# [time 36] RE: [time 27] Turing machines under difeomorphisms?

Sat, 20 Mar 1999 12:12:08 +0900

Dear Stephen,

A Turing machine is a local system that evolves along its local time producing
a tape. Each square cell of a tape you write is a state of the LS at each
corresponding time. The total history of the LS is the infinite length tape,
and hence cannot be read by any observer due to the "infinity" of the length
(note that it is said that Turing machine has a finite length tape, i.e. the
effective number of holes on the tape is finite. But there is no finite method
of judging at which point of the tape the holes end). This supports your
statement

>"a infinite length tape divided into square cells..." can
>neither be read or written to by a "head which can be in in a finite
>number of internal states"

without any additional condition. I.e. "iff part" in your post is unnecessary.

Best wishes,
Hitoshi

-----Original Message-----
From: Stephen P. King <stephenk1@home.com>
Date: Thursday, March 18, 1999 1:19 AM
Subject: [time 27] Turing machines under difeomorphisms?

>Hi all,
>
> A quick note: Can we think of Turing Machines as existing under the
>diffeomorphism invariance of GR, as Hitoshi explains it? It seems to me
>that the same conditions that prohibit clocks from being definable also
>imply that "a infinite length tape divided into square cells..." can
>neither be read or written to by a "head which can be in in a finite
>number of internal states" iff those cells are infinitesimal invariant
>under diffeomorphism transformations!
>
>cf. "Returning to the origin of the problem, i.e. to the idea of
>relativity theories, a cause of
> the problem of time seems to lie in associating time to each point
>which has no positive
> size. No clocks can reside in a sizeless point. At the stage of
>special theory of relativity,
> this difficulty does not appear: Time is associated to each
>inertial frame which can
> accommodate actual clocks. At the stage of general theory of
>relativity, the field
> equation with the invariance postulate with respect to
>diffeomorphisms requires one to
> eliminate the size of the frames in which clocks reside."
>
>
>Later,
>
>Stephen
>
>

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