John G
The Living Force
The math of the old compressible aether ideas is the conformal group that Ark uses for gravity.
But we have no idea what consciousness is. How to describe it? Science of consciousness is still to be developed. Science of information is already partly available. Both are somehow connected. But the question is: how? The devil is in the details, and these are lacking. How it all fits together with gravity waves, black holes, magnetic monoples, extra dimensions, Mobius bands, and prime numbers? That is the challenge of today.
Here is one of my papers touching the subject: Gravitation on a Homogeneous Domain, (2011).
From the Introduction of this paper:
William Kingdon Clifford speculated [4, p. 22] that the curvature of space is responsible for
all motions of matter and fields - the idea that has been taken over by Albert Einstein in his
theory of gravitation, through with the extra assumption of the weak equivalence and general
covariance principles. P. A. M. Dirac, originally impressed by General Relativity Theory, later
on had his doubts about the validity of general covariance, when the lessons of quantum theory
are taken into account. He tried to revive and reformulate the old idea of aether [5].
The idea that an alternative to Einstein’s gravity is needed in order to reconciliate, somehow, classical
geometry with quantum theory is, at least, an interesting one. 1
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My recent paper on Geometric (Clifford) algebra is available here: [2103.09767] On the bundle of Clifford algebras over the space of quadratic forms
But right now I am working on photons, and there Clifford algebra is not needed. In fact I am getting rid of it - for photons. They have spin 1, they are "Bosons", not "Fermions". They are the major carriers of information in our world and beyond - whatever the term "information" means. For photons time does not exist - whatever the term "time" means. So, perhaps, in a sense, information indeed is "timeless".
PabloAngello
Jedi Master
That move through space, in time, be assured!
You do not need geometric algebra to describe Maxwell equations. You need differential forms and Hodge * operator . See for instance this Wikipedia entry, sub-entry "Current 3-form, dual current 1-form".:
More general and more powerful tool. There is a big lobby for geometric algebra (David Hestenes and His Friends). Its role and usefulness is over-exaggerated. At least that is my experience (although I have been using it a lot in my book Quantum Fractals - but just for fun, not out of necessity).
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PabloAngello
Jedi Master
No. Time dimension is different. Geometric algebra usually deals with space only, leaving time alone. But there is also its spacetime version: spacetime algebra (Spacetime model). But the mathematical tool of differential forms is much more general and flexible. Differential forms are needed for geometrical understanding not only of electromagnetism, but also of gravitation, where geometrical algebra is essentially useless. It is via differential forms that we learn about vectors, bivectors, vector products etc.
But there are also some fans of quaternions, for sure. They will advocate quaternions instead of geometric algebra, and claim that the "true Maxwell equations" must be written using quaternions!
Curious Beagle
Jedi
Sorry, it is just very hard explaining things in this forum like walking on landmine. You don't know when someone just get upset with you (or banned). I'm not a native speaker but I get the message if someone called you psycho, making things up, don't follow 4th way, etc. probably it is inappropriate to continue talking about the subject further. It isn't exactly my blog even if a lot of the post later turn out to be revelation. I mean if you get banned a for a year after posting sensitive posts, I probably don't want to expand on things even when I probably can answer the big picture in greater details. Just not sure why C won't answer you directly when you asked them. I only answer spiritual questions in greater details now because I consider them as priority knowledge.
PabloAngello
Jedi Master
@Curious Beagle This thread started with mathetmatic rigor (@Cleopatre VII please continue your posts, I'm looking for them :) ) and is floating around concepts that seem to be connected each other: randomity, entropy, consciousness, observer, information theory, waves. We are trying to achieve something here not only from loose definitions perspective. I suppose noone is upset, noone will ban anyone. We just have questions and want good logic answers that may lead maybe to applicable definitions. Just @ark has most of that questions :D
I do not want someone telling me the answer. What's the point? If you discover something by your own effort - you learn something, you grow. If instead you are being told the answers, you get lazy and rotten. C's are just hinting (sometimes giving misleading hints, on purpose, to test our discerning abilities), leaving the pleasure of the discovery for us. And that is how all great teachers work. They would never do your homework. Your homework is for you to do!
C's are "us in the future". How did they get their wisdom? Through hard work. Through the hard work of "us in the now". How else?
As they say: There ain't no such thing as a free lunch. And you think there is one, then you are the lunch.
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dennis
Dagobah Resident
Information seems to come in fields
The commonality of all these different fields seems to be where something occurs (particle, motion, events, things) as opposed to nothing occurs (perhaps ether, existing in potential but not actualized).
The commonality of all these different fields seems to be where something occurs (particle, motion, events, things) as opposed to nothing occurs (perhaps ether, existing in potential but not actualized).
On the other hand "ether" can be full of motion, though yet unorganized (chaotic). Things then become "actual", when motions get "organized" into "meaningful" structures. But then, it seams to me, there is this concept at least as important as that of information: "meaning". What do we mean by meaning? Where it comes from. My guess is that it may be very close to the concept of consciousness - the hard question that, I hope, Clepatre VII will address in the near future, after being done with the subject of information.
John G
The Living Force
The actual algebra of Clifford algebra is actually rather useless, when the Cs mentioned liking geometric algebra, it was in the context of being compared to E8 and friends. For me, all Clifford algebra does is let fermions and bosons and differential forms all hang out in the same place. Your conformal group could be considered Cl(6) bivectors but other than to hang out with fermions and differential forms, I always think conformal group not however Cl(6) bivectors could be used; it's only part of an algebra that way. I think differential forms hang out in the Cl(8) 4-vectors but you likely couldn't actually use Cl(8) 4-vectors to do anything. E8 for some is a way to let things hang out together too, but I don't think it does that as well as Clifford/geometric algebra. Clifford algebra is good in a Hodge Star map kind of way, so as a map rather than an algebra, it can house differential forms I think.
In my recent paper on Clifford algebras, that I have mentioned before, in footnote 4, I wrote:
"While it is possible to consider all Clifford algebras as deformations of one algebra, the exterior algebra, invoking the tensor algebra allows us to have a ’bird view’ of the whole structure: all Clifford algebras, including the exterior algebra, have one ‘mother’, and this
mother is the tensor algebra."
The referee of this paper, in his elaborated report, was evidently not very happy with my statement, but yet he wrote:
"... I am not at all ready to consider the tensor algebra as "the mother" of the other algebras. But as a reviewer, I observe that the Author supports his thesis with interesting arguments (in other words, it is not just propaganda), and I wish his paper to become a useful contribution to debate."
