# All-Zero-Sum Counter

Ian Goddard (igoddard@netkonnect.net)
Fri, 19 Jun 1998 02:46:34 -0400

At 08:14 PM 6/18/98 -0400, Daniel Fabulich wrote:

>> So the examples of the relations of relations
>> cited have not identified any variety of free
>> identity, and as such we always have 100% holism.
>
>As I have constantly asserted, we OUGHT to get 100% holism: it's the same
>theory with different definitions. In this case, I don't see that there's
>any way that you could argue that I CANNOT define identity to refer only
>to the A-0 partial difference. It's just a definition, after all: I can
>define unicorns if I so wish. Within that context, identity is the
>partial difference if you adopt the (my?) atomism set of definitions
>and it is the net difference if you adopt the (your?) holism set of
>definitions.
>
>However, a thought occurred to me today which just might sink zero
>mechanics as a theory. (Gasp!) As we both agree, zero mechanics is
>completely compatible with Newtonian mechanics; indeed, this may be zero
>mechanics's downfall.
>
>Consider objects A and B, which comprise the entire universe. Imagine for
>a moment that when they were at rest they measured each other's lengths
>and found that both had the same length. So their identity chart for
>length would look like:
>
> A B
>A 0 0
>B 0 0
>
>There is 0 difference between A's length and A's length; nor is there any
>difference between A's length and B's length. The chart sums to zero.
>So far, so good.
>
>Now let us suppose that they change their speed relative to each other to
>something quite large; 0.6c. The velocity of A->B is 0.6c, B->A is -0.6c.
>A->A = B->B = 0. Sum them all, you get zero. Again, so far, so good.
>
>But let's go back to observing their lengths again. According to special
>relativity, A and B would EACH observe each other's lengths to have
>contracted, while their own lengths remained the same (again, relative to
>each). To be precise, A observes B's length to be 80% of what it
>once was; B observes A's length to have contracted in the same way. Let's
>call the magnitude of this change C. Now let's look at our identity
>chart:
>
> A B
>A 0 -C
>B -C 0

IAN: Motion measures will sum to 0 due to
the inclusion of direction in the measurement
of relative velocities such that we will get
a 25 mph and a -25 mph. In your matrix, the
relation is size, but only one of two dir-
ections in size is indicated (smaller, or -),
and the zero sum (of all valid measurements)
is thus found in two symmetrical matrices...

>This chart sums to -2C, violating a principle of zero mechanics, and
>ruining net identity's whole day.
>
>Of course, so long as we take on an (my) atomistic definition, we're fine.
>There is no principle of zero mechanics inherent in atomism, so we avoid
>this problem entirely. Interesting, no?

IAN: Both -C (each individual measure of
foreshortened length) and -2C (their sum)
are derived by relation to 0 (the 0 point
of measure, being the observer's ship) and

0 - (-2) = +2
-2 - 0 = -2

the net difference between -2 and 0 is zero;
and thus the inverse matrix is equally true:

A B
A 0 -
B - 0

A B
A + 0
B 0 +

Because size is relative, A appears to in-
crease in size when measuring B. As A looks
at B, observer A could equally assume he had
increased in size just as the observer in one
train looking at another train next to him out
the window seeing motion and may assume either
his train or the other is in motion, and either
assumption is equally correct. Observer B also
assumes he may have increased in size. So net
difference is found in the sum of the matrices.
One size-matrix doesn't contain all difference.

larger (+) <---0---> (-) smaller

Dan, it's a great counter(!) worthy of further
investigation, but it can only be sustained if
it can be shown that size is not relative and
thus that one matrix is more valid, but even
that "more vs less" valid is another 0 sum.

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