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From: Archimedes Plutonium on 26 Jul 2010 15:25


Archimedes Plutonium wrote:
> Archimedes Plutonium wrote:
> (snipped)
> >
> > Where there are 10^536 such numbers, all having exactly 268 digits in
> > base_268
> > not base_10 but base_268.
> > Now the question is, in base_10, do I have every number covered from 0
> > to 10^536
> > within those permutations of 268 digits in base_268? Has anyone ever
> > asked such a
> > question before?
> >

I would guess "no", since it is very easy to think that bases in
arithmetic are
meaningless outside of arithmetic, and inside arithmetic the changing
of base
has no more meaning than to think that two five dollar bills is any
different than
one ten dollar bill.



> > But whether that idea gets me into a geometry outlook is not at all
> > obvious in any sense.
> > Instead it looks as though I am deeper into numbers and algrebra,
> > rather than having converted probability theory into geometry
> > concepts.
> >
>
> Unless, of course, factorial to exponental or vice versa is a
> conversion of
> geometry from say Elliptical geometry to Hyperbolic geometry.
> In the above, notice that 268! = 10^536 that the 268! is every
> possible digit
> arrangement of sequences 268 digits long in base_268. And there are
> 10^536
> such cases of string-sequences within base_268. Now if we consider
> that the Sphere
> surface is composed of string-sequences having a strip-width, can we
> not say that the
> sphere surface is 10^536 strips of 536 digits long and the
> pseudosphere that corresponds to this sphere are strips of 268 digits
> long?
>
> So that base conversion in algebra or numbers would be like geometry
> conversions. For example, a sphere has in a sense two faces as front
> and back, but a cube has six faces, yet both topologically equivalent.
> So now we can make topologically equivalent many sided objects from a
> sphere or cube and these would be different bases and base conversions
> which
> in geometry would be perhaps icosehedron or dodecahedron conversions
> from sphere.
>
> Now all I need to get is the 1/2 spin in physics from the idea that
> 268! = 10^536 where
> 268 is 1/2 of 536. So, just maybe, that 1/2 spin that is essential and
> vital throughout physics
> comes from the fact that all geometry objects originate from a sphere
> with 2 faces. Where you topologically bend the sphere into other
> objects.
>
> Maybe no-one recognized, before that a sphere has 2 faces. Maybe
> everyone assumed
> a sphere has 0 or 1 face. I sort of looked at a sphere and define a
> face as that of where
> you can only see the object via a single face, so that a cube can be
> rotated 6 times to see
> only 6 faces. A sphere can only be rotated such that 1/2 of the sphere
> is visible.
>

Alright, let me make a tentative stab at Geometrical-Probability
theory.

We certainly have 268! = 10^536 and now we apply Probability theory
which says:

In base_268 we have a total of 10^536 string-sequences all of which
are
268 digits long.

Now we are tempted to ask the question of whether, when sticking only
to base_10
whether we have every number from 0 to 10^536 listed in those base_268
string sequences?
I am confident we do.

Now we convert that information of probability theory of factorial to
exponental into geometry.

Imagine a super topologist smith-iron-worker. That you deliver him
strip sheets of iron and he
can craft any sphere and pseudosphere from these iron strips. And you
deliver him 536 strips
of iron and tell him to craft a maximum sphere with those 536 strips
of iron. And he does so.

Now you tell him the next day with another deliver of 536 strips of
iron to craft a pseudosphere
that has the same diameter as the sphere. And you return the next day
to see your pseudosphere and ask how many strips of iron did he
consume in making the pseudosphere and the answer is only 268 of the
strips out of 536 strips were used to make the pseudosphere.

So, tentatively, I suspect where probability theory of factorial
versus exponental converges into geometry is the idea that the amount
of surface material to build a sphere and its associated pseudosphere
is this factorial at about 253! and beyond that is the building of the
sphere and pseudosphere from strips. We can consider each strip as a
face and so a sphere
would be 536 faces of iron strips molded together by our expert
topologist and that the associated pseudosphere is 268 strips.

And in physics, why does all mass/matter particles have spin 1/2?
because they are from
Elliptical geometry of a sphere which has 2 faces. A particle with
spin 1 has 1 face, meaning
that it is a wave and not a geometry-object like a sphere or cube or
octogon. Now it is interesting that the neutrino also has spin 1/2,
meaning that it is not a wave but a particle
of geometrical object and which further means it must have a rest-
mass.

So I think the biggest beneficiary of Geometrical-Probability theory
is going to be Physics,
and that mathematics will only look on in curiousity.

Archimedes Plutonium
http://www.iw.net/~a_plutonium/
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
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