Notational systems and cognitive evolution
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Notational systems and cognitive evolution



October 29, 2005: “Notational Systems and Cognitive Evolution”. Presented at the 2005

October 29, 2005: “Notational Systems and Cognitive Evolution”. Presented at the 2005
Annual Conference of the American Society for Cybernetics. Paper published in conference proceedings.



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Notational systems and cognitive evolution Notational systems and cognitive evolution Document Transcript

  • Cover Page   Notational Systems and  Cognitive Evolution  Author: Jeffrey G. Long ( Date: October 29, 2005 Forum: Talk presented at the 2005 Annual Conference of the American Society for Cybernetics.  Paper published in conference proceedings.  Contents Pages 1‐9: Preprint of paper Pages 10‐28: Slides (but no 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‐nc/3.0/ or send a letter to Creative Commons, 444 Castro Street, Suite 900, Mountain View, California, 94041, USA.  Uploaded June 26, 2011 
  • Notational Systems and Cognitive Evolution Jeffrey G. Long 2160 Leavenworth Street, #404 San Francisco, CA 94133 Abstract For individual people, the process of acquiring literacy with a particular notational system seems to result in significant new analytical, descriptive, and creative capabilities. For such individuals, and for society as a whole, science must account for this apparent birth of new cognitive abilities that arise by means of new and revolutionary notational systems. Just as language is not “just another tool,” notational systems (which include language as an instance) are not just another tool: they seem to affect what we can see and think about, as well as how we calculate and communicate. The proper study of this subject will require a longitudinal and comparative approach across multiple notational systems. The goal must be an understanding of the nature of notational revolutions, and the creation of new tools allowing us to solve or dissolve currently unsolvable problems. Keywords Symbol systems; cognition; literacy; mathematics; history1. BackgroundThere has been much recent discussion about how humanity’s future development may be affected bygenetics research and by computer science research in intelligent systems. Developments in these areaswill be very important, but we can also get more efficiency and effectiveness from existing humanbiology and computers by means of improved notational systems. As of yet there has been very littlestudy of the evolution of cognition within our species, independent of genetic changes, that is evidentlycaused by the discovery and development of new notational systems. This paper argues for systematicstudy of this area, by trying to establish the basic importance of notational systems to cognition and tocivilization. Indeed the link between these areas is so strong that one may think of cognition andcivilization as co-evolving, based largely on the discovery of new notational systems, over the past fiftythousand years.The rate of this co-evolution has greatly increased in the last ten thousand years. While the humangenome may not have changed very much during that period, the way humans see the world and interactwith it has changed greatly because we have come to master new abstractions and formalized them intonotational systems. Speech, money, mathematics and music are but a few examples of things we arefamiliar with that would have been incomprehensible 50,000 years ago to a hypothetical geneticduplicate of ourselves. As humanity continues to discover new abstractions, it should be expected thathypothetical genetic duplicates of ourselves of 500, 1000, or 50,000 years into the future will be utterlyincomprehensible to us.
  • This expansion of the Sapir-Whorf Hypothesis to include all notational systems rather than “just”language asserts that the notational systems we use act as cognitive lenses that largely determine whatand how we see, think, and communicate about the world; that they are a critical interface betweenhigher forms of thought and reality; and that their study is urgently needed if we are to discover newcapabilities in science, the arts, economics, and many other areas of human activity. This papertherefore advocates the systematic, comparative, and scientific study of notational systems by theestablishment of a new discipline perhaps to be called “Notational Engineering.” Only an integrative,comparative and longitudinal study of notational systems will offer the insights that we need; the historyof any one notational system is not, by itself, adequate to bring the structure and importance ofnotational revolutions into focus.2. What is a Notational System?In order to understand this argument better, it is important to address some of the commonmisconceptions about notational systems.Most people intuitively think of a notational system as being merely a set of symbols used forabbreviating ideas that could just as well be expressed using other symbols. In this understanding theparticular notation used is not very important. While I agree that the particular symbols used are notterribly important, I suggest that the tokens of a notational system are the least important feature of anynotational system; they are like the tip of the iceberg that one