Chapter 4 I N F O R M A T I C S (c) 1991, 1993 by David G. Hays (c) 1995 by Janet Hays 4.1. INFORMATICS OF SPEECH 4.2. INFORMATICS OF WRITING 4.3. CALCULATION 4.4. INFORMATICS OF COMPUTATION 4.A. Appendix: Rankshift, 2 to 3 The rank 3 concept of energy as the measure of progress gives way in rank 4 to the concept of information- processing power. The computer itself is a model of the higher-order paradigm, since its abstract formula- tion fixes the structure and limits of a world of computation. 4.1. INFORMATICS OF SPEECH 4.1.1. Linguistic structures. The universal patterns of sapient communications ... 4.1.2. The first informatic revolution. The growth curve from primate to sapient ... 4.1.3. Evolution of language. Increasing fluency, more economical expression ... Rank 1 lives by speech alone. Although life is simple in every known society that communicates by speech alone, speech itself has eluded theoretical analysis. It is an extraordinarily complex system, the subject matter of _linguistics_. The first appearance of speech marks the biological origin of sapients. But language changes from rank to rank--like technology and cognition, it evolves. 4.1.1. Linguistic structures _Phonetics_, the study of speech sounds, is a different specialty from _phonology_, the study of sounds as units of language. By instrumental observation of the articulatory appa- ratus, which is quite accessible, and of the perceptual appara- tus, which is hidden in cavities of the skull behind the ear, and of the waveform which is in the air between speaker and hearer, phoneticians have learned a lot about sounds. They can build both mechanical and electronic simulators of articulation that sound pretty good. Simulators of detection--speech recognition machines--are not yet very good. Almost all phoneticians use a theory that assumes a small alphabet of sound types: At some level, the brain commands articulation of a word by listing its segments in order, each segment taken from the small alphabet. Each segment can be represented by listing its _features_, such as _voicing_: Are the vocal cords vibrating or not? A species must have throat and mouth properly formed, with refined neuromuscular control, to articulate speech. Likewise, the right kind of acoustic signal detector and transducer is necessary to perceive speech. Talking animals are fantasy; we and we alone on earth have the full equipment. Linguistics proper has three major branches: Phonology, syntax, and semantics. _Phonology_ screens out the phonetic characteristics that are not used for encoding messages. Thus, English has two kinds of /p/, one in 'pin' and one in 'spin'. A native speaker saying those words aloud with palm before mouth feels a puff of air in 'pin' and not in 'spin'. This difference is phonetically signif- icant, because all native speakers make the distinction and hear an oddity in the English speech of those who do not, but linguis- tically not significant just because it is automatic. Phonolo- gists also study patterns. For example, the sequence /vm/ appears at the beginning of words in Russian, and the Czech speaker puts the stress on the /r/ in the word /brno/ (name of a city). English speakers do not do either. Languages differ, but phonologists are convinced that their theory fits all languages equally well. Every sapient has a brain capable of phonological encoding and decoding. _Syntax_ studies the arrangement of meaningful, or at least informatically useful, elements. Prepositions, conjunctions, and affixes like '-ing' or '-ed' may not carry meaning in the sim- plest sense, but they are useful. The units of syntax are represented by sound sequences, but they enter into patterns that cannot be explained in phonological terms. Syntactic patterns can be formulated in terms of the rela- tion between operators and arguments. The arguments of arithme- tic addition are the numbers to be added; the arguments of a verb are the noun subject and object: + eats / \ /\ / \ / \ 17 23 John cheese Applying the operator "+" to "17" and "23", we obtain their sum, "40". Applying the operator "eats" to "John" and "cheese", we obtain a composite that we can analyze for its meaning. This approach is called _dependency gramar_ (Hays in LINGBIBL* ). Syntactic patterns can also be formulated by dividing the sentence into a subject part and a predicate part, then subdi- viding each of those, and so on down to elementary segments: S / \ / \ NP VP | /\ | / \ | V NP | | | John eats cheese [S = Sentence, NP = Noun Phrase, VP = Verb Phrase] This approach is called _phrase-structure_ grammar; it also shows how analysis of the meaning of the sentence is to be performed. Some of the patterns of syntax can be displayed with depen- dency or phrase structure, but others cannot. Noam Chomsky ( LINGBIBL* ) introduced the concept of _transformation_ to account for other kinds of patterning. Transformations provide a formal system for dealing with pattern similarities, as between active and passive: He hit her on the head. She was hit on the head. Mathematical investigations show that transformation is a power- ful technique. Let T be the class of languages with transforma- tional grammars, and let P be the class of languages with phrase structure grammars. Then some languages that belong to T do not belong to P. In my opinion, no human language "really" has a grammar of either kind. But languages that belong to T and not to P serve better as _models_ of human languages. But why do natural languages have syntax? There is no answer to this question in the literature as far as I know. My own opinion is that syntax originates to help match production and recognition. These mechanisms probably