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From: Tim Golden BandTech.com on 21 May 2010 08:43
On Apr 2, 7:56 am, James Dow Allen <jdallen2...(a)yahoo.com> wrote:
> On Apr 2, 11:43 am, Danny73 <fasttrac...(a)att.net> wrote:
>
> > But here on the three dimensional earth grid it
> > is 6 directions ---
> > North,South,East,West,Skyward,Earthward. ;-)
>
> Let me try to inject a serious question I have into
> this thread. ;-)
>
> In a hexagonal grid, each point has six immediate neighbors;
> what should their names be? (I asked this question before,
> with the only answer being the ugly "solution I was
> already using: West, Northwest, Northeast, East, SE, SW.)
>
> Hexagonal grids have big advantages over square grid
> but are seldom used. It sounds silly, but perhaps
> lack of the msot basic nomenclature is one reason!
>
> James Dow Allen

There are only three directions needed to address the plane.
Within polysign their names are
-, +, *
or 'minus', 'plus', 'star'; which are mnemonically
1, 2, 3
as these are the number of strokes to draw those symbols. These three
directions are the only directions that are required, and their
opposed directions are composed of the sum of the others:
Inverse( - 1 ) = + 1 * 1
These are what I call 'simplex coordinates' and have the behavior
- 1 + 1 * 1 = 0 .
Which is the symmetrical generalization of the real line behavior
- 1 + 1 = 0
and so we are half way to defining the three-signed numbers. Upon
defining the product, which is much easier, then you would eventually
see that these three signed numbers are equivalent to the complex
numbers:
http://bandtechnology.com/PolySigned/ThreeSignedComplexProof.html

- Tim
From: spudnik on 21 May 2010 14:46
that just makes me feel completely hopeless.

- Don't show quoted text, please -

thusNso:
ah, yes; the perfect reflector (lightsail) would
have to actually "adsorb" the momentum
of the puffy little photons, so that ... so that
-- so, there!

- Show quoted text -

thus:
I mean, they don't even have to be next to each other
(technical defintion of "next" to follow .-)

> parallel lines that do not go to infinity never converge, like in FLT, there never is a success. And that is the key to Fermat's, dood.

thusNso:
I can see that you're a victim of "General Semantics and
the Nine E-primes." what ever in Hell you think that
you were saying, it does seem that "one period
of lightwaving," howsoever properly defined, would
be a sufficient unit of h-bar as a scalar of time --
if not a dimensionless constant (a "scalar" should
be a dimensionless quantity to count some thing).

did that make any sense at all?

--Pi, the surfer's canonical value, is not constructible
with a pair of compasses .. but, could be with a pair and
a half of compasses; dyscuss.
From: Thomas Heger on 21 May 2010 23:33
Tim Golden BandTech.com schrieb:
> On Apr 2, 7:56 am, James Dow Allen <jdallen2...(a)yahoo.com> wrote:
>> On Apr 2, 11:43 am, Danny73 <fasttrac...(a)att.net> wrote:
>>
>>> But here on the three dimensional earth grid it
>>> is 6 directions ---
>>> North,South,East,West,Skyward,Earthward. ;-)
>> Let me try to inject a serious question I have into
>> this thread. ;-)
>>
>> In a hexagonal grid, each point has six immediate neighbors;
>> what should their names be? (I asked this question before,
>> with the only answer being the ugly "solution I was
>> already using: West, Northwest, Northeast, East, SE, SW.)
>>
>> Hexagonal grids have big advantages over square grid
>> but are seldom used. It sounds silly, but perhaps
>> lack of the msot basic nomenclature is one reason!
>>
>> James Dow Allen
>
> There are only three directions needed to address the plane.
> Within polysign their names are
> -, +, *
> or 'minus', 'plus', 'star'; which are mnemonically
> 1, 2, 3
> as these are the number of strokes to draw those symbols. These three
> directions are the only directions that are required, and their
> opposed directions are composed of the sum of the others:
> Inverse( - 1 ) = + 1 * 1
> These are what I call 'simplex coordinates' and have the behavior
> - 1 + 1 * 1 = 0 .
> Which is the symmetrical generalization of the real line behavior
> - 1 + 1 = 0
> and so we are half way to defining the three-signed numbers. Upon
> defining the product, which is much easier, then you would eventually
> see that these three signed numbers are equivalent to the complex
> numbers:
> http://bandtechnology.com/PolySigned/ThreeSignedComplexProof.html
>
Hi Tim
I guess, I finally understand your system. Seems -btw- similar to what I
call triality. Given an arbitrary direction, which is that point I call
observer and his timeline, I call the directions left and right, what
are spacelike and zero is timelike. These build a triangle. Than we flip
over one triangle, push it a bit down and connect the edges to get a
hexagon.
In a space build by the diagonals, that cuts a series of triangles in
the middle, those triangles would form a zigzag-line, what is a helical
screw from the side. That is the timeline for light.
In the middle we find two lines, that connect the sides on a line, that
crosses the center. One could imagine those to rotate and flip one line
to the other and something going out and in. In the zero direction, we
have the spacelike left and right swirling around an axis.
That is a bit in the way I model atoms, only that I use tetrahedrons
('in volume') and bi-quaternions. The star tetrahedron has something
equivalent to hexagons, but I forgot the name again (one of the platonic
solids). And it touches a sphere from the inside, like the other
platonic solids, too. This sphere rotates like a micro-earth. Actually
there are two twisting in opposite directions. The angle between them
corresponds to the amount of 'push' mentioned above and denotes mass.
That is between two triangles touching and have no mass, to the even
hexagon and a perfect sphere, that has infinite mass.
If we take one of those swirling lines and treat that as an axis, than
other lines would wobble around it, that were fixed in the previous way.

