Science > Physics > Unification theory for Geometry: Riem + Loba = Eucl
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Science > Physics |
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24 Mar 2006 01:13:49 PM |
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Unification theory for Geometry: Riem + Loba = Eucl |
On Tues, Feb 7 2006 12:41 pm, Archimedes Plutonium wrote the below:
Email:
Groups: sci.math, sci.physics
Below is a picture of the Magnetic Field lines of force in physics.
This same picture can be seen in physics textbooks such as Electricity
And Magnetism, Berkeley Physics Course vol 2, 1965, E. M. Purcell, on
page 366. Or it can be seen in Fundamentals of Physics, Halliday &
Resnick, 3rd ed., 1988, on page 690.
I believe
this is the best model for my grand theory of mathematics:
Loba geom + Riem geom = Eucl geom
which translates into Native-Numbers of
negative signed Adic Rationals + Adic Integers = Reals
Now I am not quite sure that I need that straightline, but I need it
according to this model. In olden days I did not have straight lines in
the formula. In olden days I thought the best model was a hole in the
plane as Lobachevsky geom and the entire rest of the plane as Riemann
geom, or in 3rd dimension the torus extending to infinity as Loba and
the donut hole as Riem. But I think this model is better than the old
one.
I need some advice from Dik Winter as to whether in the below picture
the Adic Integers could be points of those curves to the right of the
straightline. And whether the curves to the left of the straightline
could be Adic Rationals once they are given a negative sign.
`-. .-'
`-. .-'
_,..-------..._ `. .' _...-------..,_
,,-' `-.. `. | .' ..-'
`-,,
,-' `-.`. | .'.-'
`-,
__..=......._ `.\ | /.' _.......=..__
,-; _..-----...__:. | .:' __.-----.._ -,
_,' ,-' _____ '. | .`:-'_____ `- `,_
/ ,' _.-''__...:..::. | .::..:...__``-._ `, \
,' ,' ,' _,' _,,,_ | _,,,_ `,_ `, `, `,
.' / ,' / ,' `, | ,' `, \ `, \ `.
| / ,' .' ,' `,|,' `, `. `, \ |
| / | | .' `|' `. | | \ |
| | | | | | | | | | |
| | | | | | | | | | |
| \ \ \ \ /|\ / / / / |
\ \ \ \ \ / | \ / / / / /
\ \ \ `. `._ _.' ||| `._ _.' .' / / /
\ `. `._ `..___`'' / | \ ``'___..' _.' .' /
`. `._ `-..______.;;// | \\;;.______..-' _.' .'
`._ `-.._____..-'.:// | \\:-:=.._____..-' _.'
`.._ .--','/ | \`,`-._ ..'
`'------'' ,',' | `,`, ``------`'
`-._ _,-' / | \ `-,_
_.-'
`-.__ __.-' ,' `, `-.__ __.-'
`'-------'' ,' `, ``-------`'
_,' `,_
mjp ,,' `,,
A.P. further writes on 24Mar06:
Well I am finally free of some side routes taken since Febr and am back
with my most beloved mathematics research. I want to prove that Eucl
geometry is a combination of Riem geom unioned (or added with) Loba
geom. This is important not only for geometry but it unifies Algebra
and Number theory because the native numbers (intrinsic or foundation
numbers) of Eucl geom are the Reals and for Riem are the Adics and for
Loba are the negative-adics. So not only do I unify geometry into one
body but also algebra and numbers.
Progress on this magnificent and beautiful project is slow. But it is
the most worthwhile mathematics ever done. It ties mathematics as a
subset of physics and it is physics that leads and commands the way.
Above is the best model I could think of to represent this unification
of Riem + Loba = Eucl. Where we imagine that the positive right side of
the above picture for all x greater than 0 is Riemiannian geometry of
positive curvature and whose numbers are Adic integers. For all x less
than 0, or negative x values is Lobachevskian geometry and underlying
are the negative-Adic Integers where we put a negative sign onto Adic
Integers.
And the union of these two curves is the entire Euclidean Plane,except
for the straight line that is the y-axis.
So this is the new progress today. Is that I need the Complex Plane
instead of the Euclidean Plane so that I can take care of that one
straight line that seems to mess up my formula.
So my formula should be this:
Riem geom + Loba geom + i-line = Complex plane
The Complex Plane is Eucl geom with the imaginary i- line as the
y-axis.
