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Notation Systems and 

the Abstract Built 

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

Date: July 27, 2008 

Forum: Talk presented at the InterSymp 2008 Conference, sponsored by the 

International Institute for Advanced Studies in Systems Research and Cybernetics 

(IIAS).  Paper published in conference proceedings, available at 

http://iias.info/pdf_general/Booklisting.pdf

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Pages 1‐5: Preprint of Article 

Pages 6‐19: Slides (but no text) for presentation 

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Notational Systems and the Abstract Built Environment

Jeffrey G. Long jefflong@aol.com

Abstract The “Built Environment” refers to the milieu of physical manmade objects such as buildings, cities, and landscapes. Christopher Alexander has advocated since the 1960s that the built environment has design patterns we should learn from1. I suggest that there is an even more fundamental “Abstract Built Environment” which may be contrasted with this “physical built environment,” and that there are patterns in that environment, too, that we should learn from. Notational systems are fundamental to the Abstract Built Environment, for they provide new metaconcepts that are very different than any existing concepts. They provide a way to tokenize (physically represent) concepts derived from these metaconcepts. And they provide rules by which we can build complex statements by linking multiple concepts into statements (what I call rules). Rules and rule systems are thus built on top of notational systems, and allow even more complex statements to be made. Examples of rule systems are legal systems, which are generally based on language as a notational system; scientific hypotheses, which are based on mathematical and other notational systems; software systems, which use programming languages as their fundamental notations; and economic/financial systems, which are based on the notational system of money and rules of accounting. These too are part of the abstract built environment. The Abstract Built Environment we’ve created over the past 200,000 years, and especially the last 10,000 years, has created human culture as we know it. Systematic study of this environment will facilitate improving our fundamental cognitive toolset to face tomorrow’s many challenges. Key Words: Concepts; Built Environment; Notational Engineering; Memes; Representation; The Abstract Built Environment The built environment includes the physical environment that humans have created, ranging from clothing to houses to cities to landscapes, and is contrasted with the natural environment provided by nature. The World Heritage Committee has noted that these are not distinct, but phase into one another as “Cultural Landscapes.”2 But there is a major piece of culture that is missing from this paradigm, namely the various abstract entity types that constitute our abstract built environment. Abstract entity types include all concepts, rules, and beliefs, and are made possible by the various known notational systems. This environment has its own ecology and patterns, and has evolution and natural selection in the form of memes. Having developed the abstract built environment especially over the past 10,000 years, we can learn a lot from it.

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Notational Systems and Metaconcepts Notational systems are fundamental to the abstract built environment for two reasons: (1) they introduce not just new concepts, but whole new classes of concepts (metaconcepts3), and (2) they provide a means to tokenize these abstract concepts so they may become a part of our physical built environment, and we can then manipulate, store, and work with them just as we can work with any other similar physical materials. As an example of a metaconcept, natural languages provide a mechanism to declare the existence of both individual entities and classes of entities. It is like an existential operator in logic, but with the mere existence of a word or phrase implying existence (in some world, not necessarily our physical world). Exactly how a particular natural language parses the flux of experience depends on its history and the history of its users. The particular individual concepts made possible by a metaconcept – the particular trees, flowers and dogs it distinguishes – are important but secondary. Another example of a metaconcept is the notion of quantity. This presumes the existence of countable entities (i.e. individuals), and provides a way to distinguish magnitudes both absolutely and relatively. It and the operations of addition and subtraction are the fundamental metaconcepts provided by arithmetic. The particular concepts derived from this, as tokenized by a particular numeration system, are again important but secondary. Roman Numerals was a dead end notationally because it was unable to represent types of number that we now take for granted beyond integers, such as imaginary numbers, transfinite numbers, and the place-holder zero (except that this latter was represented on an abacus). Concepts and Memes Concepts are particular applications of metaconcepts. For example, the fact that English distinguishes green and blue colors, and some other languages don’t, is simply a quirk of how English treats colors. Other languages make other distinctions that its users believe are important to them. All are still performing their principal function of declaring existence, even though what is thereby said to exist may differ. All the quarter-million words of English (excluding proper names) are concepts created by making various distinctions so as to isolate some aspect of experience and give it a name. All the numbers of mathematics are examples of concepts created by making various distinctions and tokenizing them with numerals. All the musical notes and concepts of musical notation are derived from the metaconcept of “notes” and their opposite, non-notes (i.e. rests). Individual concepts may usefully be thought of as memes, and ordered collections of concepts as memeplexes4. These are passed from person to person through culture, sometimes directly by imitation (as Dawkins proposes) but also though the creation and subsequent interpretation of physical tokens. Being able to grasp and use any particular concept requires that one first become “literate” in the underlying notational system. This does not mean becoming a master of it, but simply learning how to “see” those kinds of concepts and learn how they can interact together, just as we learn to

