the hunt for new abstractions

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Uploaded June 27, 2011

The Hunt for New

Abstractions

Author: Jeffrey G. Long ([email protected])

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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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

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.

The Hunt for NewThe Hunt for New Abstractions: Notational Engineering and Ultra-StructureStructure Jeffrey G. Long

September 28, 2001j ffl @ [email protected]

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 Notational: both syntax and 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

We may have competence in using certain kinds of y p gcomplex 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 butThis is not because of the nature of the systems, but rather because our notational systems – our abstractions -- are inadequate

Complexity is not a property of systems; rather, perplexity is a property of the observer


These problems cannot be solved by working harderThese problems cannot be solved by working 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-defeatingp y g


Each primary notational system maps a different “abstraction space” Abstraction spaces are incommensurable Perceiving these is a unique human ability 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 seeAcquiring literacy in a notation is learning how to see a new abstraction space


So Far We Have Settled Maybey12 Major Abstraction Spaces


All higher forms of thinking require the use of one or g g qmore 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 acquireour 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


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


Current Analysis Methods Work Only Under Certain Conditions


Rules are a Broader Way of Describing Things

Multi-notational: can include all other notational systems

E li itl ti tExplicitly contingent

Describe both behavior and mechanismDescribe both behavior and mechanism

Thousands or millions can be assembled and acted upon by computer


And Complex Rules Can be Stored asAnd 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

F ti l t t ti fFocuses 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


The Theory Offers a Different Way to L k C l S d PLook at Complex Systems and Processes

observablebehaviors surface structure

generatesrules

f f l

middle structure

constrainsform of rules deep structure


Hypothesis: Any Type of Statement Can

Natural language statements

yp y ypBe Reformulated into an If-Then Rule

Musical scoresLogical argumentsBusiness processes Architectural drawingsMathematical statementsMathematical statements


Rules Can be Represented in

Place value assigns meaning based on content and

Place-Value (Tabular) Form

location In Hindu-Arabic numerals, this is column position In ruleforms this is column position In ruleforms, this is column position

Thousands of rules can fit in same ruleformThere are multiple basic ruleforms, not just one But the total number is still small (<100?)


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

“A i ti ” ft h littl k l d f“Animation” software has little or no knowledge of the external world


This Creates New Levels for Analysis yand Representation

Standard Terminology (if any) Ultra-Structure Instance Ultra-Structure Level U-S ImplementationStandard Terminology (if any) Ultra-Structure Instance Name

Ultra-Structure Level Name

U-S Implementation

behavior, physical entities and relationships, processes

particular(s) surface structure system behavior

rules, laws, constraints, guidelines, rules of thumb

rule(s) middle structure data and some software (animation procedures)

(no standard or common term)

ruleform(s) deep structure tables

(no standard or common universal(s) sub-structure attributes, fieldsterm)

tokens, signs or symbols token(s) notational structure character set


The Ruleform HypothesisComplex system structures are created by not-

il l d thnecessarily complex processes; and these processes are created by the animation of operating rules. Operating rules can be grouped i ll b f l h f iinto a small number of classes whose form is prescribed by "ruleforms". While the operating rules of a system change over time, the ruleforms

i ll d i d ll i fremain constant. A well-designed collection of ruleforms can anticipate all logically possible operating rules that might apply to the system,

d h d f hand constitutes the deep structure of the system.


The CoRE HypothesisWe can create “Competency Rule Engines”, or C RE i ti f 50 l f th tCoREs, consisting of <50 ruleforms, that are sufficient to represent all rules found among systems sharing broad family resemblances, e.g. all

ti Th i d fi iti d t t ill bcorporations. Their definitive deep structure will be permanent, unchanging, and robust for all members of the family, whose differences in manifest

d b h i ill b d i lstructures and behaviors will be represented entirely 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.


The Deep Structure of a System p ySpecifies 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?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,If we can answer these questions about a system, then we have achieved real understanding


Suggestion 1

To advance our mental capabilities as a species, and to address the problems we currently face as a civilization we must systematically and comparativelycivilization, we must systematically and comparatively study notational systems to create wholly new abstractions and thereby revolutionary new notational s stemsnotational systems.

This is the goal of notational engineeringThis is the goal of notational engineering.


Suggestion 2

One example of a new abstraction is ruleforms ToOne example of a new abstraction is ruleforms. To 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.


ReferencesLong, J., and Denning, D., “Ultra-Structure: A design theory for

l d ” C i i f hcomplex systems and processes.” In Communications of the ACM (January 1995)Long, J., “Representing emergence with rules: The limits of addition ” In Lasker G E and Farre G L (editors) Advancesaddition. In Lasker, G. E. and Farre, G. L. (editors), Advances in Synergetics, Volume I: Systems Research on Emergence. (1996)Long, J., “A new notation for representing business and other g, , p grules.” 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. ( t dit ) S i ti S i l I N t ti l E i i(guest editor), Semiotica Special Issue: Notational Engineering, Volume 125-1/3 (1999)
