notational evolution and revolution

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Uploaded June 19, 2011

Notation Evolution and

Revolution

Author: Jeffrey G. Long ([email protected])

Date: January 16, 1993

Forum: Talk presented at the Interdisciplinary Conference on Evolutionary Systems, sponsored by the Washington Evolutionary Systems Society.

Contents

: Proposal and Bio

Pages 2‐20: Slides intermixed with text for presentation

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Submitted for the WESS Interdisciplinary Conference

on Evolutionary Systems January 16, 1993

Notational Evolution & Revolution

Jeffrey G. Long 133-1/2 11th Street,

Washington, DC 20003 (202) 547-0268

This brief presentation will discuss the nature of notational evolution and revolution through analysis of four notational evolutions: the switch from neumatic musical notation to staff musical notation the switch from tallies to Roman numerals to Arabic numerals the switch from barter to commodity trading to money the switch from internal temporal clues to external temporal clues to abstract time. From historical data the presentation will offer several hypotheses regarding the nature of notational systems and their evolution in general, including: the philosophical and technological nature of notations the distinction between notational evolution and revolution the limitations of a notation that eventually force creation of new notations the broad technical and social consequences of introducing new notations. 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. Key questions the listener might consider in advance include: what do I think of the importance of notation? does society already have all the notations it needs for science, or might new ones be necessary? in what sense do number, note, time, and money "exist"?


A Brief Overview

Jeffrey G. Long

voice: (202) 547-0268 e-mail: [email protected]

letter: 133-1/2 11th Street, S.E., Washington, DC 20003

Presented at the WESS Interdisciplinary Conference

on Evolutionary Systems January 16, 1993

Jeffrey G. Long [1/16/1993]


Page 3 of 20

Slide 1: Cover Page I appreciate this chance to share some ideas with you. I've been interested for 20 years now in developing a new way to understand complex systems, because I think mathematics and our other primary notational systems have severe fundamental limitations in what they can represent. I've concluded from my work to date that the NOTATION we use is the limitation on our ability to understand the world around us. Today I hope to demonstrate WHY I believe that, through four examples that contrast notational EVOLUTION with notational REVOLUTION. This is work-in-progress, not final conclusions. I still have a long way to go. If want to talk more, please contact me as shown on the slide.



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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 2: Standard Definition I understand that most people think notation is irrelevant. Looking at the dictionary definition, it's easy to see why they feel this way. ONE dictionary 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. I hope to persuade you to consider the possibility that notation is very different than language, and that it can express concepts that are INEFFABLE in common language. The notation is the limitation.



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

2. Notation "A" Evolves Towards Greater Simplicity & Scope

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

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

5. Notation "B" Evolves Towards Greater Simplicity & Scope

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

7. Notation "C" is Invented, Based on Abstraction "Y"

8. Notation "C" Evolves Towards Greater Simplicity & Scope

9. Notation "C" Hits "Complexity Barrier"; Progress Stops

Cyclical Process of "Notational Fulfillment"



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Slide 3: Notational Fulfillment I believe that we can understand the TRUE nature of notation by looking at how notations progressively change over long periods of time. 1. 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 general standards for the notational 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. In spite of all refinements, the notation hits what I call the "Complexity Barrier". A. No amount of effort seems to overcome the barrier B. Progress comes, if at all, by personal insight, not analysis 4. Somehow a NEW notation is created, based on a revolutionary new ABSTRACTION that never existed before A. Characteristics: 1. Solves a broad class of problems with far less effort 2. Accessible to more people 3. Accepted only grudgingly by elite because it changes the power distribution in society B. This is what I call a Second Generation Notation. While the first generation was based on ANALOGY, the second and subsequent generations are based on far more powerful insights into the nature of what must be represented. C. An ONTOLOGICAL INVENTION is the creation of something truly new in the world, that we subsequently treat as "real" 1. Money 2. Numbers



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3. Time 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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written word:spoken word:

MAN

(Ideogram)

(Phonogram)

"M - A - N"

New Ontological Invention: Letters Slide 4: First Example = Letters



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The things that are in the "real world" are shown without boxes, while the ONTOLOGICAL INVENTIONS (i.e. NOTATIONS) are in rounded-edge boxes. We could spend a lot of time debating dates, but the dates are not as important as the precedence sequence 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 (circa 3400 BC). 3. 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 an ancient 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 useless when there were thousands of symbols to deal with and low print volumes were required. 6. The Revolution occurred when 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 (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 is a classic notational revolution. 9. But it required that we create a new entity in the world: LETTERS. WRITING is a notational SYSTEM built upon LETTERS as NOTATIONS, and it defines a number of RULES regarding the proper use of this notation. 10. 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".



