----- Original Message -----
From: "Bruno Marchal" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Tuesday, January 20, 2004 5:55 AM
Subject: Re: Is the universe computable
> Dear Stephen,
> At 13:19 19/01/04 -0500, Stephen Paul King wrote:
> >Dear Hal, and Friends,
> > Were and when is the consideration of the "physical resources"
> >for the computation going to obtain? Is my question equivalent to the old
> >"first cause" question?
> This is a good question for a physicalist. But if you accept the idea that
> the very notion of time, energy, space are secondary and "logically
> as a modality in the average memory of an average universal machine, then
> that question is solved (once we get the right measure of course).
I do not accept that the "very notion of time, energy, space are
secondary" nor do I elevate "logicality" above physicality; I take them as
having the same ontological status, this follows from the proposed dualism
of Pratt that we have discussed previously. While we can argue coherently
that all of the content of experience is that which is simulated by our
"universal machine", we still must give some accounting for these. This is
why I asked the question.
> Now, about the measure, I am not convinced by Hal Finney's attempt
> to define or compute it for reason we have already discussed a lot,
> and which has just been recalled by George Levy in his last post.
Could it be that the sought after measure is only a meaningful notion
when given from "within" a world? For example, when we consider the "White
Rabbit" problem we are taking as a base line our mutal non-experience of
White Rabbits and other "Harry Potter-ish" phenomena. This argues along a
similar line as what we find in Tipler et al's "Anthropic principle", a way
of thinking going back to Descartes: What I experience here and now must be
given a probability of 1 since I can not question that it is being
The skeptic would say: "But what if it is just an illusion or the
machinations of an "evil demon"?" (See the Bennaceraf, Lucas, Searle, etc.
debate...) In reply I would say: "Even if it is just an illusion, simulation
or whatever, the fact that it is experienced and not some thing else demands
that it be taken as probability one when we start considering "possible
worlds" and other modal ideas. You have to start somewhere and the most
obvious place is right where one is stating.
> I could add this: if you take the Universal Dovetailer (UD), you must take
> account the fact that he generates all version of all programs an infinite
> number of times. For computer science reasons it is not possible to cut
> the vast redundancy of the codes in the production of the UD.
> Now, this does not mean that some other reasons could not be invoked
> for justifying the importance of "little" programs, though.
UD, UTM, QComp or whatever, all of these depend existentially on some
kind of "physical resource", be it some portion of Platonia, infinite tape
and read/write head, Hilbert space or whatever; you can not even define your
precious AR without representing it somehow. It is this necessity of
representation that you seem to dismiss so easily.
Again: When will a consideration of "physical resources" obtain?
> >----- Original Message -----
> >From: "Hal Finney" <[EMAIL PROTECTED]>
> >To: <[EMAIL PROTECTED]>
> >Sent: Monday, January 19, 2004 12:23 PM
> >Subject: RE: Is the universe computable
> > > Kory Heath wrote:
> > > > At 1/18/04, Hal Finney wrote:
> > > > >Now consider all possible program tapes being run at the same time,
> > > > >perhaps on an infinite ensemble of (virtual? abstract?) machines.
> > > > >Of those, a fraction of 1 in 2^100 of those tapes will start with
> > > > >100 bit sequence for the program in question.
> > > > [snip]
> > > > >Now consider another program that is larger, 120 bits. By the same
> > > > >reasoning, 1 in 2^120 of all possible program tapes will start with
> > > > >particular 120-bit sequence. And so 1/2^120 of all the executions
> > > > >be of that program.
> > > >
> > > > Yes, but if we're really talking about all possible finite bit
> > > > then the number of bit strings that begin with that 100 bit program
> > > > exactly the same as the number that begin with the 120 bit program -
> > > > countably infinite. You can put them into a 1 to 1 correspondence
> > > > other, just like you can put the integers into a 1 to 1
> > > > the squares. The intuition that there must be more integers than
> > > > simply incorrect, as Galileo pointed out long ago. So shouldn't your
> > > > programs have the exact same measure?
> > >
> > > Well, I'm not a mathematician either, so I can't say for sure.
> > > And actually it's worth than this, because I spoke of infinite program
> > > tapes, so the number of programs is uncountably infinite.
> > >
> > > However, here is an alternate formulation of my argument which seems
> > > be roughly equivalent and which avoids this objection: create a random
> > > program tape by flipping a coin for each bit. Now the probability
> > > you created the first program above is 1/2^100, and for the second,
> > > 1/2^120, so the first program is 2^20 times more probable than the
> > >
> > > That seems correct, doesn't it? And it provides a similar way to
> > > that the universe created by the first program has 2^20 times greater
> > > measure than the second.
> > >
> > > Hal Finney
> > >
> > >