can see above the water, and the realsubstance of the system lies out of everyday sight.We use notational systems every day when we read or write, when we use a road map, when wecalculate using mathematics, and when we use money. These systems have been in use for centuries,and we generally take them for granted as fixed and (for all practical purposes) immutable. But theywere created, and have evolved over hundreds and thousands of years, to address real and fundamentalhuman problems. They constitute a cognitive technology that in fact has been essential for thedevelopment of modern civilization and the modern mind. Like any other technology, they havestrengths and weaknesses; their development is not yet finished. Recent examples of substantialadvances in existing notational systems can be found in fuzzy logic and fractal geometry, both of whichare still in their early stages of usage even decades after their introduction. Furthermore, there probablyare wholly new kinds of notational systems, equally as important as speech, writing, and mathematics,that are yet to be developed.We can perhaps gain a better understanding of their true nature as forces in the co-evolution of mind andcivilization by reviewing what people in very different fields have said about them. For example, themathematician and creator of modern logic Gottlob Frege (1972) wrote:"Time and again, in the more abstract regions of science, the lack of a means to avoid misunderstandingson the part of others, and also errors in ones own thought, makes itself felt. Both [shortcomings] havetheir origin in the imperfection of language, for we do have to use sensible symbols to think.... Symbolshave the same importance for thought that discovering how to use the wind to sail against the wind hadfor navigation. Thus, let no one despise symbols! A great deal depends upon choosing themproperly....And, without symbols, we would scarcely lift ourselves to conceptual thinking."
  • The mathematician Philip E. B. Jourdain (1956) commented, “It is important to realize that the long andstrenuous work of the most gifted minds was necessary to provide us with simple and expressivenotation which, in nearly all parts of mathematics, enables even the less gifted of us to reproducetheorems which needed the greatest genius to discover. Each improvement in notation seems, to theuninitiated, but a small thing: and yet, in a calculation, the pen sometimes seems to be more intelligentthan the user. Our notation is an instance of that great spirit of economy which spares waste of labouron what is already systematised, so that all our strength can be concentrated either upon what is knownbut unsystematised, or upon what is unknown.”Echoing this at a much later date, but more succinctly, the logician Alfred North Whitehead (1948)stated, "By relieving the brain of all unnecessary work, a good notation sets it free to concentrate onmore advanced problems, and in effect increases the mental power of the race."Historian Eric Havelock (1982) stated, "The Greek here introduced, when it impinges onthe Greek scene, as a piece of explosive technology, revolutionary in its effects on human culture, in away not precisely shared by any other invention." The historian James Breasted (1926) said, "Theinvention of writing and of a convenient system of records on paper has had a greater influence inuplifting the human race than any other intellectual achievement in the career of man. It was moreimportant than all the battles ever fought and all the constitutions ever devised."Historian of mathematics Florian Cajori (1974) quoted from an 1800 text in which the Frenchmathematician Arbogast stated, "To form the [calculus], it becomes necessary to introduce new signs; Ihave given this subject particular attention, being persuaded that the secret of the power of analysisconsists in the happy choice and use of signs..." The French philosopher Jean-Louis Le Moigne (1985)notes, "It is, therefore, this process of production and recognition of symbols, codes, patterns, signs, orcombinations of signs that will show itself to be at the base of a process of modelization of complexityby an intelligence."In presenting a survey of chemical notations, the National Academy of Sciences National ResearchCouncil stated in 1964 that "Certainly the history of the first twenty years of chemical codes andnotations has been characterized by much original thinking and by many ingenious schemes for handlingchemical structures. There is great need for improved methods of handling the rapidly expanding fundof chemical knowledge. Further developments in this area are awaited with great interest."All of these thinkers in all of these fields are assuredly not talking about the shape of the letter “E”, orthe benefits of abbreviation. To understand what they are talking about, we must see that there is moreto notational systems than meets the eye. Examples of notational systems include the generally-recognized notational systems of:  Sign languages such as American Sign Language  Spoken languages such as English, French, or Chinese  Alphabetic and syllabic writing systems such as the Roman, Greek or Cyrillic alphabets  Ideographic writing systems such as Chinese  Computer languages such as Java, ‘C’, or Visual Basic  Quantitative notational systems such as Hindu-Arabic numerals or Roman numerals  Other kinds of mathematical systems such as geometry and calculus  Chemical notation systems such as line-formula notation or Daltonian notation
