Date: May 27, 2010 9:29 AM
Author: Tim Golden http://bandtech.com
Subject: Re: Hexagonal grid and its three directions
On May 26, 11:10 am, Thomas Heger <ttt_...@web.de> wrote:
> Tim Golden BandTech.com schrieb:> 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:
> > 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?
> This is the trouble with the term 'dimension'. If we talk about space in
> an euclidiean way, we mean something like the distance to remote
> objects, where the objects inhabit a certain position.
> These positions are based on a certain view (ours!), because this is how
> we do it. The distance is measured in light-years and we use a vector
> space to put those distances in.
> But: the space we observe is dependent on us, because we have the
> dependency on time, because distance means age, too. Than our vision
> cannot be something 'real', but is specific to our position and movement.
> What is real than? Well, that is the question. If euclidean space is
> where we would see the objects, than that is not where they are now.
> The concept of distance seems useful, so we could assume some kind of
> space with dimensions of type distance, that is mainly invisible. We
> could see it only in the direct vicinity. And we have relativity, that
> needs timelines in various directions (to enable the objects to move).
> Than we would expect direct contact to be possible and empty space to
> move within.
> But if we alter the timeline, space seem to contract and a new space
> appears, unseen before. This could be achieved, if the axis is expanding
> to a circle and the former circumference contracts to an axis.
> This could be modeled with bi-quaternions by flipping the picture to the
> side and exchange timelike and spacelike.
> If we multiply two bi-quaternions 'sideways' (the spacelike neighbors),
> there would appear a scalar part, a vector part (with three dimensions
> of type length) and a cross-product term. If the cross-product term is
> actually responsible for material objects, the relations could be
> exchanged and material objects turn into radiation and vice versa. But
> we have still a vector space with three dimensions of type length, only
> another one. Since left and right turns into before and after, the
> timeline is altered and causal relations change from simultaneous to one
> after the other.
> Even if this sounds strange, it would be consistent with GR.
> > 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?
> The 'trick' - if you like - is, that the axis are for different spheres
> of different size. Any such sphere has only one, but they are connected
> in a specific manner like the one called Descartes configuration.
> > 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
> > about in the atomic nuclei?
> Well, we have inertia to be explained. A rotational paradigm in
> spacetime would perfectly fit (in my eyes), because more spin would make
> things more stable and that spin could be related to energy or mass.
> Energy more for things that change and mass for stability. And we could
> see why and how both be converted.
> (Than matter is kind of 'wrapped up light'.)
Within the unit shell model (constrain distance to unity in nD to
yield n-1D space) this makes temendous sense, though the possibility
of reverse spin modes would suggest some dynamics. Picture rotational
axes in toward the origin from the shell, then this direction is
nonobservable from a shell constrained object. This is a Flatland
interpretation. Anyway, the ordinary principle of rotational moment
are not necessarily to be upheld within this pardigm. Rather it
should be recovered as an extension of the paradigm, and preferably
from simpler principles, or principles that yield more consequents
than just mass. I don't think that the nonobservable concept is
complete, and that is good, since we would like to witness
interactions if we are elements of that shell. Stability as you
mention is a good thing to consider. This makes me ponder the vortex
models that some are fond of. You like those right? There are some
problems with this model, but they are there for all models. The
puzzle is what to grant and how slight can the grant be?
For me I would like to try to adapt polysign into this space, but I'm
not seeing it too well just yet.
> > 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
> It is still very difficult and I'm far from being satisfied with my
> results so far. But somehow the concept seems to lead in the right
> direction. So my idea is just an idea, or maybe call it a concept, that
> seems worth to be explored, rather than something like a theory.