Notation as a basis for societal evolution

Cover Page

Notation as a Basis for
Societal Evolution

Author: Jeffrey G. Long (jefflong@aol.com)

Date: May 12, 1993

Forum: Talk presented at the monthly dinner meeting of the Washington
Evolutionary Systems Society.

Contents
Pages 1‐2: Proposal and Bio

Pages 3‐41: Slides intermixed with text for presentation

License
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Uploaded June 19, 2011

Jeffrey G. Long [5/12/1993]

Notation as a Basis of Societal Evolution

Notation as a Basis for Societal Evolution
Jeffrey G. Long
WESS Meeting, May 12, 1993

People tend to dismiss notation as a trivial afterthought, believing that notation is mere abbreviation of
ideas that could be expressed in a variety of ways. My research over the last 20 years on new
approaches to understanding complex systems has led me to conclude that rather than being mere
abbreviation, notation is in fact the primary limitation on our ability to comprehend, create and control
any complicated situation. There is a major difference between the incremental evolution of notations
(such as we have seen in the past 300 years), and the invention of a truly revolutionary new notation
(such as the alphabet or mathematics).

Key questions the listener might consider in advance include:

 what do I think of the importance of notation?
 why is it that science cannot yet comprehend, predict and/or control the behavior of complex
systems such as weather, economics, medicine, and organizations?
 what are the limitations, if any, to mathematics as the "language of science"?
 in what sense do number, note, time, and money "exist"?
 what is the essence of complex behaviors?

This presentation will briefly discuss the nature of notational evolution and revolution through
analysis of several notational revolutions. From historical data the presentation will offer several
hypotheses regarding the nature of notational systems and their evolution in general, including:

 the philosophical basis of revolutionary notations
 the limitations of a notation that eventually force creation of new notations

The presentation will continue with a brief discussion of:

 the need for a new notation based on the limitations of existing notations
 desirable features of a new notation.
 several key distinctions of a proposed new notation for complex rules, dubbed "Ultra-Structure"

Key conclusions of the talk will include the following:

 notational systems do not merely represent certain abstractions, they invent them; notational
systems are intellectual toolsets that society creates to empower it in dealing with a complex
world
 we declare the existence of number, note, time, and money as a result of notational revolutions
that are really intellectual revolutions with broad social consequences.
 our society must develop a revolutionary new notational system focused on representing complex
"rules" if it is ever to understand complex systems.

Jeff Long graduated with an honors A.B. degree from U.C. Berkeley in 1973 after 1 year. While
writing his honors thesis on neural networks he concluded that no available analytical tools were
adequate to represent truly complex systems such as the brain. In 1975 he started the Institute for
Advanced Systems Research, a non-profit organization, but was unable to secure adequate funding.

Page 1 of 41



He then worked for several large firms as a systems design consultant, ending up with Booz, Allen &
Hamilton consulting for the Air Force and Department of Energy.

In 1980 he started his own firm, Intellinomics Corporation, to pursue the development and
commercial application of complex systems research. In 1992 he wound up that business in order to
spend full time at the Library of Congress, where he is finishing a book describing the history and
philosophy of notation; describing his proposed notation for complex rules ("Ultra-Structure"), which
he was able to apply to business organizations as systems; and demonstrating how to use that notation
to represent a wide variety of other kinds of complex system. He is currently working to apply Ultra-
Structure to systems ranging from Coast Guard navigation rules to games to physics and biology.

His motto is "The notation is the limitation".

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Notation as a Basis
for Societal Evolution
A Brief Overview

Jeffrey G. Long

voice: (202) 547-0268
e-mail: JeffLong@AOL.COM
letter: 133-1/2 11th Street, S.E., Washington, DC 20003

Presented at the
WESS Monthly Meeting
May 12, 1993

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Slide 1: Cover Page
I really appreciate this chance to share some partially-baked ideas with you.

Twenty years ago I got interested in complex systems analysis when I did simple neural net
simulations as an undergraduate at U.C. Berkeley. Since then I've been looking at a wide range of
issues in order to understand why our society doesn't seem able to comprehend, create or control large
complex systems, whether natural or manmade.

I've concluded so far that mathematics and our other primary notational systems have fundamental
limitations in what they can represent. In other words, the NOTATION we use is a critical limitation
on our ability to understand the world around us. Conversely, a new notation can resolve a large
CLASS of problems all at once.

This evening I'll talk for an hour and 15 minutes about notation as "A" basis for societal evolution. In
the first 45 minutes, I'd like to discuss the NATURE of notation. I'll show a PATTERN in notational
and societal co-evolution, and then show four examples of notational EVOLUTION and
REVOLUTION. In the last 30 minutes, I'd like to describe a NEW notation I've been working on for
complex systems, based on representing complex RULES. I call this notation ULTRA-
STRUCTURE. We'll then have about 30 minutes for any questions or comments you may have.
Please hold your questions until the end, or I'll never get through this!

