in: the Chapel of San Gottardo in Milan, constructed by Guglielmo Zelandino in 1335; Saint Paul’s Cathedral in London, constructed in 1344 by an unknown; and the much more intricate one in Pavia Castle, constructed in 1364 by Giovanni de Dondi.
Since, however, the Greeks already knew and put to use such mechanical
5 Archimedes’s principle states that a body which is weighed when wholly or partially immersed in a fluid shows an apparent loss of weight equal to the weight of the volume of fluid displaced by the immersion. It follows that an object which weighs less than the weight of an equal volume of water will float on the water, since its weight is reduced to zero when it is only partially immersed; and that an object (such as a hydrogen‑filled balloon) which weighs less than an equal volume of air will rise in the air, since its weight is then negative. [Transl.]
[p114] devices as the endless screw, gear‑trains, cog‑wheels, and so forth, we must ask: what obstacles could have prevented them from creating a calculating machine incorporating such components (as more modem machines indeed do)? The reason is simple: such technology is indeed necessary, but it is far from sufficient. Their number‑system was not based on a positional principle and had no zero: in such conditions, how can one construct, or even imagine the construction of, a calculating machine? What sort of accumulator, for example, could deal with numbers represented without regard to the positions of digits? And, even if they had come to the notion of associating each cylinder of an accumulator with a decimal order of magnitude, how would such a device actually work, if its constructors had no idea of numerals based on single digits such as 0 to 9?
In short, in the absence of a number‑system based on the principle of position possessing a zero, the problem of mechanising arithmetical calculation could never have found a solution, even if the invention of such a device had been contemplated.
Why then, we may in turn ask, did the Europeans themselves fail to solve the problem earlier, since they had already known of the Indian positional number‑system since the time of the Crusades?
For this there are many reasons. The first derives from the superstitions and mystical beliefs of the period, which blocked their minds from seeing the way to progress; the second derives from the strict rules of the mediaeval guilds; and the third, practical, reason was that the techniques of mechanics reached the required degree of perfection only in the seventeenth century and especially in the eighteenth century thanks to advances in clockwork and also in theoretical mechanics.
In the fifteenth and sixteenth centuries, the European world still existed in a climate of dogmatism, mysticism, and servility towards sacred texts – a climate maintained and upheld by the Catholic Church which desperately sought to retain control over science and philosophy and spared no effort to ensure that any advances in knowledge would be strictly in accord with the Church’s dogmas on sin, Hell, and the salvation of the soul. And it cannot be forgotten that this was also the period when superstition, witch‑hunts and the Inquisition flourished.
So it was that, in 1633, Galileo was forced to solemnly recant his revolutionary theories about the solar system. The great astronomer Kepler, Court Astronomer to the Emperor Rudolph II and to his successor Matthias, was himself obliged in 1618 to defend his own mother against the Inquisition’s accusations of witchcraft, made on the obscurantist grounds that the mother, in giving birth to a genius of such stature, must have enjoyed congress with the Devil himself! Though it seems she was not put to the torture, Kepler’s mother died soon after being set free, [p115] undoubtedly a victim of this abominable course of justice.
Such then was the climate of an era awaiting enlightenment: an era where the art of calculation was considered the preserve of the “sacred and inviolable” domain of the cerebral activity of the human species. According to the mentality of the time, calculation was a purely spiritual affair, deriving uniquely from the divine essence; it was therefore absurd and sacrilegious to contemplate any mechanisation of it.
To be finally convinced of this, think only of the problems encountered by Galileo in 1593, and by Francis Bacon some twenty‑seven years later, in attempting to achieve acceptance of the idea that the use of machines is not an act against Nature, and their creation must be acceptable to divine law” [Galileo, Le Meccaniche (1593), Francis Bacon, Novum Organum (1620)].
Such religious and mystical considerations were not, however, the only obstacles at this crucial point in the history of artificial calculation. The very construction of a suitable engine would also require the work of a most skilful maker of clockwork, who was adept in every element of precision mechanics.
“In this period, to yield a professional innovation to a different guild, or to achieve work of a nature foreign to one’s own guild, was subject to severe repression. There are numerous cases where we find financial penalties, and disciplinary, moral and even physical constraints applied against artisans who contravened the rigid rules of their guilds” [R. Ligonniere (1987)].
So we can see that even if an artisan had been asked to undertake the construction of a mechanical calculator, he might have refused outright to do so, since it would seem to be such a serious infringement of the professional ethics of the time.
And the Arabs themselves, even though they knew of the Indian discoveries and made notable progress in arithmetic and were also acquainted with the work of the Greek mechanicians, did not contemplate the mechanisation of arithmetic because their own technology was inadequate. They stood in lack of all the advances which flowed from the development of theoretical mechanics, and from the development of the high‑precision construction of clockwork mechanisms.
And there is yet another reason for the delay in developing mechanical calculation. No idea, no matter how ingenious, will be developed and implemented unless it answers fundamentally to some social need. We know that many scientific discoveries have come to nothing because society, seeing no need, would have nothing to do with them. [p116]
THE ORIGINS AND DEVELOPMENT OF THEORETICAL MECHANICS
[We close this section by tracing another stream from its origins in Antiquity up to its great flowering in the eighteenth century: the history of theoretical mechanics, which added its own head of pressure to the forces which would break down the obstacles. Transl.]
Amongst the older peoples, the Greeks and Arabs stood out by virtue of their contributions to the technology of mechanics; but their contributions to the theory of the subject were, on the other hand, relatively minor. In Europe, until at least the fifteenth century, concepts of the principles of dynamics remained dominated by Aristotle’s treatises of the physical world; but his books and his theories are full of errors of interpretation and understanding.
Only in the sixteenth century did the earliest significant further progress in this domain occur. The Italian mathematician Tartaglia (1499‑1557) began the study of mechanics and ballistics, and Gerolamo Cardano (1501‑1576) published a treatise on mechanics, and invented the “Cardan joint”.6 Gianbattista Benedetti (1530‑1590) determined the conditions for the equilibrium of moments .7 The Flemish mathematician Simon Stevin (Stevinus) (1548‑1620) published papers on the equilibrium of weights, the equilibrium of bodies on an inclined plane, on hydrostatics, etc.8
These were but preliminaries, however, to the decisive breakthrough achieved by Galileo (1564‑1642), who established the fundamental laws of dynamics. In 1603 he determined the law governing the motion of a falling body,9 out of which he drew the concept of force and the principle of inertia.10 He transferred to dynamics (the study of motion and its
6 A method of linking two rotating shafts, in which a cross‑shaped piece has two of its extremities mounted in bearings on a semi‑circular extension to one shaft, and its other two extremities similarly mounted on the other shaft, so that the rotation of one shaft can be transmitted to the other even though the two shafts may be at an angle to each other. It is, therefore, a method of making a rotation “turn a corner” through an angle which may be continuously variable; and as such it has been much used in the transmission systems of motor vehicles. [Transl.]
7 The moment of a force about a point is defined as the amount of the force, multiplied by the perpendicular distance of the point from the line of action of the force, and it is a measure of the tendency of the force, when applied to an object, to cause a rotation about the given point. The principle of equilibrium of moments is that two different forces which have equal but opposite moments will, jointly, have no tendency to cause rotation. [Transl.]
8 He seems to have been the first to see how a force, acting in a particular direction, can be “resolved” along another direction according to the cosine of the angle, in effect discovering the parallelogram of forces. [Transl.]
9 Namely, that it acquires equal increments of velocity in equal time intervals, i.e. it falls with constant acceleration, regardless of its weight; from which, the distance fallen increases in proportion to the square of the time. [Transl.]
10 That a stationary body will only move, or a moving body only change its velocity, if it is acted upon by a net force. [Transl.]
[p117] dependence on applied forces) the principle of Stevin’s parallelogram of forces (discovered in the study of the equilibrium of static configurations). In his work Dialoghi delle Nuove Scienze (1638) he explains, concerning the movement of a projectile, how this principle of superposition of forces and motions entails that “the projectile, in addition to its initial and indestructible motion in the direction of projection, will add to this movement the downwards motion acquired from the force of gravity”; since the former entails a uniform displacement (both vertically and also horizontally) by an equal amount in equal intervals of time, while the second entails a vertical motion which increases in proportion to the square of the elapsed time, it follows (as Galileo was the first to discover and announce explicitly) that the path of a projectile is a parabola.
The next steps were taken by the Dutch mathematician Christiaan Huygens (1629‑1695). His principle innovations were the discovery of the notion of centrifugal force, the definition of moment of inertia, and the theory of the movement of a pendulum (which he himself applied in 1659 in the development of an accurate clock, at the same time introducing the spiral spring and the “anchor” or “recoil” escapement mechanism). He gave a demonstration of the theorem of momentum, and in 1669 a solution of the problem of motion generated by impact by making use of conservation of momentum.11
In 1671 the English mathematician and astronomer Robert Hooke (1635‑1703) discovered his law of elasticity,12 [and he was the first to state clearly that the motion of the heavenly bodies must be seen as a problem of mechanics, thereby foreseeing the existence of the force of attraction at a distance which became the foundation of Newton’s theory of gravitation. Transl.]
At this time also, the English mathematicians John Wallis (1616‑1703) and Christopher Wren (1632‑1723)13 worked on the laws of hydrostatics, further developing the discoveries of Stevin. The Italian Giovanni Alfonso Borelli (1608‑1679) made efforts to apply Galileo’s laws of dynamics to the movements of the stars.14
[The pioneering work of Galileo came to flower and to fruit in the hands
11 The momentum of a moving body, in classical mechanics, is measured as the product of its mass with its velocity. One of the most important perceptions of these early pioneers of the development of theoretical mechanics was that the total momentum of a system of moving objects was conserved throughout time, though momentum could be transferred from one object to another. [Transl.]
12 Hooke’s Law states that the amount of extension (or compression) when an elastic object is stretched (or compressed) by a force is proportional to the magnitude of the force. [Transl.]
13 Christopher Wren, later famous as an architect, was in the first place a very able mathematician who contributed to the theories here discussed, and maintained his interest throughout his life. [Transl.]
14 He also, impressed by the new successes of mathematics applied to the mechanics of moving inanimate objects, attempted to apply mathematics to the processes of living organisms. At any rate in the domain of movement and muscular forces, he succeeded in discovering some new principles in this field which flew in the face of the received wisdom of the time. [Transl.].
[p118] of Isaac Newton (1642‑1727), whose Philosophiae Naturalis Principia Mathematica (finally published in 1687, some twenty years after he had established its most fundamental material) set out the principles of theoretical mechanics in the rigorous logical style of Euclid’s Elements, with mass, position and time as primitive concepts, velocity defined as rate of change of position, and force defined as that which causes change in the velocity of moving matter; and, as axioms, Newton’s famous three Laws of Motion.15 In this work he also expounded (in a geometrical framework) the principles and methods of the differential and integral calculus which (at the same time as Leibniz) he had discovered and developed, and of which he made great use in the solution of the problems of mechanics which were discussed in the work. His calculus enabled him, in particular, to formulate and investigate his law of universal gravitation (that two particles of matter attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them), and thereby achieve the demonstration that his system of mechanics, together with his law of gravitation, explained the known facts concerning the movements of the planets and their satellites (as they had been determined from observation by Tycho Brahe and Johannes Kepler). This great work embedded the new knowledge of the mechanics of the physical world in a coherent and intrinsically complete mathematical framework, and all subsequent work in theoretical mechanics built upon Newton’s foundations until, towards the end of the nineteenth century, difficulties with reconciling the newtonian philosophy of the Universe with the phenomena of electromagnetism led to a progressive questioning of Newton’s concepts of space, time and matter culminating in Einstein’s Special Theory of Relativity (1905) which finally forced physicists to revise these concepts. Transl.]
The Swiss mathematician Jacob Bernoulli (1654‑1705) and his brother Johannes (1667‑1748) made considerable extensions to theoretical mechanics, solving many problems of dynamics. The French mathematician Pierre Varignon (1654‑1722) established the theorem of moments (which expressed the moment of a force about one point in terms of its moment about a different point and the distance between the points).
The Swiss mathematician Leonhard Euler (1707‑1783) made further very important contributions. His Mechanica, sive Motus scientia analytica exposita (1736) brought the theory of motions and mechanics fully under the analytical symbolism of the calculus (compared with the more
15 These are: (1) that the velocity of a particle of matter remains constant unless it is acted upon by an external force; (2) that the rate of change of the momentum of a particle acted on by a force is in the same direction as, and equal to, the force; (3) that if one particle exerts a force on another, the other particle exerts an equal and opposite force on the first (“action and reaction are equal and opposite”). [Transl.]
[p119] synthetic, geometrically inspired, development of Newton’s Principia). Another of the Bernoullis, Daniel (1700‑1782), applied similar methods to the dynamics of fluids.
With the subject flourishing in so many directions, the moment for synthesis had arrived. The French mathematician jean Le Rond d’Alembert (1717‑1783) published Traite de dynamique (1743), which demonstrated that problems in dynamics could be stated as problems in statics.16 He also described mechanics in the following terms: “The object of study in mechanics is the quantitative measure of force within bodies which are moving or which have a propensity to move. Mechanics has two branches: statics, and dynamics. The subject of statics is force within bodies which are in equilibrium and have only a propensity for movement. The subject of dynamics is force, within bodies which are actually moving.” (Explications generales des connaissances humaines)
This was but the beginning of a unification of the subject, however, and it was Louis de Lagrange (1736‑1813), one of the greatest of all French mathematicians, who achieved the synthesis of the subject in a single system of equations, based on a single general principle. The principle of “virtual velocities”,17 whose origins can be found in the work of Galileo (as Lagrange himself acknowledged in considering it to be the fundamental unifying principle of mechanics), was enunciated in Lagrange’s Mecanique analytique (1788) and forms the single principle from which the theory in that work is developed. Lagrange states: “I have set myself the task of reducing the theory of mechanics, and the techniques for solving the problems encountered therein, to general formulae whose straightforward working‑out would give all of the equations required for the solution of any problem whatever … This work has also the further purpose, that it will unify and present from a single point of view all the different principles discovered hitherto for the purpose of solving problems in mechanics and will display the relations and dependencies between them, and it will bring it within our grasp to judge of their correctness and their scope.”
From this moment, theoretical mechanics became a magnificent body of doctrine, and subsequently acquired an extraordinary momentum [cf. Bouveresse, Itard and SaIle (1977); T. de Galiana (1968)].
16 This is D’Alembert’s Principle: that, by the principle of superposition of forces in equilibrium, all the forces acting on the material particles of a system, taken together with their reactions against acceleration (cf. Newton’s second and third laws), are instantaneously equivalent to a system of forces in static equilibrium. [Transl.]
17 The principle states that a material system, not subject to dissipation of energy by friction, is in equilibrium in any instantaneous configuration if, and only if, the rate at which the applied forces perform work at that instant is equal to the rate at which potential energy is gained by the system, for every possible (i.e. virtual) motion through that configuration. [Transl.]
[p120] Progress in techniques of mechanical construction had already opened the way to developing mechanical calculation. We can also, however, appreciate how much the above advances in theoretical mechanics facilitated scientific study of the great variety of mechanical assemblages which had been invented and designed through the centuries: devices which were inspired by humankind as replacements for the mechanisms of the mind, to replace the mental working‑out of mathematical operations by the (literally) mechanical execution of processes which were clearly defined in terms of the characteristics of the problem.
[Before proceeding to the next section, we may also pause to briefly survey the rapidly burgeoning load of numerical work which these developments in theoretical mechanics were imposing on the brains of scientists.
[Newton’s Principia claimed that the same simple principles of mechanics applied to all the phenomena of dynamics in the Universe. Lagrange’s Mecanique analytique had provided a system, based on a single principle, capable of generating the equations to be solved for any dynamical problem whatever. Scientific exploration, and the verification of the newtonian system of the world, required the predictions of theory to be applied to the observations of the physical world, and determination of the numerical values of the quantities of which the abstract symbols appear in the equations. The equations therefore required numerical solution, and numerical solution entails calculation.
[Equations to be solved, therefore, multiplied ferociously as scientists turned their attention to more and more phenomena and to more and more instances of these phenomena. In many cases, these were systems of differential equations, whose numerical solution18 requires manifold repetition of the same (usually long and complicated) set of procedures, since the solution proceeds by computing the state of the system represented by the equation at a slightly later time, given the state at the current time; and good accuracy requires small intervals of time and therefore many of them.
[Remarkable feats of calculation using merely sheets of paper were achieved throughout the nineteenth century, and the achievements of scientists and engineers during this period are a monument to their numerical labours. Nevertheless, this very labour made the need for methods of automation all the more insistent: in so far as a development which is technically and theoretically possible nevertheless requires the spur of human need in order to be brought about, there can be no doubt
18 The cases of differential equations whose solutions can be written down as a general algebraic formula, whose numerical evaluation would be relatively straightforward, are few and, in the various domains of science, far between; for the most part, there is no escape from the necessity of calculation if an answer is to be found at all. [Transl.]
[p121] that by the nineteenth century the need was as pressing as could be. It only remained for the attention of great minds to be turned to the problems of creating the reality from the theoretical and technical potential that existed, and of developing such further theory and technology as might be required. Transl.]
Topic Four: The Mechanical Age
Lecture Objective:
To gain an overview of the development of mechanical computation from the scientific revolution through the work of Charles Babbage to the 19th century development of mechanical desktop calculators.
Overview of Topics:
- The Industrial Revolution of Steam, Iron and Coal
- Early Calculators: Schickard, Pascal and Leibniz
- The Babbage Engines
- Practical Machines
- Electricity
- Dangerous ideas
The lecture is based on Chapter 3 of The Foundations of Computing and the Information Technology Age.
Foundations Topic 4 Overheads
Foundations Book Chapter 3
Foundations Topic 4 Tutorial
Foundations Ifrah Reading Two
The First Calculating Machines
From: Ifrah, Georges. (2001). The Universal History of Computing: From the Abacus to the Quantum Computer. John Wiley and Sons, Inc: New York. pp121-133.
[p121]
3. The Calculating Machine
THE EARLIEST CALCULATING MACHINE IN HISTORY
The first step in the direction of automatic calculation was taken in 1623, when the German astronomer Wilhelm Schickard (1592‑1635) constructed his “calculating clock”, as he called it. This machine was capable of executing all four basic arithmetical operations: addition and subtraction it could perform purely mechanically, while multiplication and division required as well several interventions by the operator between entering the numbers and reading off the result. It used cylindrical elements which operated on the same principles as “Napier’s bones”.
On 20 September 1623, Schickard wrote as follows to his friend Kepler: “The calculations which you do by hand, I have recently attempted to achieve mechanically … I have constructed a machine which, immediately and automatically, calculates with given numbers, which adds, subtracts, multiplies and divides. You will cry out with joy when you see how it carries forward tens and hundreds, or deducts them in subtractions . . .” Kepler would certainly have appreciated such an invention to aid his own work, much occupied as he then was by the calculations to create his tables of the movements of the planets and having no other tool than the logarithms invented by Napier.
For all that, this invention had no impact, neither on the general public for whom mechanical calculation had long been merely a purely theoretical idea, nor even on later inventions of calculating machines, since Schickard’s one and only copy of his own machine was destroyed by fire on 22 February 1624.
Perhaps this fire was no accident: possibly a malicious spirit, no doubt prisoner of the obscurantism of the period, had whispered to him that the machine should be destroyed since ‑ endowed as it was with the ability to calculate according to the “sacred and inviolable” human spirit it must surely have emerged from the bowels of Hell! [p122]
PASCAL’S ARITHMETICAL MACHINE
Consequently, the possibility of mechanising arithmetic was first demonstrated in public in 1642, when Blaise Pascal (1623‑1662), the great French mathematician and philosopher, then only nineteen years old and totally unaware of the achievements of his predecessor Schickard, constructed his celebrated “Pascaline”. He was spurred to invent it by the interminable calculations which he made for the accounts of his father (whom Richelieu had appointed Intendant of Rouen), which he carried out by means of an abacus with counters.
The principal characteristic of Pascal’s machine was its facility for automatic carrying. This was achieved by the use of a series of toothed wheels, each numbered from 0 to 9, linked (by weighted ratchets) in such a way that when one wheel completed a revolution the next wheel advanced by one step. The prototype had five wheels, and so could handle five‑digit numbers; later versions had six or eight wheels.
[Numbers to be added were entered by turning setting‑wheels on the front of the machine, which were linked by a series of crown gears to the wheels which displayed the results. Addition was done by first turning the setting‑wheels by hand according to the digits of one number, and then turning them according to the digits of the other. Transl.]
Essentially, this was an adding machine which could not run in reverse, so that direct subtraction was impossible. Nevertheless, it was possible to perform subtraction by the process of adding the decimal complement of the number to be subtracted.
THE START OF A COMPLETELY NEW ERA
Pascal himself made the following remark, which is as true today as it was then regarding any calculator or computer:19 “The arithmetical machine produces effects which come closer to thought than anything
19 A remark whose truth is perhaps less obvious in the most recent years, when not only is genetic and neurological research beginning to indicate that the behaviour of living organisms, including humans, may be less wilful than had been supposed, but modem computers are becoming capable of a degree of autonomy which may escape human control and understanding.
Computers can already design and construct themselves, robot‑fashion. In terms of hardware and software, protection against power failure, software and hardware faults, and unwanted intrusion is, already commonplace in environments where security and reliability are paramount. In many cases they enjoy physical mobility. New concepts in programming, such as “neural networks” and “genetic algorithms”, give computers power to learn from random experience and to experiment “genetically” with variants of their software for the sake of achieving internally defined goals not yet within their reach; after a while, the human “master” of the machine might no longer know, nor be able to decipher and understand, what programme the machine is actually running.
Now that worldwide networking of computers is in place, and communication need not depend on cables but may use radio or light waves, it is not beyond imagination that a community of computers might develop which had its own “agenda”, and whose internal economy would not be directly accessible to humans. Our understanding of them, relying solely on observation and general principles, would be on much the same level as our understanding of a dog.
Nor, should such a community of computers become “unruly”, might it be straightforward to simply shut off the power …
The question is further addressed by the author in his concluding chapter, see pp. 367ff. [Transl.]
[p123] which animals can do; but it can do nothing which might lead us to say that it possesses free will, as the animals have.” (Pensees, 486).
“My brother”, wrote Gilberte Pascal, “has invented this arithmetical machine by which you can not only do calculations without the aid of counters of any kind, but even without knowing anything about the rules of arithmetic, and with infallible reliability. This instrument was considered a marvel, for having reduced a science ‑ whose source is in the human mind ‑ to the level of a machine, by discovering how to accomplish every operation with absolute reliability and without any need for reasoning.”
In her enthusiasm, Pascal’s sister no doubt somewhat exaggerated the “absolute reliability” of the Pascaline which, in truth, was far from perfectly reliable. Its essential component, the mechanism of the setting‑wheels, had a tendency not to engage well with the wheels it was supposed to turn, while the automatic carrying mechanism tended to jam when several wheels were simultaneously at 9, necessitating several simultaneous carries.
Nevertheless, Pascal’s success opened the way to further developments, while we may note that it was also the first calculating machine to be commercialised ‑ at least a dozen, probably as many as fifty, were constructed and sold in Europe.20
The success of Pascal’s “proof of concept” is demonstrated by the multitude of inventors from many countries who launched themselves along the same path in subsequent generations: Samuel Morland (1664), in England; Tito Livio Buratini (1670), in Italy; Rene Grillet de Roven (1678), De Lepine (1724‑1725), Hillerin de Boistissandeau (1730), in France; Christian Ludwig von Gersten (1735), in Germany; Pereire (1750), in France; Lord Stanhope (1780), in England; and so on. Their conceptions were nevertheless of variable quality; while some made improvements to the basic mechanisms, others produced machines distinctly inferior to the Pascaline.
All the same, Pascal’s sister’s letter perceptively foresaw the nature of the era which her brother had just inaugurated. This era was to crown two thousand years of evolution in mechanical technique, and to mark the final break with the long age of ignorance, superstition and mysticism which above all had stopped the human race from contemplating that certain mental operations could be consigned to material structures
20 Not that it proved very popular: its cost was about a year’s salary for a middle‑income worker, and the people in a position to spend such money were the same as would consider calculation to be servants’ work. [Transl.]
[p124] made up of mechanical elements, designed to obtain the same results. Pascal, therefore, had publicly inaugurated an era soon to be marked by the rapid development of a great variety of machines which not only eased the heavy burden of tedious and repetitive operations, but, in carrying out automatically an increasingly wide field of intellectual tasks with complete reliability, would come to replace the human being who would be able to use them without having even the slightest knowledge of the physical and mathematical laws which govern their working.
THE EARLIEST KNOWN DIGITAL COUNTING MACHINES
Pascal’s Arithmetical Machine and Schickard’s Calculating Clock were not the earliest devices to make direct use of the digits. They were preceded by the podometer (from the Greek podion, foot, and metron, measure).21
Jean Errard de Bar‑le‑Duc described this instrument as “A new geographical instrument which, attached to the horse’s saddle, uses the horse’s steps to display the length of the journey one has made” or, again, “by which, and according to the step of the horse or the man, one can exactly measure the circuit of a place or the length of a journey.” [Errard de Bar‑le‑Duc (1584), Avis au Lecteur, articles 37‑381.
The oldest known instrument of this kind dates from 1525; it belonged to the French artisan Jean Fernel.
These little mechanical instruments, shaped like a watch, automatically made a count of the number of steps taken, and therefore of the distance travelled by a horse or by a walker.
They comprised a system of toothed wheels and pinions driven by the movement of a kind of swinging lever, which turned needles round the faces of four dials which successively counted units, tens, hundreds and thousands [cf. Errard de Bar‑le‑Duc (1584)].
A walker might, for example, attach it on the left of his belt, and attach the corresponding lever by a cord to his right knee. At each step, the cord would pull on the lever, and the needle of the bottom dial would advance by one unit. When this passed from 9 to 0, the needle on the tens dial would advance by one unit. When this in turn passed from 90 to 0, the needle on the hundreds dial would advance by one unit, and so on.
Since they yielded an automatic display of the units of each decimal order, these pedometers were genuine ancestors of the machines of Schickard and Pascal as well as of all our present‑day counting machines (domestic or industrial), odometers, taximeters, cyclometers, etc., and so they are the earliest counting machines of history.
21 In English, usually (and subsequently below) pedometer (from the Latin pes, peals, foot, admixed with the Greek as above). [ Transl. I
[p125] This takes no credit away from Schickard nor from Pascal, however, since they were not calculating machines: they were unable to execute any arithmetical operation save the very primitive operation of adding one unit. Their place in the history of elementary artificial calculation is similar to the place that the ancient primitive techniques of human counting occupy in the history of arithmetic.
THE EXTENSION OF MECHANICAL CALCULATION TO THE FOUR ARITHMETIC OPERATIONS
The scope of Pascaline and her younger sisters was very limited: while multiplication and division were theoretically possible, the machines had no mechanism for these purposes and carrying them out involved numerous interventions, requiring considerable effort from the hand of the operator.
