Re: basic questions

From: Hal Finney <hal.domain.name.hidden>
Date: Wed, 28 Jan 1998 14:26:23 -0800

I am still confused about the mapping between TM output and a universe.
A TM produces abstract output, a list of symbols. Do we need to also
specify some kind of mapping between the output and the universe?

Suppose we have a physical universe with some characteristics, and a TM
which is offered as an implementation for the universe. We want to
understand whether the TM actually does implement the universe. Maybe
this is in Wei's model where you input the coordinates of a region and
the TM produces the state of the region, or perhaps the earlier suggestion
that the TM produces a sequence of strings which represent time slices
of the universe.

To actually answer the question, we'd want to create a mapping between the
TM's abstract, symbolic output, and the universe. Maybe we would have one
abstract symbol corresponding to an empty location of the universe, while
other symbols correspond to the presence of certain elementary particles
at each location. Using this mapping, we could test the TM by seeing
whether its output actually corresponded to the state of the universe.

My question is whether this mapping is fundamentally important. It seems
necessary for us to interpret the TM output, but is it an important
ingredient of the TM as a model for the universe?

One issue is that there could be more than one TM which produced output
which mapped to the universe. As a trivial case, one TM could produce
binary output, while another produced the exact same output expressed
in hexadecimal. If we could map one output to a given universe, we
could about as easily map the other one to the same universe.

My real worry, although I haven't come up with a clear example, is
that this mapping might be called upon to do more of the work than
is appropriate. Is there a danger that you could shift some of the
complexity from the TM program into the mapping, leaving it ambiguous
whether a given TM program actually implements a given universe? It's
not clear to me.

Hal
Received on Wed Jan 28 1998 - 15:33:20 PST