dennis
Jedi Master
It is quite twisted thinking, but that is what Hegel’s philosophy is about.
Maybe the point is realizing the twisting futility of the contradictions of duality and just letting it go.
It is quite twisted thinking, but that is what Hegel’s philosophy is about.
Hegel is in fact understandable. Once, when I was reading Hegel's works for several days in a row, I myself began to adopt certain patterns of his thinking. It's a bit like speaking a foreign language. If you talk a lot in this language, you start to think in it.Maybe the point is realizing the twisting futility of the contradictions of duality and just letting it go.
When reading your post, the following came to my mind.Number one is certainly important (unity. Number three too (trinity). Also number 7 (seven densities). There are 3 basic quaternions and 7 basic octonions. Then there is Fibonacci. Golden spiral - Wikipedia
But whether there is a hidden informations within numbers, for instance in the series representing Pi? Or in the pattern of prime numbers? That is a good theme for sci-fi movies. Numerologists find information everywhere, but not so in numbers themselves, but rather in the circumstances in which they appear. But that is a whole new discussion.
Ark and the Cs once agreed on bimetric gravity as correct but needing some tweaking. Ark's conformal group can be a metric with a structure group for the geometric half (giving the Einstein field equations which is the problem Einstein himself had with teleparallelism). Teleparallelism can be the other half giving a proper time-like path. QM Standard Model fields can be added in a differential forms Hodge star operator way like Ark mentioned earlier. The symmetry breaking though would be horrible. Using what Ark mentioned earlier, it's I think kind of like splitting the octonion into dual quaternions and I think you end up with two teleparallel connections/structure groups, one each for the spacetime quaternion and Kaluza-Klein quaternion but only one tetrad/solder form for proper time (since it's via the conformal group Hodge dual structure). The tetrad of teleparallelism relates to the modern solder form in that it solders position/velocity to momentum (tangent to cotangent).For example, I recommend this article: The Strange Similarity of Neuron and Galaxy Networks - Issue 50: Emergence - Nautilus
In fact, there are many similarities at different levels and on many scales. At the same time, in modern physics, despite the existence of analogies, we use different theories to describe the Universe at different scales. At the subatomic level we use quantum mechanics, at the galactic and extragalactic levels we use general relativity.
Hence, I believe that one of the most important tasks of physics at the moment is to develop a theory that would be a bridge between quantum mechanics and general relativity. Perhaps both theories need some adjustments.
The approaches that have come to my mind recently are gravitoelectromagnetism and teleparallelism. Perhaps having something like UFT, the particular analogies between microscale and macroscale will become easier to explain in terms of the set of applicable laws of nature.
The first three prime numbers define everything.
Quaternions can also be associated with the number 4.Well, not exactly everything.
For example, number 4 is needed (non-prime even number, so not important at all in that sense) to define 3D space we experience; we need 4 non-coplanar points (like tetrahedron, for example) to define 3 orthogonal prime axis, vectors of base, so to have volume, not just area.
Number 4 is in fact first non-prime number showing up in sequence, maybe that 'firstness' made it special too?
We write a quaternion as
q = ae + bi + cj + dk,
where a, b, c, d are real numbers and e, i, j, k are some objects, where i, j, k can be understood as imaginary units, similar to imaginary i and e is the so-called neutral element (an element of an algebraic structure which, for a given binary operation, applied to any element will not change it.). a is called the real part of the quaternion.
This is an interesting observation. Perhaps there is some depth in this approach. Space and time are related in an interesting way, I also mentioned how Hegel noticed the relationship between them. Perhaps, in fact, some model could be formulated in which the structure of spacetime would be described in terms of quaternions.Can we say that quaternion is composed of 3D imaginary space + 1D real space, kind of like 'inversely' of physics where 4-vectors are composed of 3D real space + 1D imaginary (time) space?
In Minkowski metric we write:
ds2 = c2dt2 - dx2 - dy2 - dz2,
so there is one plus and three minuses, but the relationship of this with quaternions is not clear. You can read more about the four vectors in the context of proper time in this article: Proper time - Wikipedia
From the 12/19/98 session:When Cs suggested one additional dimension for time (5 in total), I wondered if that dimension would be real or imaginary, i.e. would we have 5-vectors composed of 2D complex time + 3D real space (real time dimension 'mixed' with 3 real space dimensions) or imaginary 2D time (with or without orthogonality between 2 axis) + 3D real space?
