Quaternions
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Quaternions
This might be useful for MM's Spin mechanics. Part 13d really summarizes their usage with 3D  Spins:
FamousMathProbs13a: The rotation problem and Hamilton's discovery of quaternions I
https://www.youtube.com/watch?v=uRKZnFAR7yw
FamousMathProbs13b: The rotation problem and Hamilton's discovery of quaternions (II)
https://www.youtube.com/watch?v=0_XoZcA1HU
FamousMathProbs13c: The rotation problem and Hamilton's discovery of quaternions III
https://www.youtube.com/watch?v=g22jAtg3QAk
FamousMathProbs13d: The rotation problem and Hamilton's discovery of quaternions
https://www.youtube.com/watch?v=MkNfQtINEjo
FamousMathProbs13a: The rotation problem and Hamilton's discovery of quaternions I
https://www.youtube.com/watch?v=uRKZnFAR7yw
FamousMathProbs13b: The rotation problem and Hamilton's discovery of quaternions (II)
https://www.youtube.com/watch?v=0_XoZcA1HU
FamousMathProbs13c: The rotation problem and Hamilton's discovery of quaternions III
https://www.youtube.com/watch?v=g22jAtg3QAk
FamousMathProbs13d: The rotation problem and Hamilton's discovery of quaternions
https://www.youtube.com/watch?v=MkNfQtINEjo
Re: Quaternions
Hey Cr6, I viewed 13a and enjoyed it. I'll need to study it
At one time I was responsible for optimizing runway navigational aids, concerning myself with dual frequencies, modulation schemes, voltage levels, phase angles, cable lengths, antenna positions, the ground plane, adjacent structures, etc. I began experimenting onmyown by modeling EM signals using two dimensional complex plane waveforms while calculating angles using transcendental functions in an effort to see "EM" structures "in space". Please don't get the impression I knew what I was doing. I never got to three dimensions, processing time was ridiculously long, and I never figured out Jordy glasses. It was fun though.
I have long since given up on transcendental functions and the infinitesmal. (By a coincidence, I started reading Amir Alexander's book, but don't want to read your post since I suspect the book is politically skewed in both religion and science). I welcome Wildberger's rational geometry, and can't wait to get back to it. I'm stretched a bit thin, but am happy that you provide such interesting subjects. I can't wait to apply it to stacked spins and pool ball mechanics.
At one time I was responsible for optimizing runway navigational aids, concerning myself with dual frequencies, modulation schemes, voltage levels, phase angles, cable lengths, antenna positions, the ground plane, adjacent structures, etc. I began experimenting onmyown by modeling EM signals using two dimensional complex plane waveforms while calculating angles using transcendental functions in an effort to see "EM" structures "in space". Please don't get the impression I knew what I was doing. I never got to three dimensions, processing time was ridiculously long, and I never figured out Jordy glasses. It was fun though.
I have long since given up on transcendental functions and the infinitesmal. (By a coincidence, I started reading Amir Alexander's book, but don't want to read your post since I suspect the book is politically skewed in both religion and science). I welcome Wildberger's rational geometry, and can't wait to get back to it. I'm stretched a bit thin, but am happy that you provide such interesting subjects. I can't wait to apply it to stacked spins and pool ball mechanics.
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Re: Quaternions
LongtimeAirman wrote:Hey Cr6, I viewed 13a and enjoyed it. I'll need to study it
At one time I was responsible for optimizing runway navigational aids, concerning myself with dual frequencies, modulation schemes, voltage levels, phase angles, cable lengths, antenna positions, the ground plane, adjacent structures, etc. I began experimenting onmyown by modeling EM signals using two dimensional complex plane waveforms while calculating angles using transcendental functions in an effort to see "EM" structures "in space". Please don't get the impression I knew what I was doing. I never got to three dimensions, processing time was ridiculously long, and I never figured out Jordy glasses. It was fun though.
I have long since given up on transcendental functions and the infinitesmal. (By a coincidence, I started reading Amir Alexander's book, but don't want to read your post since I suspect the book is politically skewed in both religion and science). I welcome Wildberger's rational geometry, and can't wait to get back to it. I'm stretched a bit thin, but am happy that you provide such interesting subjects. I can't wait to apply it to stacked spins and pool ball mechanics.
Wildeberger doesn't appear to really like irrational numbers, like Mathis, so I do see them echoing each other to a degree. I think his Rational Trig with quaternions in 3D may give a few clues into the photon/antiphoton spin mechanisms of Mathis. It could be a key to unlock things with (or maybe not). I can't work out the math per se but can sense that quaternions do provide a cancelling 1 or 1 when spheres hit head on a 2D plane (photon/antiphoton). Sorry if this explanation doesn't make a lot direct sense. Wildeberger's work is interesting and can give a few different tools to solve problems with. I think Mathis could run with this since he does strictly try to avoid irrational numbers.
I kind of see the Charge Field spin mechanics using quaternion math. It is deep though. I know a few 3D game engines use quaternions for perspective rotations/kinematics so very realistic scenarios can be created with them.
Re: Quaternions
Cr6, I went through the 4 videos of the quaternion series and believe that quaternion rotations can be simplified to transform matrices similar to the complex plane transformations I learned about in fields and waves. I'll look more closely at Java and the java script, but I'll take the long road recommended by Nevyn. Engines are great but I need to get more confidence in the math and programming. It's daunting; I thought I wouldn't need either again (feel free to slap me at any time).