have different struc- tures, with different limitations, although they work together in a feedback arrangement. The limitations on production are arbitrary to the mechanism of recognition, and vice versa. Syntax represents the arbitrary limitations of the exotic _other_ component. Linguists generally assert that every language, whatever the cognitive rank of the speakers, has a grammar of the same kind; all sapients use the most powerful syntactic devices. I am not certain that they are correct. It may be the case that the grammars of rank 1 languages can be analyzed with theories that are mathematically simpler; it might even be the case that rank 3 languages need more sophisticated theory than rank 2. But no one has analyzed grammars to test this possibility. _Semantics_ studies patterns of meanings. It sorts the nouns of syntax into _animate_ and _inanimate_, for example, and further classifies animate nouns as _human_ or _nonhuman_. Among the patterns that semantics must describe, there is _corefe- rence_: John ate an apple. He enjoyed the sharp flavor. John ate an apple. It was crisp and juicy. In the first, the pronoun "He" is coreferential with "John"; in the second, "It" is coreferential with "John". In the first, one might have said "The lad" instead of "He"; in the second, "The fruit" could be used rather than "It". Some other semantic patterns have to do with the use of definite ("the") or indefinite ("a") articles; with the scope of negation John hasn't read all the novels of Zola. (But has he read any of them?) And so on through a long list. _Pragmatics_ has been proposed as a fourth branch of lin- guistics, to deal with the relation of language to user. The patterns of phonology, syntax, and semantics give the speaker many different ways to express a thought. Pragmatics might be able to account for speakers' choices. Shall the sentence be active or passive? John ate the apple. The apple was eaten by John. That might depend on what is _topic_ and what is _comment_; if we are telling the story of the apple, and introduce John for the first time in this sentence (perhaps expanding to say "John, a street urchin who had had no fruit all winter"), then the passive is likely. Linguistics still falls short of a complete analysis of language, in my opinion, because it has almost nothing to say about _metaphor_. The capacity for abstract thought in all sapients is apparent from the use of metaphor and proverbs in rank 1 (and all other ranks). I can refer you to a recent bibliography and a paper by Benzon and me ( METAPHOR* ), but we still have to hope for a more complete study of this pervasive and powerful technique. Beyond linguistics, there is more to be understood about speech. Human vocal sounds represent language. They also indicate emotions and other conditions of the speaker. If we sense these signals and react to them well, we are socially effective. Typically neither speaker nor hearer is aware of the emotional signaling that goes on (Hall in LINGBIBL* ). Writing-- on paper or through a computer communication network--does not provide an adequate equivalent. 4.1.2. The First Informatic Revolution The brain serves for ordinary activity--seeing and doing-- and also for analysis and communication. The linguistic part is more or less isolated, with major centers in the left hemisphere. The structures of the brain at the highest biological level are complex networks, themselves organized into a number of opera- tional levels. The correlation of the linguistic part with the rest occurs at or near the highest operational level; and this is the semantic relation. The final step in our biological evolu- tion occurred, I suggest, when some small change in neural topology created this highest link. Before that final change, there had been a long slow cumula- tion of linkages in the brain in certain primates; Campbell* concludes (p. 354) that it took four million years. During the second half of that period, stone tools were used; they were simple and did not vary much in time and space. Modern skeletons have been dated to 100,000 years ago (Bar- Yosef & Vandermeersch), and a survey of DNA in various places on Earth today suggests a common ancestor in Africa about then (Wilson & Cann). Stone tools began to show great variation between 45,000 and 40,000 years ago. By then, we imagine, many parts of the speech system were running: Pre-human primates used vocal sound for social interaction and, perhaps, manual signals to co-ordinate working groups. One final biological change brought these systems together, perhaps 50,000 years ago (see Hockett; Hockett & Ascher). For interesting speculations about the intricate sequence of changes from a primate ancestor to full sapience, I recommend a book by Merlin Donald. If everyone on earth descends from the single ancestor in which the change appeared, then all sapients have the same fundamental capacity for speech and thought. Unfortunately, this question is still debated. Fagan has recently brought together the evidence and arguments for a single evolutionary origin of sapient life, and for multiple evolutionary origins in various places after some earlier form had spread out (Thorne & Wolpoff). References are in HmRvBIBL* . 