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From: Archimedes Plutonium on 29 Mar 2010 12:44


A wrote:

>
> Isn't the probability of both of two independent events occurring--the
> intersection of the set of outcomes in which event A occurs with the
> set of outcomes in which event B occurs--exactly the probability of
> event A occurring multiplied by the probability of event B occurring?
>

Excellent, excellent link up. Here is a way of relating what Algebra
is, and
whether Probability theory is bigger than algebra (which I think it
is) and
thus Algebra a subset of Probability theory.

I am beginning to think that Algebra is what the units of definition
are in Physics.
For example in Physics velocity is m*s^-1, and acceleration is m*s^-2,
and force is m*a.
Now if I were doing say mathematics instead of physics, I would be
saying that
velocity is a semigroup and that acceleration is a group and the a
force is a ring.

Anyway, a long time ago a physics Stanford professor once told me that
if I were
dissatisfied with angular momentum or "action" or force or momentum,
and if I were
so dissatisfied with those definitions and went out to invent my own
brand new set
of definitions for Physics, that exercise was all for nought. Because
whatever new
set of units of measure I ever come up with, in the end, they are
recalibrated to be
one and the same as the units of measure we currently have in place.

So I think that is what Algebra of group/ring/field are all about in
the first place. They
are a sneaky way of expressing physics in mathematics. When a
physicist talks about
energy, momentum, angular momentum, force, action, pressure,
acceleration, velocity,
what they are talking about is really what mathematicians call group,
semigroup, ring,
field, semiring, etc etc.

But let me talk more about that later, I have other things on my mind
today.

Let me stew on your question for a while and see if I can add anything
to it,
at least before 15 April, for I want
to pursue Uncertainty Principle as inverse of Geometry Principle while
my
mind is still fresh on it.

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
From: A on 29 Mar 2010 13:33
On Mar 29, 12:44 pm, Archimedes Plutonium
<plutonium.archime...(a)gmail.com> wrote:
> A wrote:
>
> > Isn't the probability of both of two independent events occurring--the
> > intersection of the set of outcomes in which event A occurs with the
> > set of outcomes in which event B occurs--exactly the probability of
> > event A occurring multiplied by the probability of event B occurring?
>
> Excellent, excellent link up. Here is a way of relating what Algebra
> is, and
> whether Probability theory is bigger than algebra (which I think it
> is) and
> thus Algebra a subset of Probability theory.
>
> I am beginning to think that Algebra is what the units of definition
> are in Physics.
> For example in Physics velocity is m*s^-1, and acceleration is m*s^-2,
> and force is m*a.
> Now if I were doing say mathematics instead of physics, I would be
> saying that
> velocity is a semigroup and that acceleration is a group and the a
> force is a ring.
>
> Anyway, a long time ago a physics Stanford professor once told me that
> if I were
> dissatisfied with angular momentum or "action" or force or momentum,
> and if I were
> so dissatisfied with those definitions and went out to invent my own
> brand new set
> of definitions for Physics, that exercise was all for nought. Because
> whatever new
> set of units of measure I ever come up with, in the end, they are
> recalibrated to be
> one and the same as the units of measure we currently have in place.
>
> So I think that is what Algebra of group/ring/field are all about in
> the first place. They
> are a sneaky way of expressing physics in mathematics. When a
> physicist talks about
> energy, momentum, angular momentum, force, action, pressure,
> acceleration, velocity,
> what they are talking about is really what mathematicians call group,
> semigroup, ring,
> field, semiring, etc etc.
>
> But let me talk more about that later, I have other things on my mind
> today.
>
> Let me stew on your question for a while and see if I can add anything
> to it,
> at least before 15 April, for I want
> to pursue Uncertainty Principle as inverse of Geometry Principle while
> my
> mind is still fresh on it.
>



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.

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.

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."



> Archimedes Plutoniumhttp://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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