Re: [PO] Re: Can a regular Turing Machine provide Protected Memory?

From: Peter Olcott (olcott_at_worldnet.att.net)
Date: 08/28/04 

Date: Sat, 28 Aug 2004 19:01:05 GMT

"Simon G Best" <s.g.best@btopenworld.com> wrote in message news:4130B2EA.5000909@btopenworld.com...
> Peter Olcott wrote:
> > "Simon G Best" <s.g.best@btopenworld.com> wrote in message news:413072ED.6040504@btopenworld.com...
> >

> You obviously need some more punishment, so:
>
> String B: "String B will never be proven to constitute a true, valid
> statement."
>
> String C: "String B will never be proven to constitute a true, valid
> statement."
>
> String B will never be proven to constitute a true, valid statement.
>
> What about string C?

String B is not a statement at all due to its infinitely recursive structure.
String C would be a true statement.

I will place everyone that has correctly refuted any one of my
arguments in my list of favorite people to talk to. You and Daryl
did a fine job in pointing out loopholes in my reasoning. I really
appreciate that because I want my argument to be either 100%
solid and irrefutable (my first choice) or completely refuted
(what I hope to avoid, yet much better than lack of closure).

> >>By the way, it's a /really/ good idea to read /all/ the way through a
> >>post /before/ even beginning to reply. You obviously haven't done this.
> >
> > This is inefficient.
>
> You need to learn what 'less haste, more speed' means.

I find that I very rarely need to go back and revise. One thing that
I will do more of, with my select set best respondents (you and Daryl)
is read them all the way through, and not skip anything.

> >>In section 1 of his 1936 paper 'On computable numbers, with an
> >>application to the Entscheidungsproblem', Turing says:-
> >>
> >>"The machine is supplied with a "tape" (the analogue of paper)..."
> >
> > <sarcasm>
>
> I'm British; sarcasm should not be marked up.
>
> > And of course everyone universally agrees that the term analogue
> > means one-and-the-same-as.
> > </sarcasm>
>
> But if you'd read just a bit further first, you would have read:
>
> >>Why an "analogue"? Because, when it comes down to it, Turing Machines
> >>are /mathematical/, /not/ physical. The seemingly physical things, such
> >>as a "tape", and so on, are really for illustrative purposes.
>
> Yes, I see now: not bothering to first read the post you're replying to
> is certainly a more efficient way of embarassing yourself.
>
> > Yet to continue with the illustration there often comes a point
> > where simplifying assumptions must be modifyed.
>
> You also need to read back what you wrote /before/ posting it.
>
> > Punched paper tape might be reliable.
>
> So what? We're talking about Turing Machines. Turing Machines are
> mathematical.

I am talking about Turing Machines as actually implemented
in reality. Any simplifying assumptions that I accept can safely
be made only because they do not change the end result. Any
assumptions that are made that can change the end result must
be specified. Exactly how the data gets to the tape is not an
assumption that can be ignored, because different options
derive different end-results.

> > I am so old that I
> > was able to have one of my homework assignments
> > written to punched paper tape.
>
> You are not the first net.kook to surprise me with your age. You come
> across as so much less mature.

You are the kook who thinks that a pencil and paper tape is a reasonable
storage device. That's one of the kookier things that I have heard.

The kookiest thing that I heard was probably the guy that proved
that no automobiles can ever possibly operate properly specifically
because they can be made to not operate properly. All that I has
to do was to substitute his reference to My Halt Analyzer with the
term Automobile. Wait no much kookier than this were to small
group of people that could never stick with reasoning more than
a tiny percent of the time.

> > Pencil written and
> > erased paper tape (your suggestion) is absurd.
>
> No, it's not my suggestion. If it's anyone's, it's Turing's. But it's
> just illustrative; Turing Machines are actually mathematical.
>
> > It is
> > a simplifying assumption that does not hold up in any
> > real-world scenarios.
>
> Turing Machines are mathematical.
>
> > Since you already agreed that
> > magnetic tape is acceptable, let's go with that.
>
> No, there are technical problems with infinitely long magnetic tapes.

They don't literally need to be infinitely long unless we
are doing something such as deriving all of PI. They only
really need to be some finite length that is as much as
needed for the specific problem at hand. Since TM's
are defined with a finite alphabet, and a finite number of
internal states, finite storage will be all that is needed to
determine if any TM halts.

>
> Anyway, Turing Machines are mathematical. (Perhaps, if I say this
> enough, you'll actually read it at some point.)
>
> > Now how
> > does a human get anything onto this tape, or review
> > the tapes contents?
>
> An off-line tape reader/writer, as I said in my previous post.
>
> It really would be a lot more efficient for you to actually read all the
> way through the posts you reply to, then you wouldn't waste time raising
> irrelevant points that have already been dealt with.
>
> > I would say that something like
> > a keyboard and CRT are logically entailed.
>
> If you like. But Turing Machines are mathematical.

The reason that I like computer science so much is that
in every case, or at least nearly every case there can be
a perfect 1-1 mathematical mapping between the mathematical
ideal, and the actual real world physical implementation.

> > Now we are back to my original method that uses
> > (1) Read Only Memory
> > (2) Protected Memory
> > (3) Write Only Memory
> > It provides the result of its halt analysis only on the CRT
> > screen, no LOOP_IF_HALTS TM can be constructed.
>
> So, you've given up with Turing Machines, and decided to return to ideas
> that have been thoroughly and repeatedly debunked many times before?

(1) I have not given up Turing Machines, I have already shown
     how the above three can be implemented as a Turng Machine.

(2) Although it has been often a valid simplfying assumption to simply
      ignore how data gets on the tape, and how humans can have access
      to examine these tape values, this can no longer be ignored in this
      case. since it effects the end-result of the proof. Because of this
      I am assuming IO devices analogous to CRT and keyboard.

      You can argue that TM's are not defined to have CRT's and
      keyboards, and in this you would be correct. The problem is
      that this is a gap that must be filled and can not simply be
      ignored. The data must get to the tape by some means, a
      pencil is absurd, thus I choose a keyboard / magnetic tape
      writer to fill this gap. This gap must be filled, or the TM
      has an incomplete specification, I simply filled it.

(3) This has never been debunked. At most my initial presentation of
      this material was not shown to apply to Turing Machines. Now it
      has been shown to apply to Turing Machines.

(4) I derived an answer to circumvent your valid refutation of my point.
     Yes you can make two different TMs that will each fool one of the
     private key values, even without knowing what the key value is.
     Simply re-run the analysis with the other key value.

> Obviously you've realised that you can't defeat the Halting Problem, and
> so have decided to resort - yet again - to various obfuscations to try
> to disguise your failure. It isn't working.
>
> The classic proof is about Turing Machines. Your extra hardware is
> irrelevant, and shall be ignored (except for the purposes of fun).
>
> Simon
>

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