C
Cleopatre VII
Guest
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.
Perhaps I will give another example related to Hegel, concerning the Zeno paradox.
In the arrow paradox, Zeno states that for motion to occur, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one (duration-less) instant of time, the arrow is neither moving to where it is, nor to where it is not. It cannot move to where it is not, because no time elapses for it to move there; it cannot move to where it is, because it is already there. In other words, at every instant of time there is no motion occurring. If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible.
Hegel proposed a rather specific solution of this paradox. He argues that movement contains a contradiction, therefore an adequate description of the movement must be logically contradictory: it should consist of two contradictory judgments, stating that "a moving object is simultaneously in a given place and not in a given place."
Considering this purely logically and from a classical perspective, Hegel's approach is unacceptable. On the other hand, in the quantum world, various kinds of strange things may happen. The issue about German philosophy is that it can be quite chaotic, inconsistent with common sense, but that's what I like about it. It is inspiring, it has unusual artistry and depth.
Wandering Star
The Living Force
When reading your post, the following came to my mind.
In the computer world, all the "creation" is made with 0 and 1. Then there are different languages (type of software) or dimensions, each one with the "rules" of creator of the programming language.
The C's have said (if memory serves me well) that all creation is made with 1, 2 and 3.
The first three prime numbers define everything.
This is where my thought came ...
As an addition, the rule of three came to me, paraphrasing: "there is good, there is evil and the specific situation that defines it."
John G
The Living Force
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).
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?
C
Cleopatre VII
Guest
All my dear ones,
I would like to wish you all the most beautiful things in the New Year. And let us wish each other a time machine!
I would like to wish you all the most beautiful things in the New Year. And let us wish each other a time machine!
C
Cleopatre VII
Guest
Quaternions can also be associated with the number 4.
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.
Unit length quaternions satisfy the equation of a three-dimensional sphere immersed in four dimensions.
These objects i, j, k fulfill certain relations and they can be written as matrices, but they will not be particularly important for us at the moment.
There were once attempts to develop quantum mechanics based on quaternions (rather than on complex numbers as usual).
In fact, it is possible to describe some phenomena relevant to this theory using quaternions, but there is no indication that they have any advantage over complex numbers in terms of quantum mechanics. Rather the opposite is true. Unlike complex numbers, quaternions are not commutative, which is sometimes a problem.
However, I think that quaternions are not entirely redundant, and that their non-commutativity will someday become an asset in some yet unknown physical theory. It seems to me that their non-commutativity may contain something unique, perhaps they contain some information about the Universe that we miss when we operate only on real or complex numbers.
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?
C
Cleopatre VII
Guest
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.
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
Speaking about 4-vectors being represented like 3D real space + 1D imaginary space (time), I was thinking about something like in Complex Spacetime Frame: Four-Vector Identities and Tensors:
Minus signs in proper time ds2 appear due to 4-vector squared being defined as product of its contravariant and covariant forms, in above paper linked through complex conjugation.
In 4-vectors, 1st component is imaginary (1D time) and remaining three are real and orthogonal to each other (3D space). In quaternions it's kinda vice versa, 1st component is real and other 3 are imaginary, just lack orthogonality to form 3D space as we know it, right?
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?
John G
The Living Force
From the 12/19/98 session:
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.
Time disk like complex plane, 2 orthogonal axes of time, connected to space hypersphere, 4 orthogonal axes representing 3D space and electrical charge?
John G
The Living Force
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.
@ark
We humans observe Universe with our apparatus, so our perception of space+time would depend on what we have at our disposal. Regarding 4+2 D space+time, we can notice that humans have 4 extremities in total, coming in 2 pairs, and 2 pairs of eyes and ears.
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.)
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'.
Observing ourselves we can notice that's not where our apparatus 'ends' with its instruments, on our hands and feet we have fingers and toes, and we also have our 5 senses (in a way resembling Duality meeting Spirit giving Trinity).
In contrast to extremities each having its quintet of On/Off bits, some of our 5 senses provide us with spatial 4D resolution (sight, hearing, touch), so situation with dimensionality of time is not so clear.
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, but we're also carrying our emotions and thoughts with us, from our past and to our future. So, that also doesn't look promising if we want to avoid falling into materialistic pit.
In that respect, what we carry with us from past and to future are our perceptions of Universe which brings our consciousness making those perceptions/observations into the picture. 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?
Anyway, I hope these few thoughts could be of any help in your work on UFT.
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John G
The Living Force
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.
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.
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.
