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Notational Systems and 

Cognitive Evolution  

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

Date: October 29, 2005 

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Notational Systems and Cognitive Evolution

Jeffrey G. Long

jefflong@aol.com 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; history

1. Background There has been much recent discussion about how humanity’s future development may be affected by genetics research and by computer science research in intelligent systems. Developments in these areas will be very important, but we can also get more efficiency and effectiveness from existing human biology and computers by means of improved notational systems. As of yet there has been very little study of the evolution of cognition within our species, independent of genetic changes, that is evidently caused by the discovery and development of new notational systems. This paper argues for systematic study of this area, by trying to establish the basic importance of notational systems to cognition and to civilization. Indeed the link between these areas is so strong that one may think of cognition and civilization as co-evolving, based largely on the discovery of new notational systems, over the past fifty thousand years. The rate of this co-evolution has greatly increased in the last ten thousand years. While the human genome may not have changed very much during that period, the way humans see the world and interact with it has changed greatly because we have come to master new abstractions and formalized them into notational systems. Speech, money, mathematics and music are but a few examples of things we are familiar with that would have been incomprehensible 50,000 years ago to a hypothetical genetic duplicate of ourselves. As humanity continues to discover new abstractions, it should be expected that hypothetical genetic duplicates of ourselves of 500, 1000, or 50,000 years into the future will be utterly incomprehensible 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 what and how we see, think, and communicate about the world; that they are a critical interface between higher forms of thought and reality; and that their study is urgently needed if we are to discover new capabilities in science, the arts, economics, and many other areas of human activity. This paper therefore advocates the systematic, comparative, and scientific study of notational systems by the establishment 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 history of any one notational system is not, by itself, adequate to bring the structure and importance of notational revolutions into focus. 2. What is a Notational System? In order to understand this argument better, it is important to address some of the common misconceptions about notational systems. Most people intuitively think of a notational system as being merely a set of symbols used for abbreviating ideas that could just as well be expressed using other symbols. In this understanding the particular notation used is not very important. While I agree that the particular symbols used are not terribly important, I suggest that the tokens of a notational system are the least important feature of any notational system; they are like the tip of the iceberg that one can see above the water, and the real substance 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 we calculate 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 they were created, and have evolved over hundreds and thousands of years, to address real and fundamental human problems. They constitute a cognitive technology that in fact has been essential for the development of modern civilization and the modern mind. Like any other technology, they have strengths and weaknesses; their development is not yet finished. Recent examples of substantial advances in existing notational systems can be found in fuzzy logic and fractal geometry, both of which are still in their early stages of usage even decades after their introduction. Furthermore, there probably are 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 and civilization by reviewing what people in very different fields have said about them. For example, the mathematician 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 misunderstandings on the part of others, and also errors in one's own thought, makes itself felt. Both [shortcomings] 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....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 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 the greatest genius to discover. Each improvement 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. Our notation is an instance of that great spirit of economy which spares waste of labour on what is already systematised, so that all our strength can be concentrated either upon what is known but 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 on more advanced problems, and in effect increases the mental power of the race." Historian Eric Havelock (1982) stated, "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." The historian James Breasted (1926) said, "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." Historian of mathematics Florian Cajori (1974) quoted from an 1800 text in which the French mathematician Arbogast stated, "To form the [calculus], it becomes necessary to introduce new signs; I have given this subject particular attention, being persuaded that the secret of the power of analysis consists 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, or combinations of signs that will show itself to be at the base of a process of modelization of complexity by an intelligence." In presenting a survey of chemical notations, the National Academy of Sciences' National Research Council stated in 1964 that "Certainly the history of the first twenty years of chemical codes and notations has been characterized by much original thinking and by many ingenious schemes for handling chemical structures. There is great need for improved methods of handling the rapidly expanding fund of 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”, or the benefits of abbreviation. To understand what they are talking about, we must see that there is more to 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 Systems

