Science > Physics > Quantum Gravity-Dark Energy as Zero-Infinity (Coded as 0-1) 21: How Fermat Discovered Coded Infinity in Quadrics and Conics
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Science > Physics |
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"OsherD" |
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14 Mar 2006 08:11:23 PM |
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Quantum Gravity-Dark Energy as Zero-Infinity (Coded as 0-1) 21: How Fermat Discovered Coded Infinity in Quadrics and Conics |
From Osher Doctorow
Pierre De Fermat of 1600s France preceded Sir Isaac Newton by some
20-30 years and discovered analytic/Cartesian geometry before
Descartes. He is most famous for the discovery of modern number
theory, which led to cryptography among other things.
Most people who look at the equations of quadrics and conics think of
the generalized second degree equation in two variables or three
variables which for conics is:
1) ax^2 + bxy + cy^2 + dx + ey + f = 0 (a, b, c, d, e, f constants)
However, we all learn in analytic/Cartesian geometry that (1) can be
rewritten for ellipses (using a, b again for brevity, although they're
not the same constants as in (1)):
2) [(x - xo)^2]/a^2 + [(y - yo)^2]/b^2 = 1
Similarly for ellipsoids which are quadrics, except that there is also
a [(z - zo)^2]/c^2 term as well. Respectively circles and spheres are
special cases with a = b or a = b = c.
But ellipsoids including spheres and ellipses including circles are
closed, while the remaining nondegenerate geometric objects are in
general open.
Notice that both terms on the left hand side of (2) are nonnegative and
sum to 1, which also occurs for the corresponding three terms of
ellipsoids. Hence the quantity 1 express a total or sum which cannot
be exceeded. Moreover, it turns out that (x - xo)^2 < = a^2 and (y -
yo)^2 < = b^2 so that each term on the left hand side of (2) is < = 1.
Likewise for the corresponding situation with ellipsoids.
Does this look familiar? Yes! The 1 of both ellipsoids and ellipses
is a sum of terms which cannot exceed 1, like probabilities. There is
no ellipsoid or ellipse where the sum exceeds 1 even "formally" or
theoretically or hypothetically. Unlike the speed of light c, 1 in
these scenarios is not a finite number which formally can be exceeded
by simply writing a larger number than c. "Exceeding 1" in ellipses
and ellipsoids doesn't merely yield an imaginary number as in sqrt(1 -
v^2/c^2) if v were to exceed c, but rather it yields nothing period.
To exceed 1 would make the whole larger than the sum of its parts
geometrically.
The open conics and quadrics are not bounded in space but go off to
infinity in one or more directions, so across different classes of
curves or surfaces we can say that 1 distinguishes between two major
types (bounded and unbounded), but within the same class such as
ellipsoids 1 does not vary. In order for 1 to have occupied an
analogous position to the speed of light, it would have to be a finite
number which neither separates two real domains nor is capable of being
exceeded without contradictions. So 1 is not analogous to c, but it
is analogous to infinity here.
Osher Doctorow
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| User: "G. L. Bradford" |
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| Title: Re: Quantum Gravity-Dark Energy as Zero-Infinity (Coded as 0-1) 21: How Fermat Discovered Coded Infinity in Quadrics and Conics |
16 Mar 2006 05:49:56 AM |
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One ("1") light second per one ("1") second = c. Measurement of space is
actually relative.
A [might be] Multiverse Gravity-plus scenario:
If I could transit the diameter of the Milky Way galaxy in one
pico-second's time, I would not be in it. I would be "outside the box"
looking down and in (to a scaled down miniture of space), so to speak.
Comparatively (relative to it), I would be scaled up in space. I would
occupy a vast lot of simultaneous space, and a vast lot of simultaneous
external time zones, all at once in each pico-second of time, and each
second of time, that I would clock internally simultaneously with the
external whole that is [there and now] simultaneous with me [here and now]
as my local ground in space and time. "300,000 kilometers of space" would be
a little bit bigger relative to me than it would be relative to Einstein's
observer standing next to a railroad track on Earth. But my ruler, my
milimeter, my centimeter, my meter, would be exactly the same length of
ruler (milimeter, centimeter, meter) to me as his would be to him. My
clock's tick of each second of time would be exactly the same for me as his
clock's tick of each second of time. My cesium atom, to me, would be his
cesium atom to him. My measurement of the speed of light in a vacuum would
be exactly the same as his measurement of the speed of light in a vacuum.
My "inertial frame of reference" (beneath my feet where I stand) would be
the entire Milky Way galaxy in whole frame or ground zero unit. His
"inertial frame of reference" (beneath his feet where he stands) would be
the entire Earth in whole frame or ground zero unit.
Each spoke of a bicycle tire turns the same number of turns at the outer
rim end of each spoke as it does at the inner hub end of each spoke in the
same time. Each tick of the a clock is the same for hub end and rim end. The
rim does not gain distance on the hub either in space or in time, or either
in position or in velocity. The rim end of the spoke has no greater distance
to go in turning, in reality, than does the hub end of the spoke. Hub and
rim, both are based on [exactly] the same dead center of zero...common to --
the same to -- both at once (simultaneously).
