September 28, 2001: “The Hunt for New Abstractions: Notational Engineering and Ultra-Structure”. Talk given at the University of Utah.

1. Cover Page
The Hunt for New
Abstractions
Author: Jeffrey G. Long (jefflong@aol.com)
Date: September 28, 2001
Forum: Talk presented at the University of Utah.
Contents
Pages 1‐2: Proposal and Bio
Pages 3‐24: Slides intermixed with text for presentation
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2. Title: The Need for New Abstractions: Notational Engineering and Ultra‐Structure
Author: Jeffrey G. Long
Date: September 28, 2001
Estimated time: 60 minutes (45 for talk, 15 for Q&A
As an introduction, this talk will present the thesis that in order to understand complex systems, and to
adequately respond to many of the other challenges facing our civilization today, we will need to
develop wholly new abstractions and thus wholly new notational systems. Civilizations have
traditionally developed notational systems by accident rather than systematically, so the hunt for new
abstractions could be greatly facilitated by the systematic study of the history and evolution of a variety
of types of notational system, e.g. the branches of mathematics, language and writing, musical notation,
chemical notation, movement and dance notation, and money. In particular this search would be helped
by a good general theory of the structure of notational revolutions, such as the introduction of Hindu‐
Arabic numerals or the infinitesimal calculus. This proposed new subject of "notational engineering"
would have as a primary goal the development and systematic testing of new abstractions in many
areas, including (e.g.) new ways of representing value besides money, and new ways of representing
complex systems besides the current tools of mathematics, computer science and natural language.
The talk will then present a theory of representation called "Ultra‐Structure Theory". This theory sees
entities, structures and relationships as by‐products of complex processes, and postulates that every
process can be represented by a finite but possibly large set of rules. It further hypothesizes that rules
in any format can be converted into an If/Then format, and can be placed into a series of tables based
on the particular form of the rules, i.e. how many "If" columns there are, and how many "Then" columns
there are, and what the columns refer to. These place‐value tables are called "ruleforms", and they
constitute a fundamental new abstraction which offers a practical and formal, yet highly abstract and
concise way of organizing and representing myriad numbers of rules.
Ultra‐Structure Theory aims to represent all world‐knowledge in tables of data rather than in the
software of the system, so that the remaining software is "merely" an inference engine that has very
little subject‐specific knowledge. Ultra‐Structure Theory thus constitutes a merger of expert system and
relational database theories which minimizes the need for software maintenance and maximizes system
flexibility. One prediction resulting from the use of the ruleform abstraction is that all the members of
each broad class of systems (e.g. all corporations, all games, all legal systems, and perhaps all biological
systems) differ from each other in terms of the specific rules governing their behavior, but not in the
form of these rules. In other words, families of systems share the same "deep structure" or collection of

3. ruleforms. Ultra‐Structure Theory should be a serious candidate for a new and general approach to
representing any kind of complex rule‐driven system.
BIO: Mr. Long is a Systems Scientist for the National Security Programs division of DynCorp, a
Washington consulting and services firm. He is currently working with the Department of Energy to
apply Ultra‐Structure Theory to the computer understanding of natural language (English) text for
purposes of classification and declassification. Prior to that he worked at The George Washington
University as a Senior Research Scientist, first as director of the Notational Engineering Laboratory and
then also as Deputy Director of the Declassification Productivity Research Center. He holds a BA degree
in Psychology from the University of California at Berkeley.

