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Notational systems and the abstract built environment


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July 25, 2008: "Notational Systems and the Abstract Built Environment". Presented at …

July 25, 2008: "Notational Systems and the Abstract Built Environment". Presented at
InterSymp 2008 Conference, sponsored by the International Institute for Advanced Studies in Systems Research and Cybernetics (IIAS). Paper published in conference proceedings.

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  • 1. Cover Page   Notation Systems and  the Abstract Built  Environment Author: Jeffrey G. Long ( 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 Contents Pages 1‐5: Preprint of Article Pages 6‐19: 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 22, 2011 
  • 2. Notational Systems and the Abstract Built Environment Jeffrey G. Long jefflong@aol.comAbstractThe “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 builtenvironment has design patterns we should learn from1. I suggest that there is an even morefundamental “Abstract Built Environment” which may be contrasted with this “physical builtenvironment,” 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 newmetaconcepts 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 bywhich we can build complex statements by linking multiple concepts into statements (what I callrules).Rules and rule systems are thus built on top of notational systems, and allow even more complexstatements to be made. Examples of rule systems are legal systems, which are generally basedon language as a notational system; scientific hypotheses, which are based on mathematical andother notational systems; software systems, which use programming languages as theirfundamental notations; and economic/financial systems, which are based on the notationalsystem 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 thelast 10,000 years, has created human culture as we know it. Systematic study of thisenvironment will facilitate improving our fundamental cognitive toolset to face tomorrow’smany challenges.Key Words: Concepts; Built Environment; Notational Engineering; Memes; Representation;The Abstract Built EnvironmentThe built environment includes the physical environment that humans have created, rangingfrom clothing to houses to cities to landscapes, and is contrasted with the natural environmentprovided by nature. The World Heritage Committee has noted that these are not distinct, butphase into one another as “Cultural Landscapes.”2 But there is a major piece of culture that ismissing from this paradigm, namely the various abstract entity types that constitute our abstractbuilt environment. Abstract entity types include all concepts, rules, and beliefs, and are madepossible by the various known notational systems. This environment has its own ecology andpatterns, and has evolution and natural selection in the form of memes. Having developed theabstract built environment especially over the past 10,000 years, we can learn a lot from it. 1
  • 3. Notational Systems and MetaconceptsNotational systems are fundamental to the abstract built environment for two reasons: (1) theyintroduce not just new concepts, but whole new classes of concepts (metaconcepts3), and (2) theyprovide a means to tokenize these abstract concepts so they may become a part of our physicalbuilt environment, and we can then manipulate, store, and work with them just as we can workwith any other similar physical materials.As an example of a metaconcept, natural languages provide a mechanism to declare the existenceof both individual entities and classes of entities. It is like an existential operator in logic, butwith the mere existence of a word or phrase implying existence (in some world, not necessarilyour physical world). Exactly how a particular natural language parses the flux of experiencedepends on its history and the history of its users. The particular individual concepts madepossible by a metaconcept – the particular trees, flowers and dogs it distinguishes – are importantbut secondary.Another example of a metaconcept is the notion of quantity. This presumes the existence ofcountable entities (i.e. individuals), and provides a way to distinguish magnitudes bothabsolutely and relatively. It and the operations of addition and subtraction are the fundamentalmetaconcepts provided by arithmetic. The particular concepts derived from this, as tokenized bya particular numeration system, are again important but secondary. Roman Numerals was a deadend notationally because it was unable to represent types of number that we now take for grantedbeyond integers, such as imaginary numbers, transfinite numbers, and the place-holder zero(except that this latter was represented on an abacus).Concepts and MemesConcepts are particular applications of metaconcepts. For example, the fact that Englishdistinguishes green and blue colors, and some other languages don’t, is simply a quirk of howEnglish treats colors. Other languages make other distinctions that its users believe areimportant to them. All are still performing their principal function of declaring existence, eventhough what