This problem was first addressed by Gottfried Wilhelm Leibniz, the German mathematician and philosopher. Unaware of Schickard’s work, and borrowing nothing from Pascal, he devised mechanisms which would carry out multiplication and division by means of successive additions and subtractions.
LEIBNIZ’S MACHINE
Conceived in 1673, but only constructed in 1694, Leibniz’s was therefore the earliest calculating machine capable of carrying out all of the four fundamental arithmetic operations by purely mechanical means.
Unlike Pascal’s machine, however, Leibniz’s was never commercialised, though a second one was made in 1704. Leibniz’s machine never worked well: its highly intricate mechanisms, much more complicated than those of the Pascaline, came up against major difficulties in fabrication since the techniques of manufacture of such mechanisms had not yet attained the degree of high precision required to put together a calculating machine both reliable and robust.22
It was, nevertheless, Leibniz even more than Pascal who opened the way for the development of mechanical calculation. In the technical domain, he made a number of important innovations, such as an inscriptor for entering a number prior to adding it; a window allowing the display of the entered number; a carriage which, in fixed position, allowed addition and subtraction to take place, while it could be moved from right to left for
22 It also gave wrong answers. By examination of the machine in 1893 it was discovered that an error in the design of the carrying mechanism meant that it faded to carry tens correctly when the multiplier was a two‑ or three‑digit number. [Transl.]
[p126] multiplication, and from left to right to allow division; a cylinder with rows of gear‑teeth affixed at increasing distances along it (the “Leibniz Gear”) such that a linked system of these could amend the display in a manner corresponding to multiplication by a single digit thereby replacing ten independent single‑digit wheels; etc.
Leibniz’s contribution was, therefore, considerable, since it is at the root of a whole pedigree of inventions which have continued to be developed until the start of the twentieth century.
Subsequent generations of inventors gradually moved away from the ideas of Pascal and their machines and brought a number of detailed improvements to his original work. Amongst these were those invented by: the Italian Giovanni Poleni (1709), which was distinguished by the use of gears with variable numbers of teeth; the Austrian Antonius Braun (1727); the German Jacob Leupold (1727), improved by Antonius Braun in 1728 and constructed in 1750 by a mechanician called Vayringe; the German Philipp Matthaus Hahn, developed in 1770, of which a series were constructed between 1774 and 1820; the English Lord Stanhope whose two calculators were constructed in 1775‑1777; the German Johann Hellfried Muller (1782‑1784); etc.
THE INDUSTRIAL REVOLUTION AND THE GROWTH OF AUTOMATIC CALCULATION
Despite all these attempts, calculating machines did not become a marketable product prior to the start of the nineteenth century. They did not meet the real needs of people faced with large amounts of real‑life calculation and, apart from being of great interest to mathematicians and inventors, were never other than curiosities.
In the nineteenth century, however, the Industrial Revolution brought about an immense increase in commercial activity and in international banking; events took an altogether different turn from that moment.
The need for automatic calculation grew enormously, while at the same time a whole new society of users came into being. Previously, serious interest was mainly confined to a scientific elite; now it spread to an increasingly vast and heterogeneous group which comprised especially “computers” ‑ calculating clerks ‑ whose job was carrying out the accounting calculations for large commercial enterprises.
Therefore, at this time, a pressing need was felt for a solution which would allow calculations to be made as rapidly and efficiently as possible, with maximum reliability and at minimum cost.
The search for a solution was pursued in two directions: firstly, the perfection of the mechanical aspects so as to achieve great simplicity of [p127] use and reliability of operation; secondly, the quest to automate the reflexes of the human operator to the maximum both in order to reduce the time taken for calculation as much as possible, and in order to bring the use of calculating machines within the reach of all.
THE THOMAS ARITHMOMETER: THE EARLIEST WIDELY‑MARKETED CALCULATOR
The first major advance after Leibniz’s invention was made by the French engineer and industrialist Charles‑Xavier Thomas of Colmar, director of a Paris insurance company, who in 1820 invented a calculator which he named the Arithmometer.
Constructed in 1822 and constantly improved during the following decades, the machine was conceived on similar lines to that of Leibniz. The “Leibniz Gears” were now fixed in position instead of sliding horizontally, the pinion which engaged each of them having, in effect, been made able to rotate about its axis.
Thomas introduced a system of automatic carrying which worked in every case (whereas that of Leibniz only worked at the first level); a mechanism for cancelling numbers (reducing the registers to zero); a blocking piece in the shape of a Maltese cross which could immobilise the parts of the mechanism when they had reached a chosen stopping point, and so on.
While such elements were already known, Thomas had put them together in such a way as to create a very robust, practical, functional and reliable machine.
His arithmometer marked a decisive stage in the history of automatic calculation, since it was the first to be commercialised on a large scale.
It was so successful that it inspired a multitude of inventors, and many companies in several countries sold it under their own brand names Saxonia, Archimedes, Unitas, TIM (“Time Is Money”), etc. ‑ either in its original form or slightly modified.
ODHNER’S AND BALDWIN’S MACHINES
From the second half of the nineteenth century, the Thomas machine was in competition with at least two other calculators.
The first of these was invented and constructed in 1875 by the American Frank S. Baldwin, pioneer of the calculating machine industry in the United States.
The second was invented in 1878 by the Swedish engineer and industrialist Willgot T. Odhner established in St Petersburg. This machine saw [p128] a massive production and was sold under licence under a variety of names: Original‑Odhner, Brunsviga, Triumphator, Marchant, Rapide, Dactyle Britannic, Arrow, Eclair, Vaucanson, etc. From the 1880s until the middle of the twentieth century it was in use worldwide.
OTHER DEVELOPMENTS IN MECHANICAL CALCULATION
The period under review saw many remarkable developments, but pride of place must go to the arithmometer invented in 1841 by the Frenchman; Maurel, and constructed in 1849 by his compatriot Jayet, which came to be called the Arithmaurel. These two inventors took Thomas’s system and greatly improved it. Amongst machines constructed on clockwork principles, this was distinguished by its high degree of inventiveness. The Arithmaurel could execute, in a few seconds, multiplications whose results were as large as 99,999,999 and divisions of numbers of similar size by divisors less than 10,000. The transmission mechanism of this machine, which was made by Winnerl (one of the best makers of marine chronometers of the time), was complex, fragile and delicate. Its cost was therefore very high, which stood in the way of successful commercialisation.
Also remarkable was the machine invented by the American Joseph Edmonson, which used a kind of circular version of the principle of the calculator made by Thomas of Colmar.
These machines, from the Thomas Arithmometer to that of Maurel, were not limited to multiplication and division since, thanks to a formula concerning the series of odd numbers, the calculation of square roots could be reduced to a series of subtractions.23 These machines readily lent, themselves to this operation.
D’Ocagne writes, on the subject of the curious machine invented by the American George B. Grant, that it “had some very original features. It was
23 The sum of successive odd numbers, starting with 1, is the square of the number of odd numbers taken.
For example,
1 = 12,
1+ 3 = 22,
1+ 3 + 5 = 32, etc.
The general formula is:
1 + 3 + 5 +. .. + (2n ‑ 1)2 = n2.
To find the square root of a number which is a square, you could subtract successive odd numbers until the result is zero; the number of subtractions made is the square root. If the number is not an exact, square, the square root lies between the number of subtractions made until the result is about to become, negative, and that number plus one.
The result thus obtained is an integer. To find the square root of a non‑square to a given number of decimal places, you could find the approximate integer square root of this number times a power of 100, and divide the result by the same power of 10. For instance, to find the square root of 2 to 2 decimal places (1.41 …) you could find the integer square root of 20,000 and divide by 100. However, the above method would require 141 subtractions of successive odd numbers. While, depending on the machine, there are manipulative tricks for accelerating this successive subtraction there are much faster ways which do not depend on the above formula ‑ if one is using a machine capable of multiplication and addition … [Transl.]
[p129] essentially composed of a series of parallel toothed rails which, on the rack‑and‑pinion principle, engaged with wheels linked to numbered drums. These rails were fixed to a carriage which was moved by two connecting rods and slid on two bars in the frame of the machine, making a forward and reverse movement for each complete turn of the manual crank‑handle. Vertical fingers, sliding in grooves whose borders were numbered from 0 to 9, lifted the corresponding rails with 0, 1, 2, … , 9 teeth. When the carriage was moved forwards, the rails acted on the ten‑toothed wheels of the numbered drums; on the reverse movement, the rails disengaged from the wheels under the action of a cam which lifted the part of the frame carrying the wheels. Moreover, it is during the return movement that the carrying takes place of digits to be carried, for each successive decimal order of magnitude. However, the machine did not lend itself to subtraction which therefore had to be carried out by using the decimal complement. A lever, at the end of the shaft carrying the numbered drums, operated a cancelling mechanism which brought all the digits to zero.”
Finally we may mention Tchebishev’s calculator of 1882, notable for its epicyclic gear mechanism for carrying numbers, as well as a component which automatically shifted the carriage during multiplication, by which this operation became almost entirely automatic.
THE NUMERIC KEYBOARD: AN IMPORTANT TECHNICAL INNOVATION
However well they worked mechanically, all these machines were deficient especially where rapidity of operation was concerned. They were in practice no faster than a human calculator of average skill.
This slow performance was largely due to the method of entering the numbers into the machines, which still required the close attention of the operator; this involved the movement of a slide or lever within a straight or curved slot and required the use of at least two fingers.
At this time of the post‑industrial race for efficiency, it became urgent to reduce the entering of numbers, and also the activation of the arithmetical operations, to the level of simple reflex on the part of the user.
For this purpose, it would seem that there was no choice more simple, precise, efficient and rapid than the numeric keyboard. To enter each digit, it is sufficient to press once with a single finger on the appropriate key which automatically returns to its starting position once released.
This advance was made in the middle of the nineteenth century, apparently under the influence of the development of the typewriter whose history, as a prelude to the story of key‑operated calculating machines, will be given in the next section. [p130]
4. The Keyboard Comes on the Scene. From Adding Machine to Cash Register
MECHANICAL AIDS TO WRITING FROM DOUBLE PEN TO TYPEWRITER
One of the most useful advances in the development of calculating machines occurred when they acquired keys which the operator could press, instead of manipulating other types of control in order to set the numbers and to initiate their operation. We begin by tracing some of the history of mechanical aids to writing, leading up to the invention and development of the typewriter. [See G. Tilghman Richards (1964); T. de Galiana (1968)].
In 1647 the English statistician and political economist William (later Sir William) Petty obtained a patent for the invention of a device endowed with two pens for double writing, i.e. a kind of copying machine.
In 1714, Queen Anne granted a patent to Henry Mill (1683‑1771) for “an artificial machine or method for the impressing or transcribing of letters, singly or progressively one after another as in writing, whereby all writings whatsoever may be engrossed in paper or parchment so neat and exact as not to be distinguished from print”24 which was the earliest project for a “writing machine” worthy of the name. However, it led to no practical result, being apparently clumsy and useless.
William A. Burt (1792‑1858), an American, invented his Typographer (1829) which had its letters arranged on a roller. This device had the major defect of being much slower than handwriting (a feature common to most of the machines which came into being around this time).
Over the next few years a number of machines were invented which merit brief mention: the Frenchman Xavier Progin’s Kryptographic Machine (1833) which carried its letters on bars in a circular arrangement, but was never exploited commercially; the Italian Giuseppe Ravizza’s Cembalo Scrivano (1837), in which the letters struck upwards, after being inked from a ribbon; the Frenchman Bidet’s writing machine (1837); the Baron von Drais de Sauerbrun’s writing machine, with 16 square keys (1838); the Frenchman Louis Jerome Perrot’s Tachygraphic Machine (1839); the Universal Compositor of Baillet Sondalo and Core (Paris, 1840); Alexander Bain and Thomas Wright’s writing machine, intended for the composition of Morse code to be sent by electric telegraph (1840); the American Charles Thuber’s Chirographer (1843), a machine which already had a radial arrangement of type but which also had a very slow action; the Raphigraphe (1843), intended for use by the blind, of Pierre Foucault who taught at the
24 Encyclopaedia Britannica, 9th edition, vol. XXIV, p. 698. [Transl.]
[p131] Institute for the Blind in Paris; Pierre Foucault’s Printing Clavier (1850); the Mechanical Typographer (1852) of John M. Jones of New York State; the New York physicist Samuel Francis’s Printing Machine (1857), which had a keyboard similar to that of a piano.
In 1866‑1867 the American printer Christopher Latham Sholes, with the help of his friends Carlos Glidden and Samuel Soule, invented his Literary Piano. This typewriter, which had independent type‑bars, was the first to have practical prospects, though certain technical difficulties meant that it would not be manufactured until 1871. Its principal defect was that the type‑bars had no return spring, falling back under their own weight and therefore slowly, so that if the keys were struck too rapidly the rising bar would jam against the recently struck descending bar. Sholes corrected this soon afterwards by introducing suitable mechanisms. Initially, in the the Sholes‑Glidden machine, the keys were arranged in alphabetical order. Then Sholes, having studied which combinations of letters occurred most frequently in English, arranged to separate the most frequent combinations on the keyboard (thereby both allowing a faster finger action and also reducing the risk of jamming). The first typewriter with a universal keyboard thus came into being. This machine wrote only in capital letters, and also, because the letters were struck on the top of the platen, they could not be read while being typed without lifting the carriage.
The Remington company (manufacturers of arms, agricultural machinery and sewing machines) now took an interest in the Sholes‑Glidden machine despite the scepticism of one of its directors who could see no interest in machines to replace people for work which they already did well. Remington constructed a series of these machines starting in 1873. They were mounted on a sewing‑machine chassis, and had a pedal to return the carriage to the start of the line. This model, christened Remington Model I, was the first typewriter marketed in the United States; the machine created by Malling Hansen in Denmark was sold in Europe starting in 1870.
In 1878, the limitation to capital letters of the Sholes‑Glidden machine was removed, and lower‑case letters could be typed as well. Finally, in 1887, the type‑bars were mounted so as to strike the platen from the front, so that the text could be read while it was being typed, and the modern form of the typewriter came into existence.
THE EARLIEST ADDING MACHINES WITH KEYBOARDS
The stream of development which brought the keyboard to the typewriter, as described above, now became yet another tributary of the development of the calculating machine and the computer, providing one of the most decisive technical improvements in the whole history of artificial calculation.
[p132] Paradoxically, however, this advance proved, in the very beginning, to be a setback.
The first arithmetical calculator with a keyboard was constructed in 1849, and patented in 1850, by the American inventor David. D. Parmalee. It was an adding machine, whose essential component was a vertical rack‑and‑pinion gear activated by the movement of a lever when a key was pressed. But the accumulator had a single wheel and therefore could only add single‑digit numbers.
In order to add numbers with several digits, it was necessary to work manually, after the fashion of handwritten arithmetic, adding separately the units, the tens, the hundreds, and so on, all the while being obliged to note on paper the partial results thus obtained and entering each such result prior to the next stage!
Numerous American and European inventors later brought in improvements to this design: Schilt (1851), Hill (1857), Arzberger (1866), Chapin (1870), Robjohn (1872), Carroll (1876), Borland and Hoffman (1878), Stettner (1882), Bouchet (1883), Bagge (1884), D’Azevedo (1884), Spalding (1884), Starck (1884), Petetin (1885), Max Mayer (1886), Burroughs (1888), Shohe Tanaka (1893), etc.
To begin with, however, the improvements were inadequate and the machines still required much preliminary manipulation and continual conscious attention on the part of the operator. Worse yet: these machines had neither speed nor numerical capacity of consequence, and were fragile in use so that they gave wrong answers if not handled with delicacy and dexterity.
FELT’S COMPTOMETER
The earliest adding machine which was really useful and usable by the general public was the comptometer, invented and constructed by the American industrialist Dorr E. Felt in 1884‑1886. It was able to carry out additions and subtractions, involving numbers with several digits, advantageously, rapidly and reliably. The Felt and Tarrant Manufacturing Company of Chicago manufactured and sold it on a large scale from 1887, and the machine enjoyed worldwide success until well into the twentieth century.
Other improvements which came in somewhat later included:
- Dalton’s intermediate register, which allowed a delayed entry of numbers which had already been set using the keyboard, so that corrections could be made prior to operating the lever which initiated the calculation;
- Runge’s compact keyboard (1896), followed by that of Hopkins (1903), [p133] which had only ten keys but worked through an automatic distributor, which allowed the operator, without displacing the hands, to enter the units, tens, hundreds, etc. successively.
A FURTHER ENHANCEMENT: THE PRINTED RECORD
To be properly adapted to the needs of commerce, such machines needed the capability to produce a printed record of transactions, using a mechanism which would print each of the quantities in the total, and the total itself, on a strip of paper. The human operator could then not only check at once that the correct numbers had been used, but also keep the print‑out as a permanent record of the calculations.
We shall deal later with the developments achieved by Charles Babbage and by the Swedes Georg and Edvard Scheutz (1853). Apart from these, the first serious attempts at developing a printing mechanism were due to the American Edmund D. Barbour who in 1872 invented an adding machine with keys and also with a “printer” which, however, was a somewhat primitive device which only printed totals and sub‑totals: the individual operations were still executed more or less manually, and the printing device operated rather in the manner of a date‑stamp.
In 1875, the American Frank S. Baldwin brought in some improvements which to some extent allowed the machine to print out its own results.
The next stage in this line of development was taken by the Frenchman Henri Pottin, whose device listed the individual items of an addition and, at about the same time, by the American inventors George Grant (1874) and A. C. Ludlum (1888). In 1882, Pottin developed one of the earliest cash registers with a printing device.
THE FIRST BURROUGHS MACHINE
The decisive developments in this area occurred between 1885 and 1893, when the American William S. Burroughs invented and perfected his Adding and Listing Machine, the first mechanical calculator with keys and a printer which was also practical, reliable, robust and perfectly adapted to the requirements of the banking and commercial operations of the time. For these reasons, his machines enjoyed a remarkable worldwide success until the outbreak of the First World War.
The complete solution of the printing problem for adding machines was also achieved at almost the same time (1889‑1893) by Dorr E. Felt who had invented the comptometer.
Topic Five: The Universal Machine
Lecture Objective:
To gain an overview of the historical development of the electronic
stored program computer in the first half of the 20th
century.
Overview of Topics:
- The Revolutions in 20th Century Science and Mathematics
- Early Punched Card Machines
- Electro-Mechanical Computing: Zuse, Stibitz and Aiken
- The First Electronic Machines: ABC and ENIAC
- Colossus and the War-Time Codebreakers
- The Post-War Stored Program Machines
The lecture is based on Chapter 4 of The Foundations of Computing and the Information Technology Age.
Foundations Topic 5 Overheads
Foundations Book Chapter 4
Foundations Topic 5 Tutorial
Topic Six: Computation in Theory
Lecture Objective:
To gain a general theoretical understanding of the concept of
a formal language and the ideas of computability and computation from a consideration of the operation of a Universal Turing
Machine.
Overview of Topics:
- The Evolution of Abstraction in Maths and Logic
- The Concepts of Computability and the Effective Method
- The Turing Machine
- A Turing Machine Program
- The Universal Turing Machine
- But What is Computation Really?
Note: There is enough material here to split the topic over two weeks, comprising Part One of the lecture overheads (The Idea of a Turing Machine) and Part Two (The Idea of a Universal Machine).
The lecture is based on Chapter 5 of The Foundations of Computing and the Information Technology Age.
Foundations Topic 6 Overheads
Foundations Book Chapter 5
Foundations Topic 6 Tutorial
Foundations Weizenbaum Reading
Foundations Bolter Reading One
Foundations Turing Test Reading
Foundations Chinese Room Reading
Topic Seven: The Von Neumann Architecture
Lecture Objective:
To gain a practical understanding of how a program executes within the von Neumann architecture.
Overview of Topics:
- The von Neumann Architecture
- The Fetch-Execute Cycle
- Instruction Set Architectures
- Basic Program Instructions
- Executing a Simple Program
- The Evolution of the von Neumann Architecture
The lecture is based on Chapter 6 of The Foundations of Computing and the Information Technology Age.
Foundations Topic 7 Overheads
Foundations Book Chapter 6
Foundations Topic 7 Tutorial
Foundations Bolter Reading Two
Logic and Computation
From: Bolter, J. David. (1984). Turing’s Man: Western Culture in the Computer Age. The University of North Carolina Press, Chapel Hill. pp. 47-49, 66-79.
[p47]
The von Neumann Computer
We have traced the logical shadow of the computer in Turing’s machine. No matter how ingenious, that device was a game for logicians and could only have had a limited impact on our culture (like the other concerns of twentieth‑century logic) if it had not found a physical embodiment as the von Neumann computer. About ten years after Turing first made his suggestion, John von Neumann and his many colleagues realized its significance and worked to apply Turing’s logical scheme to the physical materials from which information processors might be built. They sought to make a Turing machine out of vacuum tubes instead of pencil and paper; the electronic version would operate millions of times faster than a mathematician applying his rules and erasing his symbols accordingly.
Again, two parts needed to be considered: the rules of operation and the data upon which to operate. The data could sensibly be put on punched cards, represented inside the machines by some sort of electronic storage, and eventually dumped as output onto punched cards or paper. The problem was with the rules of operation, for the tendency had been to think of these rules as fixed, to express them in the very structure, the wiring of the machine. Early machines offered plugboards, something like telephone switchboards, in which wires had to be reconfigured for each new problem to be solved. The wires led out to various parts of the machine, controlling the calculations that the data would undergo. The operator literally had to wire a new machine, designed exclusively to execute that one problem. [p48]
The unique feature of the von Neumann computer is that the programs and data are stored in the same way, as strings of binary digits. The program, a set of instructions to add, subtract, or manipulate pieces of data, is loaded along with the data into the computer’s memory. The central processing unit (CPU) of the machine distinguishes between instructions and data usually only by position. It decodes and executes instructions and operates accordingly upon the data. The illustration of the von Neumann computer in figure 3‑2 [not shown here] is still quite abstract: in a current machine, each of the boxes would be electronic devices made of thousands or millions of transistors; the arrows would be wires or connections allowing electrical “information” to pass between the devices in the directions indicated. The box marked memory corresponds to the tape of the Turing machine: here the input is stored and the intermediate results are written by the CPU. The CPU corresponds to the operating rules of a universal Turing machine. Built into its electronic structure are rules for making sense of the instructions and data that it finds in the memory. The CPU goes through the memory, much as a Turing machine moves along its tape, picking out instructions one at a time and executing them.
The CPU is made up of logic circuitry and various registers. The registers hold individual instructions or small amounts of data for immediate processing. The control unit, more of a functional than a physical division in modern computers, breaks the instructions into a series of electronic actions, directing the step-by‑step operation of the whole system. (This unit replaces the plugboard of the earlier machines.) The arithmetic and logical unit (ALU) performs the actual additions, subtractions, and logical business required.
Suppose the next instruction in the memory is to add two numbers and store the result somewhere else in memory. The sequences:
- The control unit signals the memory to send the next instruction and an instruction register to receive it. Decoding circuits read the instruction and discover that it demands an addition.
- The control pulls the two numbers to be added from the memory and puts them into data registers.
- It sends these two numbers through the arithmetic unit, where they are summed, and puts the sum back into a data register.
- It sends the sum from the register hack into memory. [p49]
The process is then repeated on the next instruction and so on through the program. The computer works in cycles, each of which has two parts: fetch and execute. The fetch step is the “reading” and interpreting of the instruction (1 in the above sequence), where the decoder discovers what is to be done. The actual processing (2 through 4) of the data is the execute step.
The cycle of fetch‑and‑execute proceeds with numbing regularity perhaps millions of times each second; it is repeated for each new instruction and new packet of data. For all its extraordinary speed, the von Neumann computer operates rather like a two‑stroke gasoline engine, drawing its instructions in with the first stroke and executing them with the second. A closer analogy, perhaps, is an industrial assembly line or job shop, in which an endless stream of identical items are processed. Here the items are not automobiles or alarm clocks but electronically coded packets of information. These move at speeds that are healthy fractions of the speed of light back and forth between memory and processor; within the processor they are broken into smaller packets and recombined in electronic forms of arithmetic and logical calculus. In this fashion, the computer processes information: it begins with one string of binary digits (the program and the data) and ends by assembling another (the output) from fragments of the first.
It is the logical unity of the von Neumann, stored‑program computer that makes it so powerful. New programs, new sets of instructions, can be loaded into these machines as easily as new data. Each program in effect makes the computer into a different machine, one with a new purpose, without any change in the wiring. The same physical equipment may serve first to calculate the orbit of a spacecraft, then to alphabetize a list of names, then to determine averages and deviations of a statistical sample. Since each of these tasks calls for a logically different Turing machine, the physical equipment that can accomplish them all is a universal Turing machine. Thus logic and electronics meet at precisely this point: the von Neumann computer. [p66]
5 Embodied Symbol: Logic by Computer
The computer was built to solve mathematical problems, but it was soon realized that its power went beyond numerical calculation. It could manipulate arbitrary symbols as easily as it could add numbers. Lady Lovelace, the disciple of Charles Babbage, understood the power of machine computation in the last century when she remarked that the Analytical Engine “can arrange and combine its numerical quantities exactly as if they were letters or other general symbols; and in fact it might bring out its results in algebraical notation, were provisions made accordingly” (Morrison and Morrison, Charles Babbage and His Calculating Engines, 273). John von Neumann had come to the same understanding when he arranged for his machine to keep the programs in memory along with the numerical data and to keep them in the same binary format. The program was a coded list of commands, a binary representation of the sequence of actions to be performed by the computer in reaching an answer. The computer did not calculate these commands, rather, it interpreted and executed them; it executed commands and added numbers with equal ease. The von Neumann computer was not a calculator but a logic machine.
The machine demonstrated the unity of all systems of representation: as symbols, numerals are no different from letters, hieroglyphs, or ideographs, for all these can be manipulated in electronic circuits. It soon became clear that the manipulations of [p67] mathematics were not fundamental to the machine. Computer mathematics itself could be defined in terms of the science of symbolic logic, a science that had been developed by generations of philosophers in the nineteenth and twentieth centuries. But symbolic logic too underwent a change when it was adapted for the computer: like mathematics, it took on the peculiar qualities and limitations of the machine.
Truth and the von Neumann Machine
There is a great philosophical issue that the computer requires its programmers to confront from the first day they begin to learn their craft ‑ the nature of symbols and symbolic representation. To solve a problem, the computer must fashion some representation of the problem within its circuits and then operate, and the programmer must always be aware of the relation between the original problem and the computer’s means of representation. He must constantly attend to the symbols that stand for facets of the problem, and he is constantly impressed by the way these symbols are threaded through the processor and manipulated as they are transformed into the desired values of the output.