Greetings

TH
From: Tim Golden BandTech.com on 22 May 2010 08:56
On May 21, 11:33 pm, Thomas Heger <ttt_...(a)web.de> wrote:
> Tim Golden BandTech.com schrieb:
>
> > On Apr 2, 7:56 am, James Dow Allen <jdallen2...(a)yahoo.com> wrote:
> >> On Apr 2, 11:43 am, Danny73 <fasttrac...(a)att.net> wrote:
>
> >>> But here on the three dimensional earth grid it
> >>> is 6 directions ---
> >>> North,South,East,West,Skyward,Earthward. ;-)
> >> Let me try to inject a serious question I have into
> >> this thread. ;-)
>
> >> In a hexagonal grid, each point has six immediate neighbors;
> >> what should their names be? (I asked this question before,
> >> with the only answer being the ugly "solution I was
> >> already using: West, Northwest, Northeast, East, SE, SW.)
>
> >> Hexagonal grids have big advantages over square grid
> >> but are seldom used. It sounds silly, but perhaps
> >> lack of the msot basic nomenclature is one reason!
>
> >> James Dow Allen
>
> > There are only three directions needed to address the plane.
> > Within polysign their names are
> > -, +, *
> > or 'minus', 'plus', 'star'; which are mnemonically
> > 1, 2, 3
> > as these are the number of strokes to draw those symbols. These three
> > directions are the only directions that are required, and their
> > opposed directions are composed of the sum of the others:
> > Inverse( - 1 ) = + 1 * 1
> > These are what I call 'simplex coordinates' and have the behavior
> > - 1 + 1 * 1 = 0 .
> > Which is the symmetrical generalization of the real line behavior
> > - 1 + 1 = 0
> > and so we are half way to defining the three-signed numbers. Upon
> > defining the product, which is much easier, then you would eventually
> > see that these three signed numbers are equivalent to the complex
> > numbers:
> > http://bandtechnology.com/PolySigned/ThreeSignedComplexProof.html
>
> Hi Tim
> I guess, I finally understand your system. Seems -btw- similar to what I
> call triality. Given an arbitrary direction, which is that point I call
> observer and his timeline, I call the directions left and right, what
> are spacelike and zero is timelike. These build a triangle. Than we flip
> over one triangle, push it a bit down and connect the edges to get a
> hexagon.
> In a space build by the diagonals, that cuts a series of triangles in
> the middle, those triangles would form a zigzag-line, what is a helical
> screw from the side. That is the timeline for light.
> In the middle we find two lines, that connect the sides on a line, that
> crosses the center. One could imagine those to rotate and flip one line
> to the other and something going out and in. In the zero direction, we
> have the spacelike left and right swirling around an axis.
> That is a bit in the way I model atoms, only that I use tetrahedrons
> ('in volume') and bi-quaternions. The star tetrahedron has something
> equivalent to hexagons, but I forgot the name again (one of the platonic
> solids). And it touches a sphere from the inside, like the other
> platonic solids, too. This sphere rotates like a micro-earth. Actually
> there are two twisting in opposite directions. The angle between them
> corresponds to the amount of 'push' mentioned above and denotes mass.
> That is between two triangles touching and have no mass, to the even
> hexagon and a perfect sphere, that has infinite mass.
> If we take one of those swirling lines and treat that as an axis, than
> other lines would wobble around it, that were fixed in the previous way.
>
> Greetings
>
> TH

Hi Thomas. Your descriptions are very complex. It is impressive and I
know that you have good visualization skills. Still, there are things
fundamental which do not deserve so much complexity, which is why we
would call them fundamental. So I keep asking you to consider the
fundamentals as replaceable in the hopes that you will latch onto some
things that lay buried in false assumption.

The hexagonal shape within P3 does not require any more than those
three unit rays minus, plus, and star:
http://bandtechnology.com/PolySigned/Lattice/P3Signon.gif
The packing shape is nucleated, a word I was introduced to by a
gentleman on yahoo's synergeo group. Wouldn't you think the Fullerites
would attach onto polysign? Nope, they wish to stick with their Fuller
Bible, which is insistent on remaining in 3D rather than going general
dimensional. Urner has dissected what he calls 'quadrays' which are
very appropriately named, and nearly the same as polysign, but without
the product and without the zero sum clearly stated, which is the key
to sign generalization.

The signon is hexagonal (in P3) on its exterior, but the signon
contains directed segments:
http://bandtechnology.com/PolySigned/Lattice/Lattice.html
This exposes the polysign lattice as different from the traditional
hexagonal lattice. Some of the steps on the traditional hexagonal
lattice would be called diagonals if you tried to go in those inverse
directions.

