| Topic: |
Science > Physics |
| User: |
"Russell E. Rierson" |
| Date: |
04 Jul 2003 12:10:16 AM |
| Object: |
Symmetry Forms the Basis of Truth |
Some more thoughts...
The universal laws of nature are explained in terms of symmetry. The
completed infinities, mathematician Georg Cantor's infinite sets,
could be explained as cardinal identities, akin to "qualia" from which
finite subsets, and elements of subsets, can be derived.
Completed infinities, called "alephs" are distributive in nature,
similar to the way that a set of "red" objects has the distributive
property of redness. Predicates like "red" are numbers in the sense
that they interact algebraically according to the laws of Boolean
algebra. Take one object away from the set of red objects and the
distributive number "red" still describes the set. The distributive
identity "natural number" or "real number" describes an entire
collection of individual objects.
These alephs can be set into a one to one correspondence with a proper
subset of of themselves. The "infinite" Cantorian alephs are really
distributive.
Yet, if we have a finite set of 7 objects, the cardinal number 7 does
not really distribute over its individual subsets. Take anything away
from the set and the number 7 ceases to describe it.
Symmetry is analogous to a self evident truth and is distributive via
the laws of nature, being distributed over the entire set called
universe. A stratification of Cantorian alephs with varying degrees of
freedom. More freedom = greater symmetry = higher infinity-alephs. So
the highest aleph, the "absolute-infinity" distributes over the entire
set called universe and gives it "identity".
The highest symmetry is a distributive mathematical identity. This
fact is reflected in part, by the conservation laws.
So if an unbound-infinite-potential and a
constrained-finite-bound-potential are somehow different yet the same,
the difference and sameness relation is a duality. Freedom(higher
symmetry) and constraint(lesser symmetry) forms a relation that can be
described by an invariance principle.
On a flat Euclidean surface, the three angles of a triangle sum to 180
degrees. On the curved surface of a sphere, the three angles add up to
more than 180 degrees. The two types of surfaces are not equivalent.
There is a rotational invariance for a triangle, that seems to hold
for both types of surface though.
ABC = BCA = CAB = CBA = BAC = ACB
Does this rotational invariance hold for all geometries? I say yes,
but I am not 100% sure yet. 99.999% It seems to point towards a type
of duality for quantum mechanics and general relativity.
An interesting idea for a new "theory-conjecture" which is, that
symmetry, not logic, forms the basis of mathematical truth.
Truth = Invariance principle.
Symmetry = invariance = identity
Aristotle's law of excluded middle is really an invariance principle.
Symmetry forms the basis of logic.
A V ~A
T|F = F|T = T
f(1,0) = f(0,1)
f(x,y) = f(y,x) ?
Certain "invariants" are true for all(or most) geometries.
Let "I" stand for the generic invariant
E and N can be functions of the invariants.
For example E could stand for Euclidean geometry and N could be
"non-Euclidean" geometry.
E(I) = N(I)
So it could be possible to unify general relativity and quantum
mechanics with *symmetry*? The duality of circle and square.
Russell E. Rierson
analog57@yahoo.com
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| User: "Uncle Al" |
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| Title: Re: Symmetry Forms the Basis of Truth |
04 Jul 2003 03:43:44 PM |
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"Russell E. Rierson" wrote:
Some more thoughts...
The universal laws of nature are explained in terms of symmetry.
A relativistic universe has no global conservation laws. Pookie
pookie.
The
completed infinities, mathematician Georg Cantor's infinite sets,
could be explained as cardinal identities, akin to "qualia" from which
finite subsets, and elements of subsets, can be derived.
You just broke my ***** meter.
[snip]
So it could be possible to unify general relativity and quantum
mechanics with *symmetry*? The duality of circle and square.
No, stooopid. General Relativty and quantum mechanics are
fundamentally incompatible.
