Re: Lambda Calculus and Turing Equivalence

From: Peter Douglass (peterd_at_ccs.neu.edu)
Date: 12/02/04 

Date: Thu, 2 Dec 2004 12:07:32 -0500

"Eray Ozkural exa" <examachine@gmail.com> wrote in message
news:320e992a.0412020830.887997b@posting.google.com...
> "peter_douglass" <baisly@gis.net> wrote in message
> news:<Gwvrd.178284$HA.7808@attbi_s01>...
>> If the tape of a Turing Machine is defined to be infinite,
>> or even "actually infinite", then it is "actually infinite", even
>> though we are unlikely to experience real infinite tapes.
>> This is just as much true as if I define the set of integers to
>> be "actually infinite". Perhaps you would also argue that
>> the set of integers is only "potentially infinite", that it is only
>> a "imagined" to be an "actually infinite" set. That's fine. Go
>> off and converse with whatever community accepts your
>> terminology. But by now you should understand that you
>> are not speaking the language of the mathematics community.

> It's clear that you don't consider computer scientists like Ullman or
> Chaitin part of the mathematics community. And probably all the other
> people who said TM has an unbounded tape, not an infinite one.

> What makes you an authority on that?

It is clear that your ability to comprehend is impaired. Of course
I consider Ullman and Chaitin part of the mathematics community.
If you look again and read my post, you will see that I did not claim
that the definition of a Turing machine includes an infinite tape.
What I said was:

<< If the tape of a Turing Machine is defined to be infinite,
<< or even "actually infinite", then it is "actually infinite", even
<< though we are unlikely to experience real infinite tapes.

My point is that *if* something is defined a certain way, it is
pointless to bring up arguments about the definition violating
preconceived notions about the impossibilty of "actual infinity"
and the like. The thing is defined and you just have to
accept it. (You obviously don't, but that is another matter).
If you had argued that Turing did not claim the tape was
infinite, then that would have been an entirely different
sort of argument, and one which is resolvable by investigating
the source texts. But instead of arguing about the factual
matter of how Turing defined his theoretical machine, you
argued that "actual infinity" is not permitted by your
religion.

--PeterD

Relevant Pages

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    ... > number of tape segments, but if it starts with a blank tape, or a tape ... > the abstract quantum computer with infinitely many qubits might start ... > it seems no less finite in your sense than the abstract Turing machine ... > with its infinite but mostly zeroed tape. ...
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