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1. Notation Unique to Modern Humans

2. Notational Fulfillment & Societal Evolution

3. Evolutionary vs Revolutionary Notations

4. Complexity Barrier

5. Ontological Invention

6. Ruleform Hypothesis

7. CORE Conjecture

Seven Critical Concepts

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Slide 2: Seven Critical Concepts
This talk will be difficult for several reasons.

(1) One is that I'm still learning how to speak about these ideas so others can relate to them. The
logician George Spencer-Brown commented that, "The fact that...we have to use words and other
symbols in an attempt to express what the use of words and other symbols has hitherto obscured, tends
to make demands of an extraordinary nature on both writer and reader, and I am conscious, on my
side, of how imperfectly I succeed in rising to them" [Spencer-Brown, Laws of Form].

(2) A second is that I am basically questioning a number of unconscious assumptions that people have
about the nature of things. If successful, this would constitute a "paradigm shift", something which it
is notoriously difficult to accomplish.

(3) Thirdly, we're going to cover a lot of ground. I hope to at least INTRODUCE you to SEVEN
critical concepts that form the basis of my work, and any ONE of these could easily take quite a while
to discuss.

The first part of my talk will partially repeat and extend what I said at the January WESS conference,
but for those of you who were there hopefully it will make even MORE sense the second time.

I'd like to EMPHASIZE that this is work-in-progress, not final conclusions. When I started coming
to the Library of Congress a number of years ago to do this work, I found about 50,000 book titles on
related topics. I've narrowed that down to several thousand, but I still have a long way to go. Any
area I venture into, however, is looked at from a NOTATIONAL perspective: that is the common
denominator, lest you think I'm simply trying to understand every subject in the world!

If you'd like to talk more, I've put business cards around the tables; please feel free to contact me at
any time. Constructive criticism and general thoughts are ALWAYS appreciated.

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Solving Complex Problems

Use of Verbal or Sign Language

Complex Symbolic Behaviors

Use of Tools

Providing Assistance to Each Other

Killing Each Other

Brain:Body Weight Ratio

Planning

Self-Awareness

Notation & Other Species

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Standard Definition of Notation
the use of a system of signs or symbols to represent
words, phrases, numbers, quantities, etc.
(Webster's New World Dictionary, Second College Edition, 1984)

"For the purpose of determining logical structure it is, for instance, a matter of

complete indifference whether we represent certain features of states of affairs

by spatial arrangement rather than by sounds or shapes. Hence the unimportance

in theory of attempts to 'improve' symbolism: tokens of any properties

whatsoever can be used as the material for a complete language."

-- Max Black, Language and Philosophy, 1949, page 160

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Slide 3: Standard Definition
I understand that most people think notation is unimportant. Looking at the dictionary definition, it's
easy to see why they feel this way.

WEBSTER'S defines notation as "The use of a system of signs or symbols to represent words,
phrases, numbers, quantities, etc."

Notation is thus mere ABBREVIATION; key concepts exist OUTSIDE the notation, in LANGUAGE.
This premise is widely held, and is stated fairly clearly by the philosopher of mathematics Max Black.

Because our primary notation, the alphabet, is primarily concerned with representing the sounds of our
language, it is easy to get the two mixed up. Although many complicated things CAN be done with
language, the ORAL TRADITION is simply the starting point for REAL progress in any field. I hope
to persuade you that notation is very DIFFERENT than language, and that it can express concepts that
are INEFFABLE in ordinary language.

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Solving Complex Problems

Use of Verbal or Sign Language

Complex Symbolic Behaviors

Use of Tools

Providing Assistance to Each Other

Killing Each Other

Brain: Body Weight Ratio

Planning

Self-Awareness

Notation & Other Species

Page 10 of 41



Slide 4: Notation & Other Species
On the contrary to being trivial and uninteresting, I think there is something very BASIC and
SPECIAL about notation that can shed light both on the nature of human COGNITION and on the
nature of the UNIVERSE we live in.

In partial support of this belief, if you look at all the things that other species can do, it seems to me
that NOTATION is the only thing unique to HUMANS. Other animals can match us in all these areas
shown, but I have yet to see or hear about:

o a migrating whale consulting a nautical chart

o a lion trying to BUY a fresh carcass from another lion

o a bird writing down his SONGS to revise, improve, and teach them to others

o a dog consult a clock to decide if it's time to EAT.

Yet people do these things all the time, and in fact our society is heavily dependent upon these and
other notational TOOLS.

