Le 27-sept.-06, à 20:41, Tom Caylor a écrit :
> I've thought of bringing up the Monster group here before, but I didn't
> think anyone here would be that weird, since I even get "weird"
> reactions to my ideas about the Riemann zeta function. I've noticed
> the connection with the number 26 also. (By the way, for some unknown
> reason in my childhood 26 was my favorite number ;)
26 is 24 + 2.
24 dimensions of space + 2 dimension of time (useful for continuous
bifurcating time).
I have try to develop such a "toy" theory. But it has no fermion
although there are bizare object emerging from many sort of bosons
which could perhaps play that role.
There are too much theories like that, and my hope is to extract
constraints from the comp person point of view.
(At least now we know the difference between fiction and reality: it is
18 ;)
> In the past I've been drawn to the Monster group and the classification
> of finite simple groups, perhaps for reasons similar to other
> mathematically inclined people. There's just something mysterious
> about the fact that there are only a finite number of classes of this
> type of mathematical object. And yet it is a rather non-trivial
> number, larger than the number of spatial dimensions, and even larger
> than the number of platonic solids, or the number of faces on the
> largest platonic solid. And when you look at the order (size) of the
> largest of the finite simple groups (the Monster group), it is huge.
> And yet it is the largest. This seems to be a signpost that something
> fundamental is going on here.
Yes. But sometimes I am afraid it is just mermaid's songs. Too much
beautiful to be true.
Perhaps I should trust a bit more the "artist" in me ;)
> On the other hand, if I recall correctly without checking, rings and
> fields don't have such a classification such that there are a finite
> number of some basic type of them. I'm just shooting off at the hip,
> but I wonder if this has to do with the fact that groups have only one
> operator (addition or multiplication, say), whereas rings and fields
> have at least 2. This rings a bell with the sufficient complexity
> needed for Godel's Incompleteness Theorems (and a nontrivial G/G*?).
Yes I think you are right.
But my present speculation (not to confuse with my thesis on comp where
there is no speculation at all) is based on the hope that there is a
not too much complex universal diophantine equation, so that we can
generalize in some genuine way "Wiles modularity conjecture". If that
were true, then the third and fourth hypostases would make possible to
put full light on the godel-lobian blind spot, and verify how the laws
of physics arise with all details including where qualia come from
thanks to the G* part. If the jump of complexity is too big, well
either comp will be shown false or we will have to hope there is bigger
Monster Group, or some genuine non simple finite super giant group
related too some more complex modular form.
Matiyasevich reports the following interesting dialog between a
logician L and a number theorist N:
L: Matiyasevic has find a polynome such that all and only all its
positive value are the prime numbers.
N: Waouh! Great! Super! We will learn a lot on the prime numbers!
L: Well, actually Matiyasevic has found a way to build such a polynome
for any Recursively Enumerable set of number (any Wi).
N: Oh, what a pity, we will learn nothing on the prime numbers.
But my feeling is that now we can use number theory to learn a lot on
the Wi. The positive benefits are for the logicians. Matiyasevic result
could eventually lead to an "analytical" (complex) recursion theory.
Alas this is very complicated to do (compare the simplicity of the
notion of prime number and the difficulty of Riemann's paper).
Monstrous moonshine gives me at least the courage to do some
speculations.
> A
> similar point is that there are an infinite number of primes, whereas
> the number of classes of finite simple groups is finite. Another
> caution is to note the failure this approach in the past, notably with
> Plato's "theory of everything".
Honestly I think you are unfair with Plato. But then read Plotinus who
is clearer on numbers and forms.
Frankly! The only failure of Plato is to have kept Aristotle in the
Academy (against the advise of Xeusippus and the mathematicians) !
> We don't want to go down the path of
> numerology, which is a lot of what comes up when I google "monster
> group" and "multiverse". But on the other hand, this is part of the
> nature of exploring.
Sure. And the advantage of the Mermaid's Songs, is that even if they
take you far from the truth, they still make you enjoying beautifulness
...
Bruno
PS Those interested can take a look on Mark Ronan's recent popular
book: "Symmetry and the Monster" which tells the story of the
classification of the finite simple groups, and introduces the Monster.
For reference:
http://www.amazon.com/Symmetry-Monster-Greatest-Quests-Mathematics/dp/
0192807226
http://iridia.ulb.ac.be/~marchal/
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Received on Fri Sep 29 2006 - 06:53:23 PDT