Re: Information content of the brain

From: Gilles HENRI <Gilles.Henri.domain.name.hidden>
Date: Wed, 24 Mar 1999 14:26:22 +0100

>I want to make a brief comment about what Gilles Henri
>said to Hal Finney some days ago:
>
>>I think that nobody answered me satisfactorily on the problem of
>>"interpreting" or recognizing" a string. I could compare this problem to
>>gauge invariance in physics. It's well known that all physical theories
>>admit many equivalent representations or gauge transformations. However, to
>>represent "physically" something, they must contain quantities invariant
>>upon these transformations, that allow to recognize intrinsic features :
>>e.g. proper interval in general relativity, curvature of space-time and
>>more generally the action in any known theory.
>>You seem to admit as obvious that a computation or a string can represent,
>>or better *be* a physical state of the Universe. However when you think of
>>a real way to connect them, it seems obvious that you have to precize a way
>>of doing that. If you want to describe the positions of all atoms, or the
>>values of a field, you have to precise the coding of real numbers and so
>>on. When Bruno says that the UD will solve Wheeler-DeWitt equation, it
>>assumes some coding that allows to recognize the solution in a string. I
>>may be wrong, but I don't see how you can definie intrinsic physical
>>quantities (like the curvature of the space time for example) independantly
>>on these representations (same problem with the "matching pattern" of Hal).
>>It means also that the same string can represent (under different coding
>>schemes) different, and even quite different Universes. So it cannot posses
>>intrinsically all physical properties, and for example the presence of
>>living beings. Maybe I am wrong and you know works proving the contrary?
>
>You must take into account the fact that the "interpreter" is itself
>encoded in the string.
GH:

If you mean that a string has a unique "interpreter" encoded in itself, I
like to know where it is and how to find it!

The problem I ask is the following: we know that our Universe is such that
there are apparent external, objectively measurable quantities. If you
think you have an ontological theory, or maybe a heuristic theory deeper
than what we use currently to describe it (QM and GR), the least you can
expect is to be able to give unambiguous, objective rule to reproduce the
current theory in some limiting cases. For example even if classical
mechanics is unappropriate at some level, you still have precise
prescriptions to give sense to the mass of a particle from quantum field
theories, or to newtonian gravitational forces from general relativity in
"classical approximations".

Examining the idea that a state of the Universe could "be" a string, I just
ask how to extract "classical" quantities from a string, given the infinite
number of ways of interpreting it. If you think that there is an
interpreter, or a set of interpreters in this string, this would actually
answer this question. The prescription would be: "find the interpreter in
the string by this way, and interpret the rest of the string with this
interpreter". But I have no idea of how finding *intrinsically* an
interpreter in a string!

BM:
If you do that, you will be able to use a lot of existing invariance
results from theoretical computer science for ascribing RELATIVE
representational content to computationnal states. These "contents" depend
on the existence of a representation for the interpreter and the data, but
are invariant with respect to the choice of a representation.

GH:

I suspect all invariance results are relative to the computability or the
complexity of the string. I don't think it is enough to give numerical or
structural (e.g. topological) informations.
You could assume that a string could describe an organized world if there
exists a representation through which you can calculate from it physical
quantities actually describing this organized world (am I clear?). The
problem is taht if you do not restrict the complexity of the
representation, any (complex enough) string can represent anything. For
example, given any "regular" string with 10^400 bits, you could pick up the
bits in some convenient order to reproduce the 3D universe at the time I am
writing, or at the time you are reading, or at any other time (or any other
universe with any dimensionality..)

So I think you have to restrict yourself to "simple enough"
representations, (that means interpreters much simpler than the string
itself) for example representations implying the existence of physical
laws. In this case, lambs will never eat wolves. But then it is not
different from assuming "ontologically" physical laws and think of their
numerical implementation.

To summarize I have the feeling that if you want a string to describe
something, you have to put restrictions on the way you choose the
representation ; a string can represent an organized world only if there is
a "simple" representation through which you can derive a "simple" world
from it. But this is probably equivalent to say that the world must be
simple enough (i.e. be described by physical laws), which is a strong
restriction on the "everything" hypothesis (this is *not* anthropic
principle!).

Gilles
Received on Wed Mar 24 1999 - 05:30:21 PST