  •  Musical notational systems such as staff notation or tablature notation  Dance and movement notation systems such as Labanotation, Benesh notation, and Eshkol- Wachman notation  Other notational systems for engineering in fields such as computer science, electrical engineering, or architecture.I suggest that notational systems also include such unrecognized but ubiquitous systems as:  Value representation notations such as money, checks, accounting systems, credit cards  Opinion representation notations such as voting systems  Change representation notations such as clocks and calendars (i.e., time)3. The Foundations of Notational SystemsI suggest that what makes a notational system powerful is its ability to enable its users to see and utilizefacets of reality that they literally had not been able to see before. These systems do this by reifying andaccurately representing an abstraction space: they use physical tokens to represent a wide variety ofdistinctions among a family of abstractions. Numbers, shapes, change, relationships, instructions, andentityhood are all examples of different families of abstraction space.For example, I have come to think of natural languages as the notational systems for representingentityhood, and of musical notation and software notation as systems for representing instructions.Whether these abstraction spaces are inventions or discoveries is debatable, although I think of them asdiscoveries that any sufficiently high intelligence will eventually make, albeit using tokens that are bestsuited to their anatomy and media. The mapping of these spaces into particular notational systems is notobvious, partly because most of the notational systems we regularly use have components from othernotational systems, and partly because the mapping was almost always developed in an ad hoc, trial anderror manner rather than systematically.Each abstraction space is reified by a different notational system. Competence in a notational system isacquired through a process of learning how to see, work with, and apply the distinctions made withinthat particular abstraction space (for reading and writing we call this literacy). While learning to see andwork with new abstractions is difficult, once learned the new way of seeing offers powerful newcapabilities to its users. This process of acquiring literacy can be both intellectually and culturallyrevolutionary. People often feel threatened by change, however, especially when they are being asked tosee something they never thought was there before, so a particular notational system such as Hindu-Arabic numerals, staff musical notation, or even the use of new calendars therefore often requiresdecades or centuries for acceptance and general usage, even when in retrospect it is obvious that the newnotational system is far better than the old.While it was stated above that notational systems map an abstraction space, these are only one (major)kind of notational systems that I call “first-order” notational systems. Second- and higher-ordernotational systems do not map an abstraction space; instead, they map a lower-order notational system.Alphabetic writing systems are thus second-order notational systems that map a first-order notationalsystem such as English or another natural language. Morse Code, ASCII code (the American StandardCode for Information Interchange), and Unicode (another encoding system for computers like ASCII butincluding all major writing systems) are thus third-order notational systems. Encrypted text is a higher-
  • order notational system that has special features to make it readable only by those intended to read it,who must somehow know the correct rules for decryption to a lower-order, readable notational system.Abstraction spaces cannot be translated into one another; they are incommensurable. This means thatdifferent types of notational systems cannot be translated into one another; for example, musicalnotation cannot really be translated into mathematical notation, nor can chemical notation be translatedinto movement notation. However, an instance of one type (say English as an instance of naturallanguage) can be more-or-less successfully translated into another instance of the same type (such asFrench or Russian).In addition to mapping an abstraction space or a lower-order notational system, fully- developed(mature) notational systems also have the following critical components:  rules for combining tokens to create statements having meanings that are more than the semantic sum of the tokens (syntactical rules)  a variety of styles of usage, which are consistent with the syntax and semantics of the notational system but offer significant nuance of expression (e.g. Hemmingway vs. Shakespeare, Beethoven vs. Bach)  additional “aesthetic” rules for assessing the value of a given statement in a particular notational system (the preferences and tastes of individual users and of particular time periods and societies).Any system not having all of these components is not a developed notational system. It usually requirescenturies for a nascent notational system to develop, and even then it will continue to evolve until itreaches its useful limits.4. The Limitations of