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“see” objects as such and learn how they can act and interact. Acquiring literacy is hard, because concepts are never visible to the senses. We come to believe that they are “real” only after we directly experience their usefulness. We are born with none of this knowledge, merely an innate capability to learn to see, that is then more or less developed in various individuals. Tokens and Media The particular tokens that a notational system uses are the result primarily of historical accident, for anything physical could be (and historically has probably been) so used. The fundamental properties of tokens are determined by the medium they are inscribed upon. New media, and consequently new technologies for production and distribution, open up the possibility of new, economical, and broader usage of any notational system. Going from clay tablets to paper helped in obvious ways, as did the new production mechanism of the printing press. The printing press also helped to start the standardization of letter shapes and of spellings, and made literacy more useful, thereby ultimately shaping the notational systems it was created to support. We are now famously in the midst of another media revolution made possible by digital media (including computers, storage, and transmission) which makes new tokenizations possible. For example, Unicode now provides unique global encodings of 99,024 different characters in all languages, plus punctuation marks, mathematical symbols, technical symbols, etc. 5 It also adds new features, such as a distinction between the “-“ used as a hyphen and the same token used as a minus sign, that are known only by context in normal writing: it acknowledges that they were truly never the same token, even though they may look the same. Digital media allows for hyperlinks, text searches, and multimedia presentations whose functions were previously accomplished manually only with great effort. Statements and Rules A notational system by itself makes no statements about the world beyond the existence of its tokens; it merely provides a toolset by which concepts can be formulated and statements can be created. Using this feature we can build large and complex systems of statements, such as legal systems (based largely on the notational system of language); scientific journal articles (based largely on language but also using mathematics and other notational systems such as Feynman QED notation); and even the periodic table of chemistry (based upon chemical notation). Important characteristics of these systems are that: (1) they inherit the fundamental limitations of the notational systems they are built upon, (2) they are becoming more complex as the cultures they support become more complex; (3) we depend upon them to always work essentially correctly; and (4) in general we don’t really understand them. Any statement in any notational system can be reformulated as one or more “rules” having an If-Then format. I call them “rules” because (1) they are always conditional, (2) they are quite changeable, (3) they establish active systems by which the firing of one rule unleashes a cascade of other, subsequent rules, and I believe such inherently active abstract entities deserve a name that implies this kind of power.

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Effability Spaces and the Abstract Built Environment The tokens and metaconcepts of a notational system allow us to build ordinary concepts, and we can combine these into rules and rule systems. This provides a great deal of expressive power. I call the set of all ideas that can in theory be expressed using a particular notational system its effability space6 The abstract built environment is comprised of all existing effability spaces, and expands as new notational systems are developed and new effability spaces are added to the environment. An effability space is not useful simply for communication. I suggest we should broaden the Sapir-Whorf hypothesis of linguistic relativity beyond language (where it has been found wanting) to all notational systems:

all higher forms of thinking require the use of one or more notational systems our notational systems not only influence but determine the way we may perceive, think,

and communicate about the world

new notational systems are based on whole new types of distinction, and create an ability to think clearly about things that used to be ineffable.