The computer teaches forcefully the lesson that symbols are arbitrary, that they mean exactly and only what the programmer and the machine define them to mean. This is a lesson that might also be learned from the world of natural language, as a colleague has suggested to me. The meaning of the word “inhabitable” seems clear: “habitable, capable of supporting life.” This combination of letters is not particularly ambiguous and is not a homonym. But present the same letters to a Frenchman, and he will interpret the word in almost the opposite sense. The alphabet is the same for French and English, but the words made from that alphabet are different. There is no intrinsic meaning to the string of letters “inhabitable”; the meaning we assign is as valid as the one assigned by the French. But in order to know the meaning, we must know which “code” (language) we are using.
The computer operates with a variety of codes, but the genius of the von Neumann scheme is that the codes can all be expressed in the same binary alphabet. The computer represents numbers, letters, and programming instructions all as strings of bits (binary units of information). Just its there is a binary representation for the number 12, so there is one for the letter “a” and one for the [p68] command to copy a value from the CPU into the memory. The instruction code (the opcode) is a set of symbols that command the processor to perform its operations: to add two numbers, to store a value in memory, and so on. Then there are codes that the machine uses internally (in its CPU and memory) to represent numbers for calculation. All coded values ultimately exist only as arbitrary configurations of bits. Inside the computer, the same bit string might represent the number 115, the letter “s,” and the opcode that instructs the CPU to add two numbers. How the string is treated ‑ as number, letter, or instruction ‑ depends generally on the context: that is, the machine itself interprets each string by its relation to other strings in the memory.
Now it may seem odd that letters and punctuation should need representation in the electronic world at all. The string “01110011”, interpreted as the number 115, can sensibly be added to another string standing for another number, and so the processor can proceed through a series of meaningful calculations; but it makes no sense to add two strings that represent letters. An operation that does make sense is to compare two letters or sets of letters forming names. By simple comparisons, the computer can be programmed to search through a list of names or to sort a list into alphabetical order. The prosaic operations of sorting and searching are basic to the nonscientific uses of the computer, especially business uses, and the success of such applications has provided the resources and much of the impetus for more esoteric programming. The most sophisticated programs for playing chess still rely heavily upon the two techniques used by the telephone company in billing its customers.
There is more that can be done with strings of nonnumeric data; in fact, these strings can be “added” in a meaningful way. A two‑state system (on/off, high voltage/low voltage) may be used to denote yes or no, true or false. This logical interpretation opens for the computer a new universe of discourse, as logicians are fond of calling it: any statement that logicians regard as true or false can be represented as a bit in an electronic circuit. Such bits become the numerals of logical arithmetic, and the operations of this arithmetic are called “truth functions.” A complex science has been built from this notion.
Take the statement: “Von Neumann died in 1957.” This statement is true and earns the truth value 1. Its negation, “Von Neumann did not die in 1957,” is false and has the value 0. Logicians would assign a symbol, A, to the original statement and say that [p69] A has the value 1; the negation of A, written ~A, has the value 0. Now consider a statement that is false: “Babbage was born in 1903.” If this statement is called A, then the formulas are reversed: A has value 0 and ~A has value 1. This exhausts the possibilities for the simplest truth function, the not function, which inverts truth values according to the following table:
A ~A
0 1
1 0
The table expresses the trivial notion that if a statement is true, then its negation is false, and vice versa. The point is that by reducing this notion to a formula and representing truth as a binary digit, we make the realm of symbolic logic accessible to the computer. Here the machine is not adding numbers; it is determining truth and falsity, albeit in the precise and limited sense of the logician. Other truth functions can be defined by more complicated tables ‑ an or function, an and function ‑ and soon the whole complex structure of formal logic can be expressed in the computer’s alphabet.
This highly mathematical treatment of truth and falsehood, which the computer programmer now uses daily, was created by philosophers and mathematicians in the nineteenth and early twentieth centuries, before computers had any more concrete realization than the unassembled pieces of Babbage’s Analytical Engine. These thinkers had in mind another goal altogether: to free European logic from the hold that Aristotle had exerted since ancient times. Their complaint was that Aristotle had divorced logic from mathematics. By making logic rigorous and mathematical, they now hoped to put it at the center of European philosophy, the position it had always promised to occupy and yet never quite achieved. They felt that a logical calculus (on the model of the rigorous mathematics of nineteenth‑century analysis) ought to be the philosopher’s main tool in his search for truth. So they created the formal systems of propositional and predicate calculus, in which symbols without any intrinsic meaning were manipulated according to universally valid rules of thought, rules about contradiction, consistency, and implication.
The Principia Mathematica of Bertrand Russell and A. N. Whitehead (1910) was nothing less than an attempt to make symbolic logic the foundation of mathematics and so to provide a bridge between philosophy and the most rigorous of sciences. Russell himself elsewhere wrote that in his day “logic has become [p70] more mathematical and mathematics has become more logical. The consequence is that it has now become wholly impossible to draw a line between the two; in fact the two are one. They differ as boy and man: the logic is the youth of mathematics and mathematics is the manhood of logic” (Introduction to Mathematical Philosophy, 194).
The project to unify logic and mathematics was the height of abstraction, as a glance through the pages of the Principia shows, and by its very complexity and rigor, the new symbolic logic placed itself beyond the reach of many philosophers and most other intellectuals. The Aristotelian categories and classification of syllogisms could be understood even by humanists. Everyone knows the example:
All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.
In symbolic form, the syllogism is comparatively easy to follow:
(x) (Hx -> Mx) where Hx = x is a man,
Hs Mx = x is mortal,
therefore Ms and s = Socrates.
But once we have made the leap to symbolic representation, we begin to reason entirely abstractly (without reference to men, mortality, or Socrates) and in a layered fashion, building one level of complexity upon another. The syllogism above stands in relation to the formal reasoning of the Principia as arithmetic stands in relation to theorems of complex variable analysis ‑ it is a bare beginning. Few of us indeed can follow an argument of mature symbolic logic. For most, the incentive to learn this science was never adequate, and in any case the edifice that Russell and others had erected failed decisively in the 1930s. The work of Kurt Godel showed that there were inherent limitations to any logical system designed for constructing mathematics: the danger of contradictions or lack of completeness in such systems could not be eliminated. Symbolic logic remained a compelling but esoteric discipline of its own, influential but still too abstruse to direct the course of twentieth‑century thought.
The invention of electronic computing hardware provided a new and unexpectedly utilitarian sphere for symbolic logic. It was not a revivification, for there were important logicians throughout the first half of the twentieth century Suddenly, however, [p71] their work came down to earth when logical truth functions came to be embodied in electronic circuits. Logic and electronics married, and the offspring was the von Neumann computer. For example, put a logical truth table beside its circuit diagram […]. The difference between the circuitry and the truth table may seem to the layman to be merely the replacement of one set of symbols with another, but there is more to it. In one case, the symbols are those of logic, counters that have meaning only as we define them. In the other, the symbols stand for electronic components, which are built from such earthly materials as silicon and gold (the most pedestrian and the most princely) and set to work in the world of experience.
The central processor of the computer performs its calculations by means of just such circuitry (and gates, or gates, and the like), and engineers speak of designing the “logic” for a particular machine, the constellation of logical circuits the machine will use. Such circuits exist throughout the computer but are concentrated in the ALU, that part of the central processor through which units of data are sent to be added, compared, and otherwise manipulated. There need not be two separate sections of the ALU, one for arithmetic and one for logic, because the arithmetic operations can be performed by the same circuits that embody truth functions. A binary adder, for example, can actually be built using and, or, and not gates, which is simply another facet of the remarkable unity of design of the digital computer. Just as all numbers and other symbols are reduced to the same binary digits, so all arithmetic operations are reduced to the logical manipulation of these digits. And since computer mathematics is nothing in the end but combinations of arithmetic operations, all the mathematics of the computer age (including the most complex statistics and differential equations) depend upon the realization in circuits of a few elementary logical functions.
The Triumph of Logic
In the computer, then, symbolic logic has achieved what it could not achieve in the cryptic pages of Russell’s Principia; it has become the foundation of computerized mathematics. But to win this end, logic has had to condescend to become concrete, to clothe itself in a mantle of free‑flowing electrons and to preside over an equally concrete form of mathematics. This is an [p72] astonishing development in the modern history of ideas. Its impact has not been fully appreciated, perhaps because symbolic logic in its pre‑electronic form was not available to the intellectual community at large. Now, however, the most esoteric branch of philosophy is being put to a practical, often mundane use, and the most practical of people, engineers, are studying the rudiments of symbolic logic. This pragmatic feeling for electronic logic has worked its way into the bones of Turing’s men; it is a key part of their world view. [p73]
Logicians have often dreamt of reducing (or raising) all rational human thinking to the level of their craft. Aristotle, it is true, did not think that all fields could be reached by the syllogistic logic he had invented. It would be as unreasonable, he declared in the Nicomachean Ethics, to expect exact proofs from a politician as to accept merely probable conclusions from the mathematician. But later logicians, again with characteristic Western enthusiasm, have indeed hoped to attain mathematical perfection in religion or politics. Leibniz himself proposed a universal language in which all simple ideas could be represented by individual symbols and then combined by the rules of logic; when expressed in this language, even the truths of religion would be irrefutable.
With the computer, this hope is resurrected in a new guise. Any task the computer performs is a matter of the logical manipulation of symbols; each new problem solved is a conquest for the logical calculus of thought and gives encouragement to those who still follow Leibniz’s program. “If I were to choose a patron saint for cybernetics [the study of living organisms as logical machines] out of the history of science,” wrote Norbert Wiener in 1948, “I should have to choose Leibniz. . . . The calculus ratiocinator [calculus of reasoning] of Leibniz contains the germs of the machina ratiocinatrix, the reasoning machine” (Cybernetics, 20).
When a computer specialist speaks of his machine “thinking,” “reasoning,” “manifesting intelligence,” or “solving problems,” he means that it is operating according to the rules of its embodied symbolic logic. There seems to be no bias attached to electronic logic, as there is still to some extent to electronic mathematics. It is instead a triumph that theory can now be put so successfully into practice. After all, if formal logic is now used to sort bills and keep inventories, it is also invaluable in exploring the planets with unmanned spacecraft, deciphering data collected in particle accelerators, and, least important perhaps but most dramatic, in playing computerized chess. Many computer specialists believe that no important intellectual endeavor will stay forever outside the scope of their calculus of reasoning.
The computer is also a triumph of “logic” in another sense, the popular sense, suggesting the compulsion for tight constructions, careful definitions, and tidy arguments. The computer is the embodiment of the world as the logician would like it to be. The [p74] world of everyday experience has the annoying tendency of spilling out of the neat categories he constructs, and it has had this tendency ever since Aristotle codified logic in the fourth century B.C. For the logician, then, the digital computer has this virtue: its design is perfectly logical down to the scale of electrons; it has conquered the disorder of the natural world by the hierarchical principles of symbolic logic. Outside the computer electrons fly about obeying no final cause but only the statistical and quantized laws of physics. According to the principle of entropy, the universe as a whole moves toward greater disorder. Meanwhile, the thoughts and beliefs of men ‑ to the philosophically minded logician, entities as real as tables and chairs ‑ are equally chaotic. No philosopher has yet produced a rigorous proof for or against the existence of God that could satisfy more than a fraction of his colleagues. But in the world of the computer, a special kind of order exists. Electrons still obey the statistical laws of physics, but the circuits are so designed that these laws themselves serve the principles of logic.
Western technology has been based on the idea of subordinating nature to artifice, and it has been a more or less qualified failure. Natural laws always prove stronger than human constructs; machines are inaccurate and eventually, usually all too soon, they break down. But engineers have never had at their disposal a tool of design as precise as symbolic logic. They have never attempted to master nature on so fine a scale. Electronic technology is mankind’s most arrogant and most successful attempt to impose its own teleology upon the natural world. The or gate in a computer is really the final cause for which electrons fly about, a final cause dictated by the engineer who designed the machine. The logical world the engineer creates reminds us in this respect of the universe of a Greek cosmologist. The logic of Aristotle has been left far behind, but the typically Greek contrast between order within and chaos without remains. For Greek thinkers, the universe was a place of order; cosmos, in fact, means “order.” Beyond it there may exist nothing at all or total disorder, which is the same as nothing. The boundary between the two is all important: it is precisely where Aristotle placed his god. In a similar way, the lines of a computer circuit diagram draw a map of an ordered world. Outside the computer, there is only chaos, dust, and various contaminants from which this fragile universe of order and logic must be guarded if it is to continue to function. [p75]
The Embodiment of Logical Thought
Electronic thought is the process by which the computer fires small amounts of data back and forth through the circuits in the central processing unit. Just as the popular imagination envisions, the computer “thinks” by means of dispassionate, logical calculation. A thought in common language can be anything from an image in the mind to an emotionally charged point of view, an abstraction like justice, or a theoretical entity invented by physicists. Yet dreamy imaginings, feelings, ambiguities, and contradictions have no meaning in the central processor of a von Neumann machine. The anomaly of half‑completed thoughts, which come sometimes as we are falling asleep, also cannot be computed. In binary logic, a bit is either off or on, false or true.
There are four qualities that characterize the logical processing carried on by the CPU: it is discrete, conventional, finite, and isolated. These qualities properly belong to all formal systems, and before about 1950 such systems existed only in the pages of the logician’s notebook. Since then, they have been dancing through the circuitry of digital computers. Daily success in using formal logic is suggesting to Turing’s man that this is the only way, or at least the preferred way, by which thought (human or electronic) can proceed. These four qualities will emerge repeatedly in the chapters that follow, for they define the new views of time, space, and language that will be explored.
All information, all knowledge, must be coded in some binary representation in order to be acted upon by the computer. It must be broken into a series of discrete values. It has already been noted that even in mathematics this is a limitation, that infinitely many numbers (irrational, algebraic, transcendental) cannot be represented exactly in a digital computer because they cannot be reduced to a finite series of decimal or binary places. Approximation leads to error, the central problem of computer mathematics. On the other hand, symbolic logic has no difficulty adapting itself to discrete representation, for it is characteristic of logic to seek to reduce the continuous to the discrete, the ambiguities and uncertainties of everyday thinking to the binary scheme of true and false. What is remarkable is that the idea of a two‑valued truth function should be so well suited to representation in electronic circuits. In any case, there is no room in the computer for the continuous.
The computer is of course often called upon to process continuous [p76] data from the physical world. When a spacecraft flies by the planet Mars, the pictures it takes are like television images, made up of perhaps several hundred rows, each containing dozens of individual points. At each point, the camera records a particular intensity of light, and the intensity is converted into a numerical value, say, 1 for very dark and 20 for very bright. The whole picture then is represented by a matrix of numbers from 1 to 20, and it is these numbers that are radioed back to earth. A computer takes the received values and reconstitutes the picture, again made of individual points. The original shadings of light given off by the planet have been lost, but if the resolution is fine enough, the human observer on earth will hardly notice the difference. Newspapers print pictures by a similar technique, using dots to give the illusion of continuous shades and contours. For the computer, the continuous is always simulated by a grid of discrete values. Even recorded sounds can be digitalized, turned into a series of numerical values, and later turned back into continuous wave forms ‑ all with extraordinary fidelity.
Computer thought is wholly a matter of convention, of formal rules acting upon contentless symbols. Whether numbers or letters are represented as bit strings in the machine, the representation is one of pure denotation. The number 10 spelled out in transistors has no connotations whatever, such as the word “two” written or spoken is likely to have. For the ancient Pythagoreans, the word “two” possessed an extraordinary range of connotations, including femininity, darkness, infinity, and evil, which were all somehow associated with even numbers; for moderns, perhaps, it has connotations of harmony and completion. Bits within a computer are logical symbols that mean nothing more than they are deemed to mean in the context of a particular program. (As already noted, the same string can stand for a number, a letter, or a machine instruction depending upon the context.) The programmer, then, creates meaning within his program by convention.
Computer specialists like to speak of their machines as manipulators of symbols. This is a good characterization so long as we remember that the symbols are not literary devices or natural signs pointing to a higher reality but simply arbitrary units that the programmer may choose to interpret as words in the English language or moves in the game of chess. Indeed, chess programs are a perfect example of this quality of electronic thought. A computer playing chess is manipulating a series of conventions [p77] (the rules that determine how the pieces are to be moved), and computers play good chess only because these conventions can be clearly stated in the machine’s electronic vocabulary and manipulated by the central processor.
There is something straightforward and apparently superficial about this electronic thought process. It seems superficial because of the long Western tradition of realism, of the conviction that the human mind does not construct its ideas purely at will but that instead those ideas have some force, necessity, or reality of their own. The mind therefore discovers ideas rather than inventing them and may hope through this process of discovery to attain some higher, perhaps ultimate, knowledge. The computer suggests no such deep correspondence between thought and the world at large, such as philosophers and poets from Plato to Descartes, from Greek tragedians to French symbolists, have found. Computer thought is a triumph of nominalism. The symbols that the computer manipulates are senseless in isolation, for there is no reality “behind” the symbols, propping them up. Only when incorporated into a program and set to work, does each symbol acquire a single, unambiguous function. And the whole program is viewed as an invention rather than a discovery.
Computer thought is a sequence of operations, of fetch‑and‑execute cycles of the central processing unit. Computer thought is therefore discrete and finite in a second important sense. Not only are numbers and words represented in discrete strings, but these strings are also processed discretely ‑ from the beginning of the program to its termination. Programming shares this quality with the mathematical thought of both classical Greece and Western Europe, in which the mathematician moves step by step toward his goal. The ancient geometer made a series of verbal assertions about his figures, each linked to a preceding assertion and justified by the rules of inference. His European counterpart, especially in the nineteenth century, often expressed his assertions in equations or sentences of abstract symbols. But the principle remained that there could be no dramatic leaps in the proof, that everything should follow as the night the day. Truly creative mathematicians have always made such leaps in their preliminary thinking, in their intuitive solutions to problems. In fact, their assertions, inspired guesses really, may go unproved for decades or centuries. But when the proof comes, it must be justified at every step. Every intuition must he transformed into a deduction.
Every computer program is the electronic realization the [p78] tanible proof, of a theorem in logic. We saw in the last chapter that the mathematicians Appel and Haken actually incorporated computer programs into their proof of the four‑color theorem. Computer specialists such as Edsger Dijkstra have explicitly treated programs as mathematical entities in their elegant work on logical “correctness.” Every programmer, no matter how pragmatic or mathematically naive, is a logician with a theorem to prove. The theorem states: given a certain pattern of bits (program and data) as input, the machine will produce another pattern, the desired output. The programmer asserts such a theorem as he loads his instructions into the machine; he asserts that the program works. He claims that his square‑root program, if given the bits standing for the number 5, will indeed produce the square root of 5. The commands of the program themselves are steps of his proof, and the test comes in allowing the CPU to thresh its way line by line through the code. The logical organization of the machine (the way it executes commands) is a finite set of rules that the programmer must obey in constructing his proof, just as the mathematician must obey laws of inference in constructing his.
The word “finite” is very important. The pursuit of infinity has been a prime issue for mathematics, philosophy, and even poetry since the Middle Ages. Although the Greeks were repelled by the infinite, Western Europeans in a sense worshiped it. Was not God himself infinitely powerful and good? Should not men and women strive to come as close to God’s infinity as their own finite natures would allow? The infinite and the infinitesimal terrified and yet fascinated philosophers like Pascal, and the paradox of the infinite was still identified by Kant as a major philosophical dilemma. If the computer specialist can accept only finite numbers and finite logic, this represents a turning point in the history of ideas.
Finally, computer thought is thought in isolation. It is indeed embodied, but the embodiment remains curiously separated from the rest of the physical world. I spoke earlier of the contrast between the special organization of electrons within the machine and the disorder of the inanimate world outside. The walls that separate the two worlds, those cabinets of aluminum and colored plastic, make sure that, apart from the electric current for power, there is no contact between the computer and its environment. There is a correspondence between the two, for the equations generated by the machine may successfully describe the course of a spacecraft reentering the earth’s atmosphere But this is the [p79] tantalizing correspondence between mathematics and the world in general: it is a formal relation rather than an immediate contact. The CPU does have channels by which it can communicate with the outside, such input/output devices as tape and disk drives and television screens. But in order to communicate, these devices must themselves obey rules of representation that the CPU dictates; nothing but electronic signals standing for binary strings may come in or go out.
On the other hand, electronic thought is not introspective in any earlier philosophical sense. The processes of the CPU are open to public inspection; we need only take the cover off the machine and apply electronic probing devices (though this serves no purpose unless the machine is malfunctioning). The computer is isolated in the way that all mathematical and logical thought is isolated: it allows for no possibility of immediate union between two thinkers. Computers can and do work together in so‑called networks, and several CPUs can be combined within a single frame. But in the current technology, if one processor were to interfere with the cycles of another, the result would be chaos.
What about the historically important idea that immediate union between minds was possible and perhaps vital to the human condition? Plato believed that the task of the philosopher was to reach the world of ideas by dialectic and contemplation but certainly not by his senses (his input/output devices, to use the computer metaphor), which are mere distractions. His mind must somehow unite itself with the idea of the good and the beautiful. In the same way, many Christian philosophers aimed at some sort of mental union with God. Even the mathematician Descartes had radically separated mind and body and envisioned a community of minds with God. This kind of mental activity ‑ whether the comparatively calm unification envisioned by Plato or the more violent upward movement imagined by mystics and poets of Western Europe ‑ has no counterpart in computerized thought.
The computer does not strive; it proceeds to a predetermined goal. The striving after infinity or self‑knowledge or God, so important in the previous age, is especially foreign to electronic thought. And if the Western mind has often dreamed of overcoming its mortal limitations, its finiteness, in one way or another, the programmer has no such ambitions. The very structure of the CPU and of the languages used to program it reminds him that he must proceed a step at a time and in a finite number of steps produce a useful result
Foundations Burd Reading
Processor Technology and Architecture
From: Burd, Stephen D. (2001). Systems Architecture. Course technology, Thompson Learning, Canada. pp. 110-123.
[p110]
CPU OPERATION
Recall from Chapter 2 that a CPU has three primary components ‑ the control unit, arithmetic logic unit (ALU), and a set of registers (see Figure 4‑2). The control unit moves data and instructions between main memory and registers. The ALU performs all computation and comparison operations. Registers are storage locations that hold inputs and outputs for the ALU.
[p111] Figure 4-2 Components of the CPU
A complex chain of events occurs when the CPU executes a program. To start, the control unit reads the first instruction from primary storage. The control unit then stores the instruction in a register and, if necessary, reads data inputs from primary storage and also stores them in registers. If the instruction is a computation or comparison instruction, the control unit signals the ALU what function to perform, where the input data is located, and where to store the output data. Instructions to move data to memory, I/O devices, or secondary storage are executed by the control unit itself. When the first instruction has been executed, the next instruction is read and executed. The process continues until the final instruction of the program has been executed.
The actions performed by the CPU can be divided into two groups ‑ the fetch cycle (or instruction cycle) and the execution cycle. During the fetch cycle, data inputs are prepared for transformation into data outputs. During the execution cycle, the transformation takes place and data output is stored. The CPU constantly alternates between instruction and execution cycles. Figure 4‑3 shows the flow between instruction and execution cycles denoted by solid arrows and data and instruction movement denoted by dashed arrows.
[p112] Figure 4-3 Control and data flow during the fetch and execution cycles
During the fetch cycle, the control unit:
- Fetches an instruction from primary storage
- Increments a pointer to the location of the next instruction
- Separates the instruction into components‑the instruction code (or number) and the data inputs to the instruction
- Stores each component in a separate register
During the execution cycle, the ALU:
- Retrieves the instruction code from a register
- Retrieves data inputs from registers
- Passes data inputs through internal circuits to perform the addition, subtraction, or other data transformation
- Stores the result in a register
[p113]
At the conclusion of the execution cycle a new fetch cycle is started. The control unit keeps track of the next program instruction location by incrementing a pointer after each fetch. The second program instruction is retrieved during the second fetch cycle, the third instruction is retrieved during the third fetch cycle, and so forth.
INSTRUCTIONS AND INSTRUCTION SETS
An instruction is a command to the CPU to perform one of its primitive processing functions on specific data inputs. It is the lowest‑level command that software can direct a processor to perform. As stored in memory, an instruction is merely a bit string. The bit string logically is divided into a number of components. The first group of bits represents the unique binary number of the instruction, commonly called the op code. Subsequent groups of bits hold the input values for the instruction, called operands. The content of an operand can represent a data item (such as an integer value) or the location of a data item (such as a memory address, a register address, or the address of a secondary storage or I/O device).
Physically, an instruction directs the CPU to route electrical signals representing data input(s) through a predefined set of processing circuits that implement the desired function. Data inputs are accessed from storage or extracted directly from the operands, and stored in one or more registers. For computation and logic functions, the ALU is directed to access these registers and send the corresponding electrical signals through the appropriate processing circuitry. This circuitry transforms the input signals into output signals representing the processing result. This result is stored in a register in preparation for movement to a storage device or I/O device, or for use as input to another instruction.
Figure 4-4 An instruction containing one op code and two operands
Some instructions are executed by the control unit without assistance from the ALU. Instructions for moving or copying data, as well as some simple CPU functions like halting or restarting the CPU, are handled by the control unit alone. [p114]
In general, instructions that require transforming data inputs into new outputs are executed by the ALU. All other instructions are executed by the control unit.
The collection of instructions that a CPU can process is called the CPU’s instruction set. Instruction sets vary among CPUs in the following ways:
- Size of the instruction set
- Size of individual instructions, op codes, and operands
- Supported data types
- Number and complexity of processing operations implemented as individual instructions
Instruction set variations reflect differences in design philosophy, processor fabrication technology, class of computer system, and type of application software. CPU cost and speed depend on these design parameters.
The full range of processing operations expected of a modern computer can be implemented with approximately one dozen instructions. Such an instruction set can perform all of the computation, comparison, data movement, and branching functions for integer and boolean data types. Computation and comparison of real numbers can be accomplished by software with complex sequences of integer instructions operating separately on the whole and fractional parts. Small instruction sets were common in early CPUs and microprocessors. Details of this minimal instruction set are described in the following sections.
Data Movement
A MOVE instruction copies data bits to storage locations. MOVE can copy data among any combination of registers and primary storage locations. Data transfers from main memory into registers usually are called load operations. Data transfers from registers into primary storage usually are called store operations.
MOVE tests the bit values in the source location and places copies of those values in the destination location. The former bit values in the destination are overwritten. At the completion of the MOVE, both sending and receiving locations hold identical copies. The name “move” is a misnomer because the data content of the source location is unchanged.
MOVE also is used to access storage and I/O devices. An input or storage device writes to a specific memory location and the CPU retrieves the input by reading that memory location and copying its value into a register. Similarly, data is output or stored by writing to a predefined memory address or range of addresses. The output or storage device continually monitors the content of its assigned memory address(es) and reads newly written data for storage or output. [p115]
Data Transformations
The most primitive data transformation instructions are based on boolean logic:
- NOT
- AND
- OR
- XOR
These four boolean instructions and the ADD and SHIFT instructions (which are discussed in detail in the following sections) are the basic building blocks of all numeric comparisons and computations. They are summarized in Table 4‑1.