4.1.3. Evolution of Language Language has evolved, from the beginning until now. The communicative efficiency of educated and trained participants in rank 3 or rank 4 culture is high: They convey more thought per minute in speech or writing. Evolution includes both enhancement of vocabulary and refinement of syntax. Complex syntax suggests that conceptualization has out-run communicative skill; evolution yields simple ways of expressing complex thought. Swadesh had taken this position early, but other linguists denied evolutionary change in language until Berlin & Kay demon- strated a sequence of "basic" color terms. In the languages of the simplest societies, they found only terms for "dark" and "light". Societies a bit more complex have "red". Terms for "yellow" and "green" are next, then "blue"; "brown"; and, unor- dered, "purple", "pink", "orange", and "grey". Where several terms are used, "dark" is "black" and "light" is "white". When they wrote their book, Berlin & Kay did not believe that evolu- tionary level could be measured, but some colleagues and I used a well-known measure and confirmed their sequence. (References in LINGBIBL* ). The first careful work on evolution of syntax known to me was done by Revere Perkins ( LINGBIBL* ) when he studied with me at SUNY Buffalo. Working with 50 languages, mostly from rank 1 societies, he found several orderly sequences. (The inference* from contemporary societies to the past is disputed, but I think it is justified.) For example, forms translated as "whence" and "whither" are more likely to appear in simpler societies; more complex societies use combinations "from where" and "to where". Again, certain ideas expressed morphologically (by a syllable attached to a verb) in simple societies are expressed by indepen- dent words in more complex ones. The impression one takes is growth of flexibility. Perkins also took several published papers and ranked the societies mentioned. A notable instance is the work of Keenan and Comrie on formation of relative clauses ( LINGBIBL* ). English can form a relative clause on a subject The boy who ate the apple. or on the object of a comparison The boy than whom no one was smarter. Keenan & Comrie considered six grammatical positions and found that the subject is "accessible" to relativization in every language they examined, the object of comparison in fewest, and the other four in graded sequence. Perkins found that the number of accessible positions increases with cultural evolution, but he did not publish his finding. Little research has been done so far on evolution of lan- guage, but I foresee a plethora of strong results when the topic is finally addressed. 4.2. INFORMATICS OF WRITING 4.2.1. Two Kinds of Writing. Pictographic and phonographic 4.2.2. Significance of Writing in Cultural Evolution. Out of social context ... Cumulation 4.2.3. Effect on Speech. Formal styles ,,, Writing, in a system that represents the consonants and vowels of speech, is easy to learn. Knowledge can be retained, criticized, and extended. Those who master the art become more sophisticated in their use of speech as well. Let me tell you a story that I picked up from articles by Denise Schmand-Besserat (1986), who developed the ideas of Michael J. Harner (1980)--see WRITBIBL* . Long before writing, the rich had to entrust their goods to others for transport. For example, a few sheep to be delivered at a distance. To guarantee that all of the sheep dispatched would arrive at the intended destination, the sender would prepare a small clay box and put into it one pebble for each sheep, then seal and fire the box. Breaking it, the receiver could count the pebbles and the sheep and be content. After a time, the habit of making a mark on the lid of the box for each pebble inside got started. Still later, the box was reduced to a flat sheet of clay, and the pebbles forgotten. Thus a system of marks on a surface as a representation of meaning could arise in a sequence of small steps. For the history of writing, see WRITBIBL* . 4.2.1. Two Kinds of Writing One is pictographic, the other phonographic. A pictographic system has thousands of distinct symbols (pictures), each corresponding to a dictionary entry. Note that I do _not_ say that the picture stands for an idea; that would be not writing, but drawing. With evolution of culture, picto- graphic systems drift toward representation of "minimum meaning- ful units" of language, as the linguists say. Many words can be analyzed into meaningful parts, and it is the part rather than the whole word that modern Chinese represents with a character. Phonographic systems have symbols corresponding to segments of speech sound. A _syllabary_ has a symbol for each syllable; that is not bad for a language that has a phonological rule re- stricting every syllable to one consonant followed by one vowel. For such a language, the syllabary has on the order of magnitude of 60 characters. English has no such rule, and many other languages have syllables of more elaborate types. One writing system that started by representing a whole syllable with a character later shifted to representing a conso- nant. Representation of _consonants_ only is not bad, but decoding is somewhat too hard. The Greeks are credited with conversion of some of the consonant characters of Phoenician alphabets into _vowel_ characters. Thus the letter shape `a' descends from a consonant character that was not needed by the Greeks. It is said that syllabaries derive from pictographic systems by change of interpretation; the shape `A' was originally a pictograph for "bull" (see the nose at the top and the horns at the bottom?), but later came to stand for the first syllable of the word for "bull" at the time; the sign came to match the sound rather than the minimum meaningful unit. With an alphabet of consonants and vowels, the skill of reading and writing could be taught to anyone in a short time. No longer did writing have to be left to professional scribes, as most programming is left to professional programmers today. For example, "by the sixth or seventh century B.C., Hebrew society enjoyed a basic level of literacy" (Logan, p. 81); "a reading public" arose in Greece (Logan, p. 123, WRITBIBL* ). 