I believe my above is the finest and best model ever for Riem and Loba
geometries and it comes from the Maxwell Equations of physics.
And we know well that most higher level physics such as the Schrodinger
or Dirac Equations require Complex numbers and e and pi. We know the
famous equation:
e^(i x pi) = -1
where -1 is a Adic and pi a Real, and i is complex, but what about e.
Is there an e in Adics or is e confined to Reals?
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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| User: "" |
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| Title: Re: Unification theory for Geometry: Riem + Loba = Eucl |
04 Apr 2006 04:33:49 PM |
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wrote:
Below is a picture of the Magnetic Field lines of force in physics.
This same picture can be seen in physics textbooks such as Electricity
And Magnetism, Berkeley Physics Course vol 2, 1965, E. M. Purcell, on
page 366. Or it can be seen in Fundamentals of Physics, Halliday &
Resnick, 3rd ed., 1988, on page 690.
[..]
Just a quick remark on something you asked about a couple of
months ago - the origin of the word "washer" (perforated disk).
After buying the Oxford dictionary of word origins for a pound
in a charity shop at the weekend, I looked up the word and sure
enough it says the origin is unknown, as someone mentioned at
the time you asked.
But thinking about it the other day, I reckon the most likely
origin is "wast-sceard", combining two Saxon words: "wast"
meaning empty or vast (same as Latin "vastus" means waste),
and "sceard" means any of "fragment", "notch", or "gap",
according to the dictionary under the entry for "shard".
Presumably "shear" and "scar" comes from the same word.
.
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| User: "" |
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| Title: Re: Unification theory for Geometry: Riem + Loba = Eucl |
05 Apr 2006 01:10:11 AM |
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jhnrm wrote:
Just a quick remark on something you asked about a couple of
months ago - the origin of the word "washer" (perforated disk).
After buying the Oxford dictionary of word origins for a pound
in a charity shop at the weekend, I looked up the word and sure
enough it says the origin is unknown, as someone mentioned at
the time you asked.
But thinking about it the other day, I reckon the most likely
origin is "wast-sceard", combining two Saxon words: "wast"
meaning empty or vast (same as Latin "vastus" means waste),
and "sceard" means any of "fragment", "notch", or "gap",
according to the dictionary under the entry for "shard".
Presumably "shear" and "scar" comes from the same word.
A.P. writes:
And someone a month ago wrote that it comes from the French word
"vas" ?? Which sounds like "washer".
We would have to find where the first use of a washer ever came about,
whether as a spacer in a mechanical devise. And where the first "bolts"
in history came into use.
Whether it was viewed as some sort of keeping a watertight container by
a washer to the bolt and nut.
But this is far afield of this thread.
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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| User: "" |
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| Title: Re: Unification theory for Geometry: Riem + Loba = Eucl |
03 Apr 2006 01:51:33 AM |
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Now an interesting idea comes from the Unification of the Forces of
Physics into one Coulomb force. The idea is when does a unification
require addition and when does it require multiplication. To my earlier
post of 24Mar above I was using only + or addition to form a union of
the set of all negative adics to that of the set of all positive adics.
In Physics, the StrongNuclear force is a 3rd dimensional or volume
force whereas WeakNuclear force is 1st dimensional of rate of decay and
so when we _multiply_
3D by 1D we end up with 2D of the Coulomb inverse square force.
We see this again in Mathematics when we form the Complex numbers from
the Reals not by adding i but by the multiplying of every Real with i.
So there needs to be this detailed attention to when we multiply or add
to form a unification whether it is mathematics or physics.
So now in the above where I have the magnetic field and where I claim
the righthand portion is positive adics, then to get the lefthand
portion of negative adics, all I really need to do is what? Find
another imaginary and call it "adic imaginary".
But notice how we revert from the Complex back to the Reals by simply
dividing by i to remove the complex portion and we have a Real number.
But does that work for adic imaginaries. I would say no, because one of
the differences between an adic and a Real is that they are mirror
images such as a righthand glove is a mirror image of a lefthand glove
but we want identical. So if I dream up a imaginary adic system and
divide by this imaginary I still do not end up with a Real as per the
equation
Adics + negativeAdics = Reals.
But this complaint is not satisfied by addition either. The trouble is
that Reals are infinite strings rightward and adics infinite strings
leftward and somehow the Unification of this topic has to end up with
Reals or Complex plane.
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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