Table 4‑1 Primitive data transformation instructions
Instruction Function
NOT Each result bit is the opposite of the operand bit
AND Each result bit is true if both operand bits are true
OR Each result bit is true if either or both operand bits are true
XOR Each result bit is true if either, but not both, operand bits are true
ADD Result is the arithmetic sum of operands
SHIFT Move all bit values left or right as specified by operand
NOT A NOT instruction transforms the boolean value true (1) into false (0) and the value false into true. The rules that define the output of NOT on single bit inputs are:
NOT 0 = 1
NOT 1 = 0
With bit strings, NOT treats each bit in the bit string as a separate boolean value. For example, executing NOT on the input 10001011 produces the “opposite” result ‑ 01110100. Note that NOT has only one data input, whereas all other boolean instructions have two.
AND An AND instruction generates the result true if both of its data inputs are true. The following rules define the result of AND on single bit data inputs:
0 AND 0 = 0
1 AND 0 = 0
0 AND 1 = 0
1 AND 1 = 1
[p116]
The result of AND with two bit string inputs is shown in the following example:
10001011
AND 11101100
10001000
OR There are two types of OR operations in boolean logic. An inclusive OR instruction (the word inclusive usually is omitted) generates the value true if either or both data inputs are true. The rules that define the output of inclusive OR on single bit inputs are:
0 OR 0 = 0
1 OR 0 = 1
0 OR 1 = 1
1 OR 1 = 1
The result of inclusive OR with two bit string inputs is shown in the following example:
10001011
OR 11101100
11101111
An exclusive OR, also called XOR, instruction generates the value true if either, but not both, data inputs are true. The rules that define the output of XOR on single bit inputs are:
0 XOR 0 = 0
1 XOR 0 = 1
0 XOR 1 = 1
1 XOR 1 = 0
Note that if either operand is one the result is the complement of the other operand. Specific bits within a bit string can be inverted by XORing the bit string with a string containing zeros in all positions except the positions to be negated. For example, the following XOR inverts only the right four bit values and leaves the left four bit values unchanged:
10001011
XOR 00001111
10000100
Every bit in a bit string can be inverted by XORing with a string of ones:
10001011
XOR 11111111
01110100
[p117]
Note that XORing any input with a string of ones produces the same result as executing NOT. Thus, NOT isn’t required in a minimal instruction set.
ADD An ADD instruction accepts two numeric inputs and produces their arithmetic sum. For example:
10001011
ADD 00001111
10011010
This shows the binary addition of two bit strings. Note that the mechanics of the addition operation are the same regardless of what the bit strings represent. In this example, if the bit strings represent unsigned binary numbers, then the operation is:
13910+ 1510= 15410
If the bit strings represent signed integers in two’s complement format, then the operation is:
‑11710 + 1510 = ‑10210
Binary addition does not work for complex data types such as floating point and double precision numbers. If complex numeric data types are supported by the CPU, then a separate ADD instruction must be implemented for each type.
SHIFT The effect of a SHIFT instruction is shown in Figure 4‑5. In Figure 4‑5 (a), the value 01101011 occupies an 8‑bit storage location. Bit strings can be shifted to the right or left, and the number of positions shifted may be greater than one. Typically, a second operand is used to hold an integer value that indicates the number of bit positions by which the value will be shifted. Positive or negative values of this operand can be used to indicate shifting to the left or right.
Figure 4‑5 (b) shows the result of shifting the value two positions to the right. The resulting value is 00011010. In this case, the values in the two least significant positions of the original string have been dropped and the vacant bit positions are filled with zeroes.
Figure 4‑5 is an example of a logical SHIFT. Logical SHIFT typically is used to extract a single bit from a bit string. Figure 4‑6 shows how shifting an 8‑bit value (Figure 4‑6(a)) to the left by four bits (b) and then to the right by seven bits, creates a result (c) with the third bit of the original string in the rightmost position. Since all other bit positions contain zeros, the entire bit string can be interpreted as true or false. Shifting an 8‑bit two’s complement value to the right by seven positions is a simple way to extract and test the sign bit. [p118]
Figure 4-5 Original data byte (a) shifted two bits to the right (b)
Figure 4-6 Extracting a single bit with logical SHIFT instructions
An arithmetic SHIFT instruction performs multiplication or division, as illustrated in Figure 4‑7. If a bit string contains an unsigned binary number (Figure 4‑7(a)), then shifting to the left by one bit (b) multiplies the value by two, and shifting the original bit (a) to the right by two bits (c) divides by four. Arithmetic SHIFT instructions are more complex when applied to two’s complement values because bits must be shifted “around” the sign bit. Most CPUs provide a separate arithmetic SHIFT instruction that preserves the sign bit of a two’s complement value. [p119]
Figure 4-7 Multiplying and dividing binary values using SHIFT instructions
Sequence Control
Sequence control operations alter the flow of instruction execution in a program. These operations include:
- Unconditional branch
- Conditional branch
- Halt
Branch Operations A BRANCH (or JUMP) instruction causes the processor to depart from sequential instruction order. Recall that the control unit fetches the next instruction from memory at the conclusion of each execution cycle. The control unit consults a register to determine where the instruction is located in primary storage. BRANCH has one operand containing the memory address of the next instruction. BRANCH actually is implemented as a MOVE instruction. The BRANCH operand simply is loaded into the register that the control unit uses to fetch the next instruction.
In an unconditional BRANCH, the processor always departs from the normal execution sequence. In a conditional BRANCH, the BRANCH occurs only if a specified condition is met, such as the equivalence of two numeric variables. The condition must be evaluated and the boolean result stored in a register. The conditional BRANCH instruction checks the content of that register and only branches if the value contained there is true. [p120]
HALT A HALT operation suspends the normal flow of instruction execution in the current program. In some CPUs, it causes the CPU to cease all operations. In others it causes a BRANCH to a predetermined memory address. A portion of the operating system typically is loaded at this address, effectively transferring control to the operating system and terminating the previously executing program.
Complex Processing Operations
Complex processing operations can be performed by combining the simpler operations described previously. For example, subtraction can be implemented as complementary addition. That is, the operation A ‑ B can be implemented as A + (‑B). As described in Chapter 3, a negative two’s complement value can be derived from its positive counterpart by taking the complement of the positive value and adding one. A bit string’s complement can be generated by XORing it with a string of binary one digits.
For example, the complement of 0011 (310), represented as a two’s complement value can be derived as:
XOR(0011,1111) + 0001 = 1100 + 0001 = 1101 = -310
This result then can be added to implement a subtraction operation. For example, the result of subtracting 0011 from 0111 can be calculated as:
710 ‑310 = ADD(ADD(XOR(0011,1111),0001),0111)
= ADD(ADD(1100,0001),0111)
= ADD(1101,0111)
= 10100
Because 4‑bit values are used, the result of 10100 is truncated from the left, resulting in a value of 0100.
Comparison operations can be implemented similar to subtraction. A comparison operation generates a boolean output value. Typically, an integer value of zero is interpreted as false and any nonzero value is interpreted as true. The comparison A not equal B can be implemented by generating the complement of B and adding it to A. If the two numbers are equal, the result of the addition will be a string of zeros (interpreted as false). An equality comparison can be implemented by negating the boolean result of an inequality comparison.
Greater than and less than comparisons also can be performed with subtraction followed by extraction of the sign bit. For the condition A < B, subtracting B from A will generate a negative result if the condition is true. In two’s complement notation, a negative value always will have a one in the leftmost position (that is, the sign bit). SHIFT can be used to extract the sign bit from the remainder of the value. For example, the two’s complement value 10000111 is a negative number. [p121]
The sign bit may be extracted by shifting the value 7 bits to the right, resulting in the string 00000001. The SHIFT result may be interpreted as a boolean value (nonzero, or true, in this case).
For example, the comparison:
0111 < 0011
can be evaluated as:
SHIFT(ADD(0111,ADD(XOR(0011,1111),0001)),0011)
SHIFT(ADD(0111,ADD(1100,0001)),0011)
SHIFT(ADD(0111,1101),0011)
SHIFT(0100,0011)
0000
The second operand of the SHIFT instruction is a binary number representing the direction and number of bit positions to shift (+3, or right 3 in this example). The result is zero and is interpreted as the boolean value false.
A Short Programming Example
Consider the following high‑level programming language statement:
IF (BALANCE < 100) THEN
BALANCE = BALANCE ‑ 5
ENDIF
Such a computation may be used in a program that applies a monthly service charge to checking or savings accounts with a balance below a certain minimum. A program that implements this computation using only the previously defined low level CPU instructions is shown in Figure 4‑8. Table 4‑2 shows the register contents after each instruction is executed when the account balance is $64. An 8‑bit two’s complement is the assumed coding format for all numeric data. [p122]
Figure 4-8 A simple program using primitive CPU instructions
1 |
MOVE |
M1, R1 |
‘load BALANCE |
2 | MOVE | M2, R2 | ‘load minimum balance 10010 |
3 | MOVE | M3, R3 | ‘load service charge 510 |
4 | MOVE | M4, R4 | ‘load constant 110 |
5 | MOVE | M5, R5 | ‘load constant 710 |
6 | NOT | R2, R2 | ‘start < comparison |
7 | ADD | R2, R4, R2 | ‘ |
8 | ADD | R1, R2, R0 | ‘ |
9 | SHIFT | R0, R5 | ‘end < comparison |
10 | XOR | R0, R4, R0 | ‘invert comparison result |
11 | BRANCH | R0, 16 | ‘branch if comparison false |
12 | NOT | R3, R3 | ‘start negation of service charge |
13 | ADD | R3, R4, R3 | ‘end negation of service charge |
14 | ADD | R1, R3, R0 | ‘subtract service charge from balance |
15 | MOVE | R0, M1 | ‘store new balance |
16 | HALT | ‘terminate program |
Table 4-2 A simple program using primitive CPU instructions
Instruction | R0 | R1 | R2 | R3 | R4 | R5 |
1 | 01000000 | |||||
2 | 01100100 | |||||
3 | 00000101 | |||||
4 | 00000001 | |||||
5 | 00000111 | |||||
6 | 10011011 | |||||
7 | 10011100 | |||||
8 | 11011100 | |||||
9 | 00000001 | |||||
10 | 00000000 | |||||
11 | ||||||
12 | 11111010 | |||||
13 | 11111011 | |||||
14 | 00111011 | |||||
15 | ||||||
16 |
Instructions 1 through 5 load the account balance, minimum balance, service charge, and needed binary constants from memory locations M1 through [p123] M5. A less than comparison is performed in instructions 6 through 9. The right side of the comparison is converted to a negative value by executing a NOT instruction (instruction 6) and adding 1 to the result (instruction 7). The result is added to the account balance (instruction 8) and the sum is shifted seven places to the right to extract the sign bit (instruction 9). At this point register R0 holds the boolean result of the less than comparison.
For this example, all BRANCH instructions are assumed to be conditional on the content of a register. The BRANCH is taken if the register holds a boolean true value, and otherwise ignored. To jump beyond the code that implements the service charge if the account balance is above the minimum, we must invert the boolean result of the condition prior to branching. Instruction 10 inverts the sign bit stored in the rightmost bit of R0 by XORing it against 00000001 (stored in R5). The conditional BRANCH then is executed. Because the original sign bit was one, the inverted value is zero. Thus the BRANCH is ignored and processing proceeds with instruction 12.
Instructions 12 through 14 subtract the service charge stored in register R3 from the account balance. Instructions 12 and 13 convert the positive value to a negative value, and instruction 14 adds it to the account balance. Instruction 15 saves the new balance in memory. Instruction 16 halts execution of the program.
Foundations Cragon Reading
The Von Neumann Machine
From: Cragon, Harvey G. (2000). Computer Architecture and Implementation. Cambridge University Press, Cambridge. pp. 1-13.
[p1]
ONE
COMPUTER OVERVIEW
1.0 INTRODUCTION
The general‑purpose computer has assumed a dominant role in our world‑wide society. From controlling the ignition of automobiles to maintaining the records of Olympic Games, computers are truly everywhere. In this book a one‑semester course is provided for undergraduates that introduces the basic concepts of computers without focusing on distinctions between particular implementations such as mainframe, server, workstation, PC, or embedded controller. Instead the interest lies in conveying principles, with illustrations from specific processors.
In the modern world, the role of computers is multifaceted. They can store information such as a personnel database, record and transform information as with a word processor system, and generate information as when preparing tax tables. Computers must also have the ability to search for information on the World Wide Web.
The all‑pervasive use of computers today is due to the fact that they are general purpose. That is, the computer hardware can be transformed by means of a stored program to be a vast number of different machines. An example of this power to become a special machine is found in word processing. For many years, Wang Laboratories was the dominant supplier of word processing machines based on a special‑purpose processor with wired‑in commands. Unable to see the revolution that was coming with the PC, Wang held to a losing product strategy and eventually was forced out of the business.
Another example of the general‑purpose nature of computers is found in the electronic control of the automobile ignition. When electronic control was forced on the auto industry because of pollution problems, Ford took a different direction from that of Chrysler and General Motors. Chrysler and General Motors were relatively well off financially and opted to design special‑purpose electronic controls for their ignition systems. Ford on the other hand was in severe financial difficulties and decided to use a microprocessor that cost a little more in production but did not require the development costs of the special‑purpose circuits. With a microprocessor, Ford could, at relatively low cost, customize the controller for various engine configurations by changing the read‑only memory (ROM) holding the program. Chrysler and General Motors, however, found that they had to have a unique controller for each configuration of [p2] auto ‑ a very expensive design burden. Microprocessor control, as first practiced by Ford, is now accepted by all and is the industry design standard.
A number of special‑purpose computers were designed and built before the era of the general‑purpose computer. These include the Babbage difference engine (circa 1835), the Anatasoff‑Berry Computer (ABC) at Iowa State University in the late 1930s, and the Z3 of Konrad Zuse, also in the late 1930s. Other computers are the Colossus at Bletchley Park (used for breaking German codes in World War II) and the ENIAC (which stands for electronic numerical integrater and computer, a plug‑board‑programmed machine at The University of Pennsylvania). These computers are discussed in Subsection 1.3.1.
Each of the early computers noted above was a one‑of‑a‑kind machine. What was lacking was a design standard that would unify the basic architecture of a computer and allow the designers of future machines to simplify their designs around a common theme. This simplification is found in the von Neumann Model.
1.1 VON NEUMANN MODEL
The von Neumann model of computer architecture was first described in 1946 in the famous paper by Burks, Goldstein, and von Neumann (1946). A number of very early computers or computerlike devices had been built, starting with the work of Charles Babbage, but the simple structure of a stored‑program computer was first described in this landmark paper. The authors pointed out that instructions and data consist of bits with no distinguishing characteristics. Thus a common memory can be used to store both instructions and data. The differentiation between these two is made by the accessing mechanism and context; the program counter accesses instructions while the effective address register accesses data. If by some chance, such as a programming error, instructions and data are exchanged in memory, the performance of the program is indeterminate. Before von Neumann posited the single address space architecture, a number of computers were built that had disjoint instruction and data memories. One of these machines was built by Howard Aiken at Harvard University, leading to this design style being called a Harvard architecture.1
A variation on the von Neumann architecture that is widely used for implementing calculators today is called a tagged architecture. With these machines, each data type in memory has an associated tag that describes the data type: instruction, floating-point value (engineering notation), integer, etc. When the calculator is commanded to add a floating‑point number to an integer, the tags are compared; the integer is converted to floating point, the addition is performed, and the result is displayed in floating point. You can try this yourself with your scientific calculator.
All variations of the von Neumann that have been designed since 1946 confirm that the von Neumann architecture is classical and enduring. This architecture can be embellished but its underlying simplicity remains. In this section the von Neumann
1 The von Neumann architecture is also known as a Princeton architecture, as compared with a Harvard architecture.
[p3] architecture is described in terms of a set of nested state machines. Subsection 1.2.1 explores the details of the von Neumann architecture.
We should not underestimate the impact of the von Neumann architecture, which has been the unifying concept in all computer designs since 1950. This design permits an orderly design methodology and interface to the programmer. One can look at the description of any modern computer or microprocessor and immediately identify the major components: memory, central processing unit (CPU), control, and input/output (I/O).
The programmer interface with the von Neumann architecture is orderly. The programmer knows that the instructions will be executed one at a time and will be completed in the order issued. For concurrent processors, discussed in Chapter 6, order is not preserved, but as far as the programmer is concerned order is preserved.
A number of computer architectures that differ from the von Neumann architecture have been proposed over the years. However, the simplicity and the order of the von Neumann architecture have prevented these proposals from taking hold; none of these proposed machines has been built commercially.
State Machine Equivalent
A computer is defined as the combination of the memory, the processor, and the I/O system. Because of the centrality of memory, Chapter 4 discusses memory before Chapters 5 and 6 discuss the processor.
The three components of a computer can be viewed as a set of nested state machines. Fundamentally, the memory holds instructions and data. The instructions and the data flow to the logic, then the data (and in some designs the instructions) are modified by the processor logic and returned to the memory. This flow is represented as a state machine, shown in Figure 1. 1.
The information in memory is called the process state. Inputs into the computer are routed to memory and become part of the process state. Outputs from the computer are provided from the process state in the memory.
The next level of abstraction is illustrated in Figure 1.2. The logic block of Figure 1.1 is replaced with another state machine. This second state machine has for its memory the processor registers. These registers, discussed in Chapter 3, include the program counter, general‑purpose registers, and various dedicated registers. The logic consists of the arithmetic and logic unit (ALU) plus the logic required to support the interpretation of instructions.
Figure 1.1 State machine [p4]
Figure 1.2 State machine II
The information contained in the registers is called the processor state. The processor state consists of (1) the information needed to interpret an instruction, and (2) information carried forward from instruction to instruction such as the program counter value and various tags and flags. When there is a processor context switch, it is the processor state that is saved, so the interrupted processor state can be restored.2
When microprogramming is discussed in Chapter 5, we will see that the logic block of Figure 1.2 can also be implemented as a state machine. For these implementations, there are three levels of state machine: process state, processor state, and micromachine processor state.
We now examine the major components of a computer, starting with the memory. As discussed in the preceding paragraphs, the memory is the space that holds the process state, consisting of instructions and data. The instruction space is not only for the program in execution but also for the operating system, compilers, interpreters, and other system software.
The processor reads instructions and data, processes the data, and returns results to memory, where the process state is updated. Thus a primary requirement for memory is that it be fast; that is, reads and writes must be accomplished with a small latency.
In addition, there are two conflicting requirements for memory: memory should be both very large and very fast. Memory cost is always a factor, with low cost being very desirable. These requirements lead to the concept of hierarchical memory. The memory closest to the processor is relatively small but is very fast and relatively expensive. The memory most distant from the processor is disk memory that is very slow but very low cost. Hierarchical memory systems have performance that approaches the fast memory while the cost approaches that of the low‑cost disk memory. This characteristic is the result of the concept of locality, discussed in Chapter 4. Locality of programs and data results in a high probability that a request by the processor for either an instruction or a datum will be served in the memory closest to the processor.
The processor, sometimes called the CPU, is the realization of the logic and registers of Figure 1.2. This portion of the system fetches instructions, decodes these
2 A context switch saves the processor state and restores a previously saved processor state.
[p5] instructions, finds operands, performs the operation, and returns the result to memory. The complexity of the CPU is determined by (1) the complexity of the instruction set, and (2) the amount of hardware concurrency provided for performance enhancement.
As shown in Figure 1.2, a computer must have some method of moving input data and instructions into the memory system and moving results from the memory to the outside world. This movement is the responsibility of the I/O system. Input and output devices can have differing bandwidths and latency. For example, keyboards are low‑bandwidth devices whereas color display units have high bandwidth. In between we find such devices as disks, modems, and scanners.
The control of I/O can take a number of forms. At one extreme, each transfer can be performed by the CPU. Fully autonomous systems, such as direct memory access (DMA), however, provide high‑bandwidth transfers with little CPU involvement. I/O systems are discussed in Chapter 7.
The formal specification of a processor, its interaction with memory, and its I/O capabilities are found in its instruction set architecture (ISA). The ISA is the programmer’s view of the computer. The details of how the ISA is implemented in hardware, details that affect performance, are known as the implementation of the ISA.
1.2 THE VON NEUMANN ARCHITECTURE
The von Neumann ISA is described in this section. Except for the I/O, this architecture is complete and represents a starting point for the discussion in the following chapters. The features found in this architecture can be found in any of today’s architectures; thus a thorough understanding of the von Neumann architecture is a good starting point for a general study of computer architecture. This architecture, of which a number were actually built, is used in this book for a simple example rather than the presentation of a contrived example of a simple architecture. When a von Neumann computer was actually completed at Princeton University in 1952, it was named the Institute for Advanced Studies (IAS) computer.
The von Neumann architecture consists of three major subsystems: instruction processing, arithmetic unit, and memory, as shown in Figure 1.3. A key feature of this architecture is that instructions and data share the same address space. Thus there is one source of addresses, the instruction processing unit, to the memory. The output of the memory is routed to either the Instruction Processing Unit or the Arithmetic Unit
Figure 1.3 von Neumann architecture [p6]
Figure 1.4 Accumulator local storage
depending upon whether an instruction or a datum is being fetched. A corollary to the key feature is that instructions can be processed as data. As will be discussed in later chapters, processing instructions as data can be viewed as either a blessing or a curse.
1.2.1 THE VON NEUMANN INSTRUCTION SET ARCHITECTURE
The von Neumann ISA is quite simple, having only 21 instructions. In fact, this ISA could be called an early reduced instruction set computer (RISC) processor.3 As with any ISA, there are three components: addresses, data types, and operations. The taxonomy of these three components is developed further in Chapter 3; the three components of the von Neumann ISA are discussed below.
Addresses
The addresses of an ISA establish the architectural style ‑ the organization of memory and how operands are referenced and results are stored. Being a simple ISA, there are only two memories addressed: the main memory and the accumulator.
The main memory of the von Neumann ISA is linear random access and is equivalent to the dynamic random‑access memory (DRAM) found in today’s processors. The technology of the 1940s restricted random‑access memory (RAM) to very small sizes; thus the memory is addressed by a 12‑bit direct address allocated to the 20‑bit instructions.4 There are no modifications to the address such as base register relative or indexing. The formats of the instructions are described below in the subsection on data types.
Local storage in the processor is a single accumulator, as shown in Figure 1.4. An accumulator register receives results from the ALU that has two inputs, a datum from memory, and the datum held in the accumulator. Thus only a memory address is needed in the instruction as the accumulator is implicitly addressed.
Data Types
The von Neumann ISA has two data types: fractions and instructions. Instructions are considered to be a data type since the instructions can be operated on as data, a feature called self‑modifying code. Today, the use of self‑modifying code is considered
3 An instruction set design posited by Van der Poel in 1956 has only one instruction.
4 The Princeton IAS designers had so much difficulty with memory that only 1K words were installed with a 10‑bit address.
[p7] to be poor programming practice. However, architectures such as the Intel x86 family must support this feature because of legacy software such as MSDOS.
Memory is organized with 4096 words with 40 bits per word; one fraction or two instructions are stored in one memory word.
FRACTIONS
The 40‑bit word is typed as a 2’s complement fraction; the range is ‑1 <= f < +1:
INSTRUCTIONS
Two 20‑bit instructions are allocated to the 40‑bit memory word. An 8‑bit operation code, or op‑code, and a 12‑bit address are allocated to each of the instructions. Note that, with only 21 instructions, fewer op‑code bits and more address bits could have been allocated. The direct memory address is allocated to the 12 most significant bits (MSBs) of each instruction. The address and the op‑code pairs are referred to in terms of left and right:
Registers
A block diagram of the von Neumann computer is shown in Figure 1.5, Note that I/O connections are not shown. Although only sketchily described in the original paper on this architecture, I/O was added to all implementations of this design.
The von Neumann processor has seven registers that support the interpretation of the instructions fetched from memory. These registers and their functions are listed in Table 1.1. Note that two of the registers are explicitly addressed by the instructions and defined in the ISA (called architected registers) while the other six are not defined
Figure 1.5 Block diagram of the von Neumann architecture: MQ, multiplier quotient register; IR, instruction register; IBR, instruction buffer register; MAR, memory address register; MDR, memory data register [p8]
TABLE 1.1 VON NEUMANN ISA REGISTERS | |
Name |
Function |
Architected Registers | |
Accumulator, AC, 40 bits | Holds the output of the ALU after an arithmetic operation, a datum loaded from memory, the most‑significant digits of a product, and the divisor for division. |
Multiplier quotient register, MQ, 40 bits | Holds a temporary data value such as the multiplier, the least‑significant bits of the product as multiplication proceeds, and the quotient from division. |
Implemented Registers | |
Program counter, PC, 12 bits* | Holds the pointer to memory. The PC contains the address of the instruction pair to be fetched next. |
Instruction buffer register, IBR, 40 bits | Holds the instruction pair when fetched from the memory. |
Instruction register, IR, 20 bits | Holds the active instruction while it is decoded in the control unit. |
Memory address register, MAR, 12 bits | Holds the memory address while the memory is being cycled (read or write). The MAR receives input from the program counter for an instruction fetch and from the address field of an instruction for a datum read or write. |
Memory data register, MDR, 40 bits | Holds the datum (instruction or data) for a memory read or write cycle. |
* The program counter is a special case. The PC can be loaded with a value by a branch instruction, making it architected, but cannot be read and stored, making it implemented. | |
but are used by the control for moving bits during the execution of an instruction (called implemented registers).