4.2.2. Significance of Writing in Cultural Evolution My college tutor often said, "Can you see what I'm saying?" With writing, that question can be asked literally, and the answer is "Yes." Karl Popper, the great philosopher of science, said that writing permitted criticism of theories. Look at what you have said on paper (or a screen) and be aghast! Quick, the eraser. Editing and analytic review of documents are essential tools of thought. Also, Popper notes, burning the book is more humane than burning the theoretician. Talcott Parsons* (1966) noted that writing isolates content from the social situation of a certain speaker and a certain hearer. For cool rational analysis, that is a great advantage. The tendency to believe those with authority is all too great. Writing also permits widespread distribution and permanent retention. True, before writing some texts were memorized. But Goody (1986 in WRITBIBL* ) has checked in certain places in Africa, and found that the religious beliefs and rituals of nonliterate societies can shift rapidly. How could we expect myths or tales to be remembered without significant change? Nothing comparable has occurred within our experience. I remember the fact, but not the source of the fact, that oral histories often differ substantially from written records of what happened. (Oral histories are made by putting a tape recorder in front of participants, years after the event.) Martin Davis (1988 in COMPBIBL* ) tells how Backus, inventor of a syntax for programming, gave Davis credit in writing for inspiring Backus in lectures at Atlanta State, a place where Davis could not remember lecturing. In fact, the place never existed. But Davis had lectured for IBM at The Lamb Estate. Okay, a misprint. But the Lamb Estate lectures were given after Backus invented his syntax. What happened? Davis and Backus have talked it over, but cannot figure it out. So much for oral history, human memory, and other alternatives to written records. The printing press improves diffusion ( Eisenstein in WRITBIBL* ). In the first half century of printing from moveable type in Europe, up to 1500, some 6-35 thousand titles were printed in some 10-20 million copies ( FBCC* 401, Stein 1501 in BIBLNOTE* , and elsewhere). More sapients could be informed, amused, and persuaded--not just more, but vastly more. The press gave the literate much more to think about, and surely made possible wider literacy than before. Today, electronic editing and bulletin-board and database systems threaten to make every sapient not only a reader but also an author and a publisher. A different aspect of reading appears in pictures taken by Lassen, Ingvar, and Skinhoj (1978 COGNBIBL* ), who injected radioactive material and asked their subjects to talk, listen, do arithmetic, read, read aloud. Their pictures show how much blood is needed for the brain to do these tasks. The amount varies across the surface of the brain in each task; some areas work harder than others, given a certain job. Now, what is important here is that the combination of areas for reading is a combina- tion that could never have been active all at once before the development of writing. If, as Benzon and I asserted (1988 in COGNBIBL* ), a combination of brain areas working together is the biological implementation of a psychic mode, then _writing forced a new mode of human psychic activity_, an organization of brain areas more richly complex, more intricate, than previous modes. And THAT is the best support I have for the view that each rank generates a new, higher-level, system of thought. To deal with written text, the brain organizes itself in a new way--it achieves a new psychobiological mode. That mode pulls together a range of components that have never worked together before. Now that they can collaborate, they can attack many kinds of cogni- tive problems--and in collaboration they form a more powerful system. The new cognitive system was not achieved at a stroke. There was in history a first person who read silently without moving his lips. St. Augustine describes Ambrose doing so (_Confessions_ Book 6, Section 3). That comes surprisingly late, since writing was up to the alphabetic level before the Greeks and the Hebrews began creating moral and natural philosophy. 4.2.3. Effect on Speech Formal, elaborate, flexible styles of speech are to be found among the literate. The work of Basil Bernstein ( LINGBIBL* ) is not sufficient to give a full understanding of this phenomenon, but enough to convince me that speech takes on a new character in a culture that has writing. Bernstein says, for example, that literate sapients can speak so as to be understood by a listener who is not acquainted with the general situation in which report- ed events occurred. Illiterate speakers fail to communicate because they cannot take proper account of the listener's igno- rance. Marshall & Glock found two populations of readers, one that recalled less well after reading complex texts--containing, for example, conditional statements--and another population that recalled either kind of text equally well. Gellner* makes a suggestion about the change from rank 2 to rank 3 that should be investigated: In a traditional social order, the languages of the hunt, of harvesting, of various rituals, of the council room, of the kitchen or harem, all form autonomous systems: to conjoin statements drawn from these various disparate fields, to probe for inconsistencies between them, to try to unify them all, this would be a social solecism or worse, probably blasphemy or impiety, and the very endeavour would be unintelligible. (p. 21) If writing alters speech, that is an example of a very general process: Each new rank reworks all of the systems of its prede- cessors. 