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I'm trying to implement and fix the drawing box. Don't waste your time on it rn. The drawings are going to the void...

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finally settled on a diarypage i like... such a process

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letslearntogether eastathenaeum

3 weeks ago

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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letslearntogether 3 weeks ago

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.

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letslearntogether 3 weeks ago

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).

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letslearntogether 3 weeks ago

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.

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letslearntogether 3 weeks ago

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.).

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letslearntogether 3 weeks ago

...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.

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eastathenaeum 3 weeks ago

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.

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eastathenaeum 3 weeks ago

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.

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letslearntogether 3 weeks ago

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.

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