3 dimensions and their 6 directions [Math]

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From: BURT on 8 May 2010 14:55

On May 8, 9:33 am, Thomas Heger <ttt_...(a)web.de> wrote:
> spudnik schrieb:> you are pretending to define "complex 4-vectors,"
> > but "real" 4-vectors are part of the gross and
> > unfinished porgramme of Minkowski, to "spatialize" time,
> > while it is quite obvious that the "time part"
> > is not symmetrical with the spatial coordinates,
> > either in 4-vectors or quaternions. anyway,
> > bi-quaternions would be 8-dimensional or octonions.
>
> What I did was a bit crude and goes like this:
> I put 'physics into a shredder and sieved it' and than I looked, what
> remains in the net. So I tried to count exponents, Pis or
> sin/cos/exponential functions and tried to reassemble the pieces.
> In a way complex numbers, arc- and exponential functions and quaternions
> seem to be the most important. Quaternions with complex entries are
> bi-quaternions (or the one type of octonions - if you like. The other
> have eight components as quaternions have four.)
> Than I have drawn, what you could possible do with those numbers and
> compared it with observed phenomena.
> As being not such a good mathematician, I have searched for developed
> systems of this type and found a few, that look very convincing.
> The rest is just a bet. Minkowski was right - and all the others, that
> used such a construct: Hamilton of course, Tait, Tesla (!), Maxwell,
> Lanczos and a few in recent days like Prof. Rowland or Jonathan Scott.
> (Bi-quaternions I wanted to model 'internal curvature' as curved
> spacetime of GR: Imagine an event, described by one quaternion. Than it
> would require (at least) two, that an event could have some features. So
> these two act antagonistic and in a general case describe a straight
> worldline. Because gravity curves worldlines, gravity causes radiation,
> too.
> It is more easy to see this phenomenon in the trail of a comet.
> According to my model the trail is generated as disturbance of the solar
> wind, that is not radiating. But if those 'elements of spacetime' get
> disturbed (by a rock flying through), they get tilted and start to
> radiate. )> and, it is all obfuscation, trying to insist that
> > a phase-space tells you what time really is;
> > it's very useful for seeing patterns "in" time though,
> > as in electronics (although, NB,
> > electronics is mostly done in "1-1" complex phase-space,
> > instead of quaternions, as it could be,
> > for some reason .-)
>
> I think about programming something, because math is something, I have
> not enough knowledge about and I don't know, how to cast the model into
> formulas. This is difficult, even if you know what you want to achieve.
> Now I have no good idea about how to do that. But I could recommend
> Peter Rowlands book "Zero to infinity", what is essentially about the
> same idea.
>
> > maybe, all you and polysignosis need to do,
> > is work the math of quaternions ...
>
> Tim is among the very few, that was not rightout hostile to my ideas,
> but supported me a bit. Maybe his numbers would work even better. I
> can't tell, but it should possible to find out.> that'll take me wome time, as well. (I mean,
> > what is the difference in labeling a coordinate axis
> > with a "different sign" and a different letter,
> > whether or not negatives are even needed?)
>
> Certainly 'before' could be labeled with a minus. Since a 'now' would
> require imaginary connections, this minus could be shifted to the 'side'
> and we could label the imaginary sides with plus and minus, too.
> The usual Euclidean view would require 'preexisting' curves, but we
> know, that things evolve and do not just exist as they are. So, even a
> line in space would be static and we know, this would be our impression,
> but not a physical entity. Euclidean space is meant timeless and this is
> not the right picture for physics.
> What is the right picture than? As said, my bet would be, this
> bi-quaternion system would work best.
>
> Greetings
>
> TH

There are round curved directions in space geometry.

Mitch Raemsch

From: spudnik on 8 May 2010 16:34

stay away from polysignosis,
til he has actually explained to himself,
what could possibly accrue to such a thing.

NB, Lanczos used quaternions in _Variational Mechanics_
for special rel., and it's just "real time" and
"three ('imaginary') axes of space;" but,
this is just the original "vectors."

compare Lanczos' biquaternions
with the "Cayley-Dickerson doubling" procedure,
to go from real to complex to quaternion to octonion.

"wroldlines" are just the crappola in Minkowski's "pants,"
totally obfuscatory outside of a formalism --
time is not a dimension; time is awareness & mensurability
(of dimensionality !-)

> Spacefoam is like string-theory a model with preexisting entities (foam,
> strings). But personally I would prefer a 'nothing concept', meaning 'no
> things'. Would there be the need of something, than why should that
> exist and why should it be at the supposed place?

thus:
try a search on Gauss & Ceres. or
"go" to wlym.com.

> This problem and its solution are found in a paper by Ceplecha, 1987,
> but the details are murky to me. For two, I'm pretty much OK, but for
> three and above it escapes me. His paper covers a lot more territory
> than this problem, but this one is what intrigues me the most.

thus:
the problem appears to be,
"some observers measure the angle to the marker,
relative to the other observers,"
which would not give you the distance *on a plane*,
because of similar trigona. Gauss meaasured the curvature
of Earth with his theodolite *and* a chain measure
of distance (working for France in Alsace-Lorraine,
triangulatin' that contested area .-)

thus:
notice that no-one bothered with the "proofs" that I've seen, and
the statute of limitation is out on that, but, anyway,
I think it must have been Scalia, not Kennedy,
who changed his little, oligarchical "Federalist Society" mind.

thus:
sorry; I guess, it was Scalia who'd "mooted" a yea on WS-is-WS, but
later came to d'Earl d'O. ... unless it was Breyer, as I may
have read in an article about his retirement.