4.3. CALCULATION The techniques that made it possible for almost any sapient to learn how to obtain solutions to simple problems of addition, subtraction, multiplication, and division were not known in the West until after AD 1200. These techniques contributed to the development of science and a new rank of thought. V. Gordon Childe ( MMH* pp. 152-153) discusses the intellec- tual growth that accompanied the Urban Revolution--the shift from rank 1 to rank 2. In Egypt and Babylonia, arithmetic was taught by the case method that we use in law school, business school, and other places where the subject matter is too complex for us to extract principles or rules. The scribe went to school year after year, examining case after case. Once in the field, he was expected to solve real problems. The supervisor on a construc- tion job, faced with the task of digging a hole tomorrow, would ask the scribe how many men he needed, and how many loads of earth would come out of the hole. The scribe could answer. Childe believed that the principles were taught orally; I don't. They simply could not explain how they got their results. The Egyptian method of multiplying was by adding, although they knew about doubling and halving. Babylon had tables for multiplication by about 2000 BC. Their place notation died with their writing system. ( MMH* pages 192 and 227-228) The rules for doing anything are more abstract than the doing itself. The rules for doing any particular arithmetic process are called the algorithm, after al-Khwarizmi, the Muslim writer through whose work the Hindu systems of reckoning finally reached Europe. The person given credit for making arithmetic popular in the west is Leonard Fibonacci; he did it with _The Book of the Abacus_ (1202), which was not about the abacus but about calculation (van der Waerden). (See CALCBIBL* .) Place notation is only interesting because it makes for simple algorithms. You will have been told long ago how hard it is to multiply MDCXLIV by CMX. Arabic numbers go with easy rules for arithmetic. So: Rank 1 learns to count. Rank 2 learns to do arithme- tic, but the knowledge stands as lore, not explainable. Rank 3 learns to write algorithms for all the simple arithmetic process- es, and some that are not so simple. And I have no doubt that arithmetic is a new mode, as reading and writing are new psycho- biological modes: When a sapient learns to calculate, a new combination of parts of the brain organizes to work together. Havelock (1982 in WRITBIBL* ) holds a similar view about the importance of calculation in the Renaissance. To say that Fibonacci popularized arithmetic is not to say that everyone in Europe learned arithmetic then. Merchants still used their counter (note the word; that _is_ its origin) as an abacus--a shelf marked off in squares, with small stones to reckon the bill. One example of a textbook of business arithme- tic is by Apian (1527, CALCBIBL* ). A clown in Shakespeare's _The Winter's Tale_ (1608-1611?) makes a mess of mental arithme- tic--funny to Shakespeare's audience, I suppose, because they were all having their own troubles of that sort. But by the 18th century, many English craftsmen used arithmetic on the job; more, probably, than on the Continent. Figure 4.1 ( Fig_4_1* ) contains a chronology of calcula- tion. 4.4. INFORMATIC ANALYSIS OF COMPUTATION 4.4.1. History. The gestation of the computer ... 4.4.2. The Invention. A new gestalt ... 4.4.3. Higher-order Patterns in the Brain. Does programming enhance thinking? The computer that stores a program of instructions and a mass of data received its definitive shape from mathemati- cians working on the most sophisticated questions ever asked. Its principle is simple, but its power is enormous. Understanding how enormous power can reside in a simple principle seems to promote a new level of cognitive skill. If you want to know the difference between calculation and computation, it is just this: A calculator implements an algorithm that does arithmetic. A computer implements an algorithm that does algorithms. I have talked about higher-order patterns, and now we have one: The computer. A computer is a device, made of relays, or vacuum tubes, or transistors, or very large scale integrated circuits, that can accept as input a program to carry out any process that can be defined. Mathematicians tell us that some processes are indefinable, like the apparently simple process of proving all the theorems in a system that can handle arithmetic. But subject to the abstruse restrictions of metamathematics, any adequate computer is a universal machine. A calculator is a device, made of relays, or vacuum tubes, or transistors, or very large scale integrated circuits, that can do arithmetic. Since both are made of the same kind of parts, we have no material reason to say that the computer is of higher order. Since neither, in essence, need have more than its central apparatus (described above), input-output, and storage, we have no structural reason to say that one is of higher order. However, since the computer can emulate a calculator, but a calculator cannot emulate a computer, we do have a functional reason to say that the computer is of higher order. In the history of neuropsychology (I mean the evolution of thought), we have no material reason to say that rank 4 paradigms are of higher order than rank 3: The same part of the brain runs either. We do have functional reason, since a rank 4 person can emulate a rank 3 person, but not vice versa. As for structural reasons, that is more subtle and I postpone discussion to the end of this chapter. 