At 03:21 PM 2/10/2003 -0500, Stephen Paul King wrote:

Thank you to all of you for your ideas.Dear Jean-Michel and Hal,All good humor aside, Hal makes a good point! The conditions that would exist as one approaches the event horizon seem to be such that any signal would be randomized such that the end result would be that Nature prevents infinite information (or conclusions requiring infinite computational power) from reaching any finite part of itself. Interestingly this seems to be the same situation as what forms an event horizon (around a space-time singularity) in the first place. Could it be that this is an active example of the so-called anthropic principle? It also reminds me of a solution to the Quantum Suicide problem! Kindest regards, Stephen

Let us say that my suggestion was merely provocative.

It seems to be that hypercomputers are logically possible, but

that it is still speculative whether they are physically possible

or not.

This is Toby Ord's view in http://arxiv.org/pdf/math.LO/0209332.

I find his survey very good.

In particular, it contains a reference to "Does General relativity

Allow an Observer to View an Eternity in a Finite Time ?" by Mark L. Hogarth,

and to "Non-Turing computations via Malament-Hogarth space-times",

by Etesi and Németi, http://www.math-inst.hu/pub/algebraic-logic/turing.ps,

which will be of interest to many, and especially to Jesse Mazer, as it discusses

his question.

All the best.

Jean-Michel

----- Original Message ----- From: "Hal Finney" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> Sent: Monday, February 10, 2003 12:19 PM > Jean-Michel Veuillen writes: > > There are other possibilities to obtain hypercomputers or Infinite Time > > Turing Machines: > > > > For instance, from general relativity: put a computer in orbit around a > > black hole, > > start an infinite computation on it, arrange that the results are sent to > > you by radio, > > and jump into the black hole: > > when you reach the horizon, you get the result of the infinite computation > > (and witness the end of the rest of the universe). > > > > For a survey: arxiv.org/pdf/math.LO/0209332 > > ...and burn to death as infinite amounts of radiation fall on you in a > finite time? > > Maybe the universe is like a character from a spy novel: it could tell > us what it knows (solving the halting problem, etc.), but then it has > to kill us. > > Hal F. > >