February 24, 1996: "A Metaphysical System That Includes Numbers, Rules, and Bricks: The Evolution of Evolution." Presented at the Fourth Interdisciplinary Conference on General Evolutionary Systems, sponsored by the Washington Evolutionary Systems Society.

1. Cover Page
A Metaphysical System
that Includes Numbers,
Rules and Bricks
Authors: Jeffrey G. Long (jefflong@aol.com)
Date: February 24, 1996
Forum: Talk presented at the 4th Interdisciplinary Conference on Evolutionary
Systems, sponsored by the Washington Evolutionary Systems Society.
Contents
Page 1: Proposal
Pages 2‐14: Slides intermixed with text for presentation
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Uploaded June 22, 2011

2. Title: A Metaphysical System That Includes Numbers, Rules and Bricks
Speaker: Jeff Long, Director, Notational Engineering Laboratory, George Washington University
Address: CMEE Department, Phillips 703A, Washington, DC 20052
Contact: (202) 547-0268 or jefflong@aol.com
As a necessary tool in exploring the nature and referents of notational systems, I've postulated a pluralistic
metaphysical system that differs significantly from dualism and monism but tries to achieve the same
kinds of goals. Such a system must account for the brute facts of everyday appearances but must also
address (among other things) the question of the nature and role of fundamental abstractions such as are
studied in mathematics, and the nature and role of scientific and other laws.
The resulting system is process-oriented and has three distinct levels of form and content, each generated
from the one below it by a slow evolutionary process. I will present the notion that (not to lose
perspective on my subject!) the ontological dimensions represented by notational systems (level 1) are the
basis of and hence more fundamental than the rules they generate (level 2) or the physical reality
generated by the execution of rules (level 3). Such a metaphysical model may help in understanding the
nature and power of notational systems. It may also help in the search for new abstractions with which to
develop both powerful new explanatory theories and better communications tools.

3.
A Metaphysical System That Includes
Numbers, Rules and Bricks
The Evolution of Evolution
Jeffrey G. Long
voice: (202) 547‐0268
e‐mail: JeffLong@gnn.com
letter: 133‐1/2 11th Street, S.E., Washington, DC 20003

4. Jeffrey G. Long [2//24/1996]
A Metaphsical System that Includes Numbers, Rules, and Bricks
Slide 1: Cover Page
I appreciate this chance to share some ideas with you.
Ever since Darwin introduced his theory of the origins of species 137 years ago, evolutionary theory has
been applied to a wide range of areas. Not only do species evolve, but so do cultures, ideas, and
galaxies. Even matter can be said to evolve through a process of nucleosynthesis and then chemical
interactions.
This talk will be about the evolution of evolution, i.e., how evolution itself may have developed. The
framework will be an ontology composed of three levels of form and content, yielding six different levels
and types of reality. We already talk about three of these when we talk about numbers, rules, and
bricks. I would like to introduce three structural constrains on these, whose existence I think can also be
fairly readily acknowledged. The question is not whether these entities exist, so much as in what SENSE
do they exist.
I needn't tell you that I'm neither a physicist nor a philosopher, but I will anyway. That doesn't excuse
me from any gross errors of fact, however, and I will greatly appreciate any critique you may care to
offer of these nascent ideas. Please contact me as shown on the slide.
Page 3 of 14