If this is true, then a person a thousand years from now should be able to see, think about, and communicate about ideas and parts of the world that we can’t at present imagine. Certainly a person from a thousand years ago would be surprised at our credit card economy, amazed to hear a symphony, and astonished to learn that humans went to the moon and came back. Ever since the invention of natural language, new types of notational system have been created that have been fundamental to the evolution of the human mind and human culture. I call the limitations imposed by the limited scope of a particular effability space its “effability barrier,” for that is where our cognitive tools fail us and we see things as incomprehensibly complex and/or ineffable. Upon creation of appropriate notational systems, with new distinctions and new metaconcepts, such situations become effable and eventually even banal. Notational Engineering and the Future Although every discipline uses abstract entities, there is currently no discipline whose object of study is the abstract entities of the abstract built environment. Semioticians prefer to study “informal” sign systems, i.e. having semantics but no syntax with which to build statements; for example, political or religious icons. Philosophers focus on language and mathematics to the near exclusion of every other notational system. Mathematicians study “formal” sign systems, i.e. having syntax but no semantics with which to interpret statements. Yet the discovery, exploring, extension, and mapping of effability spaces has been the work of notational pioneers throughout humanity’s 200,000 year history. They have done this without

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any guidelines, for there is no discipline of notational engineering. A productive research program in notational engineering must be:

cross-notational and cross-cultural

longitudinal, i.e. “historically” based

scientific, i.e. seeking explanatory hypotheses, subject to experimental verification

philosophically well-grounded

geared towards better addressing and solving practical problems.

The highest payoff for success in such an undertaking would be that a revolutionary new notational system could more quickly and easily be constructed, tested and utilized. New notational systems will undoubtedly be created anyway, as they historically always have been, in spite of the lack of any disciplined approach to the subject. But why make it harder than it needs to be? The minimum payoff for success in such an undertaking would be improved understanding of these cognitive tools. We need such work now, as our current concepts have been pushed to and in some cases beyond their limits. For example, our notion of money and value must undergo deep revision, as we can no longer afford to only assign value to those things for which there is a marketplace. The greatest risk is to simply continue using the same tools we always have, hoping that they will address our 21st century problems. Maybe they will! But we should remember that we would never have had calculus, or gotten to the moon, using Roman Numerals and an abacus. End Notes and References 1 -- See works by Christopher Alexander, such as A Pattern Language and the 4-volume series The Nature of Order (Center for Environmental Structures) 2 -- UNESCO (2005); Operational Guidelines for the Implementation of the World Heritage Convention. UNESCO World Heritage Centre, Paris. 3 -- In the past I have called these “universals” or “abstract entity types”. 4 -- Dawkins doesn’t define memes this way, although I believe his definition allows this; see Dawkins, R. (1989); The Selfish Gene. Oxford University Press 5 -- The Unicode Consortium (2007); The Unicode Standard, Version 5.0. Unicode, Inc. 6 -- I used to call this its “abstraction space” but that phrase seemed unduly abstract and hard to visualize.

Notational Systems and the Abstract Built Environment

Jeffrey G LongJeffrey G. Longjefflong@aol.comIIAS Conference 7/2008

Environments

• Def: “The aggregate of surrounding things, conditions, orDef: The aggregate of surrounding things, conditions, or influences, esp. as affecting the existence or development of someone or something.” -- Webster’s Encyclopedic Unabridged Dictionary of the English Language (1988)

• built = anything created/designed by humans – buildings– buildings– cities– landscapes– products

• natural = everything else, not created by humans

July 2008 2

There are Two Built Environments

• Physical Built EnvironmentPhysical Built Environment– buildings, cities, landscapes, products

Abstract Built Environment• Abstract Built Environment– all abstract entities created by humans– ranges from fundamental abstractions (i.e. notational

systems) to complex systems of abstractions (e.g. law, science, language…)

July 2008 3

Approximate Major Events in Evolution of ABE

• 1 – First Homo sapiens sapiensp p• 140,000 – Complex language, first use of fire• 192,000 – Accounting tokens, first agriculture• 196,500 – Writing, mathematics, first cities196,500 Writing, mathematics, first cities• 201,000 – Many new notational and higher-level

representational systems

• What’s next?