In some ways you could say that the polysign lattices conserve a
unidirectional nature, except that this statement is compromised by
the quantity of directions. That statement is more of a corrective
concept on the real valued assumption. Upon entering the continuum
ordinary geometry is recovered, but within the simplex coordinate
system.

The 3D shape is the rhombic dodecahedron. The signa pack space and so
are presumably important to a calculus on polysign. Of course as you
discuss a time feature within the P3 hexagon, I ask you to consider P1
and its obvious time correspondence. Then emergent spacetime lays a
few more steps away and emergent electromagnetism nearby to that, and
product behavior as fundamental to physics, though it seems to me that
the magnitude portion requires some corrective surgery such as the 1/(x
+1) transform I've babbled on about in the past.

Is time informationally orthogonal to space? If we can still apply a
relative reference frame to a structured spacetime then is there any
conflict in identifying an anisotropic frame per particle? Is the
electron's frame of reference isotropic? These I believe are
productive directions of freedom to go toward, but I think within
their reversals of the modern standard there may be some other
fundamental constructions which will form a synergy. I take polysign
as evidence that further fundamentals remain to be discovered.

- Tim
From: Thomas Heger on 23 May 2010 02:34
Tim Golden BandTech.com schrieb:
> On May 21, 11:33 pm, Thomas Heger <ttt_...(a)web.de> wrote:
>> Tim Golden BandTech.com schrieb:

> In some ways you could say that the polysign lattices conserve a
> unidirectional nature, except that this statement is compromised by
> the quantity of directions. That statement is more of a corrective
> concept on the real valued assumption. Upon entering the continuum
> ordinary geometry is recovered, but within the simplex coordinate
> system.
>
> The 3D shape is the rhombic dodecahedron. The signa pack space and so
> are presumably important to a calculus on polysign. Of course as you
> discuss a time feature within the P3 hexagon, I ask you to consider P1
> and its obvious time correspondence. Then emergent spacetime lays a
> few more steps away and emergent electromagnetism nearby to that, and
> product behavior as fundamental to physics, though it seems to me that
> the magnitude portion requires some corrective surgery such as the 1/(x
> +1) transform I've babbled on about in the past.
>
> Is time informationally orthogonal to space?

Well, I think 'relativistic' and had to base my observations on a
special point -> me! Since the other beings seem to behave in this way
too, we grant this right to any object. That means, it is
'self-centred'. The world is observed from there and timeflow is
measured by a clock. (The clock itself is self-centred, too, but stays
in my vicinity. )

Distance is than measured as length in meters or light-years, but based
on this point of view. So I rightfully say, that this space rotates,
because I know, it doesn't exist anyhow in the way I observe it. So
there is no point in fixing the fixed stars, because I don't know where
there are (now!), only where they were many million years ago.

Things seem to rotate if we look into the sky, except if we look into
the direction of the North Star. Now I take the direction perpendicular
to our galaxy and draw a line through the centre and the Milky Way is
rotating around that. These two axes do not perfectly align, but wobble
a bit and larger radius seems to correlate with slower wobble. If I make
this faster, the disks get smaller. For very fast 'wobble', we get very
small disks.

Since all this happens at the same time, I can add the pictures together
and get a fractal pattern, that goes up or down - possibly way more
steps than we think. Since the Earth does not only rotate, but moves,
too, I assume that time is accompanied by a real movement, that we
usually can't see, because we are objects ourselves and move with it.
But objects with lesser 'wobble' move slower.

The direction is based on me (our you) and the worldline of a free
falling object would point downwards - in my FoR. But this is not a very
good view, because my clock is based on the earth rotation and we could
base the movement on a 'moon view' and see, that a vertically
free-falling object is actually performing a rotation together with me.

The rotation I call 'radiation term' and the axis 'mass term', because
the size of those spheres, the rotations are an equator of, seem to have
mass, that correlates with its size. The rotation is 'anti-symmetric',
what could be imagined as if the neighbours are twisted in the same
direction, but only the along the equator. This has to go twice around
to return to it original state. Than the rotations had to fit into the
neighbourhood. This can be done, if they represent smaller spheres, but
more. This generates a nice fractal pattern that is known as Appolonian
package. Here are two nice papers about that:
http://www.math.siu.edu/kocik/apollo/papers/44Cliff.pdf
http://arxiv4.library.cornell.edu/abs/math/0010324v3

Now I assume we only perceive radiation at a certain spot (we cannot
touch the stars), what is, what I call 'radiation term' of spheres, that
have a wobble. Than we would see things perpendicular to an axis, that
functions as a timeline. This is like a cut through this fractal and I
base it on my own clock, which is based on Earth rotation. Since what we
see are objects in what we call space, the timeline had to be
perpendicular to space. So the 'real thing' had to be something
different than what we see and I call it spacetime. (Other names would
also fit, but I'll stick to that.) This has certain subdomains, where
time is not a fractal relation, but uniform and unidirectional, what
seems to be the case for the Earth' surface, that happens to be a sphere.

Greetings

Thomas

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