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 ;)
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.
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*?). 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". 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.
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