X-Message-Number: 9260
Date:  Tue, 10 Mar 98 12:05:42 
From: Mike Perry <>
Subject: Re: CryoNet #9259

Thomas says,

> Hi Mike!
> 
> As you know, I'm (by origin) a mathematician, and I take counterexamples
> seriously. Not only that, but I understand that the authors of the article
> I referenced have gone on to actually make such a machine --- it did not
> seem to require that much.
>
I don't believe it! Give me the reference. If by "making such a 
machine" you mean they constructed it and got it working, then it 
presumably has computed a non-Turing sequence to a significant 
number of places. To quote Perry Metzger from yesterday (#9254)

>Has someone found a counterexample to the Church-Turing thesis? Pardon
>my skepticism, but anyone doing so is likely an instant Fields medal
>winner. Could we have some solid evidence here first?

Thomas again,

> I'll also add that my own philosophy of mathematics (as you know, I went into
> parallel processing) is very constructivist. A lot of the problems with
> infinities which arise in nonconstructivist mathematics do not occur; and
> of course a proof by showing that the contradiction of a proposition leads
> to a contradiction isn't allowed. It's actually possible to develop most
> of modern math along these lines, and even if the results aren't (on their
> face) quite as strong, they also tell us more (because they don't just 
> show existence of some contradiction in the abstract, they actually 
> produce it).
> 
> Unless you can somehow show that such machines CANNOT be constructed, then
> the problem remains.

This may never be done. Can you show the supernatural CANNOT 
exist? On the other hand, in my book I accept the nonexistence of the 
supernatural, because this is an important hypothesis for the 
philosophical position I develop. My arguments here are certainly 
limited--the interested reader will have to consult other authorities.
And I and these authorities could all be 
proved wrong someday anyway. But the book is long enough already 
(over 400 pages) and it just can't cover everything, or even most of 
everything.

> Furthermore, if by "digital" you simply mean quantum

> mechanics, it's quite unclear to me that this notion of digital corresponds at
> all with the notion in computer science. That too requires much more argument
> than you've given.

I argue, basically, that important events come in discrete jumps 
rather than a continuum, that our (finite) experiences form a denumerable set, 

that the same (again finite) experience, exactly, can recur over and over. This
sort of "digital" argument is convenient for some of the rest of the 
philosophical points I make. The "digital" chapter of the book is 
over 40 pages long now and tries to address everything from Deutsch's 
universal quantum simulator to Searle's Chinese room. No doubt it is 
inadequate, but I've got to stop somewhere. (But I'll be happy to let 
you or anyone else read it or the rest of the book, when it's a 
little more "finished"--hopefully soon.) On the other hand, I 
certainly wouldn't assume we would have to be "digital" as a 
requirement for immortality or the possibility of resurrection, but 
it does seem, to me, to be a reasonably solid conclusion which is 
also useful, again, for other points I make. As for the linkup 
between the computer science notion of "digital" and quantum 
mechanics, Deutsch claims to have done this in *The Fabric of 
Reality*--a book worth reading. Essentially, there is a universal 
quantum system, like a universal Turing machine, that can emulate any 
other bounded system.

Endless best,

Mike Perry

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