5. Jeffrey G. Long [2//24/1996]
A Metaphsical System that Includes Numbers, Rules, and Bricks
Foundations is One Important Area of Notational Engineering
Slide 2: Foundations is Only One Area of Notational Engineering
I want to emphasize that I see this theorizing as integral to my study of notational engineering.
This slide shows several of the major areas of notational engineering, including the evolutionary history
of notational systems, the factors that make a notational system successful, and the areas where
notational systems today are successful or not very successful.
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6. Jeffrey G. Long [2//24/1996]
A Metaphsical System that Includes Numbers, Rules, and Bricks
The area here that I've highlighted is the FOUNDATIONS of notation, i.e. the theory of what notational
systems really ARE. In looking at the nature of notational systems, we are faced with the basic questions
that have been raised in the foundations of mathematics: do the tokens of these systems refer to anything
real (called realism)? Or are they convenient and arbitrary shorthand expressions of ideas that could just
as well be expressed (if desired) in words (called formalism)? For the moment we can ignore the third
main school in mathematics that says that mathematics can be reduced to logic (called logicism), for that
just defers this question to a different notational system, namely LOGIC, in which case we must explore
the foundations of logic.
But before we go on, I want to emphasize that I am not forsaking the other areas of notational engineering
for speculative philosophy. While the users of tools need not understand them except in terms of their
functions, it would be a serious mistake for the student of tools per se to not understand where they come
from and, more importantly, where they get their strength.
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7. Jeffrey G. Long [2//24/1996]
A Metaphsical System that Includes Numbers, Rules, and Bricks
To Understand One Level, It Helps To Understand a Higher Level
Slide 3: Goal: Numbers, Rules and Bricks
Notational tools such as language, writing, number, money, time, and logic are the most powerful tools
ever created by humans, and they affect how we see the world and how we live more than any other tools.
The same is true of rules, which I think many would say exist whether we are aware of them or not. As
such I think we need a metaphysical system that somehow deals equitably with numbers, rules, and
bricks.
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8. Jeffrey G. Long [2//24/1996]
A Metaphsical System that Includes Numbers, Rules, and Bricks
The Standard Ontological Pyramid
Slide 4: The Standard Ontological Pyramid
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9. Jeffrey G. Long [2//24/1996]
A Metaphsical System that Includes Numbers, Rules, and Bricks
I think there has emerged, in the scientific and philosophical community of the last 100 years, a rough
consensus on the nature of reality. This MATERIALIST view is sketched here....
"From all this it seems to follow that events, not particles, must be the 'stuff' of physics. What has
been thought of as a particle will have to be thought of as a series of events. The series of events
that replaces a partice has certain important physical properties, and therefore demands our
attention; but it has no more substantiality than any other series of events that we might arbitrarily
single out. Thus 'matter' is not part of the ultimate material of the world, but merely a convenient
way of collecting events into bundles.
"Quantum theory reinforces this conclusion, but its chief philosophical importance is that it regards
physical phenomena as possibly discontinuous. It suggests that, in an atom (interpreted as above), a
certain state of affairs persists for a certain time, and then suddenly is replaced by a finitely different
state of affairs. Continuity of motion, which had always been assumed, appears to have been a
mere prejudice. The philosophy appropriate to quantum theory, however, has not been adequately
developed. I suspect that it will demand even more radical departures from the traditional doctrine
of space and time than those demanded by the theory of relativity."
‐‐ Bertrand Russell, A History of Western Philosophy, pp. 832‐3. Copyright 1945, 1972.
There are Challenges from Many Directions, Including Physics
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10. Jeffrey G. Long [2//24/1996]
A Metaphsical System that Includes Numbers, Rules, and Bricks
Goal: Account for Numbers, Rules and Bricks!
Slides 5‐6: There Are Many Challenges
But there are many problems with this metaphysical system.
Page 9 of 14

