🚀 go-pugleaf

In article <2206@castle.ed.ac.uk> aipdc@castle.ed.ac.uk (Paul D. Crowley) writes:
>I am a little confused by one part of this letter, which seems to
>suggest that including a randomizing device increases the problem
>solving capacity of a machine. I would have thought that that any
>non-random machine wishing to solve the same problems could explore all
>the paths that a random machine could take.

I think you are correct.  This slipped past me on the first reading, but
now I think I know what's going on, at least partly.

Moravec began the section with the randomizing technique by observing that
the inability of an algorithm to add true unprovable theorems to an
axiomatized theory is due to the finite information content of algorithms.

He explained the significance of the randomizing device in terms of its
potential for adding information to the system which is executing the
algorithm.  In support of your point, according to the Shannon/Weaver
information theory, a channel which always transmits a random signal
carries no information at all, if all "messages" are equiprobable.  Not
to mention that non-deterministic Turing machines are known to be equal
to the deterministic variety, in terms of functions computed if not speed.

I think the situation changes somewhat if the information source is not
random.  The logical procedure described by Moravec corresponds closely
to some accounts of *scientific* reasoning (as opposed to mathematical),
such as Popper's.  So let's suppose Moravec's machine is a hypothesis-
tester, and the signals it gets from the information source are like
scientific observations, perhaps increasingly precise measurements of
fundamental constants.  Then, supposing that the system can make use of
the input, it's information content can increase.  But there are very
serious problems with extending this process to full-scale science.
If a constant coding scheme is used to represent the input measurements,
the system would be unable to participate in major scientific conceptual
changes, such as relativity or QM caused.

Of course, there is always the old reliable (if mundane) technique for
increasing the information content of a system, Data Entry.  All by
itself, this everyday event shows that real computers are different from
abstract automata.