🚀 go-pugleaf

In article <182@zds-ux.UUCP> gerry@zds-ux.UUCP (Gerry Gleason) writes:
>In article <d9qn02B687oD01@amdahl.uts.amdahl.com> kp@amdahl.uts.amdahl.com (Ken Presting) writes:
>> [...]  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.
>
>If you are suggesting that limitations on the senses (input devices) would
>keep an intellegence from making paradigm shifts, then you must be willing
>to suggest that the same limitation exists for us.  In this era, we have
>many tools for making measurements, and presenting the information in a
>form our senses can digest; much of this information in inaccessable to
>out senses.  An intellegent machine would have to have access to the same
>instraments if you expect it to perform in the type of scientific domains
>in your example.

Well, I wouldn't want to imply that a computerized hypothesis-tester is
necessarily incapable of making paradigm shifts.  Actually, I do believe
that it is possible.  But Moravec's algorithm for mathematical progress
is statable using a constant notation for all theorems.  That is just fine
for mathematics, where no assertion need ever be discarded (assuming it
has been proved).  But in a paradigm shift, familiar measurements get
re-interpreted, and end up as descriptions of quite different phenomena,
in a new notation system with new semantics.  So a machine which is a lot
smarter than Moravec proposes would be needed to do revolutionary science.

I might add that I think the whole issue of advancing mathematics by adding
true unprovable assertions is completely bogus.  Every case I know of
which involves an independence theorem (a proof that some assertion is
unprovable on a given set of axioms) ends up generating at least two
distinct theories, each of which has some interest in its own right.

Take non-euclidean geometry.  A lot of people were upset that the parallel
postulate was unprovable, but negating it is just as interesting as
accepting it!  The continuum hypothesis is similar, although non-Cantorian
set theory has not yet turned out to be as useful as non-euclidean
geometry.

It surprised me that Penrose thought that the ability to see the truth
of Goedel sentences shows something important about people.  Given that
the incompletenes theorem is proven, I can't imagine any mathematical
fact *less* interesting than a Goedel sentence.  The incompleteness
theorem has the information.  The Goedel sentence adds nothing.

In mathematics, the proofs are at least as important as the theorems, if
not more so.