Jeffrey G. Long's document explores the challenges of understanding complex systems, arguing that perceived complexity is often due to inadequate notational systems rather than the systems themselves. He introduces concepts like 'notational engineering' and 'ultra-structure' to propose new ways to represent and analyze complex rules governing system behavior. The paper emphasizes the importance of developing new abstractions to improve our understanding of complex phenomena across various fields.

1. Cover Page
Why We Don’t
Understand Complex
Systems
Author: Jeffrey G. Long (jefflong@aol.com)
Date: May 21, 2000
Forum: Poster session presented at the International Conference on Complex
Systems, sponsored by the New England Complex Systems Institute.
Contents
Page 1: Abstract
Pages 2‐22: Slides (but no text) for presentation
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Uploaded June 27, 2011

2. Abstract Title: Why We Don’t Understand Complex Systems
Author: Jeffrey G. Long
Physics has sought to understand physical systems that once were considered baffling in their
behavior, and by the discovery of new abstractions – initially the creation of a new descriptive
language, the infinitesimal calculus – was able to help provide theoretical explanations that have
led to one revolution after another in the past 300 years. But as is usually the case, prior to the
development of any real understanding of (say) thermodynamics, humanity was able to
successfully harness the power of steam to launch the industrial revolution. This is characteristic
of the successes we have had with many complex systems: humanity’s successes in dealing with
these systems, great as they have been in some cases, have occurred more by trial and error
exploration than by the application of any fundamental organizing principles. Extending this
classic model of progress to other kinds of complex system, this paper presents two fundamental
theses.
The first principal thesis is that complexity is in the eye of the beholder, and is a euphemism for
perplexity. Seeming complexity can be dissolved with appropriate new ways of looking at
complex phenomena, leading to the corollary that in order to understand complex systems, we
will need to develop wholly new abstractions. Humanity has typically come across these 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 systems
(not just mathematics). I call this proposed subject “notational engineering”. I believe we need
new abstractions in many areas, including (e.g.) new ways of representing value besides money,
and new ways of representing large systems of complex rules besides the current tools of
mathematics, logic and natural language.
The second principal thesis of this talk is that seemingly-complex systems differ from simpler,
more understandable systems only in having more rules governing their behavior. In traditional
science, scientists look at the complex behavior of a system and try to develop a few simple rules
that account for that behavior. With seemingly-complex systems, there will be many rules that
must be defined. I call the complex behavior of a system its “surface structure”, and the
thousands of rules that govern it “middle structure”. These rules in turn can be grouped by their
form, and these the “deep structure” of the system. Families of systems share the same deep
structure. This process-oriented metaphysics permits a very practical, highly abstract and formal
way of organizing and representing rules. I call this approach “Ultra-Structure”, and have applied
it to a number of types of systems. It permits the creation of “spreadsheets” (called “Competency
Rule Engines) for families of systems, where one needs only to enter the rules of a system as
data into the spreadsheet to make the system accurately model the behavior of a complex
system. I think this may be a serious candidate for a new general approach to representing any
kind of complex, or seemingly-complex, system.

3. Why We Don’t Understand
Complex S t
C l Systems
Jeffrey G. Long
ICCS Conference, May 2000
jefflong@aol.com

4. Complexity is a
Euphemism for Perplexity
We may have competence in using complex systems
but we still don’t “understand” complex systems
This is not because of the nature of the systems, but
rather because our notational systems – our
abstractions -- are inadequate
These problems cannot be solved by working harder
or using faster computers

5. Complexity is not a property of systems; rather, perplexity
is a property of the observer
Many if not most problems today are fundamentally
representational in character
We don’t go sailing in automobiles; we shouldn’t (e.g.)
g g ; ( g)
use mathematics for complex conditional rules
Using the wrong, or too-limited, a notational system is
inescapably self-defeating

6. We Have Never Really Studied
Notational Systems
There are four kinds of sign system:
Formal: syntax only, e.g. formal logic and language, pure
mathematics
Informal: semantics only, e.g. art, advertising, politics,
religious symbols
Notational: have both syntax and semantics, e.g. natural
semantics e g
language, musical notation, money, cartography
Subsymbolic: neither syntax nor semantics, e.g. natural
systems
Of these, notational systems are probably the least-explored

7. 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

8. All higher forms of thinking are dependent upon the
use of one or more notational systems
The notational systems one habitually uses influences
the manner in which one perceives his environment:
the picture of the universe shifts from notation to
notation
Notational systems have been central to the
evolution of civilization

9. 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

10. So Far We Have Settled Maybe
12 Major Abstraction Spaces

11. Current Analysis Methods Work
Only Under Certain Conditions

12. Even Mathematics Has Limitations
Offers conciseness of description, and rigor
But
B t equations represent b h i
ti t behavior, not mechanism
t h i
Shorthand obscures mechanism (e.g. multiplication,
exponentiation to show repeated addition)
Deals only with entities capable of being the subject
of theorems, i.e. entities that behave additively,
without emergent properties
h

13. Rules are a Broader Way of
Describing Things
Multi-notational, including (e.g.) qualities as well as
q
quantities
Explicitly contingent
Describe both behavior and mechanism
Thousands or millions can be assembled and acted
upon by computer
Shed light on ontology or basic nature of systems

14. Ultra-Structure Theory Was Created
to Represent Systems in Terms of
Complex and Changing Rules
New theory of systems design, developed 1985
Focuses on optimal computer representation of
complex, conditional and changing rules
Based on a new abstraction called ruleforms
The breakthrough was to find the unchanging
features of changing systems

15. The Theory Offers a Different Way to
Look at Complex Syste s and Processes
oo Co p e Systems a d ocesses
observable
behaviors surface structure
generates
rules middle structure
constrains
form of rules
f f l deep structure

16. Any Type of Statement Can Be
f
Reformulated into an If-Then Rule Format
Natural language statements
Musical scores
Logical arguments
Business processes
B i
Architectural drawings
Mathematical statements

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
Thousands of rules can fit in same ruleform
There are multiple basic ruleforms, not just one
But the t t l
B t th total number i still small (<100?)
b is till ll ( 100?)

18. This Creates New Levels for Analysis
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

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

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

21. The Deep Structure of a System
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 understanding

22. Conclusion
To truly understand complex systems,
we must get beyond appearances
g y pp
(surface structure) and rules (middle
structure) to the ruleforms (deep
) ( p
structure).

23. R f
References
Long, J., and Denning, D., “Ultra-Structure: A design theory for
complex systems and processes.” In Communications of the
processes
ACM (January 1995)
Long, J., “Representing emergence with rules: The limits of
addition.
addition ” In Lasker, G E. and Farre G L (eds) Advances in
Lasker G. E Farre, G. L. (eds),
Synergetics, Volume I: Systems Research on Emergence. (1996)
Long, J., “A new notation for representing business and other
rules ” In Long, J. (guest editor) Semiotica Special Issue:
rules. Long J editor),
Notational Engineering, Volume 125-1/3 (1999)
Long, J., “How could the notation be the limitation?” In Long, J.
(guest editor) Semiotica Special Issue: Notational Engineering
editor), Engineering,
Volume 125-1/3 (1999)