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From: Archimedes Plutonium on 24 Dec 2009 01:25


Archimedes Plutonium wrote:
> My foray into the legal system and reflecting on laws that are
> contradictory to one another, unless, of course
> as in the Legal System you have an overriding principle of that of
> "precedence".
>
> So I think I may have stumbled upon something of huge importance to
> mathematics and to physics. We
> commonly understand math and physics that the concept of consistency
> is vital to them and overarching
> and prime importance, especially mathematics.
>
> But now, consider, what if true math and true physics
> have a concept of "precedence" and not that universal
> constant of consistency. That a true mathematics can have local
> contradictions of where one theorem contradicts another, but that when
> Precedence is applied, that the whole of mathematics is consistent.
>
> So yesterday I started this discussion, and was wondering whether
> Physics had a "precedence concept" already within the body of physics.
> Is Quantum Tunnelling a "precedence mechanism"?
>
> Is Renormalization in Quantum Electrodynamics the acts or actions of
> placing precedence over features or
> aspects of a physical phenomenon? Is the principle in
> Physics of Least Action, is that not a principle of Precedence?
>
> Now in mathematics it may be much harder to sift out a feature of
> precedence as it relates to consistency. But one feature of
> mathematics that has always bothered me or troubled me in a mild way
> is the idea
> that in trigonometry or in geometry that as you circumnavigate the
> globe that you come back to 0 and it is not 2pi and then 4pi and then
> 6pi etc etc. So are we in effect saying that 0 = 2pi and is that not a
> act of
> precedence?
>
> And then there is Quantum Logic which is not Aristotlean Logic.
>
> So I am wanting to focus with a sharp lens on the
> concept of consistency which everyone in mathematics takes for granted
> as a vital unmoving
> essential concept that is constant. But maybe in truth
> it is not primary but secondary and that it is more like
> a variable than a constant. And that maybe the truth of
> mathematics does not depend on consistency but rather a principle such
> as is found in the Legal System
> of Precedence.
>

I think I can point my finger at the source of why Mathematics and
Physics cannot
have a constant all encompassing Consistency but must settle for far
less. Where
Consistency is a variable, and where the Legal System with its
precedence-mechanism
can have contradictory statements yet be overall consistent.

I believe the source is Quantum Duality, in that a phenomenon must
have both a wave
nature and a particle nature and you cannot separate out the two. So
that the wave nature
is all consistent as waves but has some particle nature which would be
contradictory
to the wave. I believe this is also the root source of Quantum
Tunnelling in that being all
particle it is impossible for a particle to escape a closed well, but
since there is wave
nature the wave can have a particle materialize outside the closed-
well.

Now how does this affect mathematics? Well we can consider the wave
nature as geometry
and the particle nature as algebra. And we can see some theorems of
geometry when
compared to some of algebra are contradictory. But overall, all the
geometry theorems look
to be consistent with one another, ditto for algebra, but the two
together have contradictory
theorems without the duality.

But also, the fact that Physics is the all encompassing science and
math a subset of physics, which means that since Physics has a
variable-consistency, implies that mathematics cannot have a constant-
consistency.

For those who do not understand science well enough and wondering what
I am saying above.
Simply stated, consistency as a overall characteristic of mathematics
is not a important
characteristic of mathematics. It is not a primal feature of
mathematics but rather a secondary feature of mathematics. A feature
like mass or charge or spin are primary features of physics, whereas
color, shape, size are secondary features that vary.

The idea that consistency in mathematics is a variable changes much of
our understanding
of mathematics. For it changes our ideas of "proof of mathematics" and
that proofs are
not true everlasting but merely local-truths, or situational truths.


Archimedes Plutonium
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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