Operations
The operations of the von Neumann ISA are of three types:
- moves between the accumulator, multiplier quotient register, and memory
- ALU operations such as add, subtract, multiply, and divide
- Unconditional and conditional branch instructions that redirect program flow.5
The von Neumann ISA consists of 21 instructions, shown in Table 1.2, which are sufficient to program any algorithm. However, the number of instructions that must
5 Many computer historians credit the von Neumann ISA with the first use of conditional branching with a stored program computer. No prior computer possessed this feature and subprograms were incorporated as in‑line code. [p9]
TABLE 1.2 THE VON NEUMANN ISA | |
Move Instructions | |
1. AC <- MQ | Move the number held in the MQ into the accumulator. |
2. M(x) <- AC | Move the number in the accumulator to location x in memory. The memory address x is found in the 12 least‑significant bits of the instruction. |
3.* M(x,28:39) <- AC(28:39) | Replace the left‑hand 12 bits of the left‑hand instruction located at position x in the memory with the left‑hand 12 bits in the accumulator.** |
4.* M(x,8:19) <- AC(28:39) | Replace the left‑hand 12 bits of the right‑hand instruction in location x in the memory with the left‑hand 12 bits in the accumulator. |
ALU Instructions | |
5. ACc <- M(x) | Clear the accumulator and add the number from location x in the memory. |
6 AC <- ACc ‑ M(x) | Clear the accumulator and subtract the number at location x in the memory. |
7. AC <- ACc+ |M(x)| | Clear the accumulator and add the absolute value of the number at location x in the memory. |
8. AC <- ACc ‑ |M(x)| | Clear the accumulator and subtract the absolute value of the number at location x in the memory. |
9. AC <- AC + M(x) | Add the number at location x in the memory into the accumulator. |
10. AC <- AC ‑ M(x) | Subtract the number at location x in the memory from the accumulator. |
11. AC <- AC + |M(x)| | Add the absolute value of the number at location x in the memory to the accumulator. |
12. AC <- AC ‑ |M(x)| | Subtract the absolute value of the number at location position x in the memory into the accumulator. |
13. MQc <- M(x) | Clear the MQ register and add the number at location x in the memory into it. |
14. ACc, MQ <- M(x) x MQ | Clear the accumulator and multiply the number at location x in the memory by the number in the MQ, placing the most‑ significant 39 bits of the answer in the accumulator and the least‑significant 39 bits of the answer in the MQ. |
15. MQc, AC <- AC M(x) | Clear the register and divide the number in the accumulator by the number at location x of the memory, leaving the remainder in the accumulator and placing the quotient in MQ. |
16. AC <- AC x 2 | Multiply the number in the accumulator by 2. |
17. AC <- AC 2 | Divide the number in the accumulator by 2. |
Control Instructions | |
18. Go to M(x, 20:39) | Shift the control to the left‑hand instruction of the pair in M(x). |
19. Go to M(x, 0:19) | Shift the control to the right‑hand instruction of the pair in M(x). |
20. If AC >= 0, then PC <- M(x, 0:1 9) | If the number in the accumulator is >= 0, go to the right‑hand instruction in M(x). |
21. If AC >= 0, then PC <- M(x, 20:39) | If the number in the accumulator is >= 0, go to the left‑hand instruction in M(x) |
* These instructions move the address portion of an instruction between memory and the accumulator. These instructions are required to support address modification. Indexing, common today in all computer’s ISAs had not yet been invented. ** The notation M(x,0:1 9) means the right‑hand 20 bits of location M(x); M(x,20:39) means the left‑hand 20 bits, and so on. | |
[p10] be executed is considerably greater than that required by more modem ISAs. The instructions are grouped into three groups: move, ALU, and control. This grouping is typical of all computers based on the von Neumann architecture. A more modem terminology, not the terminology of von Neumann, is used in Table 1.2.
1.2.2 INSTRUCTION INTERPRETATION CYCLE
Interpretation of an instruction proceeds in three steps or cycles. The instruction is fetched, decoded, and executed. These three steps are discussed in the following sub sections.
Instruction Fetch
A partial flow chart for the instruction fetch cycle is shown in Figure 1.6. Because two instructions are fetched at once, the first step is to determine if a fetch from memory is required. This test is made by testing the least‑significant bit (LSB) of the program counter. Thus, an instruction fetch from memory occurs only on every other state of the PC or if the previous instruction is a taken branch. The fetch from memory places a left (L) and a right (R) instruction in the instruction buffer register (IBR).
Instructions are executed, except for the case of a branch instruction, left, right, left, right, etc. For example, consider that an R instruction has just been completed.
Figure 1.6 Instruction fetch cycle [p11]
There is no instruction in the IBR and a reference is made to memory to fetch an instruction pair.
Normally, the L instruction is then executed. The path follows to the left, placing the instruction into the instruction register (IR). The R instruction remains in the IBR for use on the next cycle, thereby saving a memory cycle to fetch the next instruction.
If the prior instruction had been a branch to the R instruction of the instruction pair, the L instruction is not required, and the R instruction is moved to the IR. In summary, the instruction sequence is as follows:
Sequence Action
L followed by R No memory access required
R followed by L Increment PC, access memory, use L instruction
L branch to L Memory access required and L instruction used
R branch to R Memory access required and R instruction used
L branch to R If in same computer word, memory access not required
R branch to L If in same computer word, memory access not required
After the instruction is decoded and executed, the PC is incremented for the next instruction and control returns to the start point.
Decode and Execute
Instruction decode is only indicated in Figure 1.6. However, the instruction has been placed in the IR. As shown in Figure 1.7, combinatorial logic in the control unit decodes the op‑code and decides which of the instructions will be executed. In other words, decoding is similar to the CASE statement of many programming languages. The flow charts for two instruction executions are shown in Figure 1.7: numbers 21 and 6. After an instruction is executed, control returns to the instruction fetch cycle, shown in Figure 1.6.
Figure 1.7 Decode and execute [p12]
The sequencing of the instruction interpretation cycle is controlled by a hardwired state machine, discussed in Chapter 5. Each of the states is identified in flowchart form, flip flops are assigned to represent each state, and the logic is designed to sequence through the states. After the invention of microprogramming, the flow chart is reduced to a series of instructions that are executed on the micromachine. In other words, a second computer, rather than a hardwired state machine, provides the control.
Example Program
Without indexing, the complexity of programming the von Neumann ISA is illustrated with the following example shown in Table 1.3. We wish to compute the vector add of two vectors of length 1000:
Ci = Ai + Bi.
Vector A is stored in locations 1001‑2000, vector B in locations 2001‑3000, and vector C in locations 3001‑4000. The first steps of the program initialize three memory
TABLE 1.3 VECTOR ADD PROGRAM | ||
Location |
Datum/Instruction |
Comments |
0 | 999 | Count |
1 | 1 | Constant |
2 | 1000 | Constant |
Inner Loop for Each Add | ||
3L | AC <- M(3000) | Load Bi |
3R | AC <- AC+M(2000) | Bi + Ai |
4L | M(4000) <- AC | Store AC |
Loop Test and Continue/Terminate | ||
4R | AC <- M(0) | Load count |
5L | AC <- AC ‑ M(1) | Decrement count |
5R | If AC >= 0, go to M(6,0:19) | Test count |
6L | Go to M(6,20:39) | Halt |
6R | M(0) <- AC | Store count |
Address Adjustment (Decrement) | ||
7L | AC <- AC+ M(1) | Increment count |
7R | AC <- AC + M(2) | Add constant |
8L | M(3,8:19) <- AC(28:39) | Store modified address in 3R |
8R | AC <- AC+ M(2) | Add constant |
9L | M(3,28:39) <- AC | Store modified address in 3L |
9R | AC <- AC + M(2) | Add constant |
10L | M(4,28:39) <- AC | Store modified address in 4L |
10R | Go to M(3,20:39) | Unconditional branch to 3L |
[p 13] locations with the count 999, the constant 1000 (for testing the number of times the operation is performed), and the constant 1 (for a decrement value).
1.2.3 LIMITATIONS OF THE VON NEUMANN INSTRUCTION SET ARCHITECTURE
There are a number of major limitations of the von Neumann ISA highlighted by the vector add program of Table 1.3. The first limitation has been noted in Subsection 1.2.2: there are no facilities for automatic address modification as with modern processors. Thus the addresses in the instructions must be modified by other instructions to index through an array. This is the self‑modifying code that is very prone to programming error.
In addition, modular programming was unknown at the time of the von Neumann ISA development. Thus the architecture provides no base register mode to assist in partitioning instructions and data.
Another major limitation can be found in the vector add program of Table 1.3. With this architecture, the program counter is an implemented register All modem processors have an architected program counter; thus the PC can be stored and restored, thereby enabling the programming concepts of subroutines and procedure calls. These concepts cannot be used on the von Neumann ISA with its implemented program counter.
Finally, as mentioned in Subsection 1.2.1, the I/O was only briefly mentioned in the original paper on the von Neumann ISA. The implementation of the I/O on this and other computers will be discussed in Chapter 7.
1.3 HISTORICAL NOTES
Indexing. Apparently, the first incorporation of indexing to an ISA was with the Mark 1, developed by Kilburn and Williams at The University of Manchester, 1946‑1949, and produced by Ferranti Corp. The first Ferranti machine was installed in 1951. Although this machine is well known for the development and the use of virtual memory, the pioneering work regarding indexing is equally important. Indexing was provided as an adjunct function, called the B lines or B box.
The IBM 704, announced in 1954, has three index registers. These registers, along with floating point, provided the hardware support for the development of FORTRAN (Blaauw and Brooks 1997). It is interesting to note that the IBM 701, first installed in 1953, required program base address modification, as did the von Neumann ISA.
Subroutines: A subroutine is a program that executes only when called by the main program. After execution, the main program is then restarted. Because subroutines require a return to the main program, a necessary condition for subroutine support is that the program counter must be saved. As the von Neumann ISA had no provisions for saving the program counter, the ISA cannot execute subroutines.
This problem was first solved by Wheeler for the EDSAC at Cambridge University under the direction of Maurice Wilkes (Wilkes, Wheeler, and Gill 1951). The program counter became architected, permitting its contents to be saved and restored.
Topic Eight: Computing with Circuits and Switches
Lecture Objective:
To gain a practical understanding of how an electronic computer
performs basic calculations.
Overview of Topics:
- Boolean Logic
- Circuits and Relays
- Storage Circuits
- Circuit Notation
Supplementary Topics:
- Boolean Arithmetic
- Boolean Selection
- The Arithmetic and Logic Unit
Note: The supplementary lecture and tutorial material are needed for the second assignment and require the scheduling of another two-hour lecture and one-hour tutorial.
The lecture is based on Chapter 6 of The Foundations of Computing and the Information Technology Age (see the Lecture Chapter for Topic Seven).
Foundations Topic 8 Overheads
Foundations Topic 8 Additional Overheads
Foundations Topic 8 Tutorial
Foundations Topic 8 Additional Exercises
Topic Nine: Information Technology in Theory
Lecture Objective:
To gain a general theoretical understanding of the concept of
information technology and its role in social organisation and
control.
Overview of Topics:
- Taking a Critical Stance
- Defining Technology
- The Connection between Science and Technology
- Information Technology
- Networks and Hierarchies
- What is Information Technology?
The lecture is based on Chapter 7 of The Foundations of Computing and the Information Technology Age.
Foundations Topic 9 Overheads
Foundations Book Chapter 7
Foundations Topic 9 Tutorial
Foundations Ellul Reading
The Technological System
From: Ellul, Jacques (1977/1980). The Technological System. The Continuum Publishing Corporation, New York. pp87-93.
[p87]
Nonetheless, there is a further error to be avoided here. We should not believe that if technology is considered in this way, it is an object, or that, in relation to technology, man is a subject. Yet that is what we hear all the time. After all, technology merely supplies things, and man does whatever he likes with them. Thus, everything depends on their good or bad use . . . Remarkably, moreover, the very same people declare that the technological system does not exist as such and that there are only technological objects. In point of fact, however, those objects are not scattered and unrelated, they are included in a system. Furthermore, man, who is to act upon this system, who is to use these technological objects, is not a man per se, an absolute subject either. He himself is incorporated in a technological society.
We have to zero in on this current opinion. First of all, it belongs to the “man in the street,” who, of course, does not perceive a technological ensemble; he thinks he is dealing with his car, his TV, his modern accounting register, the IBM machine, and the airplane. Separate elements, distinct uses, an absence of reflection on their coherence and continuity. But this attitude results just as much from specialization. Each sector develops independently of the others (in appearance). Each of us is immersed in a separate technological domain. Each man knows his professional technology, and only that. He is aware (theoretically) that other technologies exist side by side with his, but he does not see the inner coherence of the sectors, and he can dream about all those vast and free fields which are ruled by independence and imagination‑his own field being that of rigor, efficiency, and enslavement. Last but [p88] not least, among intellectuals, this attitude results from a systematic refusal to consider this reality: If technology is truly a system, then freedom of thought is a mere decoy, man’s sovereignty is threatened, etc.; and since this cannot be, then technology cannot possibly be a system.
This panicky reflex dominates most intellectual judgments on the nonexistence of technology per se. It is really so convenient and so reassuring to consider only completely unrelated devices, objects, methods. One can then imagine sovereign man throning in this collection and acting upon it in full independence. All technological elements come from him, have no existence outside of him, and return to him; in short, man gives them their coherence. For there is great reluctance to admit that a specific organization of technology exists, relatively independent of man, a sort of schematizing of life by technology. This reluctance is manifest in the following: romantic reactions, (which explains a whole portion of modern literature); the intellectual impugnment of this possibility; and the elaboration of false concepts to account for our society, to attest that ultimately nothing has changed, man is still man, society is still society, nature is still nature. Society is still formally and substantially the same‑i.e., nothing has essentially changed in two centuries. Of course, there is speed, urbanization, and so on, but . . .
At bottom, those intellectuals maintain the image of an intact society (and an intact human being): a society whose structures are comparable to those of the past (not the same, to be sure), whose groups, culture, work are subject to the same principles and the same analyses (though we perceive the differences, to be sure). Society (the same old society) is thought of as consisting, still, of classes (with similar class relationships) and obeying the same old dialectics . . . In other words, there is a permanent reality undergoing surface modifications, the reality of man for some, the reality of society for others, the reality of classes; and this reality is joined by an ensemble of processes, objects, work methods, machines, which certainly change one or two aspects of the society, but ultimately integrate into it, add to it. This image recurs endlessly, even among the most “forward‑looking” people‑the image of a modern society, which, in short, is merely the traditional society plus technologies. Naturally, it is not put in that way, but the type of analysis presented shows that such is the (hidden) assumption. And that is exactly what Lefebvre assumes in the statement quoted above. It is very hard to accept that we live in a society having no [p89] common measure with earlier societies, and that the experiences and thoughts of our ancestors are no longer of any use to us […]
The technological system is a qualitatively different phenomenon from an addition of multiple technologies and objects. We cannot absolutely understand them if we consider them separately or isolate one field of action from technology; we have to study them inside of, and in terms of, the overall technological [p90] system. How could we evaluate the influence of rapid communications if we separate them from the methods of modern work, the forms of housing, the technologies of government and administration, the demands of production and distribution, etc.?
The mere act of isolating one aspect completely falsifies the issue as a whole. To understand the technological phenomenon, to analyze its sociology, the first condition is to regard it as a whole, in its unity. So long as we look at the technologies separately, we can certainly study each one’s formation, its specific methods, its particular influences; but that sheds no light for us on the society in which we live or on the reality of the technological milieu. We would therefore have a false view of not only the whole, but also every particular technology; for each one can be truly comprehended only in its relationship to the others. To what extent does that one technology spark the development of other technologies; to what extent is it based on other technologies, etc.? This is a decisive methodological problem. We have to study the technological system in itself; and it is only this approach that makes it possible to study the different technologies.
Having said that, we can attempt a quick first view of this system by naming certain of its aspects.
The first aspect of the system is obviously its specificity. Technologies are not comparable to anything else. That which is not a technology has no point in common with that which is. And they possess, among themselves, similar characteristics; one can find traits common to all technologies. But we have to go further. All [p91] the parts are correlated, a correlation accentuated by the technicizing of information. The consequences are twofold. First of all, one cannot modify a technology without causing repercussions and modifications in a huge number of other objects or methods. Secondly, the combinations of technologies produce technological effects, engendering new objects or new methods. And these combinations take place necessarily, inevitably. But beyond that, the technological world, like any system, has a certain tendency to regulate itself, i.e., to constitute an order of development and functioning which makes technology engender both its own accelerators and its own brakes. Nevertheless, as we shall see, this aspect is the most uncertain. The system thus seems highly independent of man (just as the natural environment used to be).
This system exists basically not because a mechanical relationship has established itself between the different factors (by no means should we imagine the technological system like the different parts of a clockwork); but because we have a denser and denser ensemble of information relationships. We already know this on the level of our own interpretation. Information theory, which is all the rage nowadays, is an “interscientific technology . . . that allows us both to systematize scientific concepts and schematize diverse technologies.” Information theory is not a new science, nor a technology among technologies. It has developed because the technological system exists as a system by dint of the relationships of information. It is neither a chance thing nor a brilliant human discovery. It is a response to man’s need to understand the new universe. Information theory is a mediating thought among the various technologies (but also among the various sciences, and between the sciences and the technologies). “It comes into play as a science of technologies and a technology of sciences.”
But if that is so, if information theory now appears to be a means of finally penetrating that system, then it is because information has done its share in structuring the system itself. The various technologies have unified into a system by dint of the information transmitted from one to another and utilized technologically in each sector. One can fittingly apply Norbert Wiener’s statement (Cybernetics) to the technological system: “Just as the amount of information of a system measures its degree of organization, so too the entropy of a system measures its degree of disorganization.
Once every technological object or method no longer had just the function of doing the exact task it was created for, but also acted as a transmitter of information; once every technological object or [p92] method started not only to function as such, but also to register the information transmitted by the whole technological environment (aside from what comes from the natural environment); and finally, once everyone took all that information into account‑that was the point at which there was a system.
It is not only the emergence of information theory which forces us to note this, but also the multiplication of devices transmitting information and of information technologies. The technological system has thus become a demander in these areas. The more technology develops, the further the labors of information increase as a condition of that development. Material output and the movements of physical objects have become less important than these nonmaterial activities. The information explosion was necessary for the creation of the system; it is not a mere accidental product of our capacity to produce information. The moment the system tends to organize itself, the demand for information becomes explicit; that is to say, a new informational sector appears, which is itself made up of technologies whose sole specific feature is to produce, transmit, and gather information. At present, ninety percent of this information is produced by technologies of action and intervention, and its purpose is to allow other technological sectors to improve or adjust.
Thus, what we have is an intertechnological relationship, the emergence of an ensemble of mediations; and that is what constitutes technology into a system. It is not just a matter of (though this is important) communicating, and reading about, scientific discoveries, innovations, (the international grid of information that will integrate the present‑day electronic data banks, for instance). Far more significant is the permanent relation, on a concrete, often very humble level, between everything that is performed and everything that could be performed in the neighboring operational areas. Scientific information has always been highly attractive and unsettling, but it is not the center of our world; it is the permanent movement of thousands of bits of operational data from one technological sector to another. Now this movement has been decisively facilitated by the appearance of computers. And it is in this context that we must ask about the new technological ensemble, thanks to which the technological system is completing the process of constituting itself.
The importance of the computer is obviously tied to the fact that the further we advance, the more significant a part of our world information becomes (this is already a platitude). We are no longer [p93] a society dominated by the imperative of production; now, we are ruled by the transmission, circulation, reception, and interpretation of multiple information. And that is exactly how the system is completing its constitution. The parts are not coordinated or even connected with one another; they are not materially linked. But each part is a receiver of information, and the system is held together by the network of endlessly renewed information. What makes it flexible and ungraspable at a given moment is that one can never draw up any sort of “inventory of the system,” because that would mean coagulating the information, hence negating the system itself.
Topic Ten: The Origins of the Information Tecxhnology Age
Lecture Objective:
To gain a general understanding of historical background to the information technology revolution.
Overview of Topics:
- Pax Britannica
- The Rise of the Corporation
- The World Wars
- The Post-War World Order
The lecture is based on Chapter 8 of The Foundations of Computing and the Information Technology Age.
Foundations Topic 10 Overheads
Foundations Book Chapter 8
Foundations Beniger Reading
The Control Revolution
From: Beniger, James R. (1986). The Control Revolution. Harvard University Press, Cambridge, Massachusetts. Pp426-436.
[p426]
10 Conclusions: Control as Engine of the Information Society
The great scientific revolution is still to come. It will ensue when men systematically use scientific procedures for the control of human relationships and the direction of the social effects of our vast technological machinery … The story of the achievement of science in physical control is evidence of the possibility of control in social affairs. ‑John Dewey, Philosophy and Civilization (1931)
ONLY SINCE World War II have the industrial economies of the United States, Canada, Western Europe, and Japan appeared to give way to information societies, so named because the bulk of their labor force engages in informational activities and the wealth thus generated comes increasingly from informational goods and services. Although all human societies have depended on hunting and gathering, agriculture, or the processing of matter and energy to sustain themselves, such material processing, it would seem, has begun to be eclipsed in relative importance by the processing of information.
How did this come to be ‑ and why? Despite scores of technical and popular books and articles documenting the advent of the Information Society no one seems to have even raised, much less answered, these crucial questions. Among the many things that human beings value, how did information, embracing both goods and services, come to dominate the world’s largest and most advanced economies? Material culture has also been crucial throughout human history, and yet capital did not begin to displace land as an economic base until the Industrial Revolution. To what comparable technological and economic “revolution” might we attribute the similar displacement of the industrial capital base by information and information‑processing goods and services, or the overshadowing of the Industrial by the Information Society?
The answer, as we have seen, is the Control Revolution, a complex [p427] of rapid changes in the technological and economic arrangements by which information is collected, stored, processed, and communicated and through which formal or programmed decisions can effect societal control. From its origins in the last decades of the nineteenth century the Control Revolution has continued unabated to this day and in fact has accelerated recently with the development of microprocessing technologies. In terms of the magnitude and pervasiveness of its impact upon society, intellectual and cultural no less than material, the Control Revolution appears to be as important to the history of this century as the Industrial Revolution was to the last. Just as the Industrial Revolution marked an historical discontinuity in the ability to harness energy, the Control Revolution marks a similarly dramatic leap in our ability to exploit information.
Why did the Control Revolution begin in America at mid‑nineteenth century, closely following the Industrial Revolution? Such questions of timing become easier to answer if we consider, as we did in Chapter 5, that national economies constitute concrete open processing systems engaged in the continuous extraction, reorganization, and distribution of environmental inputs to final consumption. Until the last century these functions, even in the largest and most developed national economies, still were carried on at a human pace, with processing speeds enhanced only slightly by draft animals and wind and water power and with system control increased correspondingly by modest bureaucratic structures. So long as the energy used to process and move material throughputs did not much exceed that of human labor, individual workers in the system could provide the information processing required for its control.
Once energy consumption, processing and transportation speeds, and the information requirements for control are seen to be interrelated, the Industrial Revolution takes on new meaning. By far its greatest impact from this perspective was to speed up society’s entire material processing system, thereby precipitating a crisis of control, a period in which innovations in information‑processing and communication technologies lagged behind those of energy and its application to manufacturing and transportation.
Crisis and Revolution
[p428]
Table 10. 1. Selected crises in the control of transportation, production, distribution, and consumption, 1840‑1889 | |
Year | Crisis |
1841 | Western Railroad collision kills two, injures seventeen; Massachusetts Legislature investigation |
1849 | Freight must be processed through nine transshipments between Philadelphia and Chicago, impeding distributional networks |
1851‑54 | Erie Railroad, first trunk line connecting East and West, begins operations in “utmost confusion,” misplaces cars for months |
1850s | With the growing network of grain elevators and warehouses, and the mounting demand for mass storage and shipment, transporters have increasing difficulty keeping track of individual shipments of grain and cotton; |
1850s & 1860s | Mercantile firms are increasingly unable to control the growing commerce in wheat, corn, and cotton; Commission merchants are increasingly unable to handle the distribution of mass‑produced consumer goods |
1860s | With the advent of fast‑freight and express companies, railroads experience difficulty monitoring the location and mileage of “foreign” cars on their lines Wholesalers scramble to integrate movement of goods and cash among hundreds of manufacturers and thousands of retailers Petroleum producers adopting continuous‑processing technologies increase output three to six times while halving unit costs, confront need to stimulate consumption, differentiate products, build brand loyalty |
Late 1860s | Rail mills adopting Bessemer process struggle to control increased speeds of steel production Large wholesalers and retailers like department stores confront need to maintain high rates of stock turn |
1870s | Railroad companies (except the Pennsylvania) delay building large systems because they lack means to control them Producers of basic materials ‑ iron, copper, zinc, glass – struggle to maintain competitively fast throughputs within their plants Large wholesale houses, among the most differentiated organizational structures in the nineteenth century, find need to integrate a growing number of highly specialized operating units |
1882 | Henry Crowell, adopting continuous‑processing technology to oatmeal, produces twice national consumption, confronts need to create new markets |
1880s | Metalworking industries‑from castings and screws to sewing machines, typewriters, and electric motors‑struggle to process materials at the volume and speed of the metal producers Producers of flour, soap, cigarettes, matches, canned foods, and film adopt continuous‑processing technologies, confront needs to create new markets and to stimulate and control consumption Growing scope, complexity and speed of information processing‑inventory, billing, sales analysis‑needed to run large business begins to strain capacity of manual handling systems |
[p429]
Table 10.1 summarizes the crisis in control that moved progressively through the American economy of the nineteenth century, from transportation (railroads) to distribution (commission trading and wholesaling), then to production (rail mills, other metal‑making and metalworking industries), and finally to marketing (continuous-processing industries). As we have seen, what began as a crisis of safety on the railroads in the early 1840s hit distribution in the 1850s, production in the late 1860s, and marketing and the control of consumption in the early 1880s.