4. The Hunt for New
Abstractions: Notational
Engineering and Ultra-
Structure Jeffrey G. Long
September 28, 2001
jefflong@aol.com
j ffl @ l

5. We Have Never Really Studied
Notational Systems per se
All systems can be categorized into four types:
y g yp
 Formal: syntax only, e.g. formal logic, formal
language theory, pure mathematics
 Informal: semantics only, e.g. art, advertising,
politics, religious symbols
 Notational: both syntax and semantics, e g
semantics e.g.
natural language, musical notation, money,
cartography
 Subsymbolic: neither syntax nor semantics, e.g.
natural systems
September 28, 2001 Copyright 2001 Jeff Long 2

6. We may have competence in using certain kinds of
y p g
complex systems but we still don’t understand them
 climate and weather
 economics, finance, markets
, ,
 medicine, physiology, biology, ecology
This is not because of the nature of the systems but
systems,
rather because our notational systems – our
abstractions -- are inadequate
Complexity is not a property of systems; rather,
perplexity is a property of the observer
September 28, 2001 Copyright 2001 Jeff Long 3

7. These problems cannot be solved by working harder,
harder
using faster computers, or moving to OO techniques
Many if not most problems today are fundamentally
representational in character
Using the wrong, or too-limited, a notational system is
inescapably self-defeating
p y g
September 28, 2001 Copyright 2001 Jeff Long 4

8. Each primary notational system maps a different
“abstraction space”
 Abstraction spaces are incommensurable
 Perceiving these is a unique human ability
Abstraction spaces are discoveries, not inventions
 Abstraction spaces are real
Acquiring literacy in a notation is learning how to see
a new abstraction space
September 28, 2001 Copyright 2001 Jeff Long 5

9. So Far We Have Settled Maybe
y
12 Major Abstraction Spaces
September 28, 2001 Copyright 2001 Jeff Long 6

10. All higher forms of thinking require the use of one or
g g q
more notational systems
The notational systems we habitually use influence
the manner in which we perceive our environment:
our picture of the universe shifts as we acquire
literacy in new notational systems
Notational systems have been central to the
evolution of the modern mind and modern civilization
September 28, 2001 Copyright 2001 Jeff Long 7

11. Every notational system has limitations: a
y y
“complexity barrier”
The problems we face now as a civilization are, in
many cases, notational
We need a more systematic way to develop and
settle abstraction spaces: notational engineering
September 28, 2001 Copyright 2001 Jeff Long 8

12. Current Analysis Methods Work
Only Under Certain Conditions
September 28, 2001 Copyright 2001 Jeff Long 9

13. Rules are a Broader Way of
Describing Things
Multi-notational: can include all other notational
systems
Explicitly
E li itl contingent
ti t
Describe both behavior and mechanism
Thousands or millions can be assembled and acted
upon by computer
September 28, 2001 Copyright 2001 Jeff Long 10

14. And Complex Rules Can be Stored as
Data in a Relational Database
Ultra-Structure Theory is a general theory of systems
representation, developed/tested starting 1985
Focuses on optimal computer representation of
F ti l t t ti f
complex, conditional and changing rules
Based on a new abstraction called ruleforms
The breakthrough was to find the unchanging
features of changing systems
September 28, 2001 Copyright 2001 Jeff Long 11

15. The Theory Offers a Different Way to
Look
L k at Complex S
C l Systems and Pd Processes
observable
behaviors surface structure
generates
rules middle structure
constrains
form of rules
f f l deep structure
September 28, 2001 Copyright 2001 Jeff Long 12

16. Hypothesis: Any Type of Statement Can
yp y yp
Be Reformulated into an If-Then Rule
Natural language statements
Musical scores
Logical arguments
Business processes
Architectural drawings
Mathematical statements
September 28, 2001 Copyright 2001 Jeff Long 13

17. Rules Can be Represented in
Place-Value (Tabular) Form
Place value assigns meaning based on content and
location
 In Hindu-Arabic numerals, this is column position
 In ruleforms, this is column position
ruleforms
Thousands of rules can fit in same ruleform
There are multiple basic ruleforms, not just one
 But the total number is still small (<100?)
September 28, 2001 Copyright 2001 Jeff Long 14

18. Structured and Ultra-Structured
Data are Different
Structured data separates algorithms and data, and is
good for data processing and information retrieval
tasks,e.g. reports, queries, data entry
Ultra-Structured data has only rules, formatted in a
manner that allows a small software engine to
reason with them using standard deductive logic
“Animation” ft
“A i ti ” software h littl or no knowledge of
has little k l d f
the external world
September 28, 2001 Copyright 2001 Jeff Long 15