If I could transit the diameter of a hundred billion galaxies worth of
space in one pico-second's time, I would not be anywhere among them. I would
be "outside the box" looking in to a scaled down miniature of space, so to
speak. Comparatively (relative to them), I would be scaled up in space. I
would occupy a vast lot of simultaneous space, and a vast lot of
simultaneous external time zones, all at once in each pico-second of time,
and each second of time, that I would clock internally simultaneously with
the external whole that is [there and now] simultaneous with me [here and
now] as my local ground in space and time. "300,000 kilometers of space"
would be a little bit bigger relative to me than it would be relative
to...... My measurement of the speed of light in a vacuum would be exactly
the same as [their measurements] of the speed of light in a vacuum.
My inertial frame of reference would be the ground of..... while
Einstein's observer's inertial frame of reference would be the ground of
Earth. It would be no bigger relative to me than his would be relative to
him. Locally, my observation of an atom, a proton, or an electron, and a
photon, and all atomic and subatomic qualities, quantities, behaviors, etc.,
would be identical to his (local to him). Locally, my observation of physics
would be identical to his (local to him). Locally, my observation of an
expanding universe, my universe, accelerating in expansion, would be
identical to his observation of an expanding universe, his universe,
accelerating in expansion. It would not be the same universe, though his
universe would be contained within mine. His dimensions of universe now
being simply a subset of mine.
Could you even begin to imagine what my navigational problems would be to
get back to our local universe, the Milky Way within it, and Earth? What
awesome turns and braking [accelerations] it would entail even if I had a
good hyper-dimensional map and navigating guide to go by to get back from
the universe (the position and the velocity) I would be in? What mass, and
what energy, relative solely to our local universe, to the Milky Way, and to
Earth, I and my vessel would either have to gain, or have to lose, depending
upon one's viewpoint? Relative to the Earth, infinity. Relative to me that
would be an ignorant moron's answer. I gained no more mass nor did I gain
any more energy (as I am, where I am). All that imaginary difference in mass
and energy would be real only in the difference [between] Earth and me
(neither existing there at that end nor here on my end). I would be having
only to lose magnitudes of order of dimensional differential [between] to
gain the relativity to our local universe, the Milky Way, and to Earth, I
would be wanting. And I had better be or have a great pilot and navigator,
and equally great [hyper-dimensional] maps and guide instructions.
As the traveler, I never traveled at any velocity whatsoever I could
measure. What would be my grounded measuring tool for velocity with me in an
all but complete vacuum? A vacuum where the speed of light is always
constant ("c"), even to me? All I could know was that I was changing
relative positions and proportional distance-sizes, swallowing into my local
frame of reference first the Milky Way then later on universes of hundreds
of billions of galaxies each. Every time I weighed myself on the scale in my
cabin I knew we were still doing an acceleration boost of 2g's, constant.
Externally, the infinite constant of [Multiversal Gravity] helped grease the
skids of acceleration more and more to ever increasing speeds (ever
accelerating expansion, relatively speaking that is) smoothly and
seamlessly...inertialessly. The turns and braking accelerations, or even
just shutting down the constant boost drive, switches my external
gravitational orientation to whatever the most local gravitational field
(most local or relative to me) would be.
End [might be] scenario.
One ("1") light second per one ("1") second = c. Measurement of space is
actually relative.
GLB
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| User: "OsherD" |
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| Title: Re: Quantum Gravity-Dark Energy as Zero-Infinity (Coded as 0-1) 21: How Fermat Discovered Coded Infinity in Quadrics and Conics |
14 Mar 2006 08:33:58 PM |
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From Osher Doctorow
The section of this thread on unit balls/spheres in functional analysis
can be regarded as simply an extension of the above considerations to
function spaces whether or not Cartesian coordinates are used. That
is to say, in a "real Cartesian representation of functions," the
ellipse/ellipsoid ideas hold, so they arguably carry through in
general. Or they can hold in modified norms. Or, to take a leaf out
of Einstein's book, they can even be postulated as an axiom (with no
formal violations, however). In a worst case scenario, norms of 1
would simply be the boundary of < 1 and >1 cases, which is O.K.
Osher Doctorow
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| User: "Zodness" |
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| Title: Re: Quantum Gravity-Dark Energy as Zero-Infinity (Coded as 0-1) 21: How Fermat Discovered Coded Infinity in Quadrics and Conics |
15 Mar 2006 09:59:58 PM |
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"OsherD" <> wrote in message
news:1142390038.000461.21210@e56g2000cwe.googlegroups.com...
From Osher Doctorow
The section of this thread on unit balls/spheres in functional analysis
can be regarded as simply an extension of the above considerations to
function spaces whether or not Cartesian coordinates are used. That
is to say, in a "real Cartesian representation of functions," the
ellipse/ellipsoid ideas hold, so they arguably carry through in
general. Or they can hold in modified norms. Or, to take a leaf out
of Einstein's book, they can even be postulated as an axiom (with no
formal violations, however). In a worst case scenario, norms of 1
would simply be the boundary of < 1 and >1 cases, which is O.K.
1 = Osher Doctorow = <1 again, just infinitesimally small
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