Re: Can the 'Turing Problem' be deflated?

Charlie-Boo wrote:
On Mar 29, 9:05 pm, John Jones <jonescard...@xxxxxxx> wrote:
Someone here said that "the Turing machine M will halt on input x" is a
mathematical statement. 'Halting' traditionally means that the machine
has picked up a command and fulfilled it.

This anthropomorphism allows Turing to claim that we cannot discern if a
command has been made by the machine without our knowing it. From there
we reason that there are some commands for which there are no
fulfillment criteria, except those criteria given by the machine. This
in turn means that we cannot tell whether the Turing machine will halt
or not.

But the fact that a machine has or has not halted is an inconsequential
fact of engineering and is irrelevant to the Turing problem. Each step
that the machine takes can be viewed as picking up a command and
fulfilling it, or starting and halting. 'Halting' is therefore
uninformative. The machine has no sense of 'process', or even of a
first, next, or last step. It is up to us to decide which step fulfills
our command.

We cannot avoid the machine's limitation in being unable to show us the
fulfillment of a command by commanding or programming the Turing machine
to, as it were, 'switch off all the lights when you're done'; for we
still need to know when to instruct the machine to 'turn off the
lights'. If we claim that we can give a command or an instruction for
which we have no idea how it looks when it is fulfilled, then we can
hardly say that we have given a command, for a command knows its
fulfillment.

With the failure of the notion and legitimate domain of use of the terms
'instruction' and 'command', the Turing problem is at least deflated; if
not dissolved?

You are right (including the characterizing of an undetectable command
as being meaningless) up until the point of your conclusion. The
conclusion is not that the problem is immaterial, but rather that the
HALT command is immaterial - which is true.

You are talking about the general problem of telling if a given
program executes any given command (or a TM uses a given tuple in its
definition) being undecidable. This allows us to quickly dispose of
related problems e.g. "Does a given TM reach a given state 3 or more
times?" as also being undecidable.

Now where do you continue your analysis?

C-B

So the 'halt when finished' command cannot be made if we cannot tell when a halt is 'finished'. And there again, the machine halts at each step. We cannot get around this vaguery of a when a 'halt' is a 'last' halt by stipulating a 'finish' halt from a halt in a sequence of halts. So we must know for each halt whether there is a command associated with it. But there is no command associated with 'not halting'.

If the machine recirculates a conclusion and carries on ticking away, then I would say that that is simply an engineering artifact. I am hard put to see any significance in it for a Turing problem. As long as we can associate a halt with a fulfillment of a command, then the machine is carrying out a TRUE TASK.

But even if we can associate ALL halts with a fulfillment of a command(s) and the machine is consequently carrying out a true task, then we might want to attach some significance to the fact that it is circulating a result. Do we have a command for circulation or repetition for a last halt? If we don't then the TM is not carrying out a true task. That is, it is not effectively computing, or the program has an oversight as we are getting unexpected outcomes in the machine.
.

Relevant Pages

  • Re: Can the Turing Problem be deflated?
    ... Marshall wrote: ... a fulfillment of a command. ... You do NOT GET to tell US what "halt" means. ...
    (sci.logic)
  • Re: Can the Turing Problem be deflated?
    ... a fulfillment of a command. ... WE TELL YOU what "halt" means. ... radiation oncologist who had studied the hard details of the ...
    (sci.logic)
  • Can the Turing Problem be deflated?
    ... This anthropomorphism allows Turing to claim that we cannot discern if a command has been made by the machine without our knowing it. ... This in turn means that we cannot tell whether the Turing machine will halt or not. ... Each step that the machine takes can be viewed as picking up a command and fulfilling it, or starting and halting. ... We cannot avoid the machine's limitation in being unable to show us the fulfillment of a command by commanding or programming the Turing machine to, as it were, 'switch off all the lights when you're done'; for we still need to know when to instruct the machine to 'turn off the lights'. ...
    (sci.logic)
  • Re: Can the Turing Problem be deflated?
    ... fulfillment of a command. ... Please stop pretending that you know what you are talking about. ... TMs are SYMBOLIC. ...
    (sci.logic)
  • Re: Can the Turing Problem be deflated?
    ... 'Halting' traditionally means that the machine ... command has been made by the machine without our knowing it. ... fulfillment criteria, except those criteria given by the machine. ... in turn means that we cannot tell whether the Turing machine will halt ...
    (sci.logic)
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