> I know of at least three "proofs" that WS was WS, but
> I recently found a text that really '"makes the case,"
> once and for all (but the Oxfordians, Rhodesian Scholars, and
> others brainwashed by British Liberal Free Trade,
> capNtrade e.g.).
> what ever it says, Shapiro's last book is just a polemic;
> his real "proof" is _1599_;
> the fans of de Vere are hopelessly stuck-up --
> especially if they went to Harry Potter PS#1.
> http://www.google.com/url?sa=D&q=http://entertainment.timesonline.co....

--Light: A History!
http://wlym.com

--Waxman's capNtrade#2 [*]:
"Let the arbitrageurs raise the cost of your energy as much as They
can ?!?"
* His first such bill was in '91 under HW on NOx & SO2 viz acid rain;
so?

From: Thomas Heger on 9 May 2010 02:13

spudnik schrieb:
> stay away from polysignosis,
> til he has actually explained to himself,
> what could possibly accrue to such a thing.
>
> NB, Lanczos used quaternions in _Variational Mechanics_
> for special rel., and it's just "real time" and
> "three ('imaginary') axes of space;" but,
> this is just the original "vectors."
>
> compare Lanczos' biquaternions
> with the "Cayley-Dickerson doubling" procedure,
> to go from real to complex to quaternion to octonion.
>
> "wroldlines" are just the crappola in Minkowski's "pants,"
> totally obfuscatory outside of a formalism --
> time is not a dimension; time is awareness & mensurability
> (of dimensionality !-)
>
Relativity tells us, that different points of view are equivalent, but
what is seen then is different, too. So we could see one thing as
comoving or as distant observers and our view is different then, but the
observed phenomenon is the same.
Usually we use different frames of references. In a lab peeping through
a microscope, we certainly wouldn't use a FoR based on the sun or the
center of our galaxy. Same with a telescope, if we look into the sky.
But then we would use a FoR, where the stars appear fixed.
But we could, with the same right, us one, where the observer is fixed
and the heaven rotates.
In the latter case the stars would move and the observer stays fixed. I
usually prefer this view, because we could use the same FoR as for the
microscope (and we usually prefer a comoving FoR to ourself, because
that is our 'natural' view of the world). Once this is pinned down, we
see, that all things move somehow, except ourselfs, because we define
this FoR. In this FoR we measure time, because a clock is some kind of
device we have placed near us in that lab. Since the Earth moves and
turns, this clock is performing the same movement as our FoR and we
ourselfs.
If there would be some kind of flow perpendicular to this movement, our
clock could possibly measure this flow in counting 'bumps' on our path.
To fulfill the stability condition (of ourself, the clock and the
device, we are looking through), we split off time and space. Distance
is than space and its evolution time. But this is our view, because we
define this FoR. In an other view, this would not necessarily be the
case. In that different view (from -say- Alpha Centaury) our lab would
perform some helical curve. That would mean our worldline is a real
movement (seen from Alpha Centaury) and is imaginary to us.
Since both views are of the same right, we had to take worldlines as
real movements, even if we don't perceive them as such.
More astonishing is, that we could define FoRs, from where we are
invisible. That would be, where the timeline is perpendicular to ours.
So time has a direction, in what the stability condition is fulfilled.
Along this line an objects performs a real movement, if seen by some
distant observer.

Greetings

TH

From: Karl Heinz on 9 May 2010 02:25

Thomas Heger schrieb:

> Relativity tells us, that different points of view are equivalent,

Because the projections of spaces into subspaces depends on
every possible point.

> but what is seen then is different, too.

Nope, whether you are sitting on earth watching the moon rising or
standing on moon watching mother earth rising does'nt change anything.

From: Tim Golden BandTech.com on 9 May 2010 08:46

On May 9, 2:25 am, Karl Heinz <karlhe...(a)sofort-mail.de> wrote:
> Thomas Heger schrieb:
>
> > Relativity tells us, that different points of view are equivalent,
>
> Because the projections of spaces into subspaces depends on
> every possible point.
>
> > but what is seen then is different, too.
>
> Nope, whether you are sitting on earth watching the moon rising or
> standing on moon watching mother earth rising does'nt change anything.

Heger has been eloquent, and Karl is not necessarily offering an
adequate contradiction here.
Here is a translation of Einstein:
"If the principle of relativity were not valid we should therefore
expect that the direction of motion of the earth at any moment would
enter into the laws of nature, and also that physical systems in their
behaviour would be dependent on the orientation in space with respect
to the earth."
- http://www.bartleby.com/173/5.html
I'm sure there is some more apt quote, but already I see ways to
falsify Einstein's argument. The sun shines on just half of the earth,
for instance. Physical systems certainly do behave differently
depending on their orientation with respect to the earth. This is why
we see ice sheets near the poles, jungles near the equator.

Too simpleminded? I would argue for primitive thinking, and getting
these postulates ironed out in a standalone fashion. When we dissect
down to say the electron modern science tells us that the electron
does have an inherent magnetic moment. This is an anisotropic
construction, in comparison to the raw isotropic charge which was
assumed in Maxwell's time.

- Tim