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Cover Page      Notation Evolution and           Revolution  Author: Jeffrey G. Long (jefflong@aol.com) Date: January 16, ...
Submitted for the                                      WESS Interdisciplinary Conference                                  ...
Notational Evolution & Revolution                     A Brief Overview                      Jeffrey G. Long               ...
Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution  Slide 1: Cover PageI appreciate this chance to share some id...
Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution                                  Standard Definition of Notat...
Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution  Slide 2: Standard DefinitionI understand that most people th...
Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution            1. Notation "A" is Invented, Based on Analogy     ...
Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution  Slide 3: Notational FulfillmentI believe that we can underst...
Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution                      3. Time5. Now this notation, too, goes t...
Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution                                         (Ideogram)           ...
Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution  The things that are in the "real world" are shown without bo...
Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution              six things                      seven things    ...
Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution  Slide 5: Second Example = Numbers1. Again, theres something ...
Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution                                                  440New Ontol...
Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution  Slide 6: Third Example = Notes1. Again, theres something in ...
Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution  variety of musicians. This permitted, ultimately, the creati...
Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution                                                          Salt...
Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution  Slide 7: Last Example = Dollars1. This is a little different...
Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution  Eventually we ended up with FIAT MONEY (circa 1934), not bas...
Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution                                 Conclusion1. Notational evolu...
Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution  Slide 7: ConclusionsQuestions?                              ...
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Notational evolution and revolution

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January 16, 1993: "Notational Evolution and Revolution". Presented at the Interdisciplinary Conference on Evolutionary Systems, sponsored by the Washington Evolutionary Systems Society.

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Notational evolution and revolution

