SERVING THE QUANTITATIVE FINANCE COMMUNITY

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GrenvilleCroll
Topic Author
Posts: 357
Joined: July 29th, 2004, 8:03 am

### Void, Monoids, Spheroids & Kawaguchi spaces

After a while, the Void got bored and created a Monoid for company. The Monoid ran all around the space shouting "where the hell are you its time for dinner". The Void got pissed off with this behaviour night after night, so created another Monoid, just like the first. Things got even worse - the first Monoid starting bitching with the second Monoid, as well as the Void. The second Monoid also ran around the entire space looking for the Void asking for more money.And so: is the Void and the Monoid a Kawaguchi space, and of what order and whats the notation? Are the Void and the Monoid spherical, as they do a dance looking for where the Fuck they both are. Are the first and second Monoids also a Kawaguchi space - are they spherical? And finally are the Void, and both Monoids, also a little happy family, being also a Kawaguchi space, and of what order and whats the notation and the Topology.Your answers appreciated whilst I drag my knuckles off to the pub. My dinner is in the dog.

mama
Posts: 93
Joined: April 29th, 2003, 6:40 am

### Void, Monoids, Spheroids & Kawaguchi spaces

QuoteOriginally posted by: GrenvilleCrollAfter a while, the Void got bored and created a Monoid for company. The Monoid ran all around the space shouting "where the hell are you its time for dinner". The Void got pissed off with this behaviour night after night, so created another Monoid, just like the first. Things got even worse - the first Monoid starting bitching with the second Monoid, as well as the Void. The second Monoid also ran around the entire space looking for the Void asking for more money.And so: is the Void and the Monoid a Kawaguchi space, and of what order and whats the notation? Are the Void and the Monoid spherical, as they do a dance looking for where the Fuck they both are. Are the first and second Monoids also a Kawaguchi space - are they spherical? And finally are the Void, and both Monoids, also a little happy family, being also a Kawaguchi space, and of what order and whats the notation and the Topology.Your answers appreciated whilst I drag my knuckles off to the pub. My dinner is in the dog.I think you and N would make a lovely pair. The Void meets the Octonian.

Posts: 11048
Joined: February 1st, 2005, 11:21 pm

### Void, Monoids, Spheroids & Kawaguchi spaces

In the doghouse again, eh Gren?

N
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Joined: May 9th, 2003, 8:26 pm

### Void, Monoids, Spheroids & Kawaguchi spaces

Hey, I just got back from the pub (dragging my knuckles back). Monoids (semigroup with identity element) are interesting projections of certain Lie groups since they don't have an inverse (irreversible because they are short dimension(s)). Monoids usually live on an n-sphere. And symplectic (spheroids) and octonion manifolds (simple, non-trivial Lie groups, Sp(4) and Sp(8)) live in Kawaguchi space (non-Riemannian space).I guess this question has to do with the intersection of spheroids and n-spheres (interesting relationship with the Riemann conjecture and L-functions in general).Moniods are at this intersection as are prime numbers. But since prime numbers aren't cyclotomic, I'd say the Moniods aren't really on the spheriod either.I'd have to think about your question without the influence of beer, but off hand I'd say that Moniods are on an n-sphere, and the voids are in kawaguchi space (caused by the missing mapping from the Lie groups Sp(2n) n>=2.)Based on this question, I think GrenvilleCroll might be able to prove the Riemann conjecture, what do you think?Added beer corrections...
Last edited by N on November 8th, 2005, 11:00 pm, edited 1 time in total.

Posts: 11048
Joined: February 1st, 2005, 11:21 pm

### Void, Monoids, Spheroids & Kawaguchi spaces

Over to you Gren...

ppauper
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Joined: November 15th, 2001, 1:29 pm

### Void, Monoids, Spheroids & Kawaguchi spaces

>> Spheroids oblate or prolate ?

