Re: Can returning a value change the value itself (in the Halting Problem)

From: Marc Goodman (marc.goodman_at_comcast.net)
Date: 08/24/04 

Date: Tue, 24 Aug 2004 17:11:16 GMT

Martin Shobe wrote:
> Of course the value changed. The *input* changed.

The context is a TM with access to its own state transition
table that can calculate the check sum of its own state
transition table. Do you finally see that even making
a "trivial" change to such a TM can cause the result produced
by such a TM to change? Or do we have to go through this
line of argument three more times?

But, both
> functions implement exactly the same, um, function.

You are free to call it "different input" if you want,
but the fact remains that if you are talking about
a TM with access to its own state transition table, the
line between "input" and "process" has been blurred.
To the extent that a seemingly local change to the
TM can have a global change to the result produced by
the TM.

  Apply the *same*
> input to both functions and you will receive the *same* output.

Yes. Too bad the input changes when you change the code.
I can keep repeating this if you find it helpful.

  That
> was my arguement (you know, the one you called naive),

It was "Ghost in the Machine's argument that I called
"naive." If you were arguing the same point, then...
I stand by the above explanation of why a local change
to a TM that has access to its own state transition table
might have a non-local affect on the result produced.

which is what
> you posted the above challenge to.
>
> Martin
>