As the crisis of control spread through the material economy, it inspired a continuing stream of innovations in control technology. These innovations, effected by transporters, producers, distributors, and marketers alike, reached something of a climax by the 1880s. With the rapid increase in bureaucratic control and a spate of innovations in industrial organization, telecommunications, and the mass media, the technological and economic response to the crisis ‑ the Control Revolution ‑ had begun to remake societies throughout the world by the beginning of this century. [p430-432]
Table 10.2. Selected innovations in the control of production, distribution, and consumption and in more generalized control, 1830‑1939 | ||||
Year | Production | Distribution | Consumption | Generalized |
1830 32 34 36 38 1840 42 44 46 48 1850 52 54 56 58 1860 61 62 63 64 65 66 67 68 69 1870 71 72 73 74 75 76 77 78 79 1880 81 82 83 84 85 86 87 88 89 1890 91 92 93 94 95 96 97 98 99 1900 01 02 03 04 05 06 07 08 09 1910 11 12 13 14 15 16 17 18 19 1920 21 22 23 24 25 26 27 28 29 1930 31 32 33 34 35 36 37 38 39 |
Machine‑tool factory
American System of manufacture
Standardized wire gauge
Commissioned industrial consultants
Continuous‑processing technology
Bessemer processing
Continuous processing of materials
Shop‑order accounting
Plant design to speed processing
Rate‑fixing department, cost control
Time recording
Staff time‑keepers for routing
Time studies
Auto plant designed for processing
Factory control by line‑and‑staff
Auto branch assembly
Scientific management
Moving auto assembly
Unattended substations
River Rouge processing architecture
Distant control of electrical transmission
Demand feedback control
Pneumatic proportional controller
Quality control course, text
PID controller Pneumatic transmitter
Lab analysis for quality control
Human relations textbook | Scheduled freight line
Telegraph Through‑freight forwarding
Packaging Commodity exchanges
Postage stamp Through bill Registered mail Railroad scale Futures
Paper money Fixed prices Postal money order
Transatlantic cable
Traveling salesmen
Mail‑order
Large chain of stores
Telephone
Telephone switchboard, exchanges
Uniform standard time
Special delivery mail
Car accountant offices
Pay telephone, travelers’ checks
Cafeteria
Vending machine Rural free delivery
Automat Pacific cable
Wristwatches
Transatlantic radio
Gyrocompass Two‑way auto radio
Franchising Parcel post Aircraft gyro-stabilizer
Self‑service store
Air mail, Fedwire
Metered mail Drive‑ins Shopping center Supermarket Transcontinental air mail, facsimile
Transatlantic telephone
Aircraft automatic pilot
Teletype service
Modern coaxial cable
Radar Transatlantic air mail |
Penny press
Daguerreotype Advertising agency
Hoe press Newspaper association
Wood pulp, rag paper
Iteration copy Typesetter Display type Advertising of Christmas
Premiums for coupons
Newspaper circulation book Trademark law Human‑interest advertising Illustrated daily paper
Advertising weekly
Full‑page advertising
New trademark law
Mass daily Newspaper syndicate
Linotype
Ad journal National publicity stunt
Standardized billboards
Print patent Full‑time copywriters
Corporate publicity bureau Million‑dollar ad campaign Modern advertising agency Advertising textbook
Advertising copy testing
Formal market research
Mail‑order ad testing
Circulation audit bureau
Household market interviewing
Market research textbook
Commercial radio
National network radio
Dry waste survey
Flasher sign Radio ratings Automobile radio
Retail‑sales index
National polls Audimeter ratings
Animated sign Commercial television |
Large‑scale formal organization
Hierarchical process control system
Formal line-and‑staff control
Modern bureaucracies with multiple departments
Typewriter with QWERTY keyboard
Business school Dow Jones news Accounting firm Bonding company
Desktop telephone
Punch‑card tabulator
Mimeograph Multiplier
Addressograph Four‑function calculator
Centralized, departmental corporate organization
Automatic card sorter
Plug‑board tabulator
Photostat
Printing tabulator
Postage meter
Electric key-punch
Decentralized corporate organization
Multiple register cumulating calculator
Machines linked for computing Electric typewriter
Electronic calculator |
Table 10.2 presents a selective summary of the more important innovations in information technology that constituted the nineteenth-century Control Revolution, at least in the United States, and its growth through the 1930s toward an Information Society. This list of innovations reveals a steady development of organizational, information‑processing, and communication technology over at least the decades of the 1850s through 1880s, a period that lags industrialization by perhaps ten to twenty years. Remarkable, in light of the Clark-Bell sequence discussed in Chapter 5, is the sharp periodization of the listing. Among the three economic sectors, virtually all of the major innovation in control through the 1860s can be found in distribution; much of that in the 1870s and later comes in production or consumption. Similarly, most of the important listings for distribution come before 1870, nearly all of those for production and consumption come after this date (major innovations in generalized control appear more sporadically throughout the period).
No less remarkable is the similar periodization in the development of information‑processing, communication, and control technologies. Each of the major sectors of the economy tended to exploit a particular area of information technology: transportation concentrated on the development of bureaucratic organization, production on the organization of material processing, including preprocessing, division of labor, and functional specialization; distribution concentrated on telecommunications, marketing on mass media. These relationships, combined with those for the three economic sectors discussed above, account for the patterns in nineteenth‑century control technology evident in Table 10.2.
Most bureaucratic innovation arose in response to the crisis of control in the railroads; by the late 1860s the large wholesale houses had fully exploited this form of control. Innovation in telecommunications (the telegraph, postal reforms, and the telephone) followed the movement of the crisis of control to distribution. Innovation in organizational [p433] technology and preprocessing (the shop‑order system of accounts, routing slips, rate‑fixing departments, cost control, uniform accounting procedures, factory timekeepers, and specialized factory clerks) followed the movement of the control crisis into the production sector in the 1870s. Most innovations in mass control (full‑page newspaper advertising, a trademark law, print patents, corporate publicity departments, consumer packaging, and million‑dollar advertising campaigns) came after the late 1870s with the advent of continuous‑processing machinery and the resulting crisis in control of consumption. Along with these innovations came virtually all of the basic mass communications technologies still in use a century later: photography, rotary-power printing, motion pictures, the wireless, magnetic tape recording, and radio.
Despite such rapid changes in mass media and telecommunications technologies, the Control Revolution also represented a restoration – although with increasing centralization ‑ of the economic and political control lost at more local levels during the Industrial Revolution. Before this time, control of government and markets had depended on personal relationships and face‑to‑face interactions; by the 1890s, as we saw in Part III, control began to be reestablished by means of bureaucratic organization, the new infrastructures of transportation and telecommunications, and system‑wide communication via the new mass media.
If the Control Revolution was essentially a response to the Industrial Revolution, however, why does it show no sign of abating more than a century later? As we saw in Chapter 7, three forces seem to sustain its development. First, energy utilization, processing speeds, and control technologies have continued to coevolve in a positive spiral, advances in any one factor causing ‑ or at least enabling ‑ improvements in the other two. Second, additional energy has increased not only the speed of material processing and transportation but their volume and predictability as well. This, in turn, has further increased both the demand for control and the returns on new applications of information technology. Increases in the volume of production, for example, have brought additional advantages to increased consumption, which manufacturers have sought to control using the information technologies of market research and mass advertising. Similarly, the increased reliability of production and distribution flows has increased the economic returns on informational activities like planning, scheduling, and forecasting. Third, information processing and flows need themselves to [p434] be controlled, so that informational technologies must continue to be applied at higher and higher layers of control ‑ certainly an ironic twist to the Control Revolution.
Information in Control
Given that a revolution in control did begin in response to a crisis generated by the Industrial Revolution, why have the technologies of information processing, preprocessing, programming, and communication played such a major part in the Control Revolution? In short, why the new centrality of information?
No study of technological innovation or economic history alone can possibly hope to answer this question, I argued in Part 1, no more than the history of organic evolution can explain the importance of information to all living things. In both cases the reasons why information plays a crucial role will not be found in historical particulars but rather in the nature of all living systems ‑ ultimately in the relationship between information and control. Life itself implies purposive activity and hence control, as we found in Chapter 2, in national economies no less than in individual organisms. Control, in turn, depends on information and activities involving information: information processing, programming, decision, and communication.
Inseparable from control are the twin activities of information processing and reciprocal communication. Information processing is essential to all purposive activity, which is by definition goal directed and must therefore involve the continual comparison of current states to future goals. Two‑way interaction between controller and controlled must also occur to communicate influence from the former to the latter and to communicate back (as feedback) the results of this action.
Each new technological innovation extends the processes that sustain human social life, thereby increasing the need for control and for improved control technology. Thus, technology appears autonomously to beget technology and, as argued in Part 11, innovations in matter and energy processing create the need for further innovation in information processing and communication. Because technological innovation is increasingly a collective, cumulative effort whose results must be taught and diffused, it also generates an increased need for technologies of information storage and retrieval.
Foremost among the technological solutions to the crisis of control – in that it served most other control technologies ‑ was the rapid growth [p435] in the late nineteenth century of formal bureaucracy and rationalization. The latter includes what computer scientists now call preprocessing, a complement to the control exercised by bureaucracy through information processing, increasingly using computers and microprocessors. Perhaps most pervasive of all rationalization is the increasing tendency to regulate interpersonal relationships in terms of a formal set of impersonal, quantifiable, and objective criteria, changes that greatly facilitate control by both government and business. The complex social systems that arose with the growth of capitalism and improved transportation and communication would have overwhelmed any information‑processing system that operated on a case‑by‑case basis or by the particularistic considerations of family and kin that characterized preindustrial societies.
Another explanation for the increasing importance of information in modern economies is suggested by the purposive nature of living systems. All economic activity is by definition purposive, after all, and requires control to maintain its various processes to achieve its goals. Because control depends on information and informational activities, these will enter the market, as both goods and services, in direct relationship to an economy’s demand for control. But if control is in fact crucial to all living systems, why has the economic demand for control ‑ in the form of informational goods and services ‑ increased so sharply, thereby precipitating the rise of the Information Society? Economic activity might indeed depend on control, and control on information, but why do these relationships seem relatively so much more important now than a century ago?
The Information Society
The Information Society has not resulted from recent changes, as we have seen, but rather from increases in the speed of material processing and of flows through the material economy that began more than a century ago. Similarly, microprocessing and computing technology, contrary to currently fashionable opinion, do not represent a new force only recently unleashed on an unprepared society but merely the most recent installment in the continuing development of the Control Revolution. This explains why so many of the components of computer control have been anticipated, both by visionaries like Charles Babbage and by practical innovators like Daniel McCallum, since the first signs of a control crisis in the early nineteenth century. [p436]
The progress of industrialization into the nineteenth century, with the resulting crisis of control, the technological and economic response that constituted the Control Revolution, and the continuing development of the Information Society, including the telematic stage just now emerging ‑ together these factors account for virtually all of the societal changes noted by contemporary observers as listed in Table 1. 1. These include the rise of a new information class (Djilas 1957; Gouldner 1979), a meritocracy of information workers (Young 1958), postcapitalist society (Dahrendorf 1959), a global village based on new mass media and telecommunications (McLuhan 1964), the new industrial state of increasing corporate control (Galbraith 1967), a scientific-technological revolution (Richta 1967; Daglish 1972; Prague Academy 1973), a technetronic era (Brzezinski 1970), postindustrial society (Touraine 1971; Bell 1973), an information economy (Porat 1977), and the micro millennium (Evans 1979).
The various transformations these observers identify may now be seen to be subsumed by major implications of the Control Revolution: the growing importance of information technology; the parallel growth of an information economy and its control by business and the state; the organizational basis of this control and its implications for social structure, whether Young’s meritocracy or Djilas’s new social class; the centrality of information processing and communication, as in McLuhan’s global village; the information basis of Bell’s postindustrial society; and indeed the growing importance of information and knowledge throughout modern culture. In short, particular attention to the material aspects of information processing, communication, and control promises to make possible a synthesis of a large proportion of this literature on contemporary social change.
Despite the Control Revolution’s importance for understanding contemporary society, however, especially the continuing impact of computers and microprocessors, the most useful lesson relates to our understanding of social life more generally. The rise of the Information Society itself, more than even the parallel development of formal information theory, has exposed the centrality of information processing, communication, and control to all aspects of human society and social behavior. It is to these fundamental informational concepts, I believe, that we social scientists may hope to reduce our proliferating but still largely unsystematic knowledge of social structure and process.
Topic Eleven: The Information Technology Revolution
Lecture Objective:
To gain a general historical understanding of the causes and e ffects of the information technology revolution.
Overview of Topics:
- The Origins of the Information Technology Revolution
- The Global Financial Order
- The Global Business Order
- Technology and Disorder
The lecture is based on Chapter 8 of The Foundations of Computing and the Information Technology Age (see the Lecture Chapter for Topic Ten).
Foundations Topic 11 Overheads
Topic Twelve: The Scientific Turn of Mind
Lecture Objective:
To gain an understanding of how science has fundamentally shaped our understanding of the world and the place of humanity within it.
Overview of Topics:
- The Scientifi c Method
- Science, Biology and the Brain
- The Computational Theory of Mind
- The Mind/Brain Problem
- Science and Society
The lecture is based on Chapter 9 of The Foundations of Computing and the Information Technology Age.
Foundations Topic 12 Overheads
Foundations Book Chapter 9
Foundations Pinker Reading
The Computational Theory of Mind
From: Pinker, Steven. (1997). How the Mind Works. Penguin Books, Australia. pp. 64-77.
[p64]
Thinking Machines
The traditional explanation of intelligence is that human flesh is suffused with a non‑material entity, the soul, usually envisioned as some kind of ghost or spirit. But the theory faces an insurmountable problem: How does the spook interact with solid matter? How does an ethereal nothing respond to flashes, pokes, and beeps and get arms and legs to move? Another problem is the overwhelming evidence that the mind is the activity of the brain. The supposedly immaterial soul, we now know, can be bisected with a knife, altered by chemicals, started or stopped by electricity, and extinguished by a sharp blow or by insufficient oxygen. Under a microscope, the brain has a breathtaking complexity of physicical structure fully commensurate with the richness of the mind.
Another explanation is that mind comes from some extraordinary form of matter. Pinocchio was animated by a magical kind of wood found by Geppetto that talked, laughed, and moved on its own. Alas, no one has ever discovered such a wonder substance. At first one might think that the wonder substance is brain tissue. Darwin wrote that the brain “secretes” the mind, and recently the philosopher John Searle has argued that the physico‑chemical properties of brain tissue somehow produce the mind just as breast tissue produces milk and plant tissue produces sugar. But recall that the same kinds of membranes, pores, and chemicals are found in brain tissue throughout the animal kingdom, not to mention in brain tumors and cultures in dishes. All of these globs of neural tissue have the same physico‑chemical properties, but not all of [p65] them accomplish humanlike intelligence. Of course, something about the tissue of the human brain is necessary for our intelligence, but the physical properties are not sufficient, just as the physical properties of bricks are not sufficient to explain architecture and the physical properties of oxide particles are not sufficient to explain music. Something in the patterning of neural tissue is crucial.
InteIligence has often been attributed to some kind of energy flow or force field. Orbs, luminous vapors, auras, vibrations, magnetic fields, and lines of force figure prominently in spiritualism, pseudoscience, and science fiction kitsch. The school of Gestalt psychology tried to explain illusions in terms of electromagnetic force fields on the surface of the brain, but the fields were never found. Occasionally the brain surface has been described as a continuous vibrating medium that supports holograms or other wave interference patterns, but that idea, too, has not panned out. The hydraulic model, with its psychic pressure building up, bursting out, or being diverted through alternative channels, lay at the center of Freud’s theory and can be found in dozens of everyday metaphors: anger welling up, letting off steam, exploding under the pressure, blowing one’s stack, venting one’s feelings, bottling up rage. But even it the hottest emotions do not literally correspond to a buildup and discharge of energy, (in the physicist’s sense) somewhere in the, brain. In Chapter 6 I will try to persuade you that the brain does not actually operate by internal pressures but contrives them as a negotiating tactic, like a terrorist with explosives strapped to his body.
A problem with all these ideas is that even if we did discover some gel or vortex or vibration or orb that spoke and plotted mischief like Geppetto’s log, or that, more generally, made decisions based on rational and pursued a goal in the face of obstacles, we would still be faced with the mystery of how it accomplished those feats.
No, intelligence does not come from a special kind of spirit or matter or energy but from a different commodity, information. Information is a correlation between two things that is produced by a lawful process (as to coming about by sheer chance). We say that the rings in a stump carry information about the age of the tree because their number correlates with the tree’s age (the older the tree, the more rings it has), and the correlation is not a coincidence but is caused by the way, trees grow. Correlation is a mathematical and logical concept; it is not defined In terms of the stuff that the correlated entities are made of.
Information itself is nothing special; it is found leave [p66] effects. What is special is information processing. We can regard a piece of matter that carries information about some state affairs as a symbol; it call “stand for” that state of affairs. But as a piece of matter, it can do other things as well ‑ physical things, whatever that kind of matter in that kind of state can do according to the laws of physics and chemistry. Tree rings carry information about age, but they also reflect light and absorb staining material. Footprints carry information about animal motions, but they also trap water and cause eddies in the wind.
Now here is an idea. Suppose one were to build a machine with parts that are affected by the physical properties of some symbol. Some lever or electric eye or tripwire or magnet is set in motion by the pigment absorbed by a tree ring, or the water trapped by a footprint, or the light reflected by a chalk mark, or the magnetic charge in a bit of oxide. And suppose that the machine then causes something to happen in some other pile of matter. It burns new marks onto a piece of wood, or stamps impressions into nearby dirt, or charges some other bit of oxide. Nothing special has happened so far; all I have described is a chain of physical events accomplished by a pointless contraption.
Here is the special step. Imagine that we now try to interpret the newly arranged piece of matter using the scheme according to which the original piece carried information. Say we count the newly burned wood rings and interpret them as the age of some tree at some time, even though they were not caused by the growth of any tree. And let’s say that the machine was carefully designed so that the interpretation of its new markings made sense ‑ that is, so that they carried information about something in the world. For example, imagine a machine that scans the rings in a stump, burns one mark on a nearby plank for each ring, moves over to a smaller stump from a tree that was cut down at the same time, scans its rings, and sands off one mark in the plank for each ring. When we count the marks on the plank, we have the age of the first tree at the time that the second one was planted. We would have a kind of rational machine, a machine that produces true conclusions from true premises – not because of any special kind of matter or energy, or because of any part that was itself intelligent or rational. All we have is a carefully contrived chain of ordinary physical events, whose first link was a configuration of matter that carries information. Our rational machine owes its rationality to two properties glued together in the entity we call a symbol: a symbol carries information, and it causes things to happen. (Tree rings correlate with the age of the tree, and they can absorb the light beam of a scanner.) [p67]
When the caused things themselves carry information, we call the whole system an information processor, or a computer.
Now, this whole scheme might seem like an unrealizable hope. What guarantee is there that any collection of thingamabobs can be arranged to fall or swing or shine in just the right pattern so that when their effects interpreted, the interpretation will make sense? (More precisely, so that it will make sense according to some prior law or relationship we find interesting; any heap of stuff can be given a contrived interpretation after the fact.) How confident can we be that some machine will make marks that actually correspond to some meaningful state of the world, like the age of a tree when another tree was planted, or the average age of the tree’s offspring, or anything else, as opposed to being a meaning‑ pattern corresponding to nothing at all?
The guarantee comes from the work of the mathematician Alan Turing. He designed a hypothetical machine whose input symbols and output symbols could correspond, depending on the details of the machine, to any one of a vast number of sensible interpretations. The machine consists of a tape divided into squares, a read‑write head that can print or read a symbol on a square and move the tape in either direction, a pointer that can point to a fixed number of tickmarks on the machine, and a set of mechanical reflexes. Each reflex is triggered by the symbol being read and the current position of the pointer, and it prints a symbol on the tape, moves the tape, and/or shifts the pointer. The machine is allowed as much tape as it needs. This design is called a Turing machine.
What can this simple machine do? It can take in symbols standing for a number or a set of numbers, and print out symbols standing for new numbers that are the corresponding value for any mathematical function that can be solved by a step‑by‑step sequence of operations (addition, multiplication, exponentiation, factoring, and so on ‑ I am being imprecise to convey the importance of Turing’s discovery without the technicalities). It can apply the rules of any useful logical system to derive true statements from other true statements. It can apply the rules of any grammar to derive well‑formed sentences. The equivalence among Turing machines, calculable mathematical functions, logics, and grammars, led the logician Alonzo Church to conjecture that any well‑defined recipe or set of steps that is guaranteed to produce the solution to some problem in a finite amount of time (that is, any algorithm) can be implemented on a Turing machine.
What does this mean? It means that to the extent that the world [p68] obeys mathematical equations that can be solved step by step, a machine can be built that simulates the world and makes predictions about it. To the extent that rational thought corresponds to the rules of logic, a machine can be built that carries out rational thought. To the extent that a language can be captured by a set of grammatical rules, a machine can be built that produces grammatical sentences. To the extent that thought consists of applying any set of well‑specified rules, a machine can be built that, in some sense, thinks.
Turing showed that rational machines ‑ machines that use the physical properties of symbols to crank out new symbols that make some kind of sense ‑ are buildable, indeed, easily buildable. The computer scientist Joseph Weizenbaum once showed how to build one out of a die, some rocks, and a roll of toilet paper. In fact, one doesn’t even need a huge warehouse of these machines, one to do sums, another to do square roots, a third to print English sentences, and so on. One kind of Turing machine is called a universal Turing machine. It can take in a description of any other Turing machine printed on its tape and thereafter mimic that machine exactly. A single machine can be programmed to do anything that any set of rules can do.
Does this mean that the human brain is a Turing machine? Certainly not. There are no Turing machines in use anywhere, let alone in our heads. They are useless in practice: too clumsy, too hard to program, too big, and too slow. But it does not matter. Turing merely wanted to prove that some arrangement of gadgets could function as an intelligent symbol‑processor. Not long after his discovery, more practical symbol-processors were designed, some of which became IBM and Univac mainframes and, later, Macintoshes and PCs. But all of them were equivalent to Turing’s universal machine. If we ignore size and speed, and give them as much memory storage as they need, we can program them to produce the same outputs in response to the same inputs.
Still other kinds of symbol‑processors have been proposed as models of the human mind. These models are often simulated on commercial computers, but that is just a convenience. The commercial computer is first programmed to emulate the hypothetical mental computer (creating what computer scientists call a virtual machine), in much the same way that a Macintosh can be programmed to emulate a PC. Only the virtual mental computer is taken seriously, not the silicon chips that emulate it. Then a program that is meant to model some sort of thinking (solving a problem, understanding a sentence) is run on the virtual mental [p69] computer. A new way of understanding human intelligence has been born.
–
Let me show you how one of these models works. In an age when real computers are so sophisticated that they are almost as incomprehensible to laypeople as minds are, it is enlightening to see an example of computation in slow motion. Only then can one appreciate how simple devices can be wired together to make a symbol‑processor that shows real intelligence A lurching Turing machine is a poor advertisement for the theory that the mind is a computer, so I will use a model with at least a vague claim to resembling our mental computer. I’ll show you how it solves a problem from everyday life‑kinship relations ‑ that is complex enough that we can be impressed when a machine solves it.
The model we’ll use is called a production system. It eliminates the feature of commercial computers that is most starkly unbiological: the ordered list of programming steps that the computer follows single‑mindedly, one after another. A production system contains a memory and a set of reflexes, sometimes called “demons” because they are simple, self‑contained entities that sit around waiting to spring into action. The memory is like a bulletin board on which notices are posted. Each demon is a knee‑jerk reflex that waits for a particular notice on the board and responds by posting a notice of its own. The demons collectively constitute a program. As they are triggered by notices on the memory board and post notices of their own, in turn triggering other demons, and so on, the information in memory changes and eventually contains the correct output for a given input. Some demons are connected to sense organs and are triggered by information in the world rather than information in memory. Others are connected to appendages and respond by moving the appendages rather than by posting more messages in memory.
Suppose your long‑term memory contains knowledge of the immediate families of you and everyone around you. The content of that knowledge is a set of propositions like “Alex is the father of Andrew.” According to the computational theory of mind, that information is embodied in symbols: a collection of physical marks that correlate with the state of the world as it is captured in the propositions.
These symbols cannot be English words and sentences, notwith-standing [p70] the popular conception that we think in our mother tongue. As, I showed in The Language Instinct, sentences in a spoken language like English or Japanese are designed for vocal communication between impatient, intelligent social beings. They achieve brevity by leaving out any information that the listener can mentally fill in from the context. In contrast, the “language of thought” in which knowledge is couched can leave nothing to the imagination, because it is the imagination. Another problem with using English as the medium of knowledge is that English sentences can be ambiguous. When the serial killer Ted Bundy wins a stay of execution and the headline reads “Bundy Beats Date with Chair,” we do a double‑take because our mind assigns two meanings to the string of words. If one string of words in English can correspond to two meanings in the mind, meanings in the mind cannot be strings of words in English. Finally, sentences in a spoken language are cluttered with articles, prepositions, gender suffixes, and other grammatical boilerplate. They are needed to help get information from one head to another by way of the mouth and the ear, a slow channel, but they are not needed inside a single head where information can be transmitted directly by thick bundles of neurons. So the statements in a knowledge system are not sentences in English but rather inscriptions in a richer language of thought, “mentalese.”
In our example, the portion of mentalese that captures family relations comes in two kinds of statements. An example of the first is Alex father‑of Andrew: a name, followed by an immediate family relationship, followed by a name. An example of the second is Alex is‑male: a name followed by its sex. Do not be misled by my use of English words and syntax in the mentalese inscriptions. This is a courtesy to you, the reader, to help you keep track of what the symbols stand for. As far as the machine is concerned, they are simply different arrangements of marks. As long as we use each one consistently to stand for someone (so the symbol used for Alex is always used for Alex and never for anyone else), and arrange them according to a consistent plan (so they preserve information about who is the father of whom), they could be any marks in any arrangement at all. You can think of the marks as bar codes recognized by a scanner, or keyholes that admit only one key, or shapes that fit only one template. Of course, in a commercial computer they would be patterns of charges in silicon, and in a brain they would be firings in sets of neurons. The key point is that nothing in the machine understands them the way you or I do; parts of the machine respond to their shapes and are [p71] triggered to do something, exactly as a gumball machine responds to the shape and weight of a coin by releasing a gumball.
The example to come is an attempt to demystify, computation, to get you to see how the trick is done. To hammer home my explanation of the trick ‑ that symbols both stand for some concept and mechanically things to happen ‑ I will step through the activity of our production system and describe everything twice: conceptually, in terms of the content of the problem and the logic that solves it, and mechanically, in terms of the brute sensing and marking motions of the system. The system is intelligent because the two correspond exactly, idea‑for‑mark, logical‑step‑for‑motion.
Let’s call the portion of the system’s memory that holds inscriptions about family relationships the Long‑Term Memory. Let’s identify another part as the Short‑Term Memory, a scratchpad for the calculations. A part of the Short‑Term Memory is an area for goals; it contains a list of questions that the system will “try” to answer. The system wants to know whether Gordie is its biological uncle. To begin with, the memory looks like this:
Long‑Term Memory Short‑Term Memory Goal
Abel parent‑of Me Gordie uncle‑of Me?
Abel is‑male
Bella parent‑of Me
Bella is‑female
Claudia sibling‑of Me
Claudia is‑female
Duddie sibling‑of Me
Duddie is‑male
Edgar sibling‑of Abel
Edgar is‑male
Fanny sibling‑of Abel
Fanny is‑female
Gordie sibling‑of Bella
Gordie is‑male
Conceptually speaking, our goal is to find the answer to a question; the answer is affirmative if the fact it asks about is true. Mechanically speaking, the system must determine whether a string of marks in the Goal column followed by a question mark (?) has a counterpart with in identical string of marks somewhere in memory. One of the demons is designed to [p72] answer these look-up questions by scanning for identical marks in the Goal and Long-Term Memory columns. When it detects a match, it prints a mark next to the question which indicates that it has been answered affirmatively. For convenience, let’s say the mark looks like this: Yes.
IF: Goal = blah‑blah‑blah
Long‑Term Memory = blah‑blah‑blah
THEN: MARK GOAL
Yes
The conceptual challenge faced by the system is that it does not explicitly know who is whose uncle; that knowledge is implicit in the other things it knows. To say the same thing mechanically: there is no uncle‑of mark in the Long‑Term Memory; there are only marks like sibling‑of and parent‑of. Conceptually speaking, we need to deduce knowledge of unclehood from knowledge of parenthood and knowledge of siblinghood. Mechanically speaking, we need a demon to print an uncle‑of inscription flanked by appropriate marks found in sibling‑of and parent‑of inscriptions. Conceptually speaking, we need to find out who our parents are, identify their siblings, and then pick the males. Mechanically speaking, we need the following demon, which prints new inscriptions in the Goal area that trigger the appropriate memory searches:
IF: Goal = Q uncle‑of P
THEN: ADD GOAL
Find P’s Parents
Find Parents’ Siblings
Distinguish Uncles/Aunts
This demon is triggered by an uncle‑of inscription in the Goal column. The Goal column indeed has one, so the demon goes to work and adds some new marks to the column:
Long‑Term Memory Short‑Term Memory Goal
Abel parent‑of Me Gordie uncle‑of Me?