GrenvilleCroll
Topic Author
Posts: 357
Joined: July 29th, 2004, 8:03 am

### Void, Monoids, Spheroids & Kawaguchi spaces

Thanks N.Please understand that I am a computer scientist trying to learn higher mathematics by Osmosis. It seems to be working, but slowly: your response is interesting and informative.The question arises out of a need to be able to understand sufficiently so that I can implement the double slit experiment in software (I have some really wierd hobbies) ie set up the crystalline structure of the material containing the slits, discover what a photon really is (if it is anything at all), fire it on its way, and observe the state change of the simulated silver halide observation mechanism. Anton Zeilinger has done the double slit experiment with Fullerenes [Carbon 60 etc] and has observed the interference effect even though the slits are much smaller than the Fullerenes.I have read many thousands of pages of material covering the application of Kawaguchi spaces to everything from the structure of Leptons to the number and location of Fish Fins (Oh yes, really!).Given a Kawaguchi Space K(M,L,N), with L parameters, N Dimensions and M derivatives, there appears to be an equivalence between a Kawaguchi space K(M,3,N) and the elementary particles: Baryons for L=3, Mesons for L=2 and Leptons for L=1. The physical configurations carried by the three/two paramters of K(M,3,N)/K(M,2,N) are identified with the three/two quarks of the baryon/meson.From memory, while I'm at it, there is an important result due to Kawaguchi and Hombu, the KH theorem, where the additional dimensions of higher order Kawaguchi spaces cancel out due to cross-differentiation such that only three dimensions are necessary and sufficient for the representation of complex phenomena, hence our observed three dimensional reality.I was trying to find out the reationship between the simplest Kawaguchi Space and the simplest and first emergent objects ex void, after the work of Bastin and Kilmister et al in the Combinatorial Heirarchy. (As well as expressing annoyance about being harried by menstrual women all the time). I had not realised that a monoid was so well defined, though the paper on the subject I recently read was 50 years old.Regarding the Reimann Conjecture: I rather doubt it would be me. [Get Real Edit Performed]
Last edited by GrenvilleCroll on November 9th, 2005, 11:00 pm, edited 1 time in total.

Posts: 11048
Joined: February 1st, 2005, 11:21 pm

### Void, Monoids, Spheroids & Kawaguchi spaces

Oh yeah, right. And because I have spoken at a couple of industry conferences I am going to win the Nobel Prize in finance. Get real.

GrenvilleCroll
Topic Author
Posts: 357
Joined: July 29th, 2004, 8:03 am

### Re: Void, Monoids, Spheroids & Kawaguchi spaces

A few months ago I completed a draft paper that showed, based upon some Monte Carlo simulation, that the distribution of primes around a quadratic was Gaussian.The quadratic is based upon the Logarithmic Integrand Li(x). This would appear to be another demonstration that the RH is true.

I now have to deveop the empirical result into an analytic proof. I am reasonably confident that I can do this.

I have never forgotten N's related comment as above. How did he know or surmise?

G

Cuchulainn
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### Re: Void, Monoids, Spheroids & Kawaguchi spaces

N had no equal on Wilmott.

rmax
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Joined: December 8th, 2005, 9:31 am

### Re: Void, Monoids, Spheroids & Kawaguchi spaces

N had no equal on Wilmott.
Agreed. I think he left just after I joined - might have down to the great schism. Either way he had such a brilliant in depth knowledge or he had a hunch on things that pointed to a very very deep understanding. I always wonder who he was and what happened to him.

rmax
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Joined: December 8th, 2005, 9:31 am

### Re: Void, Monoids, Spheroids & Kawaguchi spaces

katastrofa
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### Re: Void, Monoids, Spheroids & Kawaguchi spaces

It's so deep that I get vertigo from looking into it.

Cuchulainn
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### Re: Void, Monoids, Spheroids & Kawaguchi spaces

It's so deep that I get vertigo from looking into it.
void**

rmax
Posts: 6080
Joined: December 8th, 2005, 9:31 am

### Re: Void, Monoids, Spheroids & Kawaguchi spaces

A singular void that is dissimilar from its application in C or C++
A Void