I suggest that what makes a notational system powerful is its ability to enable its users to see and utilize facets of reality that they literally had not been able to see before. These systems do this by reifying and accurately representing an abstraction space: they use physical tokens to represent a wide variety of distinctions among a family of abstractions. Numbers, shapes, change, relationships, instructions, and entityhood are all examples of different families of abstraction space. For example, I have come to think of natural languages as the notational systems for representing entityhood, 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 as discoveries that any sufficiently high intelligence will eventually make, albeit using tokens that are best suited to their anatomy and media. The mapping of these spaces into particular notational systems is not obvious, partly because most of the notational systems we regularly use have components from other notational systems, and partly because the mapping was almost always developed in an ad hoc, trial and error manner rather than systematically. Each abstraction space is reified by a different notational system. Competence in a notational system is acquired through a process of learning how to see, work with, and apply the distinctions made within that particular abstraction space (for reading and writing we call this literacy). While learning to see and work with new abstractions is difficult, once learned the new way of seeing offers powerful new capabilities to its users. This process of acquiring literacy can be both intellectually and culturally revolutionary. People often feel threatened by change, however, especially when they are being asked to see 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 requires decades or centuries for acceptance and general usage, even when in retrospect it is obvious that the new notational 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-order notational 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 notational system such as English or another natural language. Morse Code, ASCII code (the American Standard Code for Information Interchange), and Unicode (another encoding system for computers like ASCII but including 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 that different types of notational systems cannot be translated into one another; for example, musical notation cannot really be translated into mathematical notation, nor can chemical notation be translated into movement notation. However, an instance of one type (say English as an instance of natural language) can be more-or-less successfully translated into another instance of the same type (such as French 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 requires centuries for a nascent notational system to develop, and even then it will continue to evolve until it reaches its useful limits. 4. The Limitations of Current Notational Systems Like any technology, notational systems have limits within which they work quite well; indeed they have enabled the creation of modern civilization. But beyond or outside those limits we cannot expect them to be helpful. The way to tell that we have reached the limits of a notational system is when, in using that system, we believe that the target system we are representing is “complex”. Complexity is not an attribute of any target system, but is a euphemism for the perplexity of an observer or user of the target 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, sometimes having lengthy cause-and-effect chains, but not perplexing. I call the limits of a notational system its “complexity barrier,” for that is where perplexity masquerading as complexity arises. Overcoming this barrier requires either (a) a hunt for a new abstraction space, or (b) finding and applying an existing notational system to the target system. An example of the first case is Newton’s creation of the infinitesimal calculus to help describe motion; an example of the second is Einstein’s application of non-Euclidean geometry to describe space-time. The true wonder of mathematics is not that nature obeys mathematical rules, but that humans can create so many 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 need something really new. If we have tried applying more power, more people, more money, or more computational 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 its natural limits. To not do this is wasteful and ultimately futile: if our ancestors had chosen to build a steam-powered abacus rather than switch from Roman to Hindu-Arabic numerals, modern mathematics and 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 of effort. In spite of the great success of our existing notational systems, many examples can be found where we have seemingly reached a complexity barrier. Unfortunately for all of us, many of these areas have important scientific, commercial, artistic, and/or public policy ramifications, so our inability to address them is more than a mere annoyance. Examples of areas that seem to qualify as essentially representational or notational problems include the following: (1) In software engineering we have the requirement for both substantial functionality and substantial flexibility 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 create systems that have the characteristics of both functionality and flexibility, so we settle for systems that are moderately functional (and moderately dysfunctional) and that can be changed only with great difficulty and expense. The real problem here is that we are increasingly dependent upon these software systems 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 of value. But price, and therefore monetary amounts, can only be set for those things which have a marketplace; 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 these assumptions 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. We achieve simplicity through over-simplification, when what we really need is simplicity without simplification. True solutions in these areas will not be a matter of trying harder, spending more money, building faster tools, or punishing those who fail to manage the problems. No amount of effort would have allowed us to send a man to the moon if we were still using Roman numerals; no level of effort would have permitted Beethoven to write his symphonies if there had not already existed a tool for him to express sophisticated and beautiful musical ideas. Notational revolutions happen when (a) wholly new abstraction spaces are discovered, (b) major new areas 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 the Internet. By opening up more of reality to study, notational revolutions can cause intellectual revolutions. They may also be culturally revolutionary in two distinct ways: by empowering new groups of people, and by constituting and permitting new kinds of understandings.

