The document discusses the abstract built environment, which includes all abstract concepts, rules, and beliefs made possible by notational systems. Notational systems introduce new metaconcepts and provide a means to represent abstract concepts physically. Concepts derived from metaconcepts can be combined into rule systems through various notational systems, expanding the effability space of what can be expressed. The abstract built environment has grown over human history with the development of new notational systems and will continue to evolve. The document calls for the discipline of notational engineering to systematically study and develop new notational systems.

1. Cover Page
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
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
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Uploaded June 22, 2011

2. 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.
1

3. 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
2

4. “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.
3

5. 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
4

6. 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.
5

7. Notational Systems and the
Abstract Built Environment
Jeffrey G Long
G.
jefflong@aol.com
IIAS 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 humans
July 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 = Effability
July 2008 5

12. Levels of Analysis/Representation
• Surface Structure
– processes & particulars
• Middle Structure
– rules & ruleforms
• Deep Structure
– concepts & domains
• Notational Structure
– notational inventions & notational dimensions
July 2008 6

13. Levels of Analysis/Representation
• Content
– notational inventions
– concepts
– rules
– processes
• Constrained by Form
– notational dimensions
– domains
– ruleforms
– structures
July 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 smileys
July 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
Tim
July 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 space
July 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 systems
July 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. Unicode
July 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