Planck's constant (h, enforces uncertainty in measurement; h-bar is
the fundamental unit of action), Newton's constant (Big G, scales
gravitation), and lightspeed (c, enforces information transfer delay)
define physics:
? h=h G=G c=infinity
mechanics,
electrostatics: h=zero G=zero c=infinity
classical physics: h=zero G=G c=infinity
quantum mechanics: h=h G=zero c=infinity
special relativity: h=zero G=zero c=c
general relativity: h=zero G=G c=c
quantum field theory: h=h G=zero c=c
Theory of Everything,
Grand Unified Theory: h=h G=G c=c
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!
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| User: "Russell E. Rierson" |
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| Title: Re: Symmetry Forms the Basis of Truth |
05 Jul 2003 10:03:06 PM |
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Uncle Al <UncleAl0@hate.spam.net> wrote in message news:<3F05E700.D646E042@hate.spam.net>...
"Russell E. Rierson" wrote:
Some more thoughts...
The universal laws of nature are explained in terms of symmetry.
A relativistic universe has no global conservation laws. Pookie
pookie.
You mean the present theories of the universe have no global
conservation laws ...yet.
The
completed infinities, mathematician Georg Cantor's infinite sets,
could be explained as cardinal identities, akin to "qualia" from which
finite subsets, and elements of subsets, can be derived.
You just broke my ***** meter.
Yes, bears do s**t in the woods. Does the universe have a mathematical
identity?
Are you saying that it does not?
Some interesting ideas about "category theory":
Category theory:
http://math.ucr.edu/home/baez/categories.html
http://math.ucr.edu/home/baez/symmetries.html
Interesting ideas...
http://www.mmsysgrp.com/stefanik.htm
QUOTE:
Thesis:
Scientific objectivity is best characterized by the concept of
invariance as explicated in category theory than the concept of truth
as explicated in mathematical logic.
END QUOTE
Russell E. Rierson
analog57@yahoo.com
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| User: "Anthony Cerrato" |
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| Title: Re: Symmetry Forms the Basis of Truth |
06 Jul 2003 04:14:56 AM |
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"Russell E. Rierson" <analog57@yahoo.com> wrote in message
news:c410ffa5.0307051903.6b652ba0@posting.google.com...
Uncle Al <UncleAl0@hate.spam.net> wrote in message
news:<3F05E700.D646E042@hate.spam.net>...
"Russell E. Rierson" wrote:
Some more thoughts...
The universal laws of nature are explained in terms of
symmetry.
A relativistic universe has no global conservation laws.
Pookie
pookie.
You mean the present theories of the universe have no
global
conservation laws ...yet.
The
completed infinities, mathematician Georg Cantor's
infinite sets,
could be explained as cardinal identities, akin to
"qualia" from which
finite subsets, and elements of subsets, can be
derived.
You just broke my ***** meter.
Yes, bears do s**t in the woods. Does the universe have a
mathematical
identity?
Are you saying that it does not?
Some interesting ideas about "category theory":
Category theory:
http://math.ucr.edu/home/baez/categories.html
http://math.ucr.edu/home/baez/symmetries.html
Interesting ideas...
http://www.mmsysgrp.com/stefanik.htm
QUOTE:
Thesis:
Scientific objectivity is best characterized by the
concept of
invariance as explicated in category theory than the
concept of truth
as explicated in mathematical logic.
END QUOTE
Russell E. Rierson
analog57@yahoo.com
Wow! Deep stuff. I sure have a new respect for modern
mathematical physics. If I interpret (some of) this stuff
correctly, there really is a nascent philosophy of QM and
potential TOEs here which may someday lead to complete
understanding of "it all." However it might take physicists
hundreds of years to get it all, and someone like me
thousands, if I started today. :) I gather that y'all
really think there's a big future in at least thinking 'bout
these subjects catagorically, rather than seeking other
paradigms. I am awash in a fog of faint understanding of
where physics is headed someday, wishing I had chosen the
path of math rather than chemistry way back then.
....tonyC
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