From: hughes@ah.com (Eric Hughes)
Date: Tue, 26 Jul 94 10:05:00 PDT
To: cypherpunks@toad.com
Subject: GUT and P=NP
In-Reply-To: <9407261520.AA11661@vendela.ma.utexas.edu>
Message-ID: <9407261643.AA05818@ah.com>
MIME-Version: 1.0
Content-Type: text/plain


   Okay.  So I should be so rude.  People please.  When someone, especially
   like berzerk or tcmay makes a strongly definitive statement, PLEASE try
   not to show your ignorance to the whole group.

Famous last words?

   Cantor demonstrated, near the turn of the century, that no such system
   can represent all reals in [0,1].  Boring technical explanation follows.

I think you've completely missed the point.  The proposed
computational device had as its symbol alphabet an uncountable set.
It's a perfectly good mathematical abstraction.  It's doesn't matter
that it can't be implemented.

And let's not call such a machine a Turing machine, OK?  Turing goes
on at great length in his original paper about how the symbols can't
be too similar to each other.

And to answer the point of another writer, this machine may have only
finitely many states, but the state transition table, being the
cartesian product of the states and the symbols, is also uncountable.
In fact, I would suspect that such a machine only needs a single
state; an interesting bit of research, to be sure.

Eric