is thereby said to exist may differ.All the quarter-million words of English (excluding proper names) are concepts created bymaking various distinctions so as to isolate some aspect of experience and give it a name. Allthe numbers of mathematics are examples of concepts created by making various distinctionsand tokenizing them with numerals. All the musical notes and concepts of musical notation arederived 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 asmemeplexes4. These are passed from person to person through culture, sometimes directly byimitation (as Dawkins proposes) but also though the creation and subsequent interpretation ofphysical tokens.Being able to grasp and use any particular concept requires that one first become “literate” in theunderlying notational system. This does not mean becoming a master of it, but simply learninghow to “see” those kinds of concepts and learn how they can interact together, just as we learn to 2
  • 4. “see” objects as such and learn how they can act and interact. Acquiring literacy is hard, becauseconcepts are never visible to the senses. We come to believe that they are “real” only after wedirectly experience their usefulness. We are born with none of this knowledge, merely an innatecapability to learn to see, that is then more or less developed in various individuals.Tokens and MediaThe 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 fundamentalproperties of tokens are determined by the medium they are inscribed upon. New media, andconsequently 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 paperhelped in obvious ways, as did the new production mechanism of the printing press. Theprinting press also helped to start the standardization of letter shapes and of spellings, and madeliteracy 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. Forexample, Unicode now provides unique global encodings of 99,024 different characters in alllanguages, plus punctuation marks, mathematical symbols, technical symbols, etc. 5 It also addsnew features, such as a distinction between the “-“ used as a hyphen and the same token used asa minus sign, that are known only by context in normal writing: it acknowledges that they weretruly never the same token, even though they may look the same. Digital media allows forhyperlinks, text searches, and multimedia presentations whose functions were previouslyaccomplished manually only with great effort.Statements and RulesA notational system by itself makes no statements about the world beyond the existence of itstokens; it merely provides a toolset by which concepts can be formulated and statements can becreated. Using this feature we can build large and complex systems of statements, such as legalsystems (based largely on the notational system of language); scientific journal articles (basedlargely on language but also using mathematics and other notational systems such as FeynmanQED 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 ofthe notational systems they are built upon, (2) they are becoming more complex as the culturesthey support become more complex; (3) we depend upon them to always work essentiallycorrectly; 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 quitechangeable, (3) they establish active systems by which the firing of one rule unleashes a cascadeof other, subsequent rules, and I believe such inherently active abstract entities deserve a namethat implies this kind of power. 3
  • 5. Effability Spaces and the Abstract Built EnvironmentThe tokens and metaconcepts of a notational system allow us to build ordinary concepts, and wecan combine these into rules and rule systems. This provides a great deal of expressive power. Icall the set of all ideas that can in theory be expressed using a particular notational system itseffability 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 theenvironment.An effability space is not useful simply for communication. I suggest we should broaden theSapir-Whorf hypothesis of linguistic relativity beyond language (where it has been foundwanting) 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, andcommunicate about ideas and parts of the world that we can’t at present imagine. Certainly aperson from a thousand years ago would be surprised at our credit card economy, amazed to heara 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 createdthat have been fundamental to the evolution of the human mind and human culture. I call thelimitations 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 complexand/or ineffable. Upon creation of appropriate notational systems, with new distinctions andnew metaconcepts, such situations become effable and eventually even banal.Notational Engineering and the FutureAlthough every discipline uses abstract entities, there is currently no discipline whose object ofstudy 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; forexample, political or religious icons. Philosophers focus on language and mathematics to thenear 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 ofnotational pioneers throughout humanity’s 200,000 year history. They have done this without 4
