From: Ian Goddard (Ian@Goddard.net)
Date: Fri Sep 25 1998 - 01:05:21 MDT
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ZEROING IN ON IDENTITY
- Identity Defined -
Identity defines the fundamental nature of every
thing, whether that thing is an objective physical
entity or a subjective mental construct. To under-
stand the nature of things we must first under-
stand the nature of identity.
Exceeding the standard definition of identity as
just "self-similarity," the structure of identity
expresses a duality of (1) self-similarity and (2)
other-difference, since we can say that a thing (a
part of all) is the same as itself if, and only if,
we can say it is different than something else. As
we shall see, these two aspects of identity create
Absolute and Relative identity attributes. This
then is the dual definition of identity:
DEFINITION OF IDENTITY:
(1) ABSOLUTE: zero difference; the uncondi-
tional nature of a thing that is not derived
from external relation; the product of inter-
nal self-similarity. Example: She must be
Mary since she is the same as Mary.
(2) RELATIVE: nonzero difference; the condi-
tional nature of a thing, n, derived from the
difference between n and not(n); the product
of external other-difference. Example: Smith
is best since he scored more than the others.
The identity of a thing is simultaneously (1) and (2).
Example: the difference between 4 and 4 is 0 (4 is the
same as 4) because the difference between 4 and 0 is 4.
So a thing, n, is defined at the same time by both its
similarity to itself and by its difference from not(n);
and thus difference (from zero difference to nonzero
differences) defines the whole structure of identity.
SYNTHETIC IDENTITY ANALYSIS
Numbers are synthetic identities that serve as ideal
subjects for the study of identity. It is because they
are the ideal model of identity structure that numbers
and their relations, while synthetic, are unparalleled
in their ability to model the natural world.
"Treat the laws and relationships
of integers like those of the
celestial bodies." George Cantor
The structure of identity is ideally expressed as a
numeric scale of difference from zero to infinity.
Zero is no difference, or similarity, and all other
numbers to infinity are degrees of difference defin-
ed by their difference, or displacement, from zero.
0____1____2____3...
scale of difference
scale of identities
Each number-identity along the continuum is defined
by its difference from zero (n - 0 = n), which de-
fines the Primary Relative (PR) identity attribute
of an identity. For example, 3 is 3 because 3 is 3
more then 0. A number n also has Secondary Relative
(SR) identity attributes, which express the differ-
ence between n and other numbers that are nonzero.
We can see this in the differentiation matrix below.
PR = Primary Relative identity attribute
SR = Secondary Relative identity attributes
AI = Absolute Identity attribute
Listed in the vertical column below each number on
the top of the matrix below are its identity attri-
butes as derived from relations to the numbers
listed along the left side. The identity attributes
derived from the relation of two numbers are found
at their intersections (fixed-pitch font required):
0 1 2 3
____________
0 | 0 1 2 3 |
| |
1 |-1 0 1 2 |
| |
2 |-2 -1 0 1 |
| |
3 |-3 -2 -1 0 |
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Using number 3 as our example:
Attributes of 3: (3,2,1,0)
by relations to: (0,1,2,3)
PR of 3 is 3 relative to 0
SR of 3 are (2,1) relative to (1,2)
AI of 3 is 0 relative to 3 (self)
Example of SR attribute: 3 is 2 more than 1. "3 is 2
more" is a statement about the identity of 3 relative
to 1, thus "2 more" is a SR identity attribute of 3.
In the same way, "Smith is 2 feet taller" defines a
SR identity attribute (+2ft) that belongs to Mr Smith
relative to Mr Jones. Smith is also 4 feet shorter
(-4ft) than an elephant just as 3 is also 6 less than
9. Therefore, a thing, n, has as many SR attributes
as there are other things n can be related to, yet
n only has one PR attribute, n.
PR = Primary Relative identity attribute
SR = Secondary Relative identity attributes
AI = Absolute Identity attribute
The AI attribute of each number (found at its inter-
section with itself in the differentiation table)
and the AI of all numbers is zero. Therefore
0 = (AI of 1) = (AI of 2) = (AI of 3) = 0.
It is the relative identity attributes derived from
holistic relations that define a thing as a unique
subset of the whole. Self-similarity is Absolute
identity, it is the "home base" of "self," and,
being a null relation, is equal to zero.
The zero of Absolute identity defines the Buddhist
claim about identity, that the inherent (i.e., the
absolute) self-nature of all things is void (i.e.,
is zero), and that what we think of as the thing
is merely a product of conditional relations. So
that central Buddhist teaching is not "mystical."
CONCLUSION
The analysis of synthetic numeric identities here-
in allows us to see and thereby prove: (a) that
identity is conserved, expressed via the real num-
bers as a constant zero-sum, since, for example, n
is always as much more than x as x is less than n;
(b) that identity is therefore symmetrical; (c)
that Relative identity is holistic, since all non-
zero identity attributes are derived from other-
difference; and (d) that the Absolute (nonrelative)
identity of each and every thing equals zero.
===================================================
WHY DIFFERENCE DEFINES IDENTITY ===================
Impressed by the complex we overlook the simple, we
associate simple with that which we must pass beyond
in our quest for the ultimate understanding and truth.
Yet, just as the complex structures of a fractal de-
sign come from an infinite repetition of a relatively
simple primary form, infinite complexity comes from
the primary simplicity of difference, from zero
difference (similarity) to infinity...
The numbers along the real-number line express pro-
gressive displacement, or additional difference, re-
lative to zero, the origin. Each number is its sep-
aration, displacement, or difference, from zero,
thus n is exactly n more than 0. So the essential
nature of an identity is a state of difference.
If there was no difference, there would be no num-
bers, and if there were no numbers, there would be
no mathematics. Before you can build a mathematical
statement, first you need numbers, which are states
of difference. The same principle holds for physical
things, which are also states of difference, such
that no difference implies no things. So the funda-
mental nature of identity and thus of all things is
that of difference, from zero difference to infinity...
Therefore, difference, expressed as subtraction, is
unique among all mathematical operations in that only
difference defines the primary causal structure of
identity. The scale of difference, from zero to
infinity defines the causal structure of identity,
of what it is that makes a thing what it is, and
thus the differentiation table is the template that
defines the foundation identity and existence.
____________________________________________________
--- (c) 1998 Ian Williams Goddard ---
> free to copy nonprofit with author attribution <
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VISIT Ian Williams Goddard --------> http://Ian.Goddard.net
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