4.4.1. History The universal algorithm that can do all computations when given the programs to execute was imagined in the 1930s by Alan M. Turing, an English mathematical logician trained at Cambridge and Princeton. His invention is called the _Universal Turing Machine_. He was working on the abstruse metamathematical problem that I mentioned above, and solved the problem, but was second by a few months to Alonzo Church. But he, not Church, thought of a process accomplished over time; and time is of the essence in computing. (See COMPBIBL* .) A Turing machine is a central processor of finite size with an infinite tape. When calculation starts, the tape may be blank or may carry information. The CPU is in some state; in that state, and given the information in the current square on the tape, the CPU may Change the content of the current square Move the tape Enter a new state That's all it takes to do a computation. The CPU may implement adding, and convert a tape containing two numbers into a tape containing their sum. Or the CPU may implement "algorithm", and convert a tape containing instructions and data into a tape containing the result of applying the instructions to the data. Meanwhile, Howard Aiken of Harvard was building, with help from IBM, enormous electromechanical calculators. John V. Atanasoff of the University of Iowa was building an electronic digital calculator. And Eckert and Mauchly of the University of Pennsylvania got around to building another, with at least some knowledge of Atanasoff's, in the 1940s. But Atanasoff neither completed nor publicized his machine adequately. Eckert and Mauchly did, and went into the encyclopedia as the inventors of the computer. (See Burks & Burks in COMPBIBL* .) However, John von Neumann was there. The first Pennsylvania machine, ENIAC, was a calculator. It had a component that could change its configuration. You could set up a program by turning knobs and plugging in wires. So ENIAC was any calculator you wanted it to be, more or less, but at any moment it was only one specific calculator. The Pennsylvania group began planning a second machine, EDVAC. von Neumann got wind of the project by accident, and attended the seminars at Penn. After a while, he went home and wrote down what the Pennsylvanians needed to say but could not, a plan for an internal-stored program electronic digital computer. And EDVAC was built to his design. (See Burks, Goldstine & von Neumann; von Neumann; and Turing in COMPBIBL* ). 4.4.2. The Invention Until a few years ago, I said that von Neumann invented the computer by bringing together three ideas: 1. Instructions and data can be represented in the same alphabet. This is the _linguistic_ aspect. 2. All calculations can be performed with the same small set of operations. This is the _mathematical_ aspect. 3. All algorithms can be realized using a single control operation, the conditional jump. This is the _logical_ aspect. But then I heard Martin Davis lecture on Turing, and learned (or was reminded of) the true nature of the Universal Turing Machine. So what did von Neumann contribute? That there was a contribu- tion in 1945 is certain; the Turing Machine is not practical, since moving the tape would take much too long, and the Aiken-- Atanasoff-Eckert-Mauchly machines were calculators until von Neumann arrived. Turing knew the linguistic aspect; his tape could be binary and contain both instructions and data. Turing knew the mathematical aspect; his universal CPU could do all arithmetic, everything. Turing knew about jumps; he sent his machine from state to state freely. But since every instruction contained a jump, he did not distinguish between sequential flow and conditional jumping. Does that matter? Well, all distinctions matter, but this one does not seem to be crucial. After reflection, I submit that von Neumann contributed a sidewaysing. In my opinion, sidewaysing is the most difficult concept in this book, but we have to understand it to see what von Neumann contributed. A Turing machine has only one level: The CPU. A von Neumann machine has two levels: Control and calcula- tion. The Control level can execute any algorithm, and is there- fore comparable to the Turing machine. Calculation can do one particular algorithm, or group of algorithms: Add, subtract, multiply, divide. Subtraction alone is enough, but implementing the others in hardware makes for speed. A von Neumann machine also has some form of addressing, although Davis says, "The ACE report [Turing 1945, later date than the EDVAC report] contains explicit mention of features such as an instruction address register and truly random access to memory locations, neither of which is dealt with in the EDVAC report, although both are already to be found in Burks, Gold- stine, and von Neumann 1946." (See COMPBIBL* .) To implement sequential calculation with conditional jumps, you build a machine that works as if every storage cell had a numerical address. You use a number to represent the location in storage of the instruction that you are presently executing. When execution of this instruction is complete, you either add 1 to the address or replace the old address with a new address -- that replacement is a jump. The new address may be obtained by _adding_ an offset to the old address. Thus the implementation of logical control by conditional jumps uses the arithmetic level to manage the control level. The two are inextricably interwoven. To take two levels of a hierarchical structure and fuse them in this brilliant way, obtaining an architecture that is effec- tive in practice, is a beautiful example of sidewaysing. By sidewaysing, then, I mean looking at several hitherto independent patterns sideways, and fusing them into a new pat- tern. Robert Merton, introducing the philosopher of science I. Bernard Cohen to an audience at Columbia University, spoke of Cohen's original concept of the _transformation of ideas_ in the history of science. Benzon's word is _regestalt_. But I claim sidewaysing as my own idea, a half-finished mechanism for making transformations of ideas, i.e., regestalting. 