Abel is‑male Find me’s Parents
Bella parent‑of Me Find Parents’ Siblings
Bella is‑female Distinguish Uncles/Aunts
Claudia sibling‑of Me
Claudia is‑female
Duddie sibling‑of Me
Duddie is‑male
Edgar sibling‑of Abel
Edgar is‑male
Fanny sibling‑of Abel
Fanny is‑female
Gordie sibling‑of Bella
Gordie is‑male
[p73]
There must also be a device ‑ some other demon, or extra machinery inside this demon ‑ that minds its Ps and Qs. That is, it replaces the P label with a list of the actual labels for names: Me, Abel, Gordie, and so on. I’m hiding these details to keep things simple.
The new Goal inscriptions prod other dormant demons into action. One of them (conceptually speaking) looks up the system’s parents, by (mechanically speaking) copying all the inscriptions containing the names of the parents into Short‑Term Memory (unless the inscriptions are already there, of course; this proviso prevents the demon from mindlessly making copy after copy like the Sorcerer’s Apprentice):
IF: Goal = Find P’s Parents
Long‑Term Memory = X parent‑of P
Short‑Term Memory not = X parent‑of P
THEN: COPY TO Short‑Term Memory
X parent‑of P
ERASE GOAL
Our bulletin board now looks like this:
Long‑Term Memory Short‑Term Memory Goal
Abel parent‑of Me Abel parent‑of Me Gordie uncle‑of Me?
Abel is‑male Bella parent‑of Me Find Parents’ Siblings
Bella parent‑of Me Distinguish Uncles/Aunts
Bella is‑female
Claudia sibling‑of Me
Claudia is‑female
Duddie sibling‑of Me
Duddie is‑male
Edgar sibling‑of Abel
Edgar is‑male
Fanny sibling‑of Abel
Fanny is‑female
Gordie sibling‑of Bella
Gordie is‑male
[p74]
Now that we know the parents, we can find the parents’ siblings, Mechanically speaking: now that the names of the parents are written in Short‑Term Memory, a demon can spring into action that copies inscriptions about the parents’ siblings:
IF: Goal = Find Parent’s Siblings
Short‑Term Memory X parent‑of Y
Long‑Term Memory Z sibling‑of X
Short‑Term Memory not = Z sibling‑of X
THEN: COPY TO SHORT‑TERM MEMORY
Z sibling‑of X
ERASE GOAL
Here is its handiwork:
Long‑Term Memory Short‑Term Memory Goal
Abel parent‑of Me Abel parent‑of Me Gordie uncle‑of Me?
Abel is‑male Bella parent‑of Me Distinguish Uncles/Aunts
Bella parent‑of Me Edgar sibling‑of Abel
Bella is‑female Fanny sibling‑of Abel
Claudia sibling‑of Me Gordie sibling‑of Bella
Claudia is‑female
Duddie sibling‑of Me
Duddie is‑male
Edgar sibling‑of Abel
Edgar is‑male
Fanny sibling‑of Abel
Fanny is‑female
Gordie sibling‑of Bella
Gordie is‑male
[p75]
As it stands, we are considering the aunts and uncles collectively. To separate the uncles from the aunts, we need to find the males. Mechanically speaking, the system needs to see which inscriptions have counterparts in Long‑Term Memory with is‑male marks next to them. Here is the demon that does the checking:
IF: Goal = Distinguish Uncles/Aunts
Short‑Term Memory = X parent‑of Y
Long‑Term Memory = Z sibling‑of X
Long‑Term Memory = Z is‑male
THEN: STORE IN LONG‑TERM MEMORY
Z uncle‑of Y
ERASE GOAL
This is the demon that most directly embodies the system’s knowledge of the meaning of “uncle”: a male sibling of a parent. It adds the unclehood inscription to Long‑Term Memory, not Short‑Term Memory, because the inscription represents a piece of knowledge that is permanently true:
Long‑Term Memory Short‑Term Memory Goal
Edgar uncle‑of‑Me
Gordie uncle‑of‑Me
Abel parent‑of Me Abel parent‑of Me Gordie uncle‑of Me?
Abel is‑male Bella parent‑of Me
Bella parent‑of Me Edgar sibling‑of Abel
Bella is‑female Fanny sibling‑of Abel
Claudia sibling‑of Me Gordie sibling‑of Bella
Claudia is‑female
Duddie sibling‑of Me
Duddie is‑male
Edgar sibling‑of Abel
Edgar is‑male
Fanny sibling‑of Abel
Fanny is‑female
Gordie sibling‑of Bella
Gordie is‑male
Conceptually speaking, we have just deduced the fact that we inquired about. Mechanically speaking, we have just created mark‑for‑mark [p76] identical inscriptions in the Goal column and the Long‑Term Memory column. The very first demon I mentioned, which scans for such duplicates, is triggered to make the mark that indicates the problem has been solved.
What have we accomplished? We have built a system out of lifeless gumball‑machine parts that did something vaguely mindlike: it deduced the truth of a statement that it had never entertained before. From ideas about particular parents and siblings and a knowledge of the meaning of unclehood, it manufactured true ideas about particular uncles. The trick, to repeat, came from the processing of symbols: arrangements of matter that have both representational and causal properties, that is, that simultaneously carry information about something and take part in a chain of physical events. Those events make up a computation, because the machinery was crafted so that if the interpretation of the symbols that trigger the machine is a true statement, then the interpretation of the symbols created by the machine is also a true statement. The computational theory of mind is the hypothesis that intelligence is computation in this sense.
“This sense” is broad, and it shuns some of the baggage found in [p77] other definitions of computation. For example, we need not assume that the computation is made up of a sequence of discrete steps, that the symbols must be either completely present or completely absent (as to being stronger or weaker, more active or less active), that a correct answer is guaranteed in a finite amount of time, or that the truth be “absolutely true” or “absolutely false” rather than a probability or a degree of certainty. The computational theory thus embraces an alternative kind of computer with many elements that are active to a degree corresponding to the probability that some statement is true or false and in which the activity levels change smoothly to register new and roughly accurate probabilities. (As we shall see, that may be the way the brain works.) The key idea is that the answer to the question “What makes a system smart?” is not the kind of stuff it is made of or the kind of energy flowing through it, but what the parts of the machine stand for and how the patterns of changes inside it are designed to mirror truth‑preserving relationships (including probabilistic and fuzzy truths).
Foundations Searle Reading
The Recent History of Materialism
From: Searle, John, R. (1992). The Resdiscovery of the Mind. MIT Press, Cambridge, Massachusetts.
[p27]
Chapter 2
The Recent History of Materialism: The Same Mistake Over and Over
I. The Mystery of Materialism
What exactly is the doctrine known as “materialism” supposed to amount to? One might think that it would consist in the view that the microstructure of the world is entirely made up of material particles. The difficulty, however, is that this view is consistent with just about any philosophy of mind, except possibly the Cartesian view that in addition to physical particles there are “immaterial” souls or mental substances, spiritual entities that survive the destruction of our bodies and live on immortally. But nowadays, as far as I can tell, no one believes in the existence of immortal spiritual substances except on religious grounds. To my knowledge, there are no purely philosophical or scientific motivations for accepting the existence of immortal mental substances. So leaving aside opposition to religiously motivated belief in immortal souls, the question remains: What exactly is materialism in the philosophy of mind supposed to amount to? To what views is it supposed to be opposed?
If one reads the early works of our contemporaries who describe themselves as materialists ‑ J. J. C. Smart (1965), U. T. Place (1956), and D. Armstrong (1968), for example ‑ it seems clear that when they assert the identity of the mental with the physical, they are claiming something more than simply the denial of Cartesian substance dualism. It seems to me they wish to deny the existence of any irreducible mental phenomena in the world. They want to deny that there are any irreducible phenomenological properties, such as consciousness, or qualia. Now why are they so anxious to deny the [p28] existence of irreducible intrinsic mental phenomena? Why don’t they just concede that these properties are ordinary higher‑level biological properties of neurophysiological systems such as human brains?
I think the answer to that is extremely complex, but at least part of the answer has to do with the fact that they accept the traditional Cartesian categories, and along with the categories the attendant vocabulary with its implications. I think from this point of view to grant the existence and irreducibility of mental phenomena would be equivalent to granting some kind of Cartesianism. In their terms, it might be a “property dualism” rather than a “substance dualism,” but from their point of view, property dualism would be just as inconsistent with materialism as substance dualism. By now it will be obvious that I am opposed to the assumptions behind their view. What I want to insist on, ceaselessly, is that one can accept the obvious facts of physics ‑ for example, that the world is made up entirely of physical particles in fields of force ‑ without at the same time denying the obvious facts about our own experiences ‑ for example, that we are all conscious and that our conscious states have quite specific irreducible phenomenological properties. The mistake is to suppose that these two theses are inconsistent, and that mistake derives from accepting the presuppositions behind the traditional vocabulary. My view is emphatically not a form of dualism. I reject both property and substance dualism; but precisely for the reasons that I reject dualism, I reject materialism and monism as well. The deep mistake is to suppose that one must choose between these views.
It is the failure to see the consistency of naive mentalism with naive physicalism that leads to those very puzzling discussions in the early history of this subject in which the authors try to find a “topic‑neutral” vocabulary or to avoid something they call “nomological danglers” (Smart 1965). Notice that nobody feels that, say, digestion has to be described in a “topicneutral” vocabulary. Nobody feels the urge to say, “There is [p29] something going on in me which is like what goes on when I digest pizza.” Though they do feel the urge to say, “There is something going on in me which is like what goes on when I see an orange.” The urge is to try to find a description of the phenomena that doesn’t use the mentalistic vocabulary. But what is the point of doing that? The facts remain the same. The fact is that the mental phenomena have mentalistic properties, just as what goes on in my stomach has digestive properties. We don’t get rid of those properties simply by finding an alternative vocabulary. Materialist philosophers wish to deny the existence of mental properties without denying the reality of some phenomena that underly the use of our mentalistic vocabulary. So they have to find an alternative vocabulary to describe the phenomena.1 But on my account, this is all a waste of time. One should just grant the mental (hence, physical) phenomena to start with, in the same way that one grants the digestive phenomena in the stomach.
In this chapter I want to examine, rather briefly, the history of materialism over the past half century. I believe that this history exhibits a rather puzzling but very revealing pattern of argument and counterargument that has gone on in the philosophy of mind since the positivism of the 1930s. This pattern is not always visible on the surface. Nor is it even visible on the surface that the same issues are being talked about. But I believe that, contrary to surface appearances, there really has been only one major topic of discussion in the philosophy of mind for the past fifty years or so, and that is the mind‑body problem. Often philosophers purport to talk about something else ‑ such as the analysis of belief or the nature of consciousness ‑ but it almost invariably emerges that they are not really interested in the special features of belief or consciousness. They are not interested in how believing differs from supposing and hypothesizing, but rather they want to test their convictions about the mind‑body problem against the example of belief. Similarly with consciousness: There is surprisingly little discussion of consciousness as such; rather, [p30] materialists see consciousness as a special “problem” for a materialist theory of mind. That is, they want to find a way to “handle” consciousness, given their materialism.2
The pattern that these discussions almost invariably seem to take is the following. A philosopher advances a materialist theory of the mind. He does this from the deep assumption that some version of the materialist theory of the mind must be the correct one ‑ after all, do we not know from the discoveries of science that there is really nothing in the universe but physical particles and fields of forces acting on physical particles? And surely it must be possible to give an account of human beings in a way that is consistent and coherent with our account of nature generally. And surely, does it not follow from that that our account of human beings must be thoroughgoing materialism? So the philosopher sets out to give a materialist account of the mind. He then encounters difficulties. It always seems that he is leaving something out. The general pattern of discussion is that criticisms of the materialist theory usually take a more or less technical form, but in fact, underlying the technical objections is a much deeper objection, and the deeper objection can be put quite simply: The theory in question has left out the mind; it has left out some essential feature of the mind, such as consciousness or “qualia” or semantic content. One sees this pattern over and over. A materialist thesis is advanced. But the thesis encounters difficulties; the difficulties take different forms, but they are always manifestations of an underlying deeper difficulty, namely, the thesis in question denies obvious facts that we all know about our own minds. And this leads to ever more frenzied efforts to stick with the materialist thesis and try to defeat the arguments put forward by those who insist on preserving the facts. After some years of desperate maneuvers to account for the difficulties, some new development is put forward that allegedly solves the difficulties, but then we find that it encounters new difficulties, only the new difficulties are not so new ‑ they are really the same old difficulties. [p31]
If we were to think of the philosophy of mind over the past fifty years as a single individual, we would say of that person that he is a compulsive neurotic, and his neurosis takes the form of repeating the same pattern of behavior over and over. In my experience, the neurosis cannot be cured by a frontal assault. It is not enough just to point out the logical mistakes that are being made. Direct refutation simply leads to a repetition of the pattern of neurotic behavior. What we have to do is go behind the symptoms and find the unconscious assumptions that led to the behavior in the first place. I am now convinced, after several years of discussing these issues, that with very few exceptions all of the parties to the disputes in the current issues in the philosophy of mind are captives of a certain set of verbal categories. They are the prisoners of a certain terminology, a terminology that goes back at least to Descartes if not before, and in order to overcome the compulsive behavior, we will have to examine the unconscious origins of the disputes. We will have to try to uncover what it is that everyone is taking for granted to get the dispute going and keep it going.
I would not wish my use of a therapeutic analogy to be taken to imply a general endorsement of psychoanalytic modes of explanation in intellectual matters. So let’s vary the therapeutic metaphor as follows: I want to suggest that my present enterprise is a bit like that of an anthropologist undertaking to describe the exotic behavior of a distant tribe. The tribe has a set of behavior patterns and a metaphysic that we must try to uncover and understand. It is easy to make fun of the antics of the tribe of philosophers of mind, and I must confess that I have not always been able to resist the temptation to do so. But at the beginning, at least, I must insist that the tribe is us – we are the possessors of the metaphysical assumptions that make the behavior of the tribe possible. So before I actually present an analysis and a criticism of the behavior of the tribe, I want to present an idea that we should all find acceptable, because the idea is really part of our contemporary scientific [p32] culture. And yet, I will later on argue that the idea is incoherent; it is simply another symptom of the same neurotic pattern.
Here is the idea. We think the following question must make sense: How is it possible for unintelligent bits of matter to produce intelligence? How is it possible for the unintelligent bits of matter in our brains to produce the intelligent behavior that we all engage in? Now that seems to us like a perfectly intelligible question. Indeed, it seems like a very valuable research project, and in fact it is a research project that is widely pursued3 and incidentally, very well funded.
Because we find the question intelligible, we find the following answer plausible: Unintelligent bits of matter can produce intelligence because of their organization. The unintelligent bits of matter are organized in certain dynamic ways, and it is the dynamic organization that is constitutive of the intelligence. Indeed, we can actually artificially reproduce the form of dynamic organization that makes intelligence possible. The underlying structure of that organization is called “a computer,” the project of programming the computer is called “artificial intelligence”; and when operating, the computer produces intelligence because it is implementing the right computer program with the right inputs and outputs.
Now doesn’t that story sound at least plausible to you? I must confess that it can be made to sound very plausible to me, and indeed I think if it doesn’t sound even remotely plausible to you, you are probably not a fully socialized member of our contemporary intellectual culture. Later on I will show that both the question and the answer are incoherent. When we pose the question and give that answer in these terms, we really haven’t the faintest idea of what we are talking about. But I present this example here because I want it to seem natural, indeed promising, as a research project.
I said a few paragraphs back that the history of philosophical materialism in the twentieth century exhibits a curious pattern, a pattern in which there is a recurring tension between the materialist’s urge to give an account of mental phenomena that [p33] makes no reference to anything intrinsically or irreducibly mental, on the one hand, and the general intellectual requirement that every investigator faces of not saying anything that is obviously false, on the other. To let this pattern show itself, I want now to give a very brief sketch, as neutrally and objectively as I can, of the pattern of theses and responses that materialists have exemplified. The aim of what follows is to provide evidence for the claims made in chapter 1 by giving actual illustrations of the tendencies that I identified.
II. Behaviorism
In the beginning was behaviorism. Behaviorism came in two varieties: “methodological behaviorism” and “logical behaviorism.” Methodological behaviorism is a research strategy in psychology to the effect that a science of psychology should consist in discovering the correlations between stimulus inputs and behavioral outputs (Watson 1925). A rigorous empirical science, according to this view, makes no reference to any mysterious introspective or mentalistic items.
Logical behaviorism goes even a step further and insists that there are no such items to refer to, except insofar as they exist in the form of behavior. According to logical behaviorism, it is a matter of definition, a matter of logical analysis, that mental terms can be defined in terms of behavior, that sentences about the mind can be translated without any residue into sentences about behavior (Hempel 1949; Ryle 1949). According to the logical behaviorist, many of the sentences in the translation will be hypothetical in form, because the mental phenomena in question consist not of actual occurring patterns of behavior, but rather of dispositions to behavior. Thus, according to a standard behaviorist account, to say that John believes that it is going to rain is simply to say that John will be disposed to close the windows, put the garden tools away, and carry an umbrella if he goes out. In the material mode of speech, behaviorism claims that the mind is just behavior and dispositions to behavior. In the formal mode of speech, it consists in [p34] the view that sentences about mental phenomena can be translated into sentences about actual and possible behavior.
Objections to behaviorism can be divided into two kinds: commonsense objections and more or less technical objections. An obvious commonsense objection is that the behaviorist seems to leave out the mental phenomena in question. There is nothing left for the subjective experience of thinking or feeling in the behaviorist account; there are just patterns of objectively observable behavior.
Several more or less technical objections have been made to logical behaviorism. First, the behaviorists never succeeded in making the notion of a “disposition” fully clear. No one ever succeeded in giving a satisfactory account of what sorts of antecedents there would have to be in the hypothetical statements to produce an adequate dispositional analysis of mental terms in behavioral terms (Hampshire 1950; Geach 1957). Second, there seemed to be a problem about a certain form of circularity in the analysis: to give an analysis of belief in terms of behavior, it seems that one has to make reference to desire; to give an analysis of desire, it seems that one has to make reference to belief (Chisholm 1957). Thus, to consider our earlier example, we are trying to analyze the hypothesis that John believes that it is going to rain in terms of the hypothesis that if the windows are open, John will close them, and other similar hypotheses. We want to analyze the categorical statement that John believes that it is going to rain in terms of certain hypothetical statements about what John will do under what conditions. However, John’s belief that it is going to rain will be manifested in the behavior of closing the windows only if we assume such additional hypotheses as that John doesn’t want the rainwater to come in through the windows and John believes that open windows admit rainwater. If there is nothing he likes better than rain streaming in through the windows, he will not be disposed to close them. Without some such hypothesis about John’s desires (and his other beliefs), it looks as if we cannot begin to analyze any sentence about his original beliefs. Similar remarks can be made about the analysis of desires; such analyses seem to require reference to beliefs. [p35]
A third technical objection to behaviorism was that it left out the causal relations between mental states and behavior (Lewis 1966). By identifying, for example, the pain with the disposition to pain behavior, behaviorism leaves out the fact that pains cause behavior. Similarly, if we try to analyze beliefs and desires in terms of behavior, we are no longer able to say that beliefs and desires cause behavior.
Though perhaps most of the discussions in the philosophical literature concern the “technical” objections, in fact it is the commonsense objections that are the most embarrassing. The absurdity of behaviorism lies in the fact that it denies the existence of any inner mental states in addition to external behavior (Ogden and Richards 1926). And this, we know, runs dead counter to our ordinary experiences of what it is like to be a human being. For this reason, behaviorists were sarcastically accused of “feigning anesthesia”4 and were the target of a number of bad jokes (e.g., first behaviorist to second behaviorist just after making love, “It was great for you, how was it for me?”). This commonsense objection to behaviorism was some times put in the form of arguments appealing to our intuitions. One of these is the superactor/superspartan objection (Putnam 1963). One can easily imagine an actor of superior abilities
who could give a perfect imitation of the behavior of someone in pain even though the actor in question had no pain, and one can also imagine a superspartan who was able to endure pain without giving any sign of being in pain.
III. Type Identity Theories
Logical behaviorism was supposed to be an analytic truth. It asserted a definitional connection between mental and behavioral concepts. In the recent history of materialist philosophies of mind it was replaced by the “identity theory,” which claimed that as a matter of contingent, synthetic, empirical fact, mental states were identical with states of the brain and of the central nervous system (Place 1956; Smart 1965). According to the identity theorists, there was no logical absurdity in supposing that there might be separate mental [p36] phenomena, independent of material reality; it just turned out as a matter of fact that our mental states, such as pains, were identical with states of our nervous system. In this case, pains were claimed to be identical with stimulations of C‑fibers.5 Descartes might have been right in thinking that there were separate mental phenomena; it just turned out as a matter of fact that he was wrong. Mental phenomena were nothing but states of the brain and central nervous system. The identity between the mind and the brain was supposed to be an empirical identity, just as the identity between lightning and electrical discharges (Smart 1965), or between water and H20 molecules (Feigl 1958; Shaffer 1961), were supposed to be empirical and contingent identities. It just turned out as a matter of scientific discovery that lightning bolts were nothing but streams of electrons, and that water in all its various forms was nothing but collections of H20 molecules.
As with behaviorism, we can divide the difficulties of the identity theory into the “technical” objections and the commonsense objections. In this case, the commonsense objection takes the form of a dilemma. Suppose that the identity theory is, as its supporters claim, an empirical truth. If so, then there must be logically independent features of the phenomena in question that enable it to be identified on the left‑hand side of the identity statement in a different way from the way it is identified on the right‑hand side of the identity statement (Stevenson 1960). If, for example, pains are identical with neurophysiological events, then there must be two sets of features, pain features and neurophysiological features, and these two sets of features enable us to nail down both sides of the synthetic identity statement. Thus, for example, suppose we have a statement of the form:
Pain event x is identical with neurophysiological event y.
We understand such a statement because we understand that one and the same event has been identified in virtue of two different sorts of properties, pain properties and neurophysiological properties. But if so, then we seem to be confronted with a [p37] dilemma: either the pain features are subjective, mental, introspective features, or they are not. Well if they are, then we have not really gotten rid of the mind. We are still left with a form of dualism, albeit property dualism rather than substance dualism. We are still left with sets of mental properties, even though we have gotten rid of mental substances. If on the other hand we try to treat “pain” as not naming a subjective mental feature of certain neurophysiological events, then its meaning is left totally mysterious and unexplained. As with behaviorism, we have left out the mind. For we now have no way to specify these subjective mental features of our experiences.
I hope it is clear that this is just a repetition of the commonsense objection to behaviorism. In this case we have put it in the form of a dilemma: either materialism of the identity variety leaves out the mind or it does not; if it does, it is false; if it does not, it is not materialism.
The Australian identity theorists thought they had an answer to this objection. The answer was to try to describe the so-called mental features in a “topic‑neutral” vocabulary. The idea was to get a description of the mental features that did not mention the fact that they were mental (Smart 1965). This can surely be done: One can mention pains without mentioning the fact that they are pains, just as one can mention airplanes without mentioning the fact that they are airplanes. That is, one can mention an airplane by saying, “a certain piece of property belonging to United Airlines,” and one can refer to a yellow‑orange afterimage by saying, “a certain event going on in me that is like the event that goes on in me when I see an orange.” But the fact that one can mention a phenomenon without specifying its essential characteristics doesn’t mean that it doesn’t exist and doesn’t have those essential characteristics. It still is a pain or an afterimage, or an airplane, even if our descriptions fail to mention these facts.
Another more “technical” objection to the identity theory was this: it seems unlikely that for every type of mental state there will be one and only one type of neurophysiological state with which it is identical. Even if my belief that Denver is the [p38] capital of Colorado is identical with a certain state of my brain, it seems too much to expect that everyone who believes that Denver is the capital of Colorado must have an identical neurophysiological configuration in his or her brain (Block and Fodor 1972; Putnam 1967). And across species, even if it is true that in all humans pains are identical with human neurophysiological events, we don’t want to exclude the possibility that in some other species there might be pains that were identical with some other type of neurophysiological configuration. It seems, in short, too much to expect that every type of mental state is identical with some type of neurophysiological state. And indeed, it seems a kind of “neuronal chauvinism” (Block 1978) to suppose that only entities with neurons like our own can have mental states.
A third “technical” objection to the identity theory derives from Leibniz’s law. If two events are identical only if they have all of their properties in common, then it seems that mental states cannot be identical with physical states, because mental states have certain properties that physical states do not have (Smart 1965; Shaffer 1961). For example, my pain is in my toe, but my corresponding neurophysiological state goes all the way from the toe to the thalamus and beyond. So where is the pain, really? The identity theorists did not have much difficulty with this objection. They pointed out that the unit of analysis is really the experience of having pain, and that experience (together with the experience of the entire body image) presumably takes place in the central nervous system (Smart 1965). On this point it seems to me that materialists are absolutely right.
A more radical technical objection to the identity theory was posed by Saul Kripke (1971), with the following modal argument: If it were really true that pain is identical with C‑fiber stimulation, then it would have to be a necessary truth, in the same way that the identity statement “Heat is identical with the motion of molecules” is a necessary truth. This is because in both cases the expressions on either side of the identity statement are “rigid designators.” By this he means that each [p39] expression identifies the object it refers to in terms of its essential properties. This feeling of pain that I now have is essentially a feeling of pain because anything identical with this feeling would have to be a pain, and this brain state is essentially a brain state because anything identical with it would have to be a brain state. So it appears that the identity theorist who claims that pains are certain types of brain states, and that this particular pain is identical with this particular brain state, would be forced to hold both that it is a necessary truth that in general pains are brain states, and that it is a necessary truth that this particular pain is a brain state. But neither of these seems right. It does not seem right to say either that pains in general are necessarily brain states, or that my present pain is necessarily a brain state; because it seems easy to imagine that some sort of being could have brain states like these without having pains and pains like these without being in these sorts of brain states. It is even possible to conceive a situation in which I had this very pain without having this very brain state, and in which I had this very brain state without having a pain.
Debate about the force of this modal argument went on for some years and still continues (Lycan 1971, 1987; Sher 1977). From the point of view of our present interests, I want to call attention to the fact that it is essentially the commonsense objection in a sophisticated guise. The commonsense objection to any identity theory is that you can’t identify anything mental with anything nonmental, without leaving out the mental. Kripke’s modal argument is that the identification of mental states with physical states would have to be necessary, and yet it cannot be necessary, because the mental could not be necessarily physical. As Kripke says, quoting Butler, “Everything is what it is and not another thing.”6
In any case, the idea that any type of mental state is identical with some type of neurophysiological state seemed really much too strong. But it seemed that the underlying philosophical motivation of materialism could be preserved with a much weaker thesis, the thesis that for every token instance of a mental [p40] state, there will be some token neurophysiological event with which that token instance is identical. Such views were called “token‑token identity theories” and they soon replaced type‑type identity theories. Some authors indeed felt that a token‑token identity theory could evade the force of Kripke’s modal arguments.7
IV. Token‑Token Identity Theories
The token identity theorists inherited the commonsense objection to type identity theories, the objection that they still seemed to be left with some form of property dualism; but they had some additional difficulties of their own.