11. Jeffrey G. Long [2//24/1996]
A Metaphsical System that Includes Numbers, Rules, and Bricks
(1) It does not account for the problems physicists have been having with the reality of matter. Shown
here is an extensive quote from Bertrand Russell on this issue.
(2) It does not account for the problems physicists and philosophers have been having with understanding
the nature of physical laws.
(3) It treats notational systems as real in some sense, but merely as emergent properties of mind. But if
notational systems are merely convenient and arbitrary shorthand expressions of ideas that could just as
well be expressed (if desired) in words, then we should be able to inter-translate concepts expressed in
any notational system into language and/or into any other notational system. Thus, we could express a
symphony in mathematical terms, or a mathematical equation in words, or a visual image in geometric
terms. It does not take many attempts at this to realize that different notational systems deal with
different TYPES OF IDEAS and at best can only be CRUDELY substituted for each other.
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12. Jeffrey G. Long [2//24/1996]
A Metaphsical System that Includes Numbers, Rules, and Bricks
Three Levels of Form and Content
Slide 6: Three Levels of Form and Content
But if the tokens of notational systems do refer to something real, we must ask what they could possibly
refer to. Certainly there is not a physical "3" somewhere, nor a "C-sharp". Nor is there an ideal "3"
somewhere, any more than there is an ideal "table" somewhere.
Notational systems do NOT refer to what we see in the world around us. Instead, each notational system
is a crude attempt to map the features and properties of what I call an ONTOLOGICAL DIMENSION.
Examples of different ontological dimensions include entityhood, quantity, relation, and value.
And for each of the distinctions that can be made within each ontological dimension, a fully-developed
notational system will propose a different TOKEN. Thus in Western music we postulate an ontological
dimension of about seven 12-tone scales, each so-called "note" having a unique token.
Form
But each ontological dimension can interact with other ontological dimensions. Thus in music there is
also the notion of SEQUENCE whereby a note is played at a certain time in relation to other notes. There
is also VOLUME, and many other distinctions. Each distinction may involve a different ontological
dimension.
When these are combined in a single unit we have an instance of UNIVERSAL: the OPPORTUNITY for
a combination to exist, whether or not any particular thing in the real world makes use of it.
Level B: "Ruleforms" as form, "Rules" as content
Content
The tokens of a notational system can be combined to form "rules": all rules are combinations of the
tokens of notational systems, and all tokens of notational systems in a well-formed formula constitute a
rule or part of a rule.
Form
All rules, I will assert without explanation, can be phrased or rephrased in If/Then terms. And all rules are
expressed in terms of place-value, for the sake of compactness and clarity, where (for example) a "3" in a
certain location does not just mean the number three, but (say) 3 dollars or 3 kilograms. This allows 2 or
more ontological dimensions to be compactly represented.
Level C: "Patterns" as form, "Particulars" as content
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13. Jeffrey G. Long [2//24/1996]
A Metaphsical System that Includes Numbers, Rules, and Bricks
Content
When rules are executed they can generate very complex behavior, including more rules and also
including events. The events are strictly a by-product of the execution of rules.
We may think of these events as a blanket that has been tossed on top of several children playing. We
can't see the children but we believe they are there; we do see the blanket moving and think that in some
sense its behavior is a consequence of the behavior of the children. In reality, all we can ever see is the
blanket, and the children are what I call the ANIMATION of RULES.
Form
The events that occur -- the movement of the blanket -- may seem to have patterns, depending on the
point of view and observational capabilities of an observer. These PATTERNS may have meaning, for
example some patterns we call matter, other patterns we call energy, life, mind, etc..
THUS we have three levels of form and content. I call these:
FORM: a SEMIOTIC structure comprised of PATTERNS
CONTENT: a SURFACE structure comprised of EVENTS
CONTENT: a MIDDLE structure comprised of RULES
FORM: a DEEP structure comprised of the form of rules, RULEFORMS
FORM: a SUB structure comprised of UNIVERSALS
CONTENT: a NOTATIONAL structure composed of TOKENS
As an example, let's use this with CELLULAR AUTOMATA....
In this model, we can see that the LOWER structures of the world are DETERMINISTIC, while the
HIGHER structures are PROBABILISTIC and may often even look like FREE WILL. We can create a
probabilistic, quantum surface structure from deterministic lower structures.
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14. Jeffrey G. Long [2//24/1996]
A Metaphsical System that Includes Numbers, Rules, and Bricks
The Evolution of Form and Content
Slide 7: The Evolution of Form and Content
These each have had their own evolutionary history, evolving from the lower levels to the higher levels.
As in biological evolution we see simple life forms evolve into more complex life-forms, here reality
itself becomes more complex over time! There is an evolution of evolution, whereby the laws of
biological evolution themselves can emerge only after a foundation has been laid for the existence of
ANY laws.
I think we are ALL hoping for a simple ultimate ontology composed of one substance, whether mind
(IDEALISM) or matter (MATERIALISM). But the world seems to have MULTIPLE levels of reality
whose entities are each fundamentally different and not inter-translatable, although they are highly inter-
connected. Like the ancient Greeks, we tend to think our place in this hierarchy -- surface structure --
constitutes the center of the universe. But it doesn't; it is merely one of 6 levels.
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15. Jeffrey G. Long [2//24/1996]
A Metaphsical System that Includes Numbers, Rules, and Bricks
Like the ancient Greeks, who believed that the universe had to be composed of perfect spheres, and that
these could not be blemished (as by, for example, sun spots), I think we will have to settle for a messier
description of a complex universe.
Page 14 of 14