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seven things

six things

eight things

New Ontological Invention: Number



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Slide 5: Second Example = Numbers 1. Again, there's something in the "real world" that we want to represent, such as how many spikes we see or how many ovals we see. 2. The first generation of quantitative notation was TALLIES that represented by ANALOGY (circa 30,000 BC). These were based on the idea of a 1:1 CORRESPONDENCE. 3. These evolved to be able to represent larger numbers more easily through the use of ROMAN NUMERALS, where (e.g.) a "V" could represent five "IIIII" (circa 500 BC). 4. This worked pretty well in ancient society, where commerce required mainly just the basic operations of arithmetic. But eventually they hit the COMPLEXITY BARRIER: many important concepts could not be represented (e.g. irrational numbers), and working with large numbers was often cumbersome. 5. Continuing on that path of adding new symbols or simplifying existing symbols would have been fruitless: we could never send a man to the moon using Roman Numerals. 6. The 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" was identified by the arbitrary ideogram "7" (circa 1202 in the West). 7. With this new approach, and the additional convention that the value of each symbol was defined absolutely by its location from the decimal place rather than by the symbols surrounding it, society was able to perform mental arithmetic and to do more complex operations without an abacus. 8. Thus the SCOPE of what could be represented was greatly increased, as well as the NUMBER and TYPE of OPERATIONS. This too is a classic notational revolution. 9. But it required that we create a new entity in the world: NUMBERS. MATHEMATICS is a notational SYSTEM built upon NUMBERS as NOTATIONS, and it defines a number of RULES regarding the proper use of this notation. 10. As the result of this ontological invention, society was able to create a better way to describe certain aspects of the behavior of the world. Thus mathematics became the "language of science".



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440

New Ontological Invention: Notes



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Slide 6: Third Example = Notes 1. Again, there's something in the "real world" that we want to represent, such as certain musical sounds. To understand music we have to realize that a note played on an instrument does not typically 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. 2. The first generation notation was NEUMES that represented by ANALOGY (circa 900 AD). So A. actus (later virga) indicated raising of voice B. gravis (later punctum) indicated lowering of voice C. these were fine for monophonic music (singing in unison) 3. These evolved to be able 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: A. four symbols B. each was 3x duration of the previous (perfect) or 2x (imperfect) 4. But eventually they hit the COMPLEXITY BARRIER: they were unable to communicate enough information for multiple simultaneous pitches, for coordinating the timing of diverse themes, or of providing a basis for tuning multiple instruments 5. 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 a Beethoven symphony 6. The Revolution occurred when someone decided to represent the INPUT to the instrument rather than its OUTPUT (circa 1000 AD). 7. By this device, after several hundred years of evolution, we are now able to represent a wide range of pitches for a wide range of instruments, and to coordinate their pitch, timing, and volume. We can do POLYPHONIC music of great complexity. 8. 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 (composed on the spot), folk music (memorized, traditional), or plainsong (written but very simple). 9. But it required that we create a new entity in the world: NOTES. Musical composition, the notational SYSTEM built upon NOTES as notations, added a number of other rules about the proper use of this notation. 10. As the result of this ontological invention, composers were able to write polyphonic music down and then edit and refine it, and were able to create simultaneous complex sets of instructions to a



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variety of musicians. This permitted, ultimately, the creation of complex symphonic and other scores. If you listen to Gregorian chants and then listen to a Beethoven symphony, you'll really FEEL the power of this.



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Twenty

Dollars

Pay to the order of:

companionship

food

Salt

ATTRIBUTES:

(value)

$20

New Ontological Invention: Dollar



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Slide 7: Last Example = Dollars 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 (i.e. practical) VALUE by ANALOGY. Examples include cattle and salt. 3. Like all notations, commodity money evolved over time. 4. But eventually it hit a COMPLEXITY BARRIER: these items were awkward to divide and/or measure, perishable, and inconvenient logistically. Sometimes one had to trade with a third person to make a deal happen (explain). Commerce was still very difficult, and the more complex an economy got the more problems were caused by commodity money. 5. Continuing on that path would have been fruitless: 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. 6. The Revolution occurred when someone noticed that VALUE could exist INDEPENDENTLY of any object, by COMMON CONSENT. They set out to designate arbitrary objects as commonly accepted SYMBOLS of DECLARED VALUE. The intrinsic PRACTICAL VALUE of these objects was nowhere near their DECLARED VALUE, and was often basically zero. Examples include cowrie seashells, wampum beads, gold and silver. The only criteria for symbols was that the objects be: 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. 7. Eventually, precious metals won this contest. But those tokens of value were subject to dilution, counterfeiting, unfair scales, and other problems, so they evolved into other equally value-less forms. TRANSFERRABLE RECEIPTS were used in the Middle Ages, and then FIDUCIARY MONEY was used in the West circa 1676. 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. America ended up being the birthplace of widespread use of paper money in the Western world. This paper money was backed by gold, an equally worthless commodity.



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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. 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 notations, 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.



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Conclusion 1. Notational evolution enhances praxis. Notational revolution invents new

abstractions, and provides a calculus for computation and communication using these new and powerful constructs.

2. Wannabe notations are that way because they have failed to distill the

"essence" of the domain they purport to deal with. Notation is not mere abbreviation, but is instead the limitation on our ability to understand the universe.

3. We have hit the "complexity barrier" in dealing with complex systems and

need a major new notation.



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Slide 7: Conclusions

Questions?

notational evolution and revolution

Technology

1 2 11th street

wess interdisciplinary conference

thenotational system built

greater simplicity

simplifying existing symbols

classic notational revolution

understand complex systems

notationalevolution