[ExI] Meaningless Symbols

[Lee Corbin]

Stathis writes

> A text or code has no life of its own. It's of trivial interest that
> multiple meanings could be attached to it: the important thing is to
> work out the originally intended meaning.

My favorite chapter of Gödel, Escher, Bach is "The Location
of Meaning". Hofstadter points out, essentially, that there
are two kinds of meaning: conventional and isomorphic (I'm
not sure after all these years whether the terminology is
mine or his).

You speak here of conventional meaning---meaning which
operates by convention. Our convention for "z-e-b-r-a"
is the large striped African mammal, though obviously
those letters could be assigned to something else.

Isomorphic meaning, however, is not at all arbitrary.
The depth and jiggles in the grooves of a vinyl playing
record have, in some cases, an objective isomorphism
to the first movement of Beethovan's fifth symphony.
That's their undeniable meaning, no two ways about it.

> With computations, however, the situation may be different.
 > If it is an inputless program the meaning ascribed to it by
 > the original programmer has no magical potency to affect it;
 > any other meaning that could possibly be mapped to it,
 > including a meaning that changes from moment to moment,
 > is just as good.

I believe I disagree here. If the computation is
isomorphic to some other ultimate entity, then that's its
meaning. We need only worry about the fidelity. To use the
often heard rainstorm analogy, an exactly detailed computation
of that rainstorm may not make anyone wet, but if there is
anything to how the rainstorm feels, then we claim that the
program feels the same way.

> This means that any physical activity which could, under some
> mapping, be seen as implementing a computation is implementing that
> computation. Like interpreting a text according to an arbitrary
> encoding this is a trivial observation in general, but it becomes
> interesting when we consider computations that create their own
> observers in virtual environments.

Well, I'll nit-pick the first sentence here: I think it
generally false that "*any* physical activity which could,
under some mapping, be seen as implementing a computation
is implementing that computation". We must not, after all,
put "too much work" into finding such a mapping. For, if
we do, then the Theory of Dust becomes acceptable, and
it no longer matters what you or I do in anything, because
the patterns of all outcomes are already out there between
the stars.

Instead, only mappings that are evident, i.e. prima facie or
manifest, can be accepted.

In fact, going back to Ben's example, a decipherment of Linear A
will only be said to succeed when there is relatively little
"stress" to such a mapping, i.e., the mapping becomes plain
and patently manifest. Anyone who, on the other hand, puts
forth a "decipherment" of Linear A that seems at all forced
will find that no one will have any interest in it. Arbitrary
mappings yield nothing and reveal nothing.

Lee

P.S. I second the motion that a medal should be struck
in your honor, to applaud your perseverance with troublesome
types like Gordon and me though thick or thin, without
showing the slightest exasperation. :)