Contrasting with these rare revolutions, notational systems undergo evolution when their tokens and/or rules change and become easier to use and clearer in their representations. This may result in cultural evolution, as when reading, voting, or the use of money became more widespread and people’s lives changed. 5. Notational Engineering as a New Discipline Unfortunately there is no field that studies notational systems per se. Instead, each field that uses notational systems has a few (maybe 1%) of its practitioners who care about the nature and limitations of the notational systems used in that field; the rest of the professionals in that field are generally uninterested in this area and are often unaware of the limitations imposed by the notational systems they use. One might think that philosophy, which is concerned (among other things) with the nature of metaphysics, 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 of other notational systems. Having taken a “linguistic turn” in the 20th century, perhaps it will yet make a broader “notational turn” in the 21st. Mathematics is the home of many distinct notational systems such as arithmetic, geometry, graph theory, topology, and calculus. But mathematicians are interested in mathematical objects and do not often become involved with objects perceived to be inherently non-mathematical such as those reified by musical notation or chemical notation. Perhaps this is because these latter notational systems, unlike many in mathematics, have not been systematized to the degree that most mathematical systems have been. One might think that semiotics, as the study of sign systems, would be the proper home for a study of notation. But modern American semiotics is focused largely on what I call informal systems, to the general exclusion of formal systems (i.e. those having syntax but no semantics, such as pure mathematics, formal language theory, and pure logic) and/or notational systems (which have both syntax and semantics). These informal systems have great meaning (semantics) but no syntax with which to express larger statements. Examples of such systems are flags, trademarks, religious symbols, coats of arms, etc. Cognitive science, as the study of intelligent systems, may seem to be the proper home for a study of notation. But cognitive science sees the problem only from the mind side of the reality/mind link. If the practical success of any notational system tells us something about cognition but also sheds light on the nature of reality, then notational engineering must involve many facets of cognitive science but also include 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 of systems. I believe complexity is a euphemism for perplexity and can be resolved (dissolved) by the use of more capable notational systems. The study of complexity was aided by the new mathematical concept of fractional dimensions (“fractals”), as well as the use of cellular automata. While both led to interesting 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 significantly improved notational systems able to dissolve entire classes of problems. This proposed discipline presupposes that an expert in (say) music who is concerned about the limitations imposed by modern musical notation could usefully speak to an expert in (say) chemistry or logic about the common areas that are representational in nature rather than subject-related. I believe this to be the case, but with the caveat that a common framework for discussing problems in notation be built as soon as possible. A “Notational Engineering Laboratory” could also add value by working on some or all of the following fourteen areas: (1) acting as a clearinghouse of information and resources for people with an interest in any notational system in any field (2) performing research into the structure of notational revolutions by studying the history of various notational systems, utilizing a comparative approach to highlight what is essential, and what is incidental, 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 associated abstractions (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 somewhat easier 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 proposed notational 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 notational systems (11) creating and maintaining an Internet web site that offers educational information about notational engineering goals and activities, a comprehensive bibliography of materials related to notational systems, 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 notational systems 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 may better 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 and communicate about the world. We thus transform ourselves. In the future, people will use notational systems that we can’t imagine today; these systems will enable them to see and do things we cannot currently conceive of, just as we can see and do things that people 1,000 or even 100 years ago could not imagine. The missing link is a deeper appreciation of the nature and role of all notational systems in human cognition and civilization. Doing this work is hard and offers no guarantees of immediate success, but it may be the only way to successfully address a wide variety of problems in today’s and tomorrow’s world. All we require is the will to investigate.

6. References Breasted, James H. (1926). The Conquest of Civilization. New York: Harper & Brothers Cajori, Florian (1974). A History of Mathematical Notations. LaSalle, IL: Open Court Publishing Company Frege, Gottlob (1972). Conceptual Notation, And Related Articles. Oxford: Clarendon Press Havelock, Eric A. (1982). The Literate Revolution in Greece and its Cultural Consequences. Princeton: Princeton University Press Jourdain, Philip E. B. (1956). The Nature of Mathematics. In James R. Newman, The World of Mathematics, Volume I. New York: Simon and Schuster Le Moigne, Jean-Louis (1985). The intelligence of complexity. In The Science and Praxis of Complexity. Tokyo: The United Nations University Long, Jeffrey G. (1999). “How could the notation be the limitation?” Semiotica Special Issue on Notational Engineering, Vol. 125-1/3 National Research Council (1964). Survey of Chemical Notation Systems. Washington DC: National Academy of Sciences Publication 1150 Whitehead, Alfred North (1948). An Introduction to Mathematics. New York: Oxford University Press

Notational systems andNotational systems and cognitive evolutiong

Jeffrey G. LongOctober 29, 2005jefflong@aol.com

American Society for Cybernetics

Current analysis and design methods work well y gonly under certain conditions

October 29, 2005 2

W * ll * d t d t d lWe *really* need to understand complex dynamic 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

i fi k t economics, finance, markets medicine, physiology, biology, ecology, epidemiology

This is not inherent in the nature of the systems, but rather because our notational systems – our abstractions -- are inadequate

October 29, 2005 3

We therefore face “complexity barriers”We therefore face complexity barriers

What we don’t understand we call complex. But complexity is not a property of systems; rather perplexity is a property of thenot a property of systems; rather, perplexity is a property of the observer. Systems that are understood can only be complicated.

Complexity barrier problems cannot be solved by workingComplexity barrier problems cannot be solved by working harder, using faster computers, or gathering more data

Complexity barrier problems are fundamentally representationalComplexity 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 studiedFormal: human-assigned syntax only, e.g., formal logic, formal language theory pure mathematicslanguage theory, pure mathematics

Informal: human-assigned semantics only, e.g., art, advertising, politics, religious symbolsp , g y

Subsymbolic: no human-assigned syntax or semantics, but “natural” syntax and semantics (i.e., physically necessary interactions) e g natural systems DNA neural networksinteractions), e.g., natural systems, DNA, neural networks

Notational: human-assigned syntax and semantics, e.g., natural language, musical notation, money, cartography

October 29, 2005 5

G. Frege (1972) noted…Time and again, in the more abstract regions of science, the l k f id i d di h flack of a means to avoid misunderstandings on the part of others, and also errors in one's 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 thehave 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 th l A d ith t b l ld l liftthem properly... And, without symbols, we would scarcely lift ourselves to conceptual thinking.