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Re: Quaternions
I moved my review of Infinitesimal to the Non MM Topics Section. http://milesmathis.forumotion.com/t72reviewofthebookinfinitesimalbyamiralexander#594
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Rational Trigonometry  Norman Wildberger’s Divine Proportions
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Cr6, I finally started working through Norman Wildberger’s Divine Proportions. http://wildegg.com/.
I had a gratis copy  thanks  but like to purchase special books once or twice a year. He lives in Sidney and wishes he had more wealth and health, so I'll help.
I found his blog yesterday. njwildberger: tangential thoughts, mathematical ruminations and more https://njwildberger.com/.
His working address at the University of New South Wales in Sidney. http://web.maths.unsw.edu.au/~norman/Rational1.htm.
The book site, http://wildegg.com/ includes FAQs about Rational Trigonometry including the following.
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Cr6, I finally started working through Norman Wildberger’s Divine Proportions. http://wildegg.com/.
I had a gratis copy  thanks  but like to purchase special books once or twice a year. He lives in Sidney and wishes he had more wealth and health, so I'll help.
I found his blog yesterday. njwildberger: tangential thoughts, mathematical ruminations and more https://njwildberger.com/.
His working address at the University of New South Wales in Sidney. http://web.maths.unsw.edu.au/~norman/Rational1.htm.
The book site, http://wildegg.com/ includes FAQs about Rational Trigonometry including the following.
A small disappointment, knowing there be Quaternions ahead.njwildberger wrote: What about rotations and circular motion?
It turns out that rotations can be handled perfectly with rational trigonometry (the book Divine Proportions shows how). But uniform circular motion cannot be handled with rational trigonometrythe trig functions are necessary for it. The point is that trigonometry (the study of the measurement of triangles) and circular/periodic motion are two separate subjects. It is not appropriate to have a mathematical technology that covers both topics at once, as the current approach does. The reason is that the theory becomes unnecessarily complicated to incorporate two overlapping but disjoint subjects.
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 Posts : 1461
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Re: Quaternions
LongtimeAirman wrote:.
Cr6, I finally started working through Norman Wildberger’s Divine Proportions. http://wildegg.com/.
I had a gratis copy  thanks  but like to purchase special books once or twice a year. He lives in Sidney and wishes he had more wealth and health, so I'll help.
I found his blog yesterday. njwildberger: tangential thoughts, mathematical ruminations and more https://njwildberger.com/.
His working address at the University of New South Wales in Sidney. http://web.maths.unsw.edu.au/~norman/Rational1.htm.
The book site, http://wildegg.com/ includes FAQs about Rational Trigonometry including the following.A small disappointment, knowing there be Quaternions ahead.njwildberger wrote: What about rotations and circular motion?
It turns out that rotations can be handled perfectly with rational trigonometry (the book Divine Proportions shows how). But uniform circular motion cannot be handled with rational trigonometrythe trig functions are necessary for it. The point is that trigonometry (the study of the measurement of triangles) and circular/periodic motion are two separate subjects. It is not appropriate to have a mathematical technology that covers both topics at once, as the current approach does. The reason is that the theory becomes unnecessarily complicated to incorporate two overlapping but disjoint subjects.
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Thanks LTAM. I just had "hunch" that some new approaches could be found with Wildberger's approach. That's great he reached out to you and indicated there are no shortcuts with real motions.
His websiteblog is quite good and some of the commenters have good input (especially on Hilbert). He definitely leans towards measuring what is "real" in the real world. A few people found a resonance with Mathis' as well??? (Somebody we know ).
https://njwildberger.com/2014/10/06/theinfinitelyrealdelusionandmyrecentdebatewithjamesfranklin/
https://njwildberger.com/2016/04/25/viewerscommentsoninfinity/ishinden wrote:
ishinden
April 28, 2016 at 1:52 am
These comments about math taking over physics very much remind me of the essay Death by Mathematics (http://milesmathis.com/death.html). Have you read it, Norm?
Re: Quaternions
Another great comment:
https://njwildberger.com/2015/06/06/somefundamentalformulasofmetricalalgebraicgeometryseminar/
Lito P. Cruz
September 13, 2015 at 6:37 pm
I am beginning to see why you do not believe in real numbers. Is it because they are not computable? You pointed out in your debate YouTube, the necessity of being able to write things down. I accept your point. If you can not write it down you can not write an algorithm to process it. Am I in the right track in understanding you?
LPC
njwildberger: tangential thoughts Post author
September 13, 2015 at 7:01 pm
Yes that is the right direction. Being able to, at least in principle, write something down is the mathematical equivalent of being able in physics to, at least in principle, make a measurement.
https://njwildberger.com/2015/06/06/somefundamentalformulasofmetricalalgebraicgeometryseminar/
Re: Quaternions
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Please check out  Visualizing quaternions . An explorable video series. Lessons by Grant Sanderson. Technology by Ben Eater. Quaternions and 3d rotation https://eater.net/quaternions.
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Please check out  Visualizing quaternions . An explorable video series. Lessons by Grant Sanderson. Technology by Ben Eater. Quaternions and 3d rotation https://eater.net/quaternions.
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