# Re: TM Tape is Always Finite

From: Arthur J. O'Dwyer (ajo_at_nospam.andrew.cmu.edu)
Date: 01/03/04

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```Date: Fri, 2 Jan 2004 19:41:09 -0500 (EST)

```

On Thu, 1 Jan 2004, Leonard Blackburn wrote:
[re: Russell Easterly]
> It's funny that since I started reading these newsgroups a year or two
> ago, I've encountered at least half a dozen people arguing exactly the
> same point of view as you, but in different contexts. Now we're in the
> context of Turing Machines. That's very humorous to me. I didn't know
> people with your beliefs existed, and now I find that there are at least
> several of you.

I can easily understand how some people don't "get" infinity. I
myself still don't quite "get" ordinal numbers, although I've got
the cardinals down pretty well now. :)
What I don't understand is how some people who don't "get" infinity
seem to compulsively post *wrong* statements to the Internet, rather
than trying to understand *right* ones. And how a guy like Russell
can seem to have such a reasonable grasp of what a "Turing machine"
is, without having even a basic conception of the properties of the
integer numbers!

> Have you heard of this guy Phil who used to post absurd
> things like the statement that all natural numbers have finitely
> many digits? It's quite fascinating. I could write a book about it.

I remember Phil. But I must point out that you forgot to complete
that thought: All natural numbers *do* have finitely many digits!
But Phil made a leap from that true statement to the false statement
that *the number of* natural numbers was finite -- and stuck to it --
and that's what was absurd.

-Arthur

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