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Topic: 3 dimensions and their 6 directions
Replies: 214   Last Post: Jun 3, 2010 6:36 PM

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 Tim Golden http://bandtech.com Posts: 1,490 Registered: 12/13/04
Re: Hexagonal grid and its three directions
Posted: May 26, 2010 7:30 AM

On May 26, 12:07 am, Thomas Heger <ttt_...@web.de> wrote:
> Tim Golden BandTech.com schrieb:> On May 23, 2:34 am, Thomas Heger <ttt_...@web.de> wrote:
> >> Tim Golden BandTech.com schrieb:
> ...
> > 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.

>
> The idea was, that to a spheric structure we would have an associated
> axis, like the axis of earth rotation, but on many different scales and
> with different frequencies. The Earth rotates once per day and has a
> large diameter. In the spacetime-view this axis is a zero node, because
> that does not rotate, but guides the movement.
> In the bi-quaternion picture we have a crossproduct term, that is
> anti-symmetric and behaves like angular momentum. This term flips the
> sign, if it passes that axis, so it needs two rounds to return to its
> original state. This could be interpreted as electrons on atomic scale,
> where the axis is the core. Since this is a three-dimensional
> simplification of a four-dimensional relation, we have to multiply that
> picture by three (to raise the hyper-sheet into volume). Than the
> electrons are the outermost part of a kind of standing waves and
> represent the point, where the wave returns - the part we could call
> potential (or 'charge'). That is a surface and two-dimensional and has
> spin, because it is part of the rotations. And we have two (left and
> right) with opposite spin and same charge.
> (The wave is generated, if we assume this cross-product term to spin
> about an axis, while the angular momentum is converted to velocity and
> back. This would be the behavior of a quaternion field, if the
> connection between the points is multiplicative.)
>
> If we disallow temporal movement of such an 'atom', the core looks like
> a knot, because the rotations spin in volume. But for simple atoms, that
> movement is large and the frequency high. To get it fixed to the surface
> of the Earth, we need to slow that movement down and make the atoms
> larger and need more 'electrons'. And this is how the Earth looks like,
> because we find the heavy elements at the surface, what could not have
> happened, if the Earth was once molten (they would sink into the ground).
>
> The picture is a bit like that of a nut on a bolt, that screws itself up
> by spinning. So I assume some kind of invisible stream, that guides the
> movement of the earth in direction of its north pole and goes right
> through it. That would explain, why we have more land on the northern
> hemisphere, because that invisible stream hits that part first and would
> slow down and transform the matter into heavier elements.
> This could also explain the Tajmar experiments, where we have a
> dependency on the location (being on the northern or souther
> hemisphere), because those experiments seem to work in opposite
> direction on the south side. Than the gravitational potential is to the
> Earth, what is charge to an atom, but -of course- with way slower
> movement and frequency and larger size.
>
> Radiation is generally unstable, but moves. So, if we flip a structure
> like an electron a bit, they would not return to the original state
> unless they get rid of that extra angular momentum, hence have to
> radiate it away. That's why I call this rotation 'radiation term',
> because it could radiate, but usually would not. Only that extra
> momentum would be sent away. But we could make things radiate, if we
> force them on curved paths. Acceleration or gravity would do that. That
> is why I assume, that CMBR is actually a realtime process, that is
> caused by the sun or other stars. Or we could make atoms wiggle by
> electric currents and make them radiate, too. Or we could apply high
> voltages, that forces these structures away from a stable state.
>
> If we treat time like an axis, it would point somewhere, while the
> rotations around represent a potential. Both behave like an inverse to
> each other. This picture could be scaled up or down and we could treat
> galaxies this way or the nucleus of an atom and get a fractal pattern.
> But on different scales we have different axes with different associated
> frequencies. A frequency of zero could have an axis, too, and would
> denote the entire universe - seen by us.
>
> Interesting question would be, what would happen, if that is not seen by
> us, but with a timeline in an angle - say perpendicular. That is a kind
> of multiverse picture, where our matter is radiation and our time is a
> spatial axis. That doesn't need to be far away, but could be 'round the
> corner'.
>
> Greetings
>
> Thomas

I can only half follow what you are describing, but I do see that you
are exercising a recurrent phenomenon. When you step up to a bi-
quaternion aren't you now in an 8D work space?

As you are thinking in terms or rotation quite a bit, then this is a
fine area of primitive mathematics to focus on.

Can one object have several axes of rotation? Here Euler angles would
have one thing to say, but can we already accept that even within 3D
that there are multiple axes? Let's say I spin a top aligned
vertically here at roughly 43 degrees north latitude. This top may be
spinning relative to me at, say, 600 rpm. Is it also spinning about
the earths rotational axis at 6.9E-4 rpm? Experiment and math will
tell us that it will not. But what about in higher dimension? If we're
going to worry about the 'axes' of the electrons in the spinning top
then we'll have to admit that we've caused precessionary forces. What

Somehow I still feel satisfied that there can be many rotational axes,
and that all of matter can be in such a dizzying rotational flux, and
that we have no sense of it because all that is around us is in
similar flux. I've actually had this as an intense sensation before
and it was memorable. It is a bit chaotic and I don't mean to validate
it by this means, just trying really to go toward some simple math.

It is possible to constrain to a purely rotational system, by fixing
all positions to a unit radius within a 4D Euclidean space. One could
call this a unified theory from the get go, because of the unity
distance constraint. What is left is 3D freedom, but no access to the
origin. All of this 3D freedom is expressible in angular quantities,
yet there is not necessarily any distinction from standard space,
except over long distances, where it should be possible to travel in
one direction and land back at yourself again. Wouldn't it be a grand
chuckle if all those galaxies were just prior versions of us in a
kaleidoscopic array? This then would lead us to believe that we are
existent in a pocket of well behaved space, for the vast open
territory never populated. This is anathema to Einstein's postulate,
but I see no problem with it. Space is not the same in all directions.
I look left and I see a chair. I look right and I see a bucket. This
is sufficient evidence to observe that space is not the same in all
directions.

Rotation is an awfully pretty concept. That it might be defined in
terms of translation is just one way to look at things. Translation
can also be looked at as rotation. We've been programmed to work from
the Euclidean basis, at least I have, and I wish that I could make
more sense of the unified rotational approach. Anyway, it's exercise.
The 'multiple axis problem' is what I see.

- Tim

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