**Stephen P. King** (*stephenk1@home.com*)

*Mon, 16 Aug 1999 15:35:16 -0400*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Matti Pitkanen: "[time 559] Generalized reals and generalized lexicons"**Previous message:**Matti Pitkanen: "[time 557] Re: [time 553] Modeling change with nonstandard numbers & the Computation of Actuality"**In reply to:**Stephen P. King: "[time 554] Re: [time 553] Modeling change with nonstandard numbers & the Computation of Actuality"**Next in thread:**Matti Pitkanen: "[time 537] Theory of cs should predict its own discovery"

Hi Matti,

Matti Pitkanen wrote:

*>
*

*> Dear Stephen et all,
*

*>
*

*> the article about Zeno's paradox was fascinating.
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*> Some comments.
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*>
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*> 1. In TGD context quantum jump Einsteinian solution to Zeno paradox
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*> holds is modified somewhat. With respect to geometric time
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*> there is no motion: tortoise becomes 4-dimensional
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*> geometric object. With respect to subjective time
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*> the observed motion of tortoise is discretized with
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*> average time increment of about 10^4 Planck times per quantum
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*> jump: cognitive spacetime sheet jumps by this temporal distance in
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*> each quantum jump and sees new t=constant section of 4-dimensional
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*> tortoise (in good approximation).
*

Ok, but do you see that we have to allow for the existence of an

infinite (unenumerable!) number of geometric "turtles"? One question I

have is: Why do we have a geometric time at all?! We obviously have a

subjective time, but why postulate an "geometric" one? For geometry, we

only need a 3+1 manifold, M^4. As it is, as you say, static, it has no

"change" related to it. Time is a subjective measure of change.

My problem is that you seem to assume the existence of an "outside"

observer that can tell the difference between a Planck length of

duration h and \infinitesimal + h. What does this entity use to measure

the difference?

*> 2. I only now realized that every infinite prime, whose inverse is
*

*> infinitesimal is smaller than 1/0, the largest possible infinity.
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*>
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*> 3. The concept of lexicon is phantastic but I could not understand
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*> the notion of rational as novelty and subsequent claim that motion
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*> is illusion.
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Let us talk about it further... :-)

*> 4. I realized a nice manner to represent surreals (or whatever TGD
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*> version about extension of reals is). Consider definition of a finite
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*> real as pinary expansion:
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*>
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*> x= SUM(n>n0) x(n)p^(-n)
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*>
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*> a) For ordinary reals all *finite* integers n
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*> are present in series
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Can we encode a description of an arbitrary material system with them?

*> b) For extened reals also infinite integers
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*> n are present. Certainly infinite values of n correspond to infinitesimal
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*> contributions in the expansion of x in negative powers of p.
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*>
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*> c) How should one define the part of expansion for which the values of n
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*> are infinite? One can make the expansion unique by following trick: sum
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*> over all n expressible as products of finite and infinite primes!
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*> If one can construct *all* infinite primes (I have constructed quite
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*> many good candidates!) one can make sense of this expansion
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*> at least formally.
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How long does it take the Universe to "do" this summation operation?!

Consider the problem of deciding if a given number is prime. Does the

Universe have a look up table? If it does, "where" is it "written" and

how is it "accessed"?

*> 5. Riemann zeta function contains product over factors over
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*> all primes. An interesting question is whether one could understand
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*> something about zeta function by allowing
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*> also infinite primes in the product formula
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*>
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*> Z(s) = Prod(p prime) [1/(1-p^s)].
*

Does this paper give you any ideas?

http://www.cs.auckland.ac.nz/CDMTCS//researchreports/032crisRR.pdf

Onward,

Stephen

**Next message:**Matti Pitkanen: "[time 559] Generalized reals and generalized lexicons"**Previous message:**Matti Pitkanen: "[time 557] Re: [time 553] Modeling change with nonstandard numbers & the Computation of Actuality"**In reply to:**Stephen P. King: "[time 554] Re: [time 553] Modeling change with nonstandard numbers & the Computation of Actuality"**Next in thread:**Matti Pitkanen: "[time 537] Theory of cs should predict its own discovery"

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