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

Daniel Fabulich (daniel.fabulich@yale.edu)
Sun, 21 Jun 1998 16:44:37 -0400 (EDT)

On Sat, 20 Jun 1998, Ian Goddard 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.

> Size is 100% relative. There is no absolute
> size, and that's what your case requires.

It certainly does not. I'm saying that A is decreasing relative to B and
that B is decreasing relative to A. There is no "true" length without a
reference frame. However, I am also saying that because both are
decreasing relative to each other (rather than one increaseing and one
decreasing as we would expect), they are also not increasing in size
relative to anything: A remains unchanged to itself and shrinks with
respect to B; B remains unchanged to itself and shrinks with respect to A.
There is not point where A increases relative to B, and THAT'S the truth.

> 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

and zero mechanics would be saved. This is, however, NOT the situation
described above, at all. A is *NOT* growing relative to B, it is
SHRINKING relative to B. That's why we get:

A B
A 0 -C
B -C 0

which is distinctly different from the case in which B actually shrinks
relative to A.

The reason why this matrix is wrong:

A B
A 0 +C
B +C 0

is because it says something that simply isn't true: A does not increase
in size relative to B. You can't use this matrix without claiming that A
increases in size relative to B and that A increases in size relative to
B; this never actually happens. It SHOULD, according to Newtonian
mechanics, but it doesn't.