Even earlier versions of our OWN species, homo sapiens, did not seem to use notation. In spite of the
first appearance of hominids some 3 to 4 million years ago, the first KNOWN examples of
NOTATION date from 30- to 40,000 years ago, corresponding exactly with the appearance of OUR
species and the replacement of Neandertal Man. I'm referring to the cave paintings and tallies found
in southern France. Other TOOLS were used by humankind long before, as long ago as 2.5 million
years. But NOTATION is a COGNITIVE toolset, not a PHYSICAL one; and no relics of notation
have been found dating anywhere near that far back.

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1. Notation "A" is Invented, Based on Analogy

2. Notation "A" Evolves; New Tiers Emerge

3. Notation "A" Hits "Complexity Barrier"; Progress Stops

4. Notation "B" is Invented, Based on Abstraction

5. Notation "B" Evolves; New Tiers Emerge

6. Notation "B" Hits "Complexity Barrier"; Progress Stops

Notational Fulfillment & Societal Evolution

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Slide 5: Notational Fulfillment & Societal Evolution
I believe we can get a better sense of the TRUE nature of notation by looking at how notations
progressively change over long periods of time.

Based on my study thus far of TEN notations, there seems to be a broad general PATTERN in
notational and societal co-evolution. I'll describe the pattern here, then show 4 examples.

1. First, a new notation is invented, and this FIRST GENERATION notation is based on ANALOGY
with what it represents

2. This notation EVOLVES through improvement of PRAXIS, e.g.

A. symbols are STREAMLINED for greater ease of use

B. NEW symbols are introduced, e.g. lower case, punctuation

C. new and better MEDIA is used [e.g. clay -> papyrus -> paper]

D. there's a CONSENSUS on standards for USING the system.

This process is generally what people think of when they think of notational evolution, e.g. the shape
of letters, the introduction of a new punctuation mark, etc. But this is NOT where notation gets its
enormous power.

3. But in spite of all refinements, the notation hits what I call the "Complexity Barrier". No amount
of effort seems to overcome the barrier, and progress comes, if at all, by random insight, not
systematic analysis. The complexity barrier by its nature is very widespread, affecting entire fields of
activity at a time. Characteristics of this complexity barrier are that:

A. there is a large class of problems that thwarts resolution

B. increased money and effort produce FEW, if ANY, results

C. evolution of the underlying notation provides the only examples of progress
in dealing with the problems, but the progress is slight

4. Next, somehow a NEW notation is created, based on a revolutionary new ABSTRACTION that
never existed before. This often leads to, or co-exists with, a tremendous boom in cultural evolution.
It is what I call a Second Generation Notation. While the first generation was based on
ANALOGY, the second and subsequent generations are based on ABSTRACTIONS, which are far
more powerful insights into the nature of what must be represented.

A. Characteristics:

1. Solves a broad class of problems with far less effort

2. Accessible to more people

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3. Accepted only grudgingly by elite because it changes the
power distribution in society

B. This new abstraction is embodied in what I call an ONTOLOGICAL INVENTION,
which is the creation of something truly new in the world, that we subsequently treat as "real"

1. Numbers
2. Musical notes
3. Money
4. Time

C. What we call "literacy" is tearning the existence and proper use of various
ontological inventions.

5. Now this notation, too, goes through the same KIND of evolutionary refinement that its
predecessor did, but eventually it hits its OWN complexity barrier.

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(Ideogram)

(Phonogram)

spoken word: written word:
MAN "M - A - N"

New Ontological Invention: Letters

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Slide 6: New Ontological Invention: Letters
The first example of this pattern is the development of the ALPHABET. In this and the subsequent
examples, the things that are in the "real world" are shown without boxes, while the ONTOLOGICAL
INVENTIONS (i.e. NOTATIONS) are in rounded-edge boxes. Also, we could spend a lot of time
debating dates, but the dates are not as important as the precedence SEQUENCE, i.e. the PATTERN.

1. In writing, there's something in the "real world" that we want to represent, such as this man.

2. First generation was PICTOGRAMS that represented by ANALOGY, starting in about 3400 BC.

3. After about 600 years, these evolved to be able to represent IDEAS and ACTIONS through the use
of IDEOGRAMS (where ideas are communicated through clever combinations of symbols) and
PHONOGRAMS (where concepts are hinted at by symbols that represent something that evokes a
particular sound) (circa 2800 BC).

4. This worked pretty well in ancient society, but eventually they hit the COMPLEXITY BARRIER:
several thousand symbols are needed to convey the concepts of even a so-called "primitive" culture.

5. Continuing on that path of adding new symbols or simplifying existing symbols would have been
fruitless: you can imagine what a Shakespeare play might be like if every symbol was subject to
personal interpretation. Further, the printing press, originally invented by the Chinese long before the
western world had it, was far less useful when thousands of symbols were required.

