X-Message-Number: 9335
From: Thomas Donaldson <>
Subject: Re: CryoNet #9332 - #9333
Date: Sun, 22 Mar 1998 15:07:14 -0800 (PST)

Hi again!

To Mr Metzger once more:

I am glad to be considered a Markov chain. It is an interesting state to be in.
Thank you for the compliment.

As for "statistical functional equivalence", IF we can simulate a human being
without running into the chaos problem, THEN I will accept your notion of
statistical functional equivalence. I believe I have explained why the
information we have is not enough to decide that a simulation of a human being
won't run into the chaos problem.

By the way, have you read the Siegelmann article or are you merely running on
ideas which you have previously learned were true?

My own sources do not raise the need for a stack in defining recursion. What

do yours say? And by the way, just what have you simulated and on what machines?

And now about Turing machines: you have agreed, yourself, that their use
lies in showing the IMPOSSIBILITY of a computation, as distinct from its
possibility. That is why we cannot use them to decide whether or not simulation
of a human being is possible. We must use finite automata only. And yes, even
a finite Turing machine with a finite tape seems to me to be an inadequate
model to show POSSIBILITY of a computation. You want many more processors,
first of all, and we'll have to pay attention not only to the topology by
which they are connected but also the actual mode of connection. Why many
more processors? Because we want our simulation to work in something at least
approximating real time. 

Furthermore, you are simply wrong when you claim to have solved the problem
of a finite tape. The machine can do 4 things: halt, mark 0, mark 1, or  move
forward or backward. To have it accept a new length of tape you must
allow additional instructions. Does it then continue to be a Turing machine?
Well, it never was, since its tape was finite to begin. Not only that, but
you yourself (in a sense) become part of this machine: you sit and watch it
to find out when it needs more tape. Frankly that role seems to me to be
far worse than just being a Markov chain. Would you like to trade places for
a while?

To play games with Turing-like machines, we must define the exact operations
such machines can perform. We must do so for finite automata too. If we
want to add tape, then we must give the operations involved, in detail, as
mathematical constructs. The finite Turing-like automaton you envision must
presumably have the ability to restart itself if more tape is added, at a
minimum. And if more tape is to be added, just what operations does it 
perform to cause that? For that matter, if more tape has been welded on,
how does it perceive that it has more tape? Your model is incomplete.

I am sure that you can devise a suitable model here, though it will most
certainly lack the simple beauty of a true Turing machine. But then if we
aren't allowed to work with anything infinite, we have to accept some 
restrictions. (And I have been raising the question of whether those 
restrictions might prevent us from simulating a human being).  

As for Turing machines, I plead guilty to bringing up the Siegelmann article,

not because I was taking any special position but because it looked 
interesting.We are not going to remain static in our theories of computation any
more
than in any other field, and here was in interesting direction. I'll add
that (given the existence of such a machine, just as we admit the existence
of a Turing machine to obtain some results in computer theory) it did make
me wonder whether Turing machines could provide an adequate simulation of
brains. (Note, please, the word "wonder" here. And don't criticise me unless
you read the article and can criticise the machines described --- as theoret-
ical machines). I will point out, however, that the idea that we might use
some kind of computer to simulate ourselves has been rife on Cryonet for
years, and any discussion of that idea will come upon the issue of just what
computations are possible. To repeat, what computations are POSSIBLE, not
what computations are IMPOSSIBLE. 

In any case, I shall now return to being a Markov chain, and you may return
to being a part of your semifinite Turing machine. Just don't be slow about
welding on that extra tape. We're all interested in the result of your 
machine's computation.

			Best wishes and long long life,

				Thomas Donaldson

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