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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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letslearntogether 3 months 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 months 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 months 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 months 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 months 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 months 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 months 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 2 months 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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ninjacoder58 2 months ago

That was deep, I'm just chillin in EONJ and your just going cosmic on us all 😂

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kips-corner 3 months ago

Thanks for the add!

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eastathenaeum 3 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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eastathenaeum 3 months ago

Filter added! Going to be spending some time to make the filter more effective with hidden text "tags" on more specific subjects, starting with the simple tag 'materials.' If you happen to check it out, please let me know if there are any others that are lacking. Also I've set up the table and code to start adding direct links for phone apps.

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eastathenaeum 3 months ago

Let's Learn Together: If you're seeing this, you should consider adding the YouTube channel Zundamon's Theorem to your list of math resources. They use anime characters to explain concepts and the demonstrations have never been clearer. https://youtu.be/HbUewIIpl6I

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eastathenaeum 3 months ago

Xanadu Quantum Technologies and Q-NEXT added

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eastathenaeum 3 months ago

I'm just now finding out after app hunting for the download links, when you save a site link shortcut, some pages will give you the option to do so in the form of an app that is not available in the app stores (Android).

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sauerbaker 3 months ago

My deepest condolences on your loss.

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derw 2 months ago

Thanks Sauer <3

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daliwali 3 months ago

instructions unclear: i have been myself this entire time.

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eastathenaeum 3 months ago

I aim to point out the absurdity of such a statement at a job. Perhaps they need a better one like, "Just be chill."

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miela583 3 months ago

I had a panel job interview where one of the interviewers became convinced I was using a fake personality and repeatedly demanded I start being myself. It was one of the most bizarre experiences of my professional life.

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eastathenaeum 3 months ago

The interviewer was being their self by being aggressively paranoid delusional? 🤣

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letslearntogether 3 months ago

😂 "You will be assimilated. Resistance is futile."

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