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YES! Thank you so much for the link! I love how they related the rotations within the multiplication of imaginary numbers to their represenation as both matrices and quaternions...To ramble crazily for a moment: These mathematical connections are *very* important for an understanding of how Steinmetz approached the relationship between energy and time when it comes to oscillating electric waves.
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"Your manuscript is both good and original, but the part that is good is not original and the part that is original is not good." -- Samuel Johnson
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Se mi devas elektu inter religio kiu kondemnas cxiuj aliaj, kaj unu kiu ne faras, tiam, sciante nur kompaton, mi cxiam devas elekti la lastan.
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letslearntogether
10 months ago
Vero estas preter ĉiuj vortoj kaj konceptoj, tamen alprenas senfinecon da esprimoj. Ĉiuj estas indaj je zorgo. * Truth is beyond all words and conceptions, yet takes on an infinity of expressions. All are worthy of care.
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zazilicious
10 months ago
updated the OS listed for my gaming PC. I got rid of Pop!_OS and have installed Ubuntu, cause I was having lots of issues with it for a while now and was getting sick of its shit
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eastathenaeum
10 months ago
Thank you as well, I see you've linked back to me. I'm impressed with how new your site is and how much work you've put into it already!
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In turn, one can visualize these rotating waves as repeatedly travelling along a type of Riemann surface. When approaching the situation topologically, it is equivalent to how a projection of the 4-D Hopf Fibration yields a 3-D Clifford Torus. Applying this model to Geometrodynamics gives us a way to unify all of the fundamental forces at all scales, providing a coherent spacetime for describing ER=EPR.
Simultaneously, one merges together a bunch of seemingly disparate fields of mathematics, Langland's Program-style...All of this is also connected to something that I've been wanting to share with you ever since you mentioned your work on Relativity: Einstein's version of Energy-Mass Equivalence (i.e.: E=mc^2) is actually a reduction of Heaviside's quadratic (i.e.: E^2 = p^2c^2+m^2c^4).
This has two solutions. The Klein-Fock-Gordon form of this equation shows how it relates to Schrödinger's work in QM. Similar to how the negative solution to Dirac's equation led to the discovery of "antimatter", the mathematician Luigi Fantappiè suggested that the negative solution to the Klein-Fock-Gordon equation implies the existence of a "reverse time", amongst other phenomena.
Modern research into Quantum Backflow seems to hint at it. Precious few have taken T-symmetry and these negative solutions to their fullest logical extent (e.g.: William James Sidis, Hannes Alfvén, etc.). However, its biological effects are measurable (e.g.: experiments demonstrating "pre-stimuli responses" in the body done by HeartMath, Vannini, et al.; Saxton Burr's work on "L-fields"; etc.).
...Phew, still barely scratching the surface there. It is challenging condensing this into something readable, so it probably looks like word salad. I hope it at least triggers some interesting ideas for you.
You're most welcome. I'm grateful you found it valuable. That video in particular should have existed 12 years ago so that quaternions would have been intuitive to me before spending entirely too much time trying to understand it. It was a nice refresher and reinforcement that clicks alongside just being told that H is the union of two C's. If only many of the visuals available to us now existed then and before.
To be clear, I never worked on relativity and never meant to insinuate it. I've only learned physics as an engineering student, and the rest is just bouncing around trying to understand every (physical/formal) scientific concept as well as I could via Wikipedia, YouTube, and downloaded pdf text books. There was a 2 year period when reading dominated my entire free time. I know of quite a lot, but I'm no physicist.
Right! A good visualization can clarify a lot. I understand too; I myself am not much of a "professional" anything, but it sure is fun to explore together! Part of me has always thought that anyone was [blank] whenever they did [blank], so everyone can be a scientist whenever they choose to practice the scientific method, for example...Anyhoo, thanks again! Going to go study more.
That was deep, I'm just chillin in EONJ and your just going cosmic on us all 😂