  1. 1. Cover Page   Notation Evolution and  Revolution  Author: Jeffrey G. Long (jefflong@aol.com) Date: January 16, 1993 Forum: Talk presented at the Interdisciplinary Conference on Evolutionary Systems, sponsored by the Washington Evolutionary Systems Society.   Contents Page 1: Proposal and Bio Pages 2‐20: Slides intermixed with text for presentation   License This work is licensed under the Creative Commons Attribution‐NonCommercial 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by‐nc/3.0/ or send a letter to Creative Commons, 444 Castro Street, Suite 900, Mountain View, California, 94041, USA.  Uploaded June 19, 2011 
  2. 2. 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) 547-0268This brief presentation will discuss the nature of notational evolution and revolution through analysisof 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 notationalsystems 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"?
  3. 3. Notational Evolution & Revolution 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 Interdisciplinary Conference on Evolutionary Systems January 16, 1993
  4. 4. Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution  Slide 1: Cover PageI appreciate this chance to share some ideas with you.Ive 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 fundamentallimitations in what they can represent.Ive concluded from my work to date that the NOTATION we use is the limitation on our ability tounderstand the world around us.Today I hope to demonstrate WHY I believe that, through four examples that contrast notationalEVOLUTION 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. Page 3 of 20
  5. 5. Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution   Standard Definition of Notation the use of a system of signs or symbols to represent words, phrases, numbers, quantities, etc. (Websters New World Dictionary, Second College Edition, 1984)"For the purpose of determining logical structure it is, for instance, a matter ofcomplete indifference whether we represent certain features of states of affairsby spatial arrangement rather than by sounds or shapes. Hence the unimportancein theory of attempts to improve symbolism: tokens of any propertieswhatsoever can be used as the material for a complete language." -- Max Black, Language and Philosophy, 1949, page 160 Page 4 of 20
  6. 6. Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution  Slide 2: Standard DefinitionI understand that most people think notation is irrelevant. Looking at the dictionary definition, itseasy 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 thatit can express concepts that are INEFFABLE in common language. The notation is the limitation. Page 5 of 20
  7. 7. Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution   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 StopsCyclical Process of "Notational Fulfillment" Page 6 of 20
  8. 8. Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution  Slide 3: Notational FulfillmentI believe that we can understand the TRUE nature of notation by looking at how notationsprogressively change over long periods of time.1. A new notation is invented, and this FIRST GENERATION notation is based on ANALOGY withwhat it represents2. 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. theres 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 shapeof letters, the introduction of a new punctuation mark, etc. But this is NOT where notation gets itsenormous 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 analysis4. Somehow a NEW notation is created, based on a revolutionary new ABSTRACTION that neverexisted 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 wasbased on ANALOGY, the second and subsequent generations are based on far more powerfulinsights 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 Page 7 of 20
  9. 9. Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution   3. Time5. Now this notation, too, goes through the same KIND of evolutionary refinement that itspredecessor did, but eventually it hits its OWN complexity barrier. Page 8 of 20
  10. 10. Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution   (Ideogram) (Phonogram) spoken word: written word: MAN "M - A - N"New Ontological Invention: LettersSlide 4: First Example = Letters Page 9 of 20
  11. 11. Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution  The things that are in the "real world" are shown without boxes, while the ONTOLOGICALINVENTIONS (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 precedencesequence1. In writing, theres 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 (whereideas are communicated through clever combinations of symbols) and PHONOGRAMS (whereconcepts are hinted at by symbols that represent something that evokes a particular sound) (circa 2800BC).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 beenfruitless: you can imagine what a Shakespeare play might be like if every symbol was subject topersonal interpretation. Further, the printing press, originally invented by the Chinese long before thewestern world had it, was useless when there were thousands of symbols to deal with and low printvolumes were required.6. The Revolution occurred when someone noticed that there were a limited number of SOUNDS wemake 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 wereable 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 ofSYMBOLS 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 notationalSYSTEM built upon LETTERS as NOTATIONS, and it defines a number of RULES regarding theproper use of this notation.10. As the result of this ontological invention, society was able to create a collective memory thatsuperseded the fragile memory of the oral tradition that preceded it. This was, literally, the beginningof "history". Page 10 of 20
  12. 12. Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution   six things seven things eight thingsNew Ontological Invention: Number Page 11 of 20
  13. 13. Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution  Slide 5: Second Example = Numbers1. Again, theres something in the "real world" that we want to represent, such as how many spikes wesee or how many ovals we see.2. The first generation of quantitative notation was TALLIES that represented by ANALOGY (circa30,000 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 ROMANNUMERALS, 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 basicoperations of arithmetic. But eventually they hit the COMPLEXITY BARRIER: many importantconcepts could not be represented (e.g. irrational numbers), and working with large numbers was oftencumbersome.5. Continuing on that path of adding new symbols or simplifying existing symbols would have beenfruitless: we could never send a man to the moon using Roman Numerals.6. The Revolution occurred when someone noticed that there were commonalities among certaingroups of (say) seven things, if you eliminated everything about them but the quantity of theirmembers. This "set of all sets of seven things" was identified by the arbitrary ideogram "7" (circa1202 in the West).7. With this new approach, and the additional convention that the value of each symbol was definedabsolutely by its location from the decimal place rather than by the symbols surrounding it, societywas 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 andTYPE 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 anotational SYSTEM built upon NUMBERS as NOTATIONS, and it defines a number of RULESregarding the proper use of this notation.10. As the result of this ontological invention, society was able to create a better way to describecertain aspects of the behavior of the world. Thus mathematics became the "language of science". Page 12 of 20
  14. 14. Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution   440New Ontological Invention: Notes Page 13 of 20
  15. 15. Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution  Slide 6: Third Example = Notes1. Again, theres something in the "real world" that we want to represent, such as certain musicalsounds. To understand music we have to realize that a note played on an instrument does not typicallyjust generate one pitch or sound vibration, it generates a number of these. These are calledOVERTONES, and they form the TIMBRE or character of each different instrument. Theseovertones 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 indicatedpitch). Later (circa 1260) MENSURAL NOTATION was better able to indicate the DURATION ofeach 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 enoughinformation for multiple simultaneous pitches, for coordinating the timing of diverse themes, or ofproviding a basis for tuning multiple instruments5. Continuing on that path of adding new symbols or simplifying existing symbols would have beenfruitless: no extension of that approach would have permitted polyphonic music such as a Beethovensymphony6. The Revolution occurred when someone decided to represent the INPUT to the instrument ratherthan its OUTPUT (circa 1000 AD).7. By this device, after several hundred years of evolution, we are now able to represent a wide rangeof pitches for a wide range of instruments, and to coordinate their pitch, timing, and volume. We cando POLYPHONIC music of great complexity.8. Thus the PRECISION and SCOPE of what could be represented was greatly increased. Musiccould 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, thenotational SYSTEM built upon NOTES as notations, added a number of other rules about the properuse of this notation.10. As the result of this ontological invention, composers were able to write polyphonic music downand then edit and refine it, and were able to create simultaneous complex sets of instructions to a Page 14 of 20
  16. 16. Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution  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, youll really FEEL thepower of this. Page 15 of 20
  17. 17. Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution   Salt ATTRIBUTES: companionship $20 food (value) Twenty Dollars Pay to the order of:New Ontological Invention: Dollar Page 16 of 20
  18. 18. Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution  Slide 7: Last Example = Dollars1. This is a little different slide, showing the PRE-NOTATIONAL situation at the top. If you want totrade your duck for my cat, we may agree on a BARTER arrangement. A duck and a cat are roughlycommensurable, partly because theyre both animals and they both have some real and obvious valuesto somebody; so it is fairly easy to make that trade. But as you offer things that are less and lesscommensurable, 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/ormeasure, perishable, and inconvenient logistically. Sometimes one had to trade with a third person tomake a deal happen (explain). Commerce was still very difficult, and the more complex an economygot the more problems were caused by commodity money.5. Continuing on that path would have been fruitless: we can hardly imagine what the New YorkStock Exchange or our economy in general might be like if every transaction was paid for byweighing salt or some other physical commodity.6. The Revolution occurred when someone noticed that VALUE could exist INDEPENDENTLY ofany object, by COMMON CONSENT. They set out to designate arbitrary objects as commonlyaccepted SYMBOLS of DECLARED VALUE. The intrinsic PRACTICAL VALUE of these objectswas nowhere near their DECLARED VALUE, and was often basically zero. Examples includecowrie seashells, wampum beads, gold and silver. The only criteria for symbols was that the objectsbe: 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 wasused in the West circa 1676.From 1825 through 1875 in the United States there was a major political debate between the "papermoney 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. Thispaper money was backed by gold, an equally worthless commodity. Page 17 of 20
  19. 19. Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution  Eventually we ended up with FIAT MONEY (circa 1934), not based on the gold standard, to enablegovernments to print money as desired, independently of their actual gold reserves. and therebycontrol 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 formy cat. Since in principle anything could be traded for this symbol, the BREADTH of what could bereadily 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 itover so THEY could control its abuse.9. Again we created a new entity in the world: DOLLARS (or their equivalent). ACCOUNTING, thenotational SYSTEM built upon DOLLARS as notations, provides rules for the proper use of thisnotation.10. As the result of this ontological invention, society was able to divide work more readily intospecialized categories, for there was now a common denominator that could be used in anycommercial activity. This was the beginning of "commerce" as we know it today. Page 18 of 20
  20. 20. Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution   Conclusion1. 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. Page 19 of 20
  21. 21. Jeffrey G. Long [1/16/1993]Notational Evolution & Revolution  Slide 7: ConclusionsQuestions? Page 20 of 20

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