**Hitoshi Kitada** (*hitoshi@kitada.com*)

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

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephen P. King: "[time 37] Re:The ordering of spatial states and temporal events"**Previous message:**ca314159: "[time 35] Re: [time 34] Re: My comments of the trinity of nondeterminisms in TGD"**Next in thread:**Stephen P. King: "[time 40] The Computational Complexity of LSs"

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>

To: Time List <time@kitada.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."
*

*>
*

*>http://www.kitada.com/
*

*>
*

*>Later,
*

*>
*

*>Stephen
*

*>
*

*>
*

**Next message:**Stephen P. King: "[time 37] Re:The ordering of spatial states and temporal events"**Previous message:**ca314159: "[time 35] Re: [time 34] Re: My comments of the trinity of nondeterminisms in TGD"**Next in thread:**Stephen P. King: "[time 40] The Computational Complexity of LSs"

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