6. A Notational Revolution occurred when, about another 1,500 years later, someone noticed that
there were a limited number of SOUNDS we make in human speech, and they designed SYMBOLS to
represent those SOUNDS (first alphabet, circa 1500 BC).

7. With this new approach, and after the invention of vowels by the Greeks about 750 years later
(circa 776 BC), we were able to represent the >50,000 words known by the average adult with only 26
letters.

8. Thus the SCOPE of what could be represented was greatly increased, while the NUMBER of
SYMBOLS greatly decreased. This made the notation far more powerful and accessable to a far
greater proportion of society. As the result of this ontological invention, society was able to create a
collective memory that superseded the fragile memory of the oral tradition that preceded it. This was,
literally, the beginning of "history", and is probably the most classic notational revolution. Historian
Eric Havelock said, "The Greek alphabet...is here introduced, when it impinges on the Greek scene,
as a piece of explosive technology, revolutionary in its effects on human culture, in a way not
precisely shared by any other invention" [Havelock, 1982]. Historian James Breasted notes, "The
invention of writing and of a convenient system of records on paper has had a greater influence in
uplifting the human race than any other intellectual achievement in the career of man. It was more
important than all the battles ever fought and all the constitutions ever devised" [Breasted, 1926, pages
53-54].

9. But it required that we create a new entity in the world: LETTERS. WRITING is a notational
SYSTEM built upon LETTERS, and it defines a number of CONVENTIONS regarding the proper use
of this ontological invention.

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Lion Lion

Lion Lion Lion

Lion Lion
Soldier

Soldier
Soldier
Soldier five lions
Soldier
Soldier one lion
Soldier one lion

one soldier five soldiers seven
one soldier things

New Ontological Invention: Number

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Slide 7: New Ontological Invention: Numbers
1. Again, there's something in the "real world" that we want to represent, such as how many lions we
saw or how many enemy soldiers we saw. Needless to say, getting the number right can be very
important, although many societies had no words for numbers greater than two.

2. The first generation of quantitative notation, introduced over 30,000 years ago, was TALLIES that
represented by ANALOGY (circa 30,000 BC). These were based on the idea of a 1:1
CORRESPONDENCE. Any objects -- stones, whatever-- could be used as the basis for creating a
1:1 correspondence.

3. About 22,000 years later (circa 8,000 BC), this notation evolved so that "accounting tokens"
represented both the number of items and their nature. Each commodity, and each quantity of a
commodity, could have its own clay token. Impressions of these tokens on clay envelopes, and later
on clay tablets, eventually came to be the basis of writing.

4. This worked pretty well for the commercial requirements of the first cities, but eventually it hit a
COMPLEXITY BARRIER: it required too many separate and identifiable symbols. Continuing to
ADD new symbols or SIMPLIFY existing symbols would have been fruitless.

5. Over 6,000 years later, a Notational Revolution occurred when someone noticed that there were
commonalities among certain groups of (say) seven things, if you eliminated everything about them
but the quantity of their members. This "set of all sets of seven things", although it wasn't thought of
that way at the time, was the FIRST TIME that numerical concepts were represented BY
THEMSELVES. Examples of this are Egyptian hieroglyphic numerals (1900 BC), and ROMAN
NUMERALS (circa 500 BC), where (e.g.) a "V" could represent five "IIIII". This was a revolution in
SPECIFICATION, that moved us from E-NUMERATION to NUMERATION.

6. This worked very well in the ancient empires, where use of arithmetic was very limited and
numbers tended to be small by current standards. But eventually this too hit a COMPLEXITY
BARRIER: many important concepts could not be represented (e.g. irrational numbers, large
numbers).

7. Continuing to ADD new symbols or SIMPLIFY existing symbols would have been fruitless: we
could never send a man to the moon using Roman Numerals.

8. So about 1,500 years later (in the West), a Second Notational Revolution occurred (circa 1202)
when we borrowed an idea from the Arabs that they had borrowed from the Hindus in India.
Someone in India noticed that the operations of the abacus (the computational device used up to then)
could be simulated by using symbols for the counters of the abacus. This required use of zero as a
place-holder for counters with no beads on them.

9. By defining the MEANING of each symbol absolutely by its LOCATION rather than by the
symbols SURROUNDING it (place-value versus relative value), the groundwork was set for
mathematics to move beyond simple arithmetic using the abacus. In particular, the concepts of
number line and more abstract operations on numbers could be contemplated. However, this was not
an easily accepted idea: for 400 years (1100 AD to 1500 AD), there was a long and sometimes bitter
fight between the "abacists" and the "algorists". Eventually the algorists won, so since the 18th

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century few people in the West use an abacus for calculations. In 1525 the decimal point was
introduced, and complex numbers were introduced in 1545.