Current Notational SystemsLike any technology, notational systems have limits within which they work quite well; indeed theyhave enabled the creation of modern civilization. But beyond or outside those limits we cannot expectthem to be helpful. The way to tell that we have reached the limits of a notational system is when, inusing that system, we believe that the target system we are representing is “complex”. Complexity isnot an attribute of any target system, but is a euphemism for the perplexity of an observer or user of thetarget system. It exists solely in the eye (mind) of the beholder and can be eliminated by use of a more-powerful notational system. The target system may then appear to a user to be complicated, sometimeshaving lengthy cause-and-effect chains, but not perplexing.I call the limits of a notational system its “complexity barrier,” for that is where perplexitymasquerading as complexity arises. Overcoming this barrier requires either (a) a hunt for a newabstraction space, or (b) finding and applying an existing notational system to the target system. Anexample of the first case is Newton’s creation of the infinitesimal calculus to help describe motion; anexample of the second is Einstein’s application of non-Euclidean geometry to describe space-time. Thetrue wonder of mathematics is not that nature obeys mathematical rules, but that humans can create somany notational systems that one can be found to fit almost any situation.As a society we need to be able to recognize when we have reached a complexity barrier and needsomething really new. If we have tried applying more power, more people, more money, or morecomputational capability to solve a given problem, and have been unsuccessful (i.e. are still faced with
  • great complexity), then we need to consider the possibility that our notational technology has reached itsnatural limits. To not do this is wasteful and ultimately futile: if our ancestors had chosen to build asteam-powered abacus rather than switch from Roman to Hindu-Arabic numerals, modern mathematicsand technology would not exist. Problems that have this characteristic may be thought of as primarily“representational problems,” as contrasted with those caused by lack of data, lack of theory, or lack ofeffort.In spite of the great success of our existing notational systems, many examples can be found where wehave seemingly reached a complexity barrier. Unfortunately for all of us, many of these areas haveimportant scientific, commercial, artistic, and/or public policy ramifications, so our inability to addressthem is more than a mere annoyance. Examples of areas that seem to qualify as essentiallyrepresentational or notational problems include the following:(1) In software engineering we have the requirement for both substantial functionality and substantialflexibility of functionality at the same time. We can create multi-functional systems that don’t change,or highly changeable systems that are simple (i.e. not multi-functional). We don’t know how to createsystems that have the characteristics of both functionality and flexibility, so we settle for systems thatare moderately functional (and moderately dysfunctional) and that can be changed only with greatdifficulty and expense. The real problem here is that we are increasingly dependent upon these softwaresystems for all aspects of our life and safety.(2) In determining corporate and public policy we are faced with the use of money as the only tokens ofvalue. But price, and therefore monetary amounts, can only be set for those things which have amarketplace; and the most important things – family, friends, clean air, drinkable water, stable climate,ecological diversity, etc – have no marketplace and therefore, under our current system of accounting,have no value. How can we make wise decisions in such a situation?(3) In trying to understand complex man-made and natural systems such as we find in medicine,economics, and climatology, we are forced to make numerous simplifying assumptions. We know theseassumptions are not really valid but without them our mathematical representations become unsolvable,so we use the limited models, and often need to make grave decisions that can affect many people. Weachieve simplicity through over-simplification, when what we really need is simplicity withoutsimplification.True solutions in these areas will not be a matter of trying harder, spending more money, building fastertools, or punishing those who fail to manage the problems. No amount of effort would have allowed usto send a man to the moon if we were still using Roman numerals; no level of effort would havepermitted Beethoven to write his symphonies if there had not already existed a tool for him to expresssophisticated and beautiful musical ideas.Notational revolutions happen when (a) wholly new abstraction spaces are discovered, (b) major newareas of an existing abstraction space are discovered and reified by a new or extended notational system,or (c) a new notational order is developed, usually to make fuller use of new media as in printing or theInternet. By opening up more of reality to study, notational revolutions can cause intellectualrevolutions. They may also be culturally revolutionary in two distinct ways: by empowering new groupsof people, and by constituting and permitting new kinds of understandings.
