X-Message-Number: 9259
From: Thomas Donaldson <>
Subject: Re: CryoNet #9251 - #9252
Date: Mon, 9 Mar 1998 21:59:51 -0800 (PST)

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'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. 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. (The problem comes from incommensurability, as you can
guess). If space is not digital, then eventually any digital model of it
will fail because distances are cannot be assimulated to integer multiples of
a single distance. That does not make such models useless, only incorrect,
in a way which increases with time). 

As for immortality, of interest to both of us, it seems to me that we have
no requirement at all for the universe to be digital, or ourselves to be
digital, if we are to be immortal -- whatever is to be meant by "digital".

Finally, if you have a draft of your arguments I would be very happy to 
read them.  

			Best and long long life,

				Thomas Donaldson

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