10. Thus the SCOPE of what could be represented was greatly increased -- twelve basic symbols,
including the decimal point and "i", could represent all possible numbers. This advance also permitted
an extension of the type of OPERATIONS possible, such as taking the square root of any number.
This was a classic notational revolution, both in SPECIFICATION and in CALCULATION. The
logician Alfred North Whitehead stated, "By relieving the brain of all unnecessary work, a good
notation sets it free to concentrate on more advanced problems, and in effect increases the mental
power of the race" (An Introduction to Mathematics).

11. So we have again created new entities in the world: NUMBERS. MATHEMATICS started as a
notational SYSTEM built upon NUMBERS, and it defines a number of CONVENTIONS regarding
the proper use of this ontological invention. Mathematics has evolved to deal with OTHER
ENTITIES besides numbers, such as geometrical figures and vectors. In general I think it MAY be
said that mathematics deals with ANY commensurable abstractions, and is designed to determine their
equivalence or non-equivalence.

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me di a vi ta ...

440

me di a vi ta ...

New Ontological Invention: Notes

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Slide 8: New Ontological Invention: Notes
To understand musical notation we have to realize that a note played on an instrument does not just
generate ONE pitch or sound vibration, it generates a NUMBER of these. These are called
OVERTONES, and they form the TIMBRE or character of each different instrument. These
overtones are very IMPORTANT to music.

1. The first generation of Western musical notation that we really know about was developed only
1,000 years ago. NEUMES represent the rising or lowering of the voice by an upward or downward
line. This was thus a first generation notation by ANALOGY (circa 900 AD).

2. These evolved over the next 600 years to a dead-end. They were changed to represent pitch better
through the use of HEIGHTENED NEUMES (where relative spacing indicated pitch) and
LIGATURES (where the broader part of a line indicated pitch). Later (circa 1260) MENSURAL
NOTATION was better able to indicate the DURATION of each note, using four symbols, each with
3x duration of the previous (perfect) or 2x (imperfect).

3. These were fine for simple music sung in unison, or even for the later organum music sung in fixed
intervals. But they eventually hit the COMPLEXITY BARRIER: they were unable to represent
simultaneous different pitches, to coordinate the timing of diverse themes, or to provide a reliable
basis for tuning multiple instruments. They were incapable of really representing the kind of complex
POLYPHONIC MUSIC we are used to.

4. Continuing on that path of adding new symbols or simplifying existing symbols would have been
fruitless: no extension of that approach would have permitted polyphonic music such as Handel's
"Messiah".

5. A Notational Revolution occurred around the year 1,000, when Guido de Arrezo, a music teacher
trying to find a better way to teach music to his students, started a separate developmental path
involving LINES around the notation; defining separate NOTES and, equally important, RESTS; and
"pinning" the notes to a particular PITCH. This essentially meant that the notation of music represent
the INPUT to the instrument rather than its OUTPUT. As in the second mathematical revolution, this
also represented a move from RELATIVE VALUE to PLACE-VALUE notation.

6. When this tool settled down over the next 3 centuries to a 5-line staff, composers were able to write
complex musical ideas down, and then EDIT and REFINE them. In 1325 an influential book was
published that advocated new and relatively modern forms of musical expression. Composers could
create complex sets of instructions to a variety of musicians, without being there in person, as the oral
tradition would have required.

7. Thus the PRECISION and SCOPE of what could be represented was greatly increased. Music
could be edited and COMPOSED before it was PERFORMED, unlike jazz (which is composed on the
spot) or folk music (which is memorized and traditional).

8. But it required that we create a new entity in the world: NOTES. Musical COMPOSITION, the
notational SYSTEM built upon NOTES, defines a number of CONVENTIONS about the proper use
of this ontological invention.

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Similarities:

o simple choral compositions
o multiple voices

o both popular in their times

Differences:

o polyphonic (not unison) with complex harmonies

o human voices AND instruments

o synchronized performer entry and exit

Gregorian Chant versus Modern Music

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Slide 9: Gregorian Chant versus Modern Music
The philosopher Ludwig Wittgenstein said that there's a lot that cannot be SAID, but has to be
SHOWN. I agree. Much of our culture is based on the presumption that all thought IS done or CAN
be done in WORDS. Yet this is clearly not true in an area like MUSIC.

So I propose that we take 5 minutes now to listen to a Gregorian chant that was composed in the 10th
century and was VERY POPULAR in its time. and then compare it to ANOTHER religious
composition, composed 800 years later, in the so-called Baroque period of music. I'll play 2 minutes
of each composition, so you can get the FEEL of them.

(Play music cut #6)

As you listen to this next familiar piece, try to imagine whether it could exist WITHOUT modern
musical notation, i.e. whether it could have been created and preserved in the ORAL TRADITION, or
by using earlier NEUMATIC notation. Hopefully you'll be able to directly EXPERIENCE the
difference between the kinds of thought involved in medieval and baroque music.

