# Re: All-Zero-Sum Counter... Not!

Ian Goddard (igoddard@netkonnect.net)
Mon, 22 Jun 1998 14:56:29 -0400

Daniel Fabulich (daniel.fabulich@yale.edu) wrote:

>> IAN: A reduction (-) of B in size by 1
>> unit relative to A (0) is expressed as
>> -1. -1 is LESS than 0, 0 is 1 more (+)
>> then -1, so in fact A has gotten larger!
>
>Relative to what? Not A or B.

IAN: If the only other thing is B,
A increased in size relative to B
in the fashion described above. The
simple fact that B appears to be
smaller than A means that A appears
to be larger than B to observer A.

Has A gotten larger than B? The only
way for A to know is look at B. If B
is smaller, then A has gotten larger.

The fact that both observers witness
the same thing does not break this
symmetry of relational structure.
Both observers see themselves
as larger than the other:

A B (how I appeared)
A 0 +
B + 0

and both observed the other as smaller:

B A (how the other appeared)
B 0 -
A - 0

and the sum of all valid measurements equals 0.
Nice try Dan, but time to find another counter,
I've already toppled this one three times now.

>There is not point where A increases relative to B, and THAT'S the truth.

IAN: Sorry, but that's just false and
I've already proved that it's false.

If the size of A = 1 and the size of A
= the size of B, but then B decreases
in size to .5, it is a fact that 1 is
LARGER than .5, and thus A has gotten
larger relative to B because B got
smaller relative to A. Simple.

Because B was also size 1, it could
be stated now that A = 1.5, for no
point of size-reference is absolute.

>> That the second matrix is valid is clearly
>> proven by the fact that -1 is less than
>> 0 and 0 is 1 more than -1. If we have 2
>> things in the universe, A and B, and B
>> gets smaller, it's equally true that A
>> gets larger, because size is relative.
>
>No, you don't understand. You're thinking in terms of Newtonian physics
>and not in the inherently non-intuitive terms of special relativity.
>Normally, when something gets smaller, something else gets larger relative
>to it; special relativity sys that when B appears smaller to A, A appears
>SMALLER to B, not larger. This is why it doesn't sum to 0: If B were
>actually shrinking, it would look like this:
>
>A B
>A 0 -C
>B +C 0

IAN: There is no absolute size, you cannot have
"got smaller" free from "got larger." Observer
A will measure the situation and see that there
are two sides of the relative change: he himself
got larger than B because B got smaller than A.

Your case represents the fallacy of atomism,
that we can have S (smaller) free from not-S.

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