  • Contrasting with these rare revolutions, notational systems undergo evolution when their tokens and/orrules change and become easier to use and clearer in their representations. This may result in culturalevolution, as when reading, voting, or the use of money became more widespread and people’s liveschanged.5. Notational Engineering as a New DisciplineUnfortunately there is no field that studies notational systems per se. Instead, each field that usesnotational systems has a few (maybe 1%) of its practitioners who care about the nature and limitationsof the notational systems used in that field; the rest of the professionals in that field are generallyuninterested in this area and are often unaware of the limitations imposed by the notational systems theyuse.One might think that philosophy, which is concerned (among other things) with the nature ofmetaphysics, mind, mathematical objects, and truth, would be the proper home for a study of notation.But modern American and British philosophy is focused largely on language, to the general exclusion ofother notational systems. Having taken a “linguistic turn” in the 20th century, perhaps it will yet make abroader “notational turn” in the 21st.Mathematics is the home of many distinct notational systems such as arithmetic, geometry, graphtheory, topology, and calculus. But mathematicians are interested in mathematical objects and do notoften become involved with objects perceived to be inherently non-mathematical such as those reifiedby musical notation or chemical notation. Perhaps this is because these latter notational systems, unlikemany in mathematics, have not been systematized to the degree that most mathematical systems havebeen.One might think that semiotics, as the study of sign systems, would be the proper home for a study ofnotation. But modern American semiotics is focused largely on what I call informal systems, to thegeneral exclusion of formal systems (i.e. those having syntax but no semantics, such as puremathematics, formal language theory, and pure logic) and/or notational systems (which have both syntaxand semantics). These informal systems have great meaning (semantics) but no syntax with which toexpress larger statements. Examples of such systems are flags, trademarks, religious symbols, coats ofarms, etc.Cognitive science, as the study of intelligent systems, may seem to be the proper home for a study ofnotation. But cognitive science sees the problem only from the mind side of the reality/mind link. If thepractical success of any notational system tells us something about cognition but also sheds light on thenature of reality, then notational engineering must involve many facets of cognitive science but alsoinclude physics and metaphysics as critical facets of the problem space.Efforts since the 1980s have focused on complexity as a subject in its own right, across many kinds ofsystems. I believe complexity is a euphemism for perplexity and can be resolved (dissolved) by the useof more capable notational systems. The study of complexity was aided by the new mathematicalconcept of fractional dimensions (“fractals”), as well as the use of cellular automata. While both led tointeresting results, the problem of complexity is clearly not dissolved.
  • I therefore have proposed (Long, 1999) a new interdisciplinary study called “notational engineering,”whose object of study is notational systems, and whose goal is to develop new and/or significantlyimproved notational systems able to dissolve entire classes of problems.This proposed discipline presupposes that an expert in (say) music who is concerned about thelimitations imposed by modern musical notation could usefully speak to an expert in (say) chemistry orlogic about the common areas that are representational in nature rather than subject-related. I believe thisto be the case, but with the caveat that a common framework for discussing problems in notation be builtas soon as possible.A “Notational Engineering Laboratory” could also add value by working on some or all of the followingfourteen areas:(1) acting as a clearinghouse of information and resources for people with an interest in any notationalsystem in any field(2) performing research into the structure of notational revolutions by studying the history of variousnotational systems, utilizing a comparative approach to highlight what is essential, and what isincidental, about each notational system(3) determining the limitations imposed upon their users by existing and proposed notational systems(4) studying the philosophical foundations of various notational systems and their associatedabstractions (corresponding in many ways to studies of the foundations of mathematics)(5) helping to establish criteria for adequate new notational systems in various fields(6) interviewing living creators of notational systems to learn more about how and why they did that,and what the reactions were to their work, so that future “notational engineers” might travel a somewhateasier road(7) developing experimental new notational systems for various fields of knowledge(8) developing scientifically well-grounded test problems, test data and test procedures for proposednotational systems, and carrying out such tests on selected proposed notational systems(9) organizing conferences and seminars pertaining to notational research and engineering(10) publishing a new Journal of Notational Engineering to discuss issues pertaining to notationalsystems(11) creating and maintaining an Internet web site that offers educational information about notationalengineering goals and activities, a comprehensive bibliography of materials related to notationalsystems, an online “Encyclopedia of Notation”, and online meetings(12) creating and maintaining a research library of reference materials related to notational systems
