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

*Sun, 4 Apr 1999 20:41:47 +0300 (EET DST)*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Matti Pitkanen: "[time 157] Re: [time 155] Re: [time 154] Entropy, wholeness,dialogue, algebras"**Previous message:**Stephen P. King: "[time 155] Re: [time 154] Entropy, wholeness,dialogue, algebras"**In reply to:**Matti Pitkanen: "[time 154] Re: [time 149] Re: [time 108] Re: [time 81] Entropy, wholeness, dialogue, algebras"**Next in thread:**Stephen P. King: "[time 143] Re: [time 140] Re: [time 81] Discreteness and p-adics"

On Sun, 4 Apr 1999, Ben Goertzel wrote:

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*> Hi all,
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*>
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*> to avoid getting several copies of each e-mail, let's please address
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*> messages only to
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*> time@kitada.com and not additionally to individuals within the group ;)
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*>
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*> >The point is that k can be also *infinite* as integer: these have finite
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*> >p-adic norm also. For instance 1/1-p =1+p+p^2+.... is completely well
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*> >defined p-adic number with p-adic norm one.
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*> >
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*> >One could argue that discreteness is only apparent but the fact p-adic
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*> >Fourier basis obeys Kronecker delta normalization suggests that this is
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*> >not the case.
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*>
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*> What is your definition of "discrete" if it's not cardinality ;)
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My criteria are physics based.

The behaviour of plane waves like discrete planewaves could be one

criterion. Second criterion is also physics based.

By super Virasoro invariance mass squared eigenvalues of

elementary particle states

are always non-negative integers: M^2= n in suitable units.

With respect to p-adic thermodynamics n behaves as integer.

Thermal mass squared is sum SUM p(n)n where p(n) are thermal masses and

two lowest n:s are important since p(n) behaves as p^n is converges

extremely rapidly with respect to p-adic norm.

On the other hand, the real counterparts of masses in canonical

identification with *infinite n:s allowed* fill the interval

[0,p] so that mass spectum is continuous in this sense.

By the way, the real counterpart for the spectrum of p-adic quantum

harmonic oscillator with spectrum E=n is continuous so that

p-adic quantum oscillator behaves like classical oscillator in this

respect.

MP

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**Next message:**Matti Pitkanen: "[time 157] Re: [time 155] Re: [time 154] Entropy, wholeness,dialogue, algebras"**Previous message:**Stephen P. King: "[time 155] Re: [time 154] Entropy, wholeness,dialogue, algebras"**In reply to:**Matti Pitkanen: "[time 154] Re: [time 149] Re: [time 108] Re: [time 81] Entropy, wholeness, dialogue, algebras"**Next in thread:**Stephen P. King: "[time 143] Re: [time 140] Re: [time 81] Discreteness and p-adics"

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