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                            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.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


     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:

                             / \
                            /   \
                           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_

     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-

     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

     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

     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.


     4.2.1.  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

     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

     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
     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-

     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-


     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

     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-


     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

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

     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..
 ...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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