July 2008 4

Structure of the ABE

• Levels of Analysis/ExpressionLevels of Analysis/Expression• Kinds of Analysis/Expression

Both evolving over time• Both evolving over time– randomly (little or no engineering)– non-monotonically

• Analysis/Expression = Effability

July 2008 5

Levels of Analysis/Representation

• Surface StructureSurface Structure– processes & particulars

• Middle Structure– rules & ruleforms

• Deep Structure – concepts & domains– concepts & domains

• Notational Structure– notational inventions & notational dimensions

July 2008 6

Levels of Analysis/Representation

• Content– notational inventions – concepts– rulesrules– processes

• Constrained by Form– notational dimensionsnotational dimensions– domains– ruleforms– structures– structures

July 2008 7

Kinds of Analysis/Representation

• Existence tokenized by languageExistence, tokenized by language• Quantity, tokenized by arithmetic, algebra • Shape, tokenized by geometry p , y g y• Value, tokenized by money • Instruction, tokenized by music, software, dance • Context, tokenized by cartography • Relation, tokenized by logic

Ch t k i d b ti• Change, tokenized by time • Intent/Will, tokenized by voting• Emotions tokenized by smileys

July 2008 8

• Emotions, tokenized by smileys

Kinds of Analysis/ Expression

P d P ti l

SpeechMathematical

Notation

Other Notations

Logic Notation

Processes and Particulars (Surface Structure)

Rules and Ruleforms(Middle Structure)s/

Exp

ress

ion

Concepts and Domains(Deep Structure)

Notational Inventions &evel

s of

Ana

lysi

tion)Notational Inventions & Dimensions (Notational Structure)Le

Time (Generatio

July 2008 9

Effability Space

• All abstract entities and structuresAll abstract entities and structures– rule systems (beliefs, laws, science, software…)– concepts, taxonomies, dictionaries– notational systems (letters, numbers…)

• Each new notational system expands effability space• Each new notational system expands effability space

• It takes thousands of years to explore and “settle” that space

July 2008 10

Fundamental Hypothesis

• Many problems in government, science, the arts, business, and engineering exist solely because of the way we currently represent them. These kinds of problems present an “effability barrier” thatof problems present an effability barrier that cannot be overcome with existing representational concepts, methods and tools. The only possible solution is the development of new and moresolution is the development of new and more powerful forms of representation.

July 2008 11

Future of the ABE?

R t ti l t h b t d h h dl• Representational systems have been created haphazardly

• Higher-level representational systems are built from notational systems

• Notational systems have been created haphazardlyy p y

• There are patterns to the evolution of representational and notational systemsnotational systems

July 2008 12

Patterns of Representational Revolutions• Place-value rather than relative-value assignment of meaningPlace value rather than relative value assignment of meaning

– e.g. numerals; music; cartography• Changing what is being represented

– e g representing sounds (phonograms) vs ideas directly– e.g. representing sounds (phonograms) vs. ideas directly (ideograms)

• Introduction of a new abstractione g zero musical notes– e.g. zero, musical notes

• Development of higher-order notational systems, e.g. Unicode

July 2008 13

Fragility of ABE

• The meaning of tokens is always initially communicated via aThe meaning of tokens is always initially communicated via a difficult teaching process (“literacy”)

• Any historical gap in continuous literacy means that prior• Any historical gap in continuous literacy means that prior artifacts may become incomprehensible (e.g. Linear A)

The same can occur with the loss of artifacts of the abstract• The same can occur with the loss of artifacts of the abstract built environment (e.g. Library of Alexandria, migration of digital media)

July 2008 14