4.4.3. Higher-order Patterns in the Brain Do we have structural reasons for saying that rank 4 thought is of higher order than rank 3 thought? In the end, no. The rank 4 pattern is a fusion, obtained when, for example, two cultures come into contact. In the Renaissance, the thinking of Medieval Scholasticism came into contact with both Islamic philosophy and that of ancient Greece. At present, many of the interesting areas of science have hyphenated names: physico- chemical, computational-linguistic, ... So, of course, do many uninteresting areas. You can decide whether a hyphenated name goes with an interesting development by asking whether fusion has occurred: Have they sidewaysed and obtained a new gestalt, or have they merely stapled two curricula together? A rank 4 pattern in the brain is, I surmise, as integrated as a von Neumann computer. Your highest order patterns, the ones that set the style for all the rest and thus determine the nature of reality for you, are of rank 1, 2, 3, or 4 according to your personal history. Whatever their rank, they are not implemented as supervisors of lower rank activity. They are fused, and have immediate access to concrete thought. 4.A. Rankshift 2-3 The well-known components of the shift from rank 2 to rank 3 in the West were the Renaissance, the Scientific Revolution, the Protestant Reformation, the Enlightenment, and the Industrial Revolution. In my mind, there is not question about the regression in the western part of the former Roman Empire after AD 450. Others have held the contrary, There is, in fact, no proof that any important skills of the Graeco-Roman world were lost during the Dark Ages even in the unenlightened West ..." ( MRTe* 13) But the general level of life fell, population shrank, literacy dwindled, and Europe had to climb back to rank 2, between AD 800 or 1000 and AD 1400 before it could move toward rank 3. If we recall that the original Mediterranean rankshift from 1 to 2 occurred during a period of growth that lasted 4000 to 8000 years, depending on how we fix the beginning, we need not be surprised that the next rankshift occupied 500 years. MAIN PHASES OF RANKSHIFT 2-3 1400 1580 Renaissance in northern Italy. 1517 1648 Protestant Reformation 1543 1687 Scientific Revolution; Copernicus to Newton. 1688 1782 Enlightenment; English revolution to USA constitution 1765 1830 Industrial Revolution; James Watt 1830 1914 Scientific Industrial Revolution; USA, Germany 1914 1918 World War I unseats European aristocracy Some put the beginning earlier, with Dante's _Divine Comedy_ (1321), or with Petrarch, crowned as poet laureate at Rome in 1341. And I have noted that Fibonacci's _Book of the Abacus_ (1202) was significant. By 1300, mechanical church clocks had been invented. Three artists working in Florence are generally taken as the innovators of a new art: Brunelleschi (sculptor and architect), Donatello (sculptor), and Masaccio (painter). What seems to me most significant is Masaccio's use of perspective; but it is clear that these artists brought into the world a new way of _seeing_. As we have noted, humanism as a philosophy and way of life flourished in Florence in the 15th century. And personal self- consciousness is a discovery of the Renaissance. Barbu draws on Burckhardt (1945) in discussing the Renaissance. This is one of the three periods, he says, that favored the emergence of human personality; the others were Greece in the 6th century BC and Israel at the time of the Prophets. Medieval man "was conscious of himself only as a member of a race, people, party, family, or corporation--only through some general category". (Burckhardt p. 81; Barbu p. 76). (Barbu: COGNBIBL* ; Burckhardt: SCIBIBL* ) The Protestant Reformation began with Luther's attack on the sale of indulgences in 1517, and spread across Europe; although a kind of truce was attempted in 1555, wars partly motivated by religious differences continued until the end of the Thirty Years' War in 1648. A new way of thinking is central to Protes- tantism, an expectation of personal character that can survive without the support of a priest. The Scientific Revolution began in 1543 with Copernicus's book on the revolution of the planets around the Sun. Columbus made Europe aware that ancient knowledge was incomplete. Coper- nicus had no data; but he had a "theory pleasing to the mind." He made retrograde motion of planets a "reasoned fact", and made sense of the precession of the equinoxes. (Gingerich, p. 105; SCIBIBL* ) Copernicus published reluctantly, because of Catholic opposition to a new astronomy; he was persuaded, Gingerich says, by a young Protestant student. If Copernicus's contribution was pure analysis, Vesalius added observation in the first accurate textbook of anatomy, also published in 1543. When Newton published his _Mathematical Principles of Natural Philosophy_, the revolution was complete. The completion of science came in 1887-88, when Heinrich Hertz discovered elec- tromagnetic waves, following James Clerk Maxwell's 1873 theory. In 1859, Maxwell had published a theory of gases. This work seems to me to complete the program of materialist-causalist science. And as