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From: Archimedes Plutonium on 29 Mar 2010 23:44


A wrote:
(snipped)
>
> The point I was trying to make is just that the uncertainty principle
> is by no means the first or only place in mathematics or physics where
> a number associated to an intersection of two subsets is the product
> of the numbers associated to the two subsets.
>

You put your finger on it. I do not know of any other math or physics
equation
that places numbers in association with a set. And the Uncertainty
Principle
to me places Planck's constant as a number for angular momentum in
connection
with two sets of the del_position and the del_momentum.

You say that there are other such equations. Well, I know of no other
such equation
where it has sets and numbers strewn into the equation. Seems to me,
that an Equation
has to be all or no sets, and all or no numbers. But to have an
equation that is parcelled
with both sets and numbers is hard to understand.

You say the Uncertainty Principle is not a unique equation. I say it
is.

And even the new principle of the Geometry Principle which I contend
is the inverse
of the Uncertainty Principle.

Geometry Principle:
Eucl geometry == Elliptic geom unioned with Hyperbolic geom

Even that equation involves three sets, unlike the Uncertainty
Principle which involves
two sets and a number.

So, thanks for asking the question, because the way to resolve it is
that neither the
Uncertainty Principle nor the Geometry Principle are equations for
there never is a
equal sign in there, and what there should be is a "greater than sign
>" in the
Uncertainty Principle where it can not be equal and where the Planck
constant is
singleton set having only one member {h} and where this set is smaller
than either
the position and momentum sets multiplied or intersecting and where we
have a
"order on sets with more than one member".

As for the Geometry Principle, there is no equation but rather an
equivalency relationship
which I write as "=="

So if you are aware of more, or other equations or relations in math
or physics that
has a mix of sets and numbers, please inform, for I know of no others,
at least, important
others.

> At any rate, it is not the case that probability is a subset of
> algebra, or algebra is a subset of probability--the two fields are
> independent, use different methods, and answer different questions.
>

No, I have a different opinion.

My science mind tells me that Physics is top, and that means all the
other sciences
are subsets, so we can place in a hierarchy list where chemistry is
closer to physics than
say geology and that biology is closer to physics than is sociology
but all of these sciences
reduce to what the physics is going on. And that logic also says that
every math subject falls into a hierarchy of subsets, and every
physics subject also falls into a hierarchy of subsets.

The heart of math is probably the dual pair of geometry and numbers.
Algebra fits somewhere
as a subset of numbers, same with probability theory and set theory.
The question is whether
probability theory is closer to Number theory over that of algebra and
over that of set theory.
Example: chemistry is closer to physics than is biology or geology.

So that we have Quantum Mechanics as the heart of Physics and where
thermodynamics
is a subset of Quantum Mechanics and where Maxwell Equations and
electrodynamics
are each subsets of QM and where each of these fit as subsets, whether
one is closer
to QM than another is fun to find out.


> I also do not know what you mean when you write that "velocity is a
> semigroup and that acceleration is a group and the a force is a ring."

I was making an observation. An observation that noone in mathematics
ever addressed the question why is Algebra so filled up with group,
ring and field when it was first borne by
Galois to solve the quintic and so, why is modern math so saturated
with this group ring and
field speak? So no mathematician ever squarely faced or answered that
question.

But I have answered it. Math is a subset of Physics, and so, where in
physics is this
structural importance. A group, ring and field is no more than a
classification-structure.
We define a structure like a group or a ring. It must meet specific
criteria. Then we can
make deductions. So if math is a subset of Physics, then physics must
have these
"classification structures" just like math. And it is not far to look
into Physics to see where
classification structures exist. In fact, probably the first day in a
Physics class you learn a few structures: You learn mass is "m" and
that length or distance is "d" and that time is "t",
but then in advanced physics you get some bigger structures of F = ma,
or acceleration
is m*s^-2, or pressure is dyne*cm^-2 or density is g*cm^-3 or
resistivity is ohm*cm,
or angular momentum erg*s

Each of these structures in physics, the units of the definition, are
the same structures
that Algebra gives to calling a semigroup or a group or a ring etc
etc.

So on one side of the table, a physicist playing around with momentum,
force, energy,
inductance etc etc, is the same thing as the mathematician on the
other side of the table
playing around with groups, rings, fields. Both are playing with
classified structures in
their science.

Now do not hold me to saying that a force is a ring in physics. That
was never my intention.
What I was trying to say is that all the structures of physics of
their parameters, is similar to
the mathematician with all his structures of algebra. Do not think
that a force is a ring, but rather, think that the entire spectrum of
group ring and field is the akin to the entire spectrum
of physics unit-dimensions.

And obviously, noone can do physics without doing these unit-
dimensions of Force =ma
and that is why Algebra group ring and field keep cropping up all over
the place in
math.

And why noone before me could ever explain the above, because noone
before me ever
realized that Physics comes first and explains all of mathematics in
its proper perspective.

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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