  • (13) facilitating development of a television series on the history and impact of various major notationalsystems for the general public(14) creating and maintaining a Notational Museum of notational systems throughout history and pre-history, and describing their role in the continuing evolution of the human mind, so that the public maybetter understand and appreciate the value and importance of notational systems.By creating new and improved notational systems we create new and improved ways to see, think andcommunicate about the world. We thus transform ourselves. In the future, people will use notationalsystems that we can’t imagine today; these systems will enable them to see and do things we cannotcurrently conceive of, just as we can see and do things that people 1,000 or even 100 years ago could notimagine. The missing link is a deeper appreciation of the nature and role of all notational systems inhuman cognition and civilization. Doing this work is hard and offers no guarantees of immediatesuccess, but it may be the only way to successfully address a wide variety of problems in today’s andtomorrow’s world. All we require is the will to investigate.6. ReferencesBreasted, James H. (1926). The Conquest of Civilization. New York: Harper & BrothersCajori, Florian (1974). A History of Mathematical Notations. LaSalle, IL: Open Court PublishingCompanyFrege, Gottlob (1972). Conceptual Notation, And Related Articles. Oxford: Clarendon PressHavelock, Eric A. (1982). The Literate Revolution in Greece and its Cultural Consequences. Princeton:Princeton University PressJourdain, Philip E. B. (1956). The Nature of Mathematics. In James R. Newman, The World ofMathematics, Volume I. New York: Simon and SchusterLe Moigne, Jean-Louis (1985). The intelligence of complexity. In The Science and Praxis ofComplexity. Tokyo: The United Nations UniversityLong, Jeffrey G. (1999). “How could the notation be the limitation?” Semiotica Special Issue onNotational Engineering, Vol. 125-1/3National Research Council (1964). Survey of Chemical Notation Systems. Washington DC: NationalAcademy of Sciences Publication 1150Whitehead, Alfred North (1948). An Introduction to Mathematics. New York: Oxford University Press
  • Notational systems andcognitive evolution g Jeffrey G. Long October 29, 2005 jefflong@aol.comAmerican Society for Cybernetics
  • Current analysis and design methods work well y gonly under certain conditionsOctober 29, 2005 2
  • W * ll * need t understand complexWe *really* d to d t d ldynamic systems much better Modern society may have competence in using certain kinds of complex systems but we still don’t understand them  climate and weather  economics, fi i finance, markets k t  medicine, physiology, biology, ecology, epidemiology This is not inherent in the nature of the systems, but rather because our notational systems – our abstractions -- are inadequateOctober 29, 2005 3
  • We therefore face “complexity barriers” complexity barriers What we don’t understand we call complex. But complexity is not a property of systems; rather perplexity is a property of the rather, observer. Systems that are understood can only be complicated. Complexity barrier problems cannot be solved by working harder, using faster computers, or gathering more data Complexity barrier problems are fundamentally representational problems. Using the wrong, or too-limited, a representational (notational) system is inescapably self-defeating.October 29, 2005 4
  • Other system types have long been studied Formal: human-assigned syntax only, e.g., formal logic, formal language theory, pure mathematics theory Informal: human-assigned semantics only, e.g., art, advertising, p politics, religious symbols , g y Subsymbolic: no human-assigned syntax or semantics, but “natural” syntax and semantics (i.e., physically necessary interactions), e.g., interactions) e g natural systems DNA neural networks systems, DNA, Notational: human-assigned syntax and semantics, e.g., natural language, musical notation, money, cartographyOctober 29, 2005 5
  • G. Frege (1972) noted… Time and again, in the more abstract regions of science, the lack f l k of a means to avoid misunderstandings on the part of id i d di h f others, and also errors in ones own thought, makes itself felt. Both have their origin in the imperfection of language, for we do have to use sensible symbols to think.... Symbols have the same importance for thought that discovering how to use the wind to sail against the wind had for navigation. Thus, let no one despise symbols! A great deal depends upon choosing them properly... A d without symbols, we would scarcely lift th l And, ith t b l ld l ourselves to conceptual thinking.October 29, 2005 6
  • P E B Jourdain (1956) notedP. E. B. noted… It is important to realize that the long and strenuous work of the most gifted minds was necessary to provide us with simple and expressive notation which, in nearly all parts of mathematics, enables even the less gifted of us to reproduce theorems which needed th greatest genius t discover. E h i d d the t t i to di Each improvement i t in notation seems, to the uninitiated, but a small thing: and yet, in a calculation, the pen sometimes seems to be more intelligent than the user.October 29, 2005 7
  • A. N. Whitehead (1948) noted… 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.October 29, 2005 8