we shall see, completion was followed immediate- ly by overthrow. The Enlightenment began in England with the Glorious Revolu- tion and continued in France. It has been said that French replaced Latin as the language of diplomacy when the leaders of the Earth became convinced that French philosophy taught the right approach to reality. These philosophers corresponded with the leaders of the American Revolution, who contributed to the conceptual structure and also wrote the Declaration of Indepen- dence and the Constitution and Bill of Rights that made the new way of thinking the basis of a government. Humanism, born in Florence 350 years earlier, had grown up and was ready to fulfill an adult role. The entire period of rankshift was a time of economic growth. Braudel rather tentatively concludes "that industrial production multiplied at least five times, in Europe, between 1600 and 1800. I also believe that circulation expanded and improved its range." ( FBCC* p. 2:181) Until the middle of the 18th century, workmanship and materials were inadequate to realize the grand ideas that came to the imagination of many dreamers, of whom Leonardo is only the most famous. The first new source of power was introduced by Newcomen and his predecessors, but it was Watt's version of the steam engine that could be improved by a long series of small steps to drive the factories and vehicles of the Earth. If it is true that Watt used knowledge gained from the scientist James Black in reconceptualizing the steam engine as a heat engine rather than a mechanical device like all the rest, then besides the workmanship and materials we must blame the weakness of science, and scientific thinking, for the late start of the Industrial Revolution. By 1830, the revolutionary system was in place. For the first time, however, the new idea was progress: Change, invention, improvement were now to be the ordinary work of everyday life. Alteration of technology that had been con- fined to brief spurts would now be continuous. As the first Industrial Revolution culminated in Britain, however, another began in Germany and the USA. The first was only moderately influenced by science. Probably it could not have occurred without science, but the revolutionaries were not scientists and were not educated by scientists. (See Mokyr, p. 113 BIBLNOTE* .) "The innovations that revolutionized the British iron industry in the eighteenth century were not made by research scientists working in obscure laboratories, but rather by ironmasters attempting to solve particu- lar technical or economic problems. (Hyde, p. 7, InRvBIBL* ) Later, in both Germany and America, scientists and engineers trained by scientists took over. Laboratories were founded for the improvement of technology--Edison (1876), the Bell system, and Eastman Kodak were early. The University of Berlin had a chemical laboratory in 1867, and by 1890 United Alkali had one in Britain. It was in America that the second revolution produced the factory system of mass production with interchangeable parts. In my opinion, the passage from rank 2 to rank 3 was not complete until World War I. Before that time the aristocrats of Europe, who did not accept rank 3 education for themselves and who relied on their control of land for their power, remained politically ascendant. Their younger sons took university degrees, but it was the educated middle class that conducted the affairs of business, government, and science for the most part. World War II unseated the aristocrats, as a century of upheaval across Europe had not done. Summing it up in a growth curve: 2222..Rank 3.. IIIII2 EEEI SEE SS S S SS SSS RRSS RRRRR ...Rank 2..RRRRR | | | | | | 1400 1500 1600 1700 1800 1900 R: Renaisssance S: Scientific Revolution E: Enlightenment I: Industrial Revolution 2: Second Industrial Revolution As a footnote, we may add that a new urban revolution occurred in Europe during this same period. Islam and eastern successor of the Roman Empire (governed from Constantinople) had cities AD 500-800, and so did other parts of Earth, but Europe in the Dark Ages scarcely did. After AD 1000, towns began to grow and almost 400 places had 10,000 population or more in the years from 1500 to 1800. De Vries ( InRvBIBL* ) tabulates the data. "The whole story of the Renaissance shows within the limits of the city-state how the exhilarating rise of an urban civilization is liable to issue in a process of secularization--the priest as well as the noble loses the power that he was able to possess in a more conservative agrarian world. Something parallel has happened over and over again in the case of nation- states when not only have towns become really urban in character--which is late in the case of England, for example--but when a sort of leadership in society has passed to the towns ..." (Butterfield, p. 67, quoted PWTr 109 n26; see SCIBIBL* ) As for the regestalt that fixed the higher-order paradigm of rank 3, historians give such a prominent place to Descartes's _Discourse on Method_, published in 1637, that we can only agree. And why should we want to? Descartes stands squarely in the middle of the Scientific Revolution, and teaches us to take apart intellectual problems as if they were machines. Descartes completes what Galileo began, for the concept of _machine_ was Galileo's contribution. He abstracted the machine from the individual machines that had been consid- ered each of its own kind. All machines are combinations of the elementary devices, the levers and such, known to the Greeks. Galileo saw that a theory of mechanics could apply to all of them. (Mokyr, p. 75, in BIBLNOTE* ).
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