Cover Page The Evolution of Abstractions Author: Jeffrey G. Long (firstname.lastname@example.org) Date: September 11, 1997 Forum: Talk presented at a luncheon meeting of the Washington Evolutionary Systems Society. Contents Page 1: Proposal Pages 2‐22: 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 http://creativecommons.org/licenses/by‐nc/3.0/ or send a letter to Creative Commons, 444 Castro Street, Suite 900, Mountain View, California, 94041, USA. Uploaded June 22, 2011
Title: The Evolution of AbstractionsSpeaker: Jeff Long, Director, GWU Notational Engineering LaboratoryDate: September 11, 1997 at NoonLocation: Faculty Club, The George Washington University (call ahead forlunch reservations please!)What is it that gives notational systems their power? Are they merelyconvenient collections of arbitrary tokens and rules that just happen tohave a useful application in the real world? Or might there be a deeperconnection between notational systems and reality?This talk will explore this question, and answer in the affirmative. Wewill discuss the conventional definitions of "abstraction" and theirinadequacies, and seek a new definition. To do this we will sketch atheoretical framework -- a metaphysical system that attempts to accountfor the the law-abiding nature of physical objects, the nature of laws,and, ultimately, the nature of abstractions.The talk will discuss the notion of an "abstraction space" such as thefield of numbers, and how three such spaces historically have beenexplored and tokenized ("settled"). The talk will end with a briefoutline of a plan for improving the abstraction space settlement process.This plan is essentially an agenda for the proposed new field of"notational engineering".
My Work in Notational Engineering y g g Involves Four Main Areas
What Does An Analytical Tool That Works Say (If Anything) About Ontology? NotationalOntology Systems Any connection?
Sections of this Talk S ti f thi T lk1. The hi i l process of exploring abstractions h historical f l i b i2. An alternative metaphysical system3.3 A general strategy for improving the correlation process
Part OneThe Historical Process of Exploring Abstractions
There A M Th Are Many Definitions of ‘Abstractions’ D fi iti f ‘Ab t ti ’ Anything not concrete or physically perceivable (love, hi h i ll i bl (l nations) Ideal/perfect forms in the noumenal world (perfect justice, justice perfect sphere) Ideas or classifications formed by mental separation from particulars (rules, sets) Entities lacking causal powers (universals, numbers, ideas) Referents of words that are not proper nouns (dogs, cats) (dogsThese have not been very useful distinctions – they conflate things that must be distinguished
AT Taxonomy of Ab t ti f Abstractions Tokens & Operators Expressions composed of tokens, generated by operators Expressions referred to by other expressions Entities, classes & ideas named by expressions Expressions further delimited by their position in statements Variables acting as position-holders within statements Ruleforms composed of ordered sets of variables Particular laws/rules are the resolution of ruleforms
Exploring N Ab t ti S E l i a New Abstraction Space Is Very Diffi lt I V Difficult Requires exploring and mapping into useful tokens and i l i d i i f l k d syntax By definition entity was never before imagined definition, (discoverer seems nuts) There is no predefined language available for the concepts involved Users require training and practice to “see” the entities (literacy)
Settling “Q tit S S ttli “Quantity Space” Required Centuries ”R i dC t i Tallies: 30,000 BP lli Accounting tokens: 8,000 BC Whole numbers: 1,900 BC 1 900 Rational numbers: 500 BC Zero and real numbers: 200 Complex (imaginary) numbers: 1545 Transfinite numbers: c. 1900
Settling “F S ttli “Form Space” Required Centuries S ”R i dC t i Euclidean geometry: c. 325 BC lid Non-Euclidean (hyperbolic, elliptic) geometries: c. 1850 Fractal geometry: c. 1975 c
Settling “Id tit S S ttli “Identity Space” Required Centuries ”R i dC t i Speech: 100,000 BP? h Pictograms: 3,400 BC Ideograms: 2,200 BC 2 200 – Syllabic writing: 3,000 BC – Consonantal alphabet: 1,500 BC – Full alphabet: c. 776 BC Stroke: 1969
But W HB t We Have Done It Informally Many Times D I f ll M Ti
Part TwoAn Alternative Metaphysical System for Exploring the Basic Issues
The P Th Prevailing (Materialist) Paradigm ili (M t i li t) P di Universe consists solely of matter/energy (physicalism) This substance follows certain laws, sought by science The universe is becoming more uniform over time (2nd Law) These laws and all such abstractions are useful fictions (nominalism) ( i li ) Metaphysical questions are pseudo-questions (positivism)But this paradigm leaves unanswered many questions viewed as non-scientific – why is the universe lawful? – what are laws/rules, really? Do they have component parts?
An Alternative (Ultra-Structural) Paradigm A Alt ti (Ult St t l) P di The material world doesn’t follow laws, it is l h i l ld d f ll l i laws – We perceive and define entities according to the laws they happen to follow A natural law is an ordered set of noumenal abstractions – e.g. identity & group & form, form&quantity & state ‘L ‘Laws’ are the name we give to the interaction of ’ th i t th i t ti f noumenal abstractions Interaction of rules produces processes which generate p p g “events” – what we perceive to be the material world – eventually these include mental abstractions t ll th i l d t l b t ti Noumenal abstractions become more complex over time – they operate on themselves and evolve
Examples of Noumenal Abstractions E l fN l Ab t ti Possible Identity ibl d i Possible Group Possible Relation Possible Form Possible Quantity Possible State
This I li C t i F t Thi Implies Certain Features of Noumenal Abstractions fN l Ab t ti Each i a fundamentally different type of entity h is f d ll diff f i – Each has unique types of possible relations with other noumenal abstractions – One cannot be fully translated into another They are self-referential Th are combinable or able to have interactions They bi bl bl t h i t ti We can perceive them only by mind – Similar to how we learn to perceive physical objects They exist independently of any mind
Part Three h A General Strategy forImproving the Correlation Process
Study R l ti St d Revolutionary Notational Systems N t ti l S t Discovery of new noumenal abstractions i f l b i – quantities, sets, infinitessimals, value, form, relation Progressive exploration of noumenal abstractions – imaginary numbers, fractal geometry, fuzzy sets Improved praxis with better tokens, media and teaching – Leibniz versus Newton’s tokenization, printing versus hand- lettering, writing versus oral tradition
Develop Complete List of p p Current and Potential Noumenal Abstractions Identify all current notational systems (20+) d if ll i l ( ) Determine uniqueness, i.e. inter-translatability (6+) Is there any pattern, a la Mendeleev? (probably not!) pattern Are there practical and/or logical limitations for each noumenal abstraction?
Improve Communication Among p g Notational Researchers Define scope, nature, basic concepts of subject fi b i f bj Identify sources of information/participants – people (maybe 1% of each group using a NS) – books, articles, Web sites (esp. foreign language) Establish clearinghouse – Internet discussions (notation listserver) – conferences (NOTATE’97 at SSA) – publications p
Conclusion C l i Alternative paradigm can be tested by its utility l i di b db i ili – an effective mental abstraction says something about noumenal abstractions Broaden the “linguistic turn” to be a “notational turn” – metaphysics is important after all – limitations are not just those of language, but all NS language – language is not the only tool or reference point We can speed up the process of settling abstractions – make it more of a regular discipline than an ad hoc event