19. This Creates New Levels for Analysis
y
and Representation
Standard Terminology (if any) Ultra-Structure Instance Ultra-Structure Level U-S Implementation
Name Name
behavior, physical entities particular(s) surface structure system behavior
and relationships, processes
rules, laws, constraints, rule(s) middle structure data and some
guidelines, rules of thumb software (animation
procedures)
(no standard or common ruleform(s) deep structure tables
term)
(no standard or common universal(s) sub-structure attributes, fields
term)
tokens, signs or symbols token(s) notational structure character set
September 28, 2001 Copyright 2001 Jeff Long 16

20. The Ruleform Hypothesis
Complex system structures are created by not-
necessarily complex processes; and these
il l d th
processes are created by the animation of
operating rules. Operating rules can be grouped
into a small number of classes whose form is
i ll b f l h f i
prescribed by "ruleforms". While the operating
rules of a system change over time, the ruleforms
remain constant. A well-designed collection of
i ll d i d ll i f
ruleforms can anticipate all logically possible
operating rules that might apply to the system,
and constitutes the deep structure of the system.
d h d f h
September 28, 2001 Copyright 2001 Jeff Long 17

21. The CoRE Hypothesis
We can create “Competency Rule Engines”, or
CoREs,
C RE consisting of <50 ruleforms, th t are
i ti f 50 l f that
sufficient to represent all rules found among systems
sharing broad family resemblances, e.g. all
corporations. Their definitive d
ti Th i d fi iti deep structure will b
t t ill be
permanent, unchanging, and robust for all members
of the family, whose differences in manifest
structures and b h i
d behaviors will b represented entirely
ill be d i l
as differences in operating rules. The animation
procedures for each engine will be relatively simple
compared to current applications, requiring less than
100,000 lines of code in a third generation language.
September 28, 2001 Copyright 2001 Jeff Long 18

22. The Deep Structure of a System
p y
Specifies its Ontology
What is common among all systems of type X?
What is the fundamental nature of type X systems?
What are the primary processes and entities involved
in type X systems?
What makes systems of type X different from
systems of type Y?
If we can answer these questions about a system,
then we have achieved real understanding
September 28, 2001 Copyright 2001 Jeff Long 19

23. Suggestion 1
To advance our mental capabilities as a species, and
to address the problems we currently face as a
civilization,
civilization we must systematically and comparatively
study notational systems to create wholly new
abstractions and thereby revolutionary new
notational systems.
s stems
This is the goal of notational engineering.
engineering
September 28, 2001 Copyright 2001 Jeff Long 20

24. Suggestion 2
One example of a new abstraction is ruleforms To
ruleforms.
truly understand complex systems, we must get
beyond appearances (surface structure) and rules
(middle structure) to the ruleforms (deep structure)
and beyond.
This is the goal of Ultra-Structure Theory.
September 28, 2001 Copyright 2001 Jeff Long 21

25. References
Long, J., and Denning, D., “Ultra-Structure: A design theory for
complex systems and processes.” In C
l d ” Communications of the
i i f h
ACM (January 1995)
Long, J., “Representing emergence with rules: The limits of
addition.
addition ” In Lasker, G E. and Farre G L (editors) Advances
Lasker G. E Farre, G. L. (editors),
in Synergetics, Volume I: Systems Research on Emergence.
(1996)
Long, J., “A new notation for representing business and other
g, , p g
rules.” In Long, J. (guest editor), Semiotica Special Issue:
Notational Engineering, Volume 125-1/3 (1999)
Long, J., “How could the notation be the limitation?” In Long, J.
(guest editor), S i ti S
( t dit ) Semiotica Special Issue: Notational Engineering,
i lI N t ti lE i i
Volume 125-1/3 (1999)
September 28, 2001 Copyright 2001 Jeff Long 22