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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

From: Tim Golden BandTech.com on 23 May 2010 09:27
On May 22, 12:46 pm, "Clifford J. Nelson" <cjnels...(a)verizon.net>
wrote:
> > 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.
>
> Buckminster Fuller's Synergetics coordinate system begins with four dimensions.
>
> See:
>
> http://mysite.verizon.net/cjnelson9/index.htm
>
> and
>
> http://library.wolfram.com/infocenter/search/?search_results=1;search...
>
> Cliff Nelson

The simplex coordinate system that I construct is much simpler than
Fuller's construction. Still, it lays nearby, and is even closer to
Kirby Urner's quadray analysis. Also nearby are barycentric
coordinates. As you expose, many construct the simplex from the next
dimension up as the cartesian coordinates
(1,0,0,...), (0,1,0,0,...), ...
but this is not necessary. The n-verticed simplex exists in n-1
dimensional space, where 'dimensional' is traditionally a real valued
basis. The reality that polysign exposes is that the one dimensional
behavior on the real line
- 1 + 1 = 0
is in fact generalizable, and that this statement is within the
geometry of the simplex. Sign is merely dimension, but off by one, so
that the bidirectional real number (two signs) is one dimensional. The
zero sum statement above is merely on a two verticed simplex. This
will eventually be regarded as the next step by the Fullerites but it
is too challenging to grasp when the real number is presumed
fundamental, as in the language of your post. The simplex geometry is
in fact a very compact form and beautifully recovers the complex
numbers as P3, time as P1, and spacetime as the structured progression
P1 P2 P3 | P4 ...
with a natural distance behavioral breakpoint of P4+ arithmetic
product.
That you and really all of us have overlooked emergent spacetime for
so long from a pure and simplistic arithmetic is a statement on the
the limitations of the human race. That I can put this evidence
beneath your nose and the aroma does nothing can be taken as even more
evidence
http://bandtechnology.com/PolySigned
I don't mean any harm by positing this. I mean to point out that
productive constructions lay buried, and that the modern mathematical
methods may not be those which yield productive results. How else
could polysign go overlooked? There are likely more such fundamental
constructions, and this is a positive conclusion that makes the
subject alive. This is not a dead religion that we practice. Those
books are not bibles, are they? Well you Fullerites sure do have alot
of fun in the practice, but there is a simpler and more general way.

- Tim
From: spudnik on 23 May 2010 14:00
yeah; first, do no harm, or assign yourself
to an automatic "opt-in to your killfile,
thank *me*."

anyway, that is not Bucky's sytem, but Cliff's. at least,
he is not among the fanatics, who beleive what Bucky saith,
that he alleviated the need for math with Nature's Co-ordinating
System
-- as important as some of that is.

"to remove me from your killfile,
sends you Social Security Number to tim(a)polysignosis.org;
thank *you*."

>    http://bandtechnology.com/PolySigned

thsNso:
"pressure equals a third of energy density" -- really?... well,
a tetrahedron is a third of the volume of the parallelopiped
that it's inscribed in; so, there.

"spacetime" is a totally useless word for concepts, since
it is merely phase-space of ordinary space;
just use quaternions, real part as time. (funny thing:
I just read that Hoagland's "hyperdimensional physics" was
nothing but quaternions "a la Maxwell," Yahoo!TM .-)

thusNso:
I don't see any neccesary resaon for *any* irrational number
to have a maximum run of any digit in what ever integral base; so,
rake one coal over yourself for propitiating such a silly idea!

on the wayside,
0.999.... does not = 1;
it equals 1.000...., the "real"number, one;
take a hop, a skip & a jump over Tony Robinson's bed
(of coals).

> Many irrational numbers have this property that there is a maximum run of
> one or all digits. Despite the fact that the probability of this occuring is

thusNso:
the second part of the question is clearly trivial, and
the first part seems to be its inverse, or what ever.

have Farey sequences ever been used for continued fractions, or
does that make any sense, at all?

> Example: The fraction 4 / 97 occur in the place 197 of
> the Farey's sequence of order 113. How can I know it
> without calculate all the smaller terms?

--Pi, the surfer's canonical value -- good to at least one place!
http://wlym.com
From: Tim Golden BandTech.com on 25 May 2010 07:08
On May 23, 2:34 am, Thomas Heger <ttt_...(a)web.de> wrote:
> Tim Golden BandTech.com schrieb:
snip
> 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.pdfhttp://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

I took a look at the first paper. Very readable, though I disagree
with the 2D interpretation of electron spin. I don't think his analogy
is so strong. I made it to the Appolonian construction which I do see
as an interesting blend of continuous and discrete but it is awfully
arbitrary.

I keep seeing your references to the time axis as a spatial reference.
It is good that you are thinking this way, but according to polysign
that time component will be zero dimensional. This is a geometrical
argument. We are fairly large scale conglomerations of finer material,
and we exist at fluid temperature levels. These details may deny us
the pure perception that we seek. Still, under spacetime unification
it seems appropriate that there will be the sort of symmetry that you
are trying. I guess to me the point would be that the algebra carries
the components within a structure, but the rendering of that algebra
will not grant that time a direction that you can point to. I remember
your statements in the past were apt in this region.