One was this. If two people who are in the same mental state are in different neurophysiological states, then what it is about those different neurophysiological states that makes them the same mental state? If you and I both believe that Denver is the capital of Colorado, then what is it that we have in common that makes our different neurophysiological squiggles the same belief? Notice that the token identity theorists cannot give the commonsense answer to this question; they cannot say that what makes two neurophysiological events the same type of mental event is that it has the same type of mental features, because it was precisely the elimination or reduction of these mental features that materialism sought to achieve. They must find some nonmentalistic answer to the question, “What is it about two different neurophysiological states that makes them into tokens of the same type of mental state?” Given the entire tradition within which they were working, the only plausible answer was one in the behaviorist style. Their answer was that a neurophysiological state was a particular mental state in virtue of its function, and this naturally leads to the next view.
V. Black Box Functionalism
What makes two neurophysiological states into tokens of the same type of mental state is that they perform the same function in the overall life of the organism. The notion of a [p41] function is somewhat vague, but the token identity theorists fleshed it out as follows. Two different brain‑state tokens would be tokens of the same type of mental state iff the two brain states had the same causal relations to the input stimulus that the organism receives, to its various other “mental” states, and to its output behavior (Lewis 1972; Grice 1975). Thus, for example, my belief that it is about to rain will be a state in me which is caused by my perception of the gathering of clouds and the increasing thunder; and together with my desire that the rain not come in the windows, it will in turn cause me to close them. Notice that by identifying mental states in terms of their causal relations ‑ not only to input stimuli and output behavior, but also to other mental states ‑ the token identity theorists immediately avoided two objections to behaviorism. One was that behaviorism had neglected the causal relations of mental states, and the second was that there was a circularity in behaviorism, in that beliefs had to be analyzed in terms of desires, desires in terms of beliefs. The token identity theorist of the functionalist stripe can cheerfully accept this circularity by arguing that the entire system of concepts can be cashed out in terms of the system of causal relations.
Functionalism had a beautiful technical device with which to make this system of relations completely clear without invoking any “mysterious mental entities.” This device is called a Ramsey sentence,8 and it works as follows: Suppose that John has the belief that p, and that this is caused by his perception that p; and, together with his desire that q, the belief that p causes his action a. Because we are defining beliefs in terms of their causal relations, we can eliminate the explicit use of the word “belief” in the previous sentence, and simply say that there is a something that stands in such‑and‑such causal relations. Formally speaking, the way we eliminate the explicit mention of belief is simply by putting a variable, “x,” in place of any expression referring to John’s belief that p; and we preface the whole sentence with an existential quantifier (Lewis 1972). The whole story about John’s belief that p can then be told as follows: [p42]
($x) (John has x & x is caused by the perception that p & x together with a desire that q causes action a)
Further Ramsey sentences are supposed to get rid of the occurrence of such remaining psychological terms as “desire” and “perception.” Once the Ramsey sentences are spelled out in this fashion, it turns out that functionalism has the crucial advantage of showing that there is nothing especially mental about mental states. Talk of mental states is just talk of a neutral set of causal relations; and the apparent “chauvinism” of type‑type identity theories ‑ that is, the chauvinism of supposing that only systems with brains like ours can have mental states ‑ is now avoided by this much more “liberal” view.9 Any system whatever, no matter what it was made of, could have mental states provided only that it had the right causal relations between its inputs, its inner functioning, and its outputs. Functionalism of this variety says nothing about how the belief works to have the causal relations that it does. It just treats the mind as a kind of a black box in which these various causal relations occur, and for that reason it was sometimes labeled “black box functionalism.”
Objections to black box functionalism revealed the same mixture of the commonsensical and the technical that we have seen before. The commonsense objection was that the functionalist seems to leave out the qualitative subjective feel of at least some of our mental states. There are certain quite specific qualitative experiences involved in seeing a red object or having a pain in the back, and just describing these experiences in terms of their causal relations leaves out these special qualia. A proof of this was offered as follows: Suppose that one section of the population had their color spectra reversed in such a way that, for example, the experience they call “seeing red” a normal person would call “seeing green”; and what they call “seeing green” a normal person would call “seeing red” (Block and Fodor 1972). Now we might suppose that this “spectrum inversion” is entirely undetectable by any of the usual color blindness tests, since the abnormal group makes exactly the [p43] same color discriminations in response to exactly the same stimuli as the rest of the population. When asked to put the red pencils in one pile and the green pencils in another they do exactly what the rest of us would do; it looks different to them on the inside, but there is no way to detect this difference from the outside.
Now if this possibility is even intelligible to us ‑ and it surely is ‑ then black box functionalism must be wrong in supposing that neutrally specified causal relations are sufficient to account for mental phenomena; for such specifications leave out a crucial feature of many mental phenomena, namely, their qualitative feel.
A related objection was that a huge population, say the entire population of China, might behave so as to imitate the functional organization of a human brain to the extent of having the right input‑output relations and the right pattern of inner cause‑and‑effect relations. But all the same, the system would still not feel anything as a system. The entire population of China would not feel a pain just by imitating the functional organization appropriate to pain (Block 1978).
Another more technical‑sounding objection to black box functionalism was to the “black box” part: Functionalism so defined failed to state in material terms what it is about the different physical states that gives different material phenomena the same causal relations. How does it come about that these quite different physical structures are causally equivalent?
VI. Strong Artificial Intelligence
At this point there occurred one of the most exciting developments in the entire two‑thousand‑year history of materialism. The developing science of artificial intelligence provided an answer to this question: different material structures can be mentally equivalent if they are different hardware implementations of the same computer program. Indeed, given this answer, we can see that the mind just is a computer program [p44] and the brain is just one of the indefinite range of different computer hardwares (or “wetwares”) that can have a mind. The mind is to the brain as the program is to the hardware (Johnson‑Laird 1988). Artificial intelligence and functionalism coalesced, and one of the most stunning aspects of this union was that it turned out that one can be a thoroughgoing materialist about the mind and still believe, with Descartes, that the brain does not really matter to the mind. Because the mind is a computer program, and because a program can be implemented on any hardware whatever (provided only that the hardware is powerful and stable enough to carry out the steps in the program), the specifically mental aspects of the mind can be specified, studied, and understood without knowing how the brain works. Even if you are a materialist, you do not have to study the brain to study the mind.
This idea gave birth to the new discipline of “cognitive science.” I will have more to say about it later (in chapters 7, 9, and 10); at this point I am just tracing the recent history of materialism. Both the discipline of artificial intelligence and the philosophical theory of functionalism converged on the idea that the mind was just a computer program. I have baptized this view “strong artificial intelligence” (Searle 1980a), and it was also called “computer functionalism” (Dennett 1978).
Objections to strong AI seem to me to exhibit the same mixture of commonsense objections and more or less technical objections that we found in the other cases. The technical difficulties and objections to artificial intelligence in either its strong or weak version are numerous and complex. I will not attempt to summarize them. In general, they all have to do with certain difficulties in programming computers in a way that would enable them to satisfy the Turing test. Within the AI camp itself, there were always difficulties such as the “frame problem” and the inability to get adequate accounts of “nonmonotonic reasoning” that would mirror actual human behavior. From outside the AI camp, there were objections such as those of Hubert Dreyfus (1972) to the effect that the [p45] way the human mind works is quite different from the way a computer works.
The commonsense objection to strong AI was simply that the computational model of the mind left out the crucial things about the mind such as consciousness and intentionality. I believe the best‑known argument against strong AI was my Chinese room argument (Searle 1980a) that showed that a system could instantiate a program so as to give a perfect simulation of some human cognitive capacity, such as the capacity to understand Chinese, even though that system had no understanding of Chinese whatever. Simply imagine that someone who understands no Chinese is locked in a room with a lot of Chinese symbols and a computer program for answering questions in Chinese. The input to the system consists in Chinese symbols in the form of questions; the output of the system consists in Chinese symbols in answer to the questions. We might suppose that the program is so good that the answers to the questions are indistinguishable from those of a native Chinese speaker. But all the same, neither the person inside nor any other part of the system literally understands Chinese; and because the programmed computer has nothing that this system does not have, the programmed computer, qua computer, does not understand Chinese either. Because the program is purely formal or syntactical and because minds have mental or semantic contents, any attempt to produce a mind purely with computer programs leaves out the essential features of the mind.
In addition to behaviorism, type identity theories, token identity theories, functionalism, and strong AI, there were other theories in the philosophy of mind within the general materialist tradition. One of these, which dates back to the early 1960s in the work of Paul Feyerabend (1963) and Richard Rorty (1965), has recently been revived in different forms by such authors as P. M. Churchland (1981) and S. Stich (1983). It is the view that mental states don’t exist at all. This view is called “eliminative materialism” and I now turn to it. [p46]
VII. Eliminative Materialism
In its most sophisticated version, eliminative materialism argued as follows: our commonsense beliefs about the mind constitute a kind of primitive theory, a “folk psychology.” But as with any theory, the entities postulated by the theory can only be justified to the extent that the theory is true. Just as the failure of the phlogiston theory of combustion removed any justification for believing in the existence of phlogiston, so the failure of folk psychology removes the rationale for folk psychological entities. Thus, if it turns out that folk psychology is false, then we would be unjustified in believing in the existence of beliefs, desires, hopes, fears, etc. According to the eliminative materialists, it seems very likely that folk psychology will turn out to be false. It seems likely that a “mature cognitive science” will show that most of our commonsense beliefs about mental states are completely unjustified. This result would have the consequence that the entities that we have always supposed to exist, our ordinary mental entities, do not really exist. And therefore, we have at long last a theory of mind that simply eliminates the mind. Hence, the expression “eliminative materialism.”
A related argument used in favor of “eliminative materialism” seems to me so breathtakingly bad that I fear I must be misunderstanding it. As near as I can tell, here is how it goes:
Imagine that we had a perfect science of neurobiology. Imagine that we had a theory that really explained how the brain worked. Such a theory would cover the same domain as folk psychology, but would be much more powerful. Furthermore, it seems very unlikely that our ordinary folk psychological concepts, such as belief and desire, hope, fear, depression, elation, pain, etc., would exactly match or even remotely match the taxonomy provided by our imagined perfect science of neurobiology. In all probability there would be no place in this neurobiology for expressions like “belief,” “fear,” “hope” and “desire,” and no smooth reduction of these supposed phenomena would be possible. [p47]
That is the premise. Here is the conclusion:
Therefore, the entities purportedly named by the expressions of folk psychology, beliefs, hopes, fears, desires, etc., do not really exist.
To see how bad this argument really is, just imagine a parallel argument from physics:
Consider our existing science of theoretical physics. Here we have a theory that explains how physical reality works, and is vastly superior to our commonsense theories by all the usual criteria. Physical theory covers the same domain as our commonsense theories of golf clubs, tennis rackets, Chevrolet station wagons, and split‑level ranch houses. Furthermore, our ordinary folk physical concepts such as “golf club,” “tennis racket,” “Chevrolet station wagon,” and “split‑level ranch house” do not exactly, or even remotely, match the taxonomy of theoretical physics. There simply is no use in theoretical physics for any of these expressions and no smooth type reductions of these phenomena is possible. The way that an ideal physics – indeed the way that our actual physics ‑ taxonomizes reality is really quite different from the way our ordinary folk physics taxonomizes reality.
Therefore, split‑level ranch houses, tennis rackets, golf clubs, Chevrolet station wagons, etc., do not really exist.
I have not seen this mistake discussed in the literature. Perhaps it is so egregious that it has simply been ignored. It rests on the obviously false premise that for any empirical theory and corresponding taxonomy, unless there is a type-type reduction of the entities taxonomized to the entities of better theories of basic science, the entities do not exist. If you have any doubts that this premise is false, just try it out on anything you see around you ‑ or on yourself!10
With eliminative materialism, once again, we find the same pattern of technical and commonsense objections that we noted earlier. The technical objections have to do with the fact [p48] that folk psychology, if it is a theory, is nonetheless not a research project. It isn’t itself a rival field of scientific research, and indeed, the eliminative materialists who attack folk psychology, according to their critics, are often unfair. According to its defenders, folk psychology isn’t such a bad theory after all; many of its central tenets are quite likely to turn out to be true. The commonsense objection to eliminative materialism is just that it seems to be crazy. It seems crazy to say that I never felt thirst or desire, that I never had a pain, or that I never actually had a belief, or that my beliefs and desires don’t play any role in my behavior. Unlike the earlier materialist theories, eliminative materialism doesn’t so much leave out the mind, it denies the existence of anything to leave out in the first place. When confronted with the challenge that eliminative materialism seems too insane to merit serious consideration, its defenders almost invariably invoke the heroic‑age‑of‑science maneuver (P. S. Churchland 1987). That is, they claim that giving up the belief that we have beliefs is analogous to giving up the belief in a flat earth or sunsets, for example.
It is worth pointing out in this entire discussion that a certain paradoxical asymmetry has come up in the history of materialism. Earlier type‑type identity theories argued that we could get rid of mysterious, Cartesian mental states because such states were nothing but physical states (nothing “over and above” physical states); and they argued this on the assumption that types of mental states could be shown to be identical with types of physical states, that we would get a match between the deliverances of neurobiology and our ordinary notions such as pain and belief. Now in the case of eliminative materialism, it is precisely the alleged failure of any such match that is regarded as the vindication of the elimination of these mental states in favor of a thoroughgoing neurobiology. Earlier materialists argued that there aren’t any such things as separate mental phenomena, because mental phenomena are identical with brain states. More recent materialists argue that there aren’t any such things as separate mental phenomena [p49] because they are not identical with brain states. I find this pattern very revealing, and what it reveals is an urge to get rid of mental phenomena at any cost.
VIII. Naturalizing Content
After half a century of this recurring pattern in debates about materialism, one might suppose that the materialists and the dualists would think there is something wrong with the terms of the debate. But so far the induction seems not to have occurred to either side. As I write this, the same pattern is being repeated in current attempts to “naturalize” intentional content.
Strategically the idea is to carve off the problem of consciousness from the problem of intentionality. Perhaps, one admits, consciousness is irreducibly mental and thus not subject to scientific treatment, but maybe consciousness does not matter much anyway and we can get along without it. We need only to naturalize intentionality, where “to naturalize intentionality” means to explain it completely in terms of ‑ to reduce it to ‑ nonmental, physical phenomena. Functionalism was one such attempt at naturalizing intentional content, and it has been rejuvenated by being joined to externalist causal theories of reference. The idea behind such views is that semantic content, that is, meanings, cannot be entirely in our heads because what is in our heads is insufficient to determine how language relates to reality. In addition to what is in our heads, “narrow content,” we need a set of actual physical causal relations to objects in the world, we need “wide content.” These views were originally developed around problems in the philosophy of language (Putnam 1975b), but it is easy to see how they extend to mental contents generally. If the meaning of the sentence “Water is wet” cannot be explained in terms of what is inside the heads of speakers of English, then the belief that water is wet is not a matter solely of what is in their heads either. Ideally one would like an account of intentional content stated solely in terms of causal relations between people, on [p50] the one hand, and objects and states of affairs in the world, on the other.
A rival to the externalist causal attempt to naturalize content, and I believe an even less plausible account, is that intentional contents can be individuated by their Darwinian, biological, teleological function. For example, my desires will have a content referring to water or food iff they function to help me obtain water or food (Milliken 1984).
So far no attempt at naturalizing content has produced an explanation (analysis, reduction) of intentional content that is even remotely plausible. Consider the simplest sort of belief. For example, I believe that Flaubert was a better novelist than Balzac. Now, what would an analysis of that content, stated in terms of brute physical causation or Darwinian natural selection, without using any mental terms, look like? It should be no surprise to anyone that these attempts do not even get off the ground.
Once again such naturalized conceptions of content are subject to both technical and commonsense objections. The most famous of the technical problems is probably the disjunction problem (Fodor 1987). If a certain concept is caused by a certain sort of object, then how do we account for cases of mistaken identity? If “horse” is caused by horses or by cows that are mistakenly identified as horses, then do we have to say that the analysis of “horse” is disjunctive, that it means either horse or certain sorts of cows?
As I write this, naturalistic (externalist, causal) accounts of content are all the rage. They will all fail for reasons that I hope by now are obvious. They will leave out the subjectivity of mental content. By way of technical objections there will be counterexamples, such as the disjunction cases, and the counterexamples will be met with gimmicks ‑ nomological relations, and counterfactuals, or so I would predict ‑ but the most you could hope from the gimmicks, even if they were successful in blocking the counterexamples, would be a parallelism between the output of the gimmick and intuitions about mental content. You still would not get at the essence of mental content. [p51]
I do not know if anyone has yet made the obvious commonsense objection to the project of naturalizing intentional content, but I hope it is clear from the entire discussion what it will be. In case no one has done it yet, here goes: Any attempt to reduce intentionality to something nonmental will always fail because it leaves out intentionality. Suppose for example that you had a perfect causal externalist account of the belief that water is wet. This account is given by stating a set of causal relations in which a system stands to water and to wetness and these relations are entirely specified without any mental component. The problem is obvious: a system could have all of these relations and still not believe that water is wet. This is just an extension of the Chinese room argument, but the moral it points to is general: You cannot reduce intentional content (or pains or “qualia”) to something else, because if you could they would be something else, and they are not something else. The opposite of my view is stated very succinctly by Fodor: “If aboutness is real, it must really be something else” (1987, p. 97). On the contrary, aboutness (i.e., intentionality) is real, and it is not something else.
A symptom that something is radically wrong with the project is that the intentional notions are inherently normative. They set standards of truth, rationality, consistency, etc., and there is no way that these standards can be intrinsic to a system consisting entirely of brute, blind, nonintentional causal relations. There is no normative component to billiard ball causation. Darwinian biological attempts at naturalizing content try to avoid this problem by appealing to what they suppose is the inherently teleological, normative character of biological evolution. But this is a very deep mistake. There is nothing normative or teleological about Darwinian evolution. Indeed, Darwin’s major contribution was precisely to remove purpose and teleology from evolution, and substitute for it purely natural forms of selection. Darwin’s account shows that the apparent teleology of biological processes is an illusion.
It is a simple extension of this insight to point out that notions such as “purpose” are never intrinsic to biological organisms, (unless of course those organisms themselves have [p52] conscious intentional states and processes). And even notions like “biological function” are always made relative to an observer who assigns a normative value to the causal processes. There is no factual difference about the heart that corresponds to the difference between saying
- The heart causes the pumping of blood.
and saying,
- The function of the heart is to pump blood.
But 2 assigns a normative status to the sheer brute causal facts about the heart, and it does this because of our interest in the relation of this fact to a whole lot of other facts, such as our interest in survival. In short, the Darwinian mechanisms and even biological functions themselves are entirely devoid of purpose or teleology. All of the teleological features are entirely in the mind of the observer.11
IX. The Moral So Far
My aim so far in this chapter has been to illustrate a recurring pattern in the history of materialism. This pattern is made graphic in table 2.1. I have been concerned not so much to defend or refute materialism as to examine its vicissitudes in the face of certain commonsense facts about the mind, such as the fact that most of us are, for most of our lives, conscious. What we find in the history of materialism is a recurring tension between the urge to give an account of reality that leaves out any reference to the special features of the mental, such as consciousness and subjectivity, and at the same time account for our “intuitions” about the mind. It is, of course, impossible to do these two things. So there are a series of attempts, almost neurotic in character, to cover over the fact that some crucial element about mental states is being left out. And when it is pointed out that some obvious truth is being denied by the materialist philosophy, the upholders of this view almost invariably resort to certain rhetorical strategies [p53]
Table 2.1
The general pattern exhibited by recent materialism.
Theory | Common‑sense objections | Technical objections |
Logical behaviorism | Leaves out the mind: superspartan/superactor objections | 1. Circular; needs desires to explain beliefs, and conversely 2. Can’t do the conditionals 3. Leaves out causation |
Type identity theory | Leaves out the mind: or else it leads to property dualism | 1. Neural chauvinism 2. Leibniz’s law 3. Can’t account for mental properties 4. Modal arguments |
Token identity theory | Leaves out the mind: absent qualia | Can’t identify the mental features of mental content |
Black box functionalism | Leaves out the mind: absent qualia and spectrum inversion | Relation of structure and function is unexplained |
Strong AI (Turing machine functionalism) | Leaves out the mind: Chinese room | Human cognition is nonrepresentational and therefore noncomputational |
Eliminative materialism (rejection of folk psychology) | Denies the existence of the mind: unfair to folk psychology | Defense of folk psychology |
Naturalizing intentionality | Leaves out intentionality | Disjunction problem |
[p54] designed to show that materialism must be right, and that the philosopher who objects to materialism must be endorsing some version of dualism, mysticism, mysteriousness, or general antiscientific bias. But the unconscious motivation for all of this, the motivation that never somehow manages to surface, is the assumption that materialism is necessarily inconsistent with the reality and causal efficacy of consciousness, subjectivity, etc. That is, the basic assumption behind materialism is essentially the Cartesian assumption that materialism implies antimentalism and mentalism implies antimaterialism.
There is something immensely depressing about this whole history because it all seems so pointless and unnecessary. It is all based on the false assumption that the view of reality as entirely physical is inconsistent with the view that world really contains subjective (“qualitative,” “private,” “touchy‑feely.” “immaterial,” “nonphysical”) conscious states such as thoughts and feelings.
The weird feature about this entire discussion is that materialism inherits the worst assumption of dualism. In denying the dualist’s claim that there are two kinds of substances in the world or in denying the property dualist’s claim that there are two kinds of properties in the world, materialism inadvertently accepts the categories and the vocabulary of dualism. It accepts the terms in which Descartes set the debate. It accepts, in short, the idea that the vocabulary of the mental and the physical, of material and immaterial, of mind and body, is perfectly adequate as it stands. It accepts the idea that if we think consciousness exists we are accepting dualism. What I believe ‑ as is obvious from this entire discussion ‑ is that the vocabulary, and the accompanying categories, are the source of our deepest philosophical difficulties. As long as we use words like “materialism,” we are almost invariably forced to suppose that they imply something inconsistent with naive mentalism. I have been urging that in this case, one can have one’s cake and eat it too. One can be a “thoroughgoing materialist” and not in any way deny the existence of (subjective, internal, intrinsic, often conscious) mental phenomena. However, [p55] since my use of these terms runs dead counter to over three hundred years of philosophical tradition, it would probably be better to abandon this vocabulary altogether.
If one had to describe the deepest motivation for materialism, one might say that it is simply a terror of consciousness. But should this be so? Why should materialists have a fear of consciousness? Why don’t materialists cheerfully embrace consciousness as just another material property among others? Some, in fact, such as Armstrong and Dennett, claim to do so. But they do this by so redefining “consciousness” as to deny the central feature of consciousness, namely, its subjective quality. The deepest reason for the fear of consciousness is that consciousness has the essentially terrifying feature of subjectivity. Materialists are reluctant to accept that feature because they believe that to accept the existence of subjective consciousness would be inconsistent with their conception of what the world must be like. Many think that, given the discoveries of the physical sciences, a conception of reality that denies the existence of subjectivity is the only one that it is possible to have. Again, as with “consciousness,” one way to cope is to redefine “subjectivity” so that it no longer means subjectivity but means something objective (for an example, see Lycan 1990a).
I believe all of this amounts to a very large mistake, and in chapters 4, 5, and 6, I will examine in some detail the character and the ontological status of consciousness.
X. The Idols of the Tribe
I said earlier in this chapter that I would explain why a certain natural‑sounding question was really incoherent. The question is: How do unintelligent bits of matter produce intelligence? We should first note the form of the question. Why are we not asking the more traditional question: How do unconscious bits of matter produce consciousness? That question seems to me perfectly coherent. It is a question about how the brain works to cause conscious mental states even though the [p56] individual neurons (or synapses or receptors) in the brain are not themselves conscious. But in the present era, we are reluctant to ask the question in that form because we lack “objective” criteria of consciousness. Consciousness has an ineliminable subjective ontology, so we think it more scientific to rephrase the question as one about intelligence, because we think that for intelligence we have objective, impersonal criteria. But now we immediately encounter a difficulty. If by “intelligence” we mean anything that satisfies the objective third‑person criteria of intelligence, then the question contains a false presupposition. Because if intelligence is defined behavioristically, then it is simply not the case that neurons are not intelligent. Neurons, like just about everything else in the world, behave in certain regular, predictable patterns. Furthermore, considered in a certain way, neurons do extremely sophisticated “information processing.” They take in a rich set of signals from other neurons at their dendritic synapses; they process this information at their somae and send out information through their axonal synapses to other neurons. If intelligence is to be defined behavioralistically, then neurons are pretty intelligent by anybody’s standards. In short, if our criteria of intelligence are entirely objective and third‑person ‑ and the whole point of posing the question in this way was to get something that satisfied those conditions ‑ then the question contains a presupposition that on its own terms is false. The question falsely presupposes that the bits do not meet the criteria of intelligence.
The answer to the question, not surprisingly, inherits the same ambiguity. There are two different sets of criteria for applying the expression “intelligent behavior.” One of these sets consists of third‑person or “objective” criteria that are not necessarily of any psychological interest whatever. But the other set of criteria are essentially mental and involve the first-person point of view. “Intelligent behavior” on the second set of criteria involves thinking, and thinking is essentially a mental process. Now, if we adopt the third‑person criteria for intelligent behavior, then of course computers ‑ not to mention [p57] pocket calculators, cars, steam shovels, thermostats, and indeed just about everything in the world ‑ engages in intelligent behavior. If we are consistent in adopting the Turing test or some other “objective” criterion for intelligent behavior, then the answer to such questions as “Can unintelligent bits of matter produce intelligent behavior?” and even, “How exactly do they do it?” are ludicrously obvious. Any thermostat, pocket calculator, or waterfall produces “intelligent behavior,” and we know in each case how it works. Certain artifacts are designed to behave as if they were intelligent, and since everything follows laws of nature, then everything will have some description under which it behaves as if it were intelligent. But this sense of “intelligent behavior” is of no psychological relevance at all.
In short, we tend to hear both the question and the answer as oscillating between two different poles: (a) How do unconscious bits of matter produce consciousness? (a perfectly good question to which the answer is: In virtue of specific ‑ though largely unknown ‑ neurobiological features of the brain); and (b) How do “unintelligent” (by first‑ or third‑person criteria?) bits of matter produce “intelligent” ( by first‑ or third‑person criteria?) behavior? But to the extent that we make the criteria of intelligence third‑person criteria, the question contains a false presupposition, and this is concealed from us because we tend to hear the question on interpretation (a).
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