October 29, 2005 6

P E B Jourdain (1956) notedP. E. B. Jourdain (1956) 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

d d th t t i t di E h i t ineeded the greatest genius to discover. Each improvement 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 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

i l h d b th i ti "precisely shared by any other invention."

October 29, 2005 9

Notational systems give us a cognitive

Each major notational s stem maps a different “abstraction

lens with which to see anew

Each major notational system maps a different “abstraction space”

Abstraction spaces areAbstraction spaces are incommensurable discoveries, not inventions real in some sense real in some sense

Acquiring literacy in a notation is learning how to see anew

Perceiving these is a uniquely human capability

October 29, 2005 10

So far we have settled maybe12 major abstraction spaces

October 29, 2005 11

All higher forms of thinking require the use of one or more

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 i t l i f t h iour environment: our analysis of events changes as we acquire

literacy in new notational systems

Notational systems have been central to the co-evolution ofNotational systems have been central to the co evolution of mind and civilization

October 29, 2005 12

Corollaries…Where would human culture be without language, writing, musical notation chemical notation mathematics maps ormusical notation, chemical notation, mathematics, maps, or logic notation?

To address the problems we currently face as a civilization, we d t l iti d i ti t l hneed new perceptual, cognitive, and communication tools, such

as… measures of value far more sophisticated than money the ability to represent millions of complex rules driving a 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 argumentsconclusions 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?

October 29, 2005 13

p g y

We can and should systematically, y y,comparatively, and longitudinally study notational systems to facilitate the

fdiscovery of new abstractions on which to base new or greatly enhanced notational systems Even if only onenotational systems. Even if only one new notational system ever came out of that effort it would repay society manythat effort, it would repay society many 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 fieldwith 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

ti h t d t i h t i ti l d h tcomparative approach to determine what is essential, and what is incidental, about each notational system

(3) determine the limitations imposed upon their users by existing(3) determine the limitations imposed upon their users by existing and proposed notational systems

(4) study the philosophical foundations of various notational t d th i i t d b t ti (lik t di f thsystems and their associated abstractions (like studies of the

foundations of mathematics)

October 29, 2005 15

(5) help to establish criteria and desiderata for new notational systems in various fieldssystems 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 th i k th t f t “ t ti l i ” i ht t ltheir work, so that future “notational engineers” might travel a somewhat easier road

(7) help to develop experimental new notational systems for various(7) help to develop experimental new notational systems for various fields of knowledge

(8) develop well-grounded test problems and test procedures for d t ti l t d t h t tproposed notational systems, and carry out such tests on

selected notational systems

October 29, 2005 16

(9) organize conferences and seminars pertaining to the history, philosophy psychology sociology engineering and applicationsphilosophy, psychology, sociology, engineering, and applications of notational systems

(10) publish a Journal of Notational Engineering to discuss issues t i i t t ti l tpertaining to notational systems

(11) create and maintain a website that offers educational information about notational engineering goals and activities an onlineabout notational engineering goals and activities, an online “Encyclopedia of Notation”, and specialized online listservers

(12) create and maintain a comprehensive bibliography of materials l t d t t ti l t d lib f f t i lrelated to notational systems, and a library of reference materials

October 29, 2005 17

ReferencesFrege, Gottlob (1972). Conceptual Notation, And Related Articles Oxford: Clarendon PressArticles. Oxford: Clarendon Press

Havelock, Eric A. (1982). The Literate Revolution in Greece and its Cultural Consequences Princeton: Princeton Universityits Cultural Consequences. Princeton: Princeton University Press

Jourdain Philip E B (1956) The Nature of Mathematics InJourdain, Philip E. B. (1956). The Nature of Mathematics. In 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 Press

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Further ReadingLong, J., and Denning, D., “Ultra-Structure: A design theory for

l d ” I C i ti f thcomplex systems and processes.” In Communications of the ACM (January 1995)Long, J., “Representing emergence with rules: The limits of addition ” In Lasker G E and Farre G L (editors) Advancesaddition. In Lasker, G. E. and Farre, G. L. (editors), Advances in Synergetics, Volume I: Systems Research on Emergence. (1996)Long, J., “A new notation for representing business and other g, , p grules.” 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. ( t dit ) S i ti S i l I N t ti l E i i(guest editor), Semiotica Special Issue: Notational Engineering, Volume 125-1/3 (1999)

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