Q: (A) Okay, now, this is one thing. At some other point we
were speaking about pentagons and hexagons and I tried to
be tricky and when it came to pentagons, I wrote a
mathematical formula, a symbol for a pentagon, and then
there was the question of signs. We needed five signs. I
asked you whether there should be four pluses and one
minus, or 3 pluses and two minus. The answer was that there
should be 3 pluses and two minuses in a pentagon. Now,
what about a hexagon? What should I put in a hexagon?
Three pluses and three minuses, or four pluses and two
minuses?
A: Four and two.
Q: (A) That is what I hoped for...
This would be 4 space-like and two time-like which would give you a Cartesian product of a time disk and a space hypersphere. In other words it's a bounded complex domain for your spacetime. In terms of basis vectors you kind of have a spacetime quaternion XYZT plus internal zt for translations and conformal degrees of freedom (for me via Tony Smith, there's also an xy for positive/color and negative/anticolor charge). So charge is kind of the internal version of transverse, translations the internal version of longitudinal and conformal the internal version of time.
It's like the boundary of the disk would be real time and the inside complex time and the boundary of the hypersphere would be 3d real space and the inside would be complex space. People differentiate topological boundaries from something called Shilov boundaries so things get more messy for the people that actually work with these things. This is only made from 4 + 2 = 6 basis vectors so no electric charge yet. You need to go up to 8 basis vectors to get electric (and color) charge (for Tony Smith). Tony would add Electroweak/color forces in a Cs-like rim of the cylinder kind of way but the math ends up a conventional Yang-Mills differential forms Hodge star thing where I think you think of really small twists of spacetime.Time disk like complex plane, 2 orthogonal axes of time, connected to space hypersphere, 4 orthogonal axes representing 3D space and electrical charge?
Q: (A) Okay, now, this is one thing. At some other point we
were speaking about pentagons and hexagons and I tried to
be tricky and when it came to pentagons, I wrote a
mathematical formula, a symbol for a pentagon, and then
there was the question of signs. We needed five signs. I
asked you whether there should be four pluses and one
minus, or 3 pluses and two minus. The answer was that there
should be 3 pluses and two minuses in a pentagon. Now,
what about a hexagon? What should I put in a hexagon?
Three pluses and three minuses, or four pluses and two
minuses?
A: Four and two.
Q: (A) That is what I hoped for...
The Cs do mention the 4th dimension as an in-out and not being able to tell left from right (curved roads looks straight). It's like the stuff on one side can be lifted out of the page and be seen on the other side too. I saw it once in a physics blog described as not being able to tie your shoes. It relates I think to the Lethbridge pentagons in third density looking like triangles in 4th thing since a regular pentagon has a line segment on one side and a point on the other.One way to observe Universe around us and ourselves within it could be to have 4 spatial dimensions, each being a pair for itself: left+right, up+down, front+back, in+out (kinda motion in nowadays science where nice trick was to introduce 'ideas' to use 'quasimotion' (from-out) as time dimension, which explains a lot why humanity couldn't lift off the veil.)
You do get a complex spacetime domain dual light cone structure going indefinitely in opposite time-like directions which Ark has recently related to the two universes (matter & antimatter) which related to the lost in the Bermuda triangle ideas.In addition to 4 spatial dimensions, our consciousness knows 2 time dimensions also: past and future, which we perceive as each stretching indefinitely from 'backwards' and to 'frontwards'... First idea was that each of 2 time dimensions we perceive would be represented with a sheet, 2D complex plane expanding indefinitely to past on one side and future on the other. But that's not how we perceive time, we perceive it as our whole being moving from past and to future, so it's not just 2D on each end. Maybe it could be our spatial 4D, like spatial 4D coming from the past and going to the future. So, that also doesn't look promising if we want to avoid falling into materialistic pit.
Our consciousness could certainly via quantum self-decoherence create its proper time teleparallel path via its 4D space/2D time real plus imaginary dual quaternion infinite vertices structure. More knowledge equalling less stuck with only the entropic probabilities.Could our consciousness be the one creating its proper time by the process of observing and in that way 'coupling' 4D (dual) spatial space with 2 'independent' imaginary/complex time dimension bundles of (quantum) probabilities, kinda quaternions with infinite imaginary dimensions?