Re: Foundation for a Formal Refutation of the Original Halting Problem?

From: >parr\(*> (gniKyruaL_at_tenretnitb.moc)
Date: 08/07/04 

Date: Sat, 7 Aug 2004 03:11:58 +0000 (UTC)

"Peter Olcott" <olcott@worldnet.att.net> wrote in message
news:VVAPc.167035$OB3.143413@bgtnsc05-news.ops.worldnet.att.net...
|
| ">parr(*>" <gniKyruaL@tenretnitb.moc> wrote in message
news:celukt$347$1@hercules.btinternet.com...
| >
| > Peter,
|
| > So where are we going to find a common language, Peter? Are you
| > expecting people to learn your language? Turing didn't. Are you
| > prepared to learn the language of your audience? Turing did.
|
| Before I can translate the ideas into a form that can be understood
by
| many, I must first have these ideas in a form that is understood by
me.

Yes. I know you _believe_ there is an error. I know you believe
that all things ought to be knowable, or computable. Right up to the
early 20h C, scientists believed that all things could be knowable if
they worked hard enough at it. Before that, people pooh-poohed the
idea of sqrt(-1), they pooh-poohed the idea of negative numbers, of
zero as a number, even.

Then along came Goedel and upset this arrogance, And Turing did for
Computing what Goedel did for Maths. I remember doing a double take
when I first saw a version of Goedel's proof. But having a solid
foundation of maths, and having familiarity with the mathod of proof
by assuming that which you are about to disprove, I was able to go
through the proof and convince myself that it was right.

It defies intuition, that I know. But I've seen weirder
counter-intuitive stuff pop out of statistical calculations.
|
| This thread is supposed to be an answer to all the objection that
| I received in all the other threads. What this thread currently
| provides is the basis from which a formal proof can be constructed.
| I had to boil the Halting Problem down to its barest essence
| before I could hope to address it on the same Turing Machine
| terms that formed the basis of the original proof.
|
| I will call this a fully elaborated sketch of an informal proof.
| There are now no crucially relevant details missing. You can
| find the additional material in my 6:41 pm posting.

Time zone? I assume GMT+7 as this tallies with a likely candidate
posted has Mon, 02 Aug 2004 23:41:40 GMT.

I will go study it.
|
| > A. You say 'Foundation'. To be a foundation, your presentation
must
| > be absolutely solid so that the refutation to come will be
soundly
| > based. The remaining comments here are aimed at helping you get
a
| > good foundation statement.
|
| When I used the word foundation I was referring to a fully
elaborated sketch
| of an informal proof, that would form the basis for a formal proof.

My offer still stands
lauryking at btinternet dot com

I will email you a cleaned version of anything you post. But there's
no point me putting it here unless you are happy with it.

|
| > B. You say 'Original Halting Problem'. What 'Original' do you
mean?
| > Adding the word 'Turing' and giving suitable references to where
the
| > 'O.H.P' was first stated, and where subsequent amendments can be
| > found. [It could be I am jumping to conclusions and that you are
not
| > considering Turing Machines.
|
| I am referring to the same place that everyone else if referring
to.

This being? If you are not explicit in all things, people will not
understand. Worse, by not making everything explicit, you, yourself,
are in danger of missing any errors you make.

| I did not study this original material directly myself. Instead I
studied
| many other references that were much easier to follow.

I don't think anyone minds how you arrived at your understanding.
But it's not an understanding about Turing's conclusion.

| Every
| example of the Halting Problem has certain features in common.
| When I was referring to the original it is more along the lines
| that my solution now directly applies to the most basic form of
| a Turing Machine, and needs nothing outside this.

Ummm. If you haven't read and understood Turing, how do you know
your result applies? More importantly, how are you going to convince
other people by pinpointing the erroneous line(s)) in Turing's method
if you haven't read and understood it?

| > D. 'SourceCode' is not in Turing's terminolgy. Therefore it must
be
| > defined using that terminology.
|
| I have been adding (parenthetically) (or Turing Machine
Description)

I think you missed the point. If you don't know what the Turing
machine equivalent is to, say 'source code', how can you expect
others to guess correctly? 

--
)>==ss$$%PARR(º>   Parr

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