**Matti Pitkanen** (*matpitka@pcu.helsinki.fi*)

*Mon, 16 Aug 1999 21:46:00 +0300 (EET DST)*

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Dear Stephen et all,

the article about Zeno's paradox was fascinating.

Some comments.

1. In TGD context quantum jump Einsteinian solution to Zeno paradox

holds is modified somewhat. With respect to geometric time

there is no motion: tortoise becomes 4-dimensional

geometric object. With respect to subjective time

the observed motion of tortoise is discretized with

average time increment of about 10^4 Planck times per quantum

jump: cognitive spacetime sheet jumps by this temporal distance in

each quantum jump and sees new t=constant section of 4-dimensional

tortoise (in good approximation).

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

infinitesimal is smaller than 1/0, the largest possible infinity.

3. The concept of lexicon is phantastic but I could not understand

the notion of rational as novelty and subsequent claim that motion

is illusion.

4. I realized a nice manner to represent surreals (or whatever TGD

version about extension of reals is). Consider definition of a finite

real as pinary expansion:

x= SUM(n>n0) x(n)p^(-n)

a) For ordinary reals all *finite* integers n

are present in series

b) For extened reals also infinite integers

n are present. Certainly infinite values of n correspond to infinitesimal

contributions in the expansion of x in negative powers of p.

c) How should one define the part of expansion for which the values of n

are infinite? One can make the expansion unique by following trick: sum

over all n expressible as products of finite and infinite primes!

If one can construct *all* infinite primes (I have constructed quite

many good candidates!) one can make sense of this expansion

at least formally.

5. Riemann zeta function contains product over factors over

all primes. An interesting question is whether one could understand

something about zeta function by allowing

also infinite primes in the product formula

Z(s) = Prod(p prime) [1/(1-p^s)].

Best,

Matti Pitkanen

**Next message:**Matti Pitkanen: "[time 557] Re: [time 553] Modeling change with nonstandard numbers & the Computation of Actuality"**Previous message:**Stephen P. King: "[time 555] Re: [time 554] Re: [time 553] Modeling change with nonstandard numbers & the Computation of Actuality"**Next in thread:**Stephen P. King: "[time 558] Re: [time 556] Modeling change with nonstandardnumbers"

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