(Play music cut #13)

Thus more powerful notation permits the creation of symphonies and other complex musical forms.
The development of polyphonic music has been called "The most important development in Western
music" (Elliott Schwartz, Music: Ways of Listening)

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Salt

ATTRIBUTES:
companionship $20
food (value)

Twenty
Dollars

Pay to the order of:

New Ontological Invention: Dollar

Page 24 of 41



Slide 10: New Ontological Invention: the Dollar
I'd like to talk now about an UNRECOGNIZED NOTATION, namely MONEY.

1. This is a little different slide, showing the PRE-NOTATIONAL situation at the top. If you want to
trade your duck for my cat, we may agree on a BARTER arrangement. A duck and a cat are roughly
commensurable, partly because they're both animals and they both have some real and obvious values
to somebody; so it is fairly easy to make that trade. But as you offer things that are less and less
commensurable, it gets harder to make a trade.

2. The first generation of notation was COMMODITY MONEY that represented a certain REAL,
PRACTICAL VALUE. Examples include cattle, salt, and tobacco. This was widely used up until
about 4,000 years ago; tobacco was the principal medium of exchange for several centuries in
Maryland and Viginia; and as recently as 1935, salt was still used in Ethiopia.

3. Like all notations, commodity money evolved over time. Any item having real value could be
used, preferably meeting the following criteria:

A. known to many people
B. recognizable in value
C. scarce
D. portable (at least not too bulky)
E. physically stable over time (preferably imperishable)
F. easily sub-divided.

4. But eventually this basis for exchange hit a COMPLEXITY BARRIER: these items were
logistically inconvenient. Commerce was thus still very DIFFICULT, and the more COMPLEX an
economy got the more problems were caused by commodity money. We can hardly imagine what the
New York Stock Exchange or our economy in general might be like if every transaction was paid for
by weighing salt or some other physical commodity;
continuing on that path would have been fruitless.

5. A Notational Revolution occurred about 5,000 years ago (3000 B.C.) when people noticed that
VALUE could exist INDEPENDENTLY of an object, i.e. the concept of ABSTRACT VALUE.
People and, later, governments, designated arbitrary objects as commonly accepted SYMBOLS of this
abstract value. The intrinsic PRACTICAL VALUE of these objects was nowhere near their
DECLARED VALUE, and was often basically zero. Examples include seashells, beads (strung
together = "wampum"), gold, silver, and copper.

6. Eventually, the precious metals (particularly silver) won this contest, especially with the help of
government LAWS that regulated their availability and use. But those tokens of value were subject to
dilution, unfair scales, and other problems, so they evolved into other equally value-less forms. So
after another 750 years (2250 B.C.), COINS having a declared FACE VALUE were introduced.
These dominated for over 4000 years, until recently, although TRANSFERRABLE RECEIPTS were
introduced in the Middle Ages, and then FIDUCIARY MONEY in the form of BANK NOTES was
introduced by the government of Sweden in 1656.

From 1825 through 1875 in the United States there was a major political debate between the "paper
money men" and the "gold bugs" about how abstract value should be represented in America.

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America ended up being the birthplace of widespread use of paper money in the Western world. This
paper money was initially backed by gold (an equally worthless commodity?)

Eventually we ended up with FIAT MONEY (circa 1934), not based on the gold standard, to enable
governments to print money as desired, independently of their actual gold reserves, and thereby
control aspects of their economy through monetary policy. Now we use an evolutionary advance over
that, namely checks and credit cards, where actual "money" does not even change hands during a
transaction, but waits until a later and more convenient time.

8. Thus VALUE-IN-THE-ABSTRACT came to be REAL, and could be traded like a real duck for
my cat. Since in principle anything could be traded for this symbol, the BREADTH of what could be
readily traded was greatly increased, and this EASE OF USE encouraged more commercial activity.
Once governments understood the power of this notation, they regulated it and then completely took it
over so THEY could control its abuse.

9. Again we created a new entity in the world: DOLLARS (or their equivalent). ACCOUNTING, the
notational SYSTEM built upon DOLLARS as ontological inventions, provides rules for the proper use
of this notation.

10. As the result of this ontological invention, society was able to divide work more readily into
specialized categories, for there was now a common denominator that could be used in any
commercial activity. This was the beginning of "commerce" as we know it today. I wasn't able to
find a quotation about the impact of money on societal evolution, but I think you'd all agree that
money is important in society!

-----

So much for the past; Janus-like, we must also look to the future. The history of notation shows
ongoing evolution punctuated by periodic revolution. Have we reached the end of the road? Do we
already have all the notations we need? I don't think so.