  • E. Havilock (1982) noted… The Greek 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 b any other i i l h d by th invention." ti "October 29, 2005 9
  • Notational systems give us a cognitivelens with which to see anew Each major notational system maps a different “abstraction s stem space” Abstraction spaces are  incommensurable  discoveries, not inventions  real in some sense Acquiring literacy in a notation is learning how to see anew Perceiving these is a uniquely human capabilityOctober 29, 2005 10
  • So far we have settled maybe12 major abstraction spacesOctober 29, 2005 11
  • The notational hypothesis All higher forms of thinking require the use of one or more notational systems The notational systems we use influence the way we perceive our environment: our analysis of events changes as we acquire i t l i f t h i literacy in new notational systems Notational systems have been central to the co-evolution of co evolution mind and civilizationOctober 29, 2005 12
  • Corollaries… Where would human culture be without language, writing, musical notation chemical notation mathematics maps or notation, notation, mathematics, maps, logic notation? To address the problems we currently face as a civilization, we need new perceptual, cognitive, and communication t l such d t l iti d i ti tools, h as…  measures of value far more sophisticated than money  the ability to represent millions of complex rules driving a rule-based system such as a climate or a cell biology model  semantic tools that allow us to mechanically integrate scientific hypotheses so as to automatically generate new conclusions from the integrated arguments Why rely, as we have so far, on pure chance to develop such tools when we can attempt to design them deliberately? p g yOctober 29, 2005 13
  • We can and should systematically, y y, comparatively, and longitudinally study notational systems to facilitate the discovery of new abstractions on which f to base new or greatly enhanced notational systems. Even if only one systems new notational system ever came out of that effort, it would repay society many effort times over.October 29, 2005 14
  • Notational engineering tasks(1) provide a clearinghouse of information and resources for people with an interest in any kind of notational system in any field(2) perform research into the structure of notational revolutions by studying the history of various notational systems, utilizing a comparative approach t determine what i essential, and what ti h to d t i h t is ti l d h t is incidental, about each notational system(3) determine the limitations imposed upon their users by existing and proposed notational systems(4) study the philosophical foundations of various notational systems and their associated abstractions (lik studies of the t d th i i t d b t ti (like t di f th foundations of mathematics)October 29, 2005 15
  • (5) help to establish criteria and desiderata for new notational systems in various fields(6) interview living creators of notational systems to learn more about how and why they did that, and what the reactions were to their th i work, so th t future “notational engineers” might t k that f t “ t ti l i ” i ht travel a l somewhat easier road(7) help to develop experimental new notational systems for various fields of knowledge(8) develop well-grounded test problems and test procedures for proposed notational systems, and carry out such t t on d t ti l t d t h tests selected notational systemsOctober 29, 2005 16
  • (9) organize conferences and seminars pertaining to the history, philosophy, psychology, sociology, engineering, philosophy psychology sociology engineering and applications of notational systems(10) publish a Journal of Notational Engineering to discuss issues pertaining to notational systems t i i t t ti l t(11) create and maintain a website that offers educational information about notational engineering goals and activities an online activities, “Encyclopedia of Notation”, and specialized online listservers(12) create and maintain a comprehensive bibliography of materials related t notational systems, and a lib l t d to t ti l t d library of reference materials f f t i lOctober 29, 2005 17
  • References Frege, Gottlob (1972). Conceptual Notation, And Related Articles. Articles Oxford: Clarendon Press Havelock, Eric A. (1982). The Literate Revolution in Greece and its Cultural Consequences Princeton: Princeton University Consequences. Press Jourdain, Jourdain Philip E B (1956) The Nature of Mathematics In E. B. (1956). Mathematics. James R. Newman, The World of Mathematics, Volume I. New York: Simon and Schuster Whitehead, Alfred North (1948). An Introduction to Mathematics. New York: Oxford University PressOctober 29, 2005 18
  • Further Reading Long, J., and Denning, D., “Ultra-Structure: A design theory for complex systems and processes.” I C l d ” In Communications of th i ti f the ACM (January 1995) Long, J., “Representing emergence with rules: The limits of addition. addition ” In Lasker G E and Farre G. L. (editors), Advances Lasker, G. E. Farre, G L (editors) in Synergetics, Volume I: Systems Research on Emergence. (1996) Long, J., “A new notation for representing business and other g, , p g rules.” In Long, J. (guest editor), Semiotica Special Issue: Notational Engineering, Volume 125-1/3 (1999) Long, J., “How could the notation be the limitation?” In Long, J. (guest editor), S i ti S ( t dit ) Semiotica Special Ii l Issue: N t ti Notational E i l Engineering, i Volume 125-1/3 (1999)October 29, 2005 19