  • 6. any guidelines, for there is no discipline of notational engineering. A productive researchprogram 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 newnotational system could more quickly and easily be constructed, tested and utilized. Newnotational systems will undoubtedly be created anyway, as they historically always have been, inspite of the lack of any disciplined approach to the subject. But why make it harder than it needsto be? The minimum payoff for success in such an undertaking would be improvedunderstanding of these cognitive tools.We need such work now, as our current concepts have been pushed to and in some cases beyondtheir limits. For example, our notion of money and value must undergo deep revision, as we canno longer afford to only assign value to those things for which there is a marketplace. Thegreatest risk is to simply continue using the same tools we always have, hoping that they willaddress our 21st century problems. Maybe they will! But we should remember that we wouldnever have had calculus, or gotten to the moon, using Roman Numerals and an abacus.End Notes and References1 -- 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. UNESCOWorld 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 Press5 -- 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. 5
  • 7. Notational Systems and theAbstract Built EnvironmentJeffrey G Long G.jefflong@aol.comIIAS Conference 7/2008
  • 8. Environments • Def: “The aggregate of surrounding things, conditions, or The 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 – cities – landscapes – products • natural = everything else, not created by humansJuly 2008 2
  • 9. There are Two Built Environments • Physical Built Environment – buildings, cities, landscapes, products • 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
  • 10. Approximate Major Events in Evolution of ABE • 1 – First Homo sapiens sapiens p p • 140,000 – Complex language, first use of fire • 192,000 – Accounting tokens, first agriculture • 196,500 – Writing, mathematics, first cities • 201,000 – Many new notational and higher-level representational systems • What’s next?July 2008 4
  • 11. Structure of the ABE • Levels of Analysis/Expression • Kinds of Analysis/Expression • Both evolving over time – randomly (little or no engineering) – non-monotonically • Analysis/Expression = EffabilityJuly 2008 5
  • 12. Levels of Analysis/Representation • Surface Structure – processes & particulars • Middle Structure – rules & ruleforms • Deep Structure – concepts & domains • Notational Structure – notational inventions & notational dimensionsJuly 2008 6
  • 13. Levels of Analysis/Representation • Content – notational inventions – concepts – rules – processes • Constrained by Form – notational dimensions – domains – ruleforms – structuresJuly 2008 7
  • 14. Kinds of Analysis/Representation • Existence, Existence tokenized by language • Quantity, tokenized by arithmetic, algebra • Shape, tokenized by geometry p , yg y • Value, tokenized by money • Instruction, tokenized by music, software, dance • Context, tokenized by cartography • Relation, tokenized by logic • Change, t k i d b ti Ch tokenized by time • Intent/Will, tokenized by voting • Emotions, Emotions tokenized by smileysJuly 2008 8
  • 15. Kinds of Analysis/ Expression l ca ion s h ati m n tat ati on c t ee the tio No No Sp Ma Nota g ic her Lo Ot Processes and P ti l P d Particulars evels of Analysis/Expression (Surface Structure) Rules and Ruleforms (Middle Structure) Concepts and Domains (Deep Structure) n ) Notational Inventions & tio Le Dimensions (Notational Structure) era en e (G TimJuly 2008 9
  • 16. Effability Space • All abstract entities and structures – rule systems (beliefs, laws, science, software…) – concepts, taxonomies, dictionaries – notational systems (letters, numbers…) • Each new notational system expands effability space • It takes thousands of years to explore and “settle” that spaceJuly 2008 10
  • 17. 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” that effability barrier cannot be overcome with existing representational concepts, methods and tools. The only possible solution is the development of new and more powerful forms of representation.July 2008 11
  • 18. Future of the ABE? • Representational systems h R t ti l t have b been created h h t d haphazardly dl • Higher-level representational systems are built from notational systems • Notational systems have been created haphazardly y p y • There are patterns to the evolution of representational and notational systemsJuly 2008 12
  • 19. Patterns of Representational Revolutions • Place value Place-value rather than relative-value assignment of meaning relative value – e.g. numerals; music; cartography • Changing what is being represented – e g representing sounds (phonograms) vs. ideas directly e.g. vs (ideograms) • Introduction of a new abstraction – e g zero musical notes e.g. zero, • Development of higher-order notational systems, e.g. UnicodeJuly 2008 13
  • 20. Fragility of ABE • The meaning of tokens is always initially communicated via a difficult teaching process (“literacy”) • 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 built environment (e.g. Library of Alexandria, migration of digital media)July 2008 14