In the area of complex systems, for example, we have poor empirical results, and there are
fundamental theoretical limitations that are not possible to overcome. The strength of mathematics is
that it can address equalities and inequalities; but much of what we need to represent about the
universe has nothing to do with that aspect of entities.

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o Represent a New Ontological Invention

o Far Richer Capacity to Represent or Express Ideas

o Reasonable Ease of Learning & Use (years okay)

o Often, Better Utilize a New Media

o Permit More Powerful Methods of "Computation"

Desiderata for a New Notation

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Slide 11: Desiderata for a New Notation
If we were to try to deliberately create a notational revolution -- let's say to issue an RFP -- what
criteria might we use?

1. The FUNDAMENTAL REQUIREMENT of a revolutionary notation is that it represent something
different and more BASIC about the subject domain than the existing notations it is designed to
supersede.

2. Obviously the new notation must represent a superset, not a subset, of the target domain of the
existing notation,

3. There has to be reasonable ease of learning and using the notation, although a lengthy "literacy"
curve would not be at all unreasonable.

4. We might also want to re-examine the media available to us, to see whether a new notation could
utilize a new medium.

5. Finally, if it is a domain where computations would be useful (such as complex systems theory),
we will want a greatly extended computational ability as the result of a new notation.

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Complex
System Complex Behavior

d = 1/2 g t2

Rules

Ruleforms

New Ontological Invention: Ruleforms

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Slide 12: New Ontological Invention: Ruleforms
1. So let's look at our basic model of notational evolution. Again, there's something in the "real
world" that we want to represent, namely a complex system (e.g. an ecosystem). The pre-notational
situation was that we could describe the structure, behavior, inputs or outputs of a complex system in
NATURAL LANGUAGE.

2. The first generation of notation was graphical and quantitative, e.g. E-R DIAGRAMS or
MATHEMATICAL FORMULAS. These represented by ANALOGY the OUTPUT of the system.

3. These evolved, but eventually hit a COMPLEXITY BARRIER: somehow, pressure/temperature
functions or economic elasticity curves have failed to describe the behavior of weather and economies.
I suggest that this is because they focus upon and represent the wrong ASPECT of systems, primarily
their BEHAVIOR. They are DESCRIPTIVE, not PRESCRIPTIVE, in nature.

5. Continuing on that path, we could enhance our ability to describe system outputs and behaviors by
getting bigger computers and more facts. But some theorists have postulated that many systems are
UNKNOWABLE due to either:

o sensitive dependency on initial conditions,
o the existence of free will in systems involving humans, or
o intrinsic quantum randomness at the lowest levels of physical systems.

6. If there is to be a revolution in this area, it will require that we represent some OTHER aspect of
complex systems than their input, processes and output; namely RULES. Currently we can represent
"rules" as:

o procedural computer code
o symbolic logic statements
o English statements (e.g. law)
o mathematical formulas.

But that still leaves us with too much complexity to really understand the systems we are dealing with.
Simply representing RULES is not ENOUGH.

To abstract to a higher level, we must focus on RULES, but notice that there are COMMONALITIES
in the FORMAT of the rules in complex systems. Thus many instances of rules may have the same
form but different content. Each such "set of all rules having the same form" can be represented by a
simple relational table. Thus the next level of abstraction is the idea of RULEFORMS, wherein all
rules having the same FORMAT are grouped together.

7. With this focus on ruleFORMS rather than mere RULES, we may be able to represent seemingly
complex systems, with tens of thousands of rules, using just a few basic relational database tables.
These will be implemented on that wonderful new N-dimensional MEDIUM called the COMPUTER.

8. Thus we can SPECIFY rules better (more explicitly and rigorously), and also perform sophisticated
COMPUTATIONS easily, using a common ruleform notation for any kind of complex system.

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9. But this will require that we deal with a new entity in the world: RULEFORMS. ULTRA-
STRUCTURE is a notational SYSTEM built upon RULEFORMS, and it defines a number of
conventions regarding the proper use of this ontological invention.

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Ontological Real-World System Ultra-Structure Model
Level
Surface Particulars (Manifest Event Records and Rule
Structure Behavior & Structure) Considerations
Middle Operating Rules Rule Records
Structure
Deep Structure Ruleforms Relational Tables

Sub-Structure Universals Attributes (Fields)

Animation Energy Software
Procedures

Ultra-Structure Ontological Levels

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Slide 13: Ultra-Structure Ontological Levels
In other words, we can define the world as a PROCESS having different ontological LEVELS:

First, there is the structure, appearance and behavior of a system, that we will call SURFACE
STRUCTURE.

Next, the essence of this complexity can be captured by RULES having an IF...THEN format.
Defining phenomena in a compressed manner via RULES is the principal activity of science,
developed by the Greeks.

This activity will result in tens of thousands of seemingly varied rules, called the MIDDLE
STRUCTURE.