Here is a perception that sometimes feels strong to me: the past,
while we consider it to be fixed, is actually gone. We are its ghosts,
and this disappearing act of the past is only challenged by our
records. So long as those records are incomplete then this position is
established, since the ability to regain that lost information is
nonexistent.

I'm all for new attempts Thomas and support your active position and
hope merely to feedback to keep flowing. Still, these moves should
somehow go to axioms that are granted, and then the consequents. Well,
it is wise not to jump into axioms before they are correct. Still,
mistakes are allowed so I think it would be wise to attempt this
level. You are free to do so. I'm right nearby trying to do so as
well.

The main thing that I've got going is polysign. They simplify much of
mathematics and yield emergent spacetime. In some ways they are the
ultimate foundation for a physics theory. Well, I see that there is
still something missing.

Within the quaternionic theories you have a 4D math that claims to
render out 3D geometry, so isn't the 4th real valued component
supposed to be time related?

The polysign progression
P1 P2 P3 | P4 ...
builds out a structure of unsigned components
a11
a21, a22
a31, a32, a33
a41, a42, a43, a44
...
The option of working out some interdimensional behaviors exists. It
is fairly easy to upcast or downcast in dimension. Any time you draw a
real line on a piece of paper you've essentially upcasted that one
dimensional structure into two dimensions, and of course we typically
allow that the paper actually exists in three dimensional space. Yet
for some reason we face a perceptional challenge when we upcast the
zero dimensional ray onto the paper, and still claim it to be zero
dimensional. Perhaps here you are more coherent than I, for above I've
argued that you can't do this. Well, you are doing this, and I am at
the edge of my understanding and do see this problem as open due to
these interdimensional behaviors. Orthogonality is nearby to these
concerns, and is not a necessary assumption for a clean theory, as
polysign already denies it's necessity. Then too some surprises are
claimed by established math as one continues into higher dimensions.

I am trying to discuss pure geometry and one would hope that the
physical naturally maps there in such a way that the basis is
unmistakeable. Still, this is a step of construction and we are living
within assumptions that are not necessarily visible. These ghosts of
ghosts are problematic. To challenge them is a necessary part of the
construction. Something needs to be pulled out of thin air here and it
will be fairly fundamental.

- Tim; Prisoner of spacetime, ghost of the past...
From: Thomas Heger on 25 May 2010 13:13
Tim Golden BandTech.com schrieb:
> On May 23, 2:34 am, Thomas Heger <ttt_...(a)web.de> wrote:

> ...
> The option of working out some interdimensional behaviors exists. It
> is fairly easy to upcast or downcast in dimension. Any time you draw a
> real line on a piece of paper you've essentially upcasted that one
> dimensional structure into two dimensions, and of course we typically
> allow that the paper actually exists in three dimensional space. Yet
> for some reason we face a perceptional challenge when we upcast the
> zero dimensional ray onto the paper, and still claim it to be zero
> dimensional. Perhaps here you are more coherent than I, for above I've
> argued that you can't do this. Well, you are doing this, and I am at
> the edge of my understanding and do see this problem as open due to
> these interdimensional behaviors. Orthogonality is nearby to these
> concerns, and is not a necessary assumption for a clean theory, as
> polysign already denies it's necessity. Then too some surprises are
> claimed by established math as one continues into higher dimensions.
>
> I am trying to discuss pure geometry and one would hope that the
> physical naturally maps there in such a way that the basis is
> unmistakeable. Still, this is a step of construction and we are living
> within assumptions that are not necessarily visible. These ghosts of
> ghosts are problematic. To challenge them is a necessary part of the
> construction. Something needs to be pulled out of thin air here and it
> will be fairly fundamental.
>

Well, I think it is difficult to think in four dimensions, but not that
much as many people think. We know a lot about how time behaves. E.g. we
know, that thing do not happen for nothing, but have some kind of input.
The output then is gained in the future.
So, if we want to have a result in the future, we had to do something
now. And somehow we don't want that to happen somewhere, but where we
could utilize it. That is, where we would be - in the future.
The other influences, that we have not caused, we may call 'ghosts' - or
other intentions - alien to ours. But in the view of those, who have
created them, they are real.

Usually things are drawn on a blackboard or on paper, what is
essentially two-dimensional. This has to represent somehow abstract
ideas, that are not two-dimensional. If we want to consider the
influence of time, we get a 3+1 picture. If we take time relativistic,
we come to a four-dimensional view, where there is no specific
time-dimension. Only our (!) view 'cuts' this into a 3+1 view and a
stability condition requires to treat imaginary movement as time.
If we would follow the four-dimensional paradigm, we could say, that
imaginary movement is time. That is because we don't really move in time
(e.g. sitting on a chair). This movement, accompanied with time, is
invisible, because we move with it.

Greetings
Thomas
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