These can be grouped by format into ruleFORMS, the collection of which is called DEEP
STRUCTURE. Thus the DEEP STRUCTURE of any system will be a set of 10-50 ruleforms will
represent any particular complex system.

By representing these ruleforms as TABLES in a relational database, and the rules as RECORDS in
the tables, we can implement complex system models in a very concise manner.

Finally, below that are the UNIVERSALS, represented by the FIELDS in a table. These constitute the
SUB-STRUCTURE of the system.

The rules are ANIMATED or EXECUTED by very small amounts of procedural code.

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The perceived structures and behaviors of any system are artifacts of
"animation procedures" executing "operating rules."

These operating rules can be grouped into a small number of classes whose
format is described by "ruleforms".

While the operating rules of a system may change over time, the ruleforms
are constant.

Ruleforms anticipate all logically possible operating rules that might apply to
a subject domain and constitute the deep structure of that domain.

The Ruleform Hypothesis

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Slide 14: The Ruleform Hypothesis
Another way to state this is what I call the RULEFORM HYPOTHESIS:

"The perceived STRUCTURES and BEHAVIOR of any system are ARTIFACTS of 'animation
procedures' executing 'operating rules'.

These operating rules can be grouped into a small number of classes whose format is described by
'ruleforms'.

While the operating RULES of a system may CHANGE over time, the RULEFORMS are
CONSTANT. Ruleforms anticipate all logically possible operating rules that might apply to the
system and constitute the deep structure of a system."

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All instances of systems within a single domain (e.g. all games, all biological
systems) may be defined by a common set of approximately 50 ruleforms.

This definitive deep structure is permanent and unchanging.

Differences in perceived structures and behaviors of instances of systems
within that domain will be represented entirely as differences in rules.

The animation procedures for these ruleforms will comprise less than 100,000
lines of code in a third generation language.

The CORE Conjecture

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Slide 15: The CORE Conjecture
Now, there's another aspect of ruleforms that is interesting. If you group rules into ruleforms for ONE
system, then ANOTHER system within the same general CLASS of systems, you will find that you do
not REPLACE one set of ruleforms with another, rather, you BROADEN the ruleforms you have so
that they can accommodate BOTH instances of systems.

I conjecture that ALL instances of systems within a single domain (e.g. all games, all rules of biology)
may be defined by a COMMON SET of approximately 50 ruleforms. This definitive deep structure
will be permanent, unchanging, and robust. Differences in perceived structures and behaviors of
various instances of systems will be represented entirely as differences in rules. The animation
procedures for these ruleforms will comprise less than 100,000 lines of code in a third generation
language.

For example, the middle structure (rules) of baseball and chess are DIFFERENT, and their surface
structure (appearance) is DIFFERENT, but the deep structure of these and indeed all games is the
SAME. I've found this a useful exercise in the business world, and invite you to spend a day with me
some Saturday, if you wish, to explore this example.

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1. Spend full-time on research and writing: test CORE Conjecture with 6-10
complex systems, and finish book entitled NOTATION (Vol 1 and 2)

2. Start new institute to focus on notation and complex systems; apply for small
NSF grant for next year.

Current Status of Project

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Slide 16: Current Status of Project
So, what's next? I realize these hypotheses need more work....

1. Finish my own study of ten key existing notational systems (alphabet, math, music, chemistry,
cartography, dance, software, money, and time), and finish my models of 6-10 complex systems
implemented using Ultra-Structure (games, weather, cell biology, physics, scientific arguments,
navigation rules, others?), and get a publishing commitment within the next year.

2. Create a team to pursue this research in greater depth, historically, cognitively, philosophically, and
in terms of applications to various complex systems.

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Conclusions

1. There are limitations to what any notation can express, based on what domain
that notation was designed to represent and consequently what abstractions it
embodies. This is true even for the "Language of Science", mathematics. A
key factor in the evolution of society is the introduction and fulfillment of
revolutionary new notational systems such as the calendar, writing,
mathematics, and money.

2 Our society currently faces a "complexity barrier" in dealing with so-called
"complex systems" such as medicine, ecology, economics, and public policy.
But complexity is in the eye of the beholder and can be eliminated by an
appropriate notation based upon a new ontological invention. Larger
computers, more data, and more money will not overcome this complexity
barrier.

3. We need to develop at least one wholly new notation, using distinctions far
beyond fractals or other fundamentally quantitative constructs. We need a new
science to study rules per se, compressing them into simple common forms to
permit a deeper understanding of the ontology of various complex systems
domains.

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Slide 17: Conclusions
1. Limitations of notations.

2. Complexity barrier exists now.

3. Need a new notation for rules OR some other basic new abstraction.

Thank you for your attention.

Are there any questions?

Page 41 of 41

Notation as a basis for societal evolution

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