I have always been an average Physicist:
Little ability in Chemistry too:
And my knowledge of Mathematics comes mainly from Biology:
Little ability in Chemistry too:
And my knowledge of Mathematics comes mainly from Biology:
The word "Bird" to me means Charlie Parker:
https://www.johnconnollybooks.com/
Who could not love Charlie Parker and Angel and Louis? Very surreal indeed. That's Jazz baby. 😛
https://www.johnconnollybooks.com/
Who could not love Charlie Parker and Angel and Louis? Very surreal indeed. That's Jazz baby. 😛
Saxophonist and Astrophysicist Stephon Alexander describes the links between jazz and physics. “One connection,” he says, is “the mysterious way that quantum particles move…. According to the rules of quantum mechanics,” they “will actually traverse all possible paths.”
Last edited:
That was one of the best things I have ever watched! Thank you. Stephon is autistic. I know this state.
Symmetry and Physics tells it all:
J.S. Bach is surely the Mathematician's favourite Musician.
Symmetry and Physics tells it all:
J.S. Bach is surely the Mathematician's favourite Musician.
Wiki has an interesting entry on Stephon Alexander (no mention of autism!): https://en.wikipedia.org/wiki/Stephon_Alexander
Particularly relevant to this thread, Alexander has done much research on gravity, including co-authoring a paper that reinterpreted Hořava–Lifshitz gravity, a theory intended to quantise gravity by using techniques of traditional quantum field theories.
He was the president of the National Society of Black Physicists and has written about the need for black academics to set a positive trend for the next generation.
Last edited:
It was how he couldn't keep his feet still that I noticed. I have little idea what that theory is about really, except I have seen something similar in superconductivity recently where the whole system is acting as one, not as individual particles.
This book is a deep discussion about symmetry in both Mathematics and Music:
I enjoyed it. The human mind is very symmetry based, which I have not explained well here. Deep stuff.
A lot of good thought experiments use symmetry to get a grip on things:
I thought about that one for days! Where is the energy? It's relative. It's all quite tricky. 🙂
This book is a deep discussion about symmetry in both Mathematics and Music:
I enjoyed it. The human mind is very symmetry based, which I have not explained well here. Deep stuff.
A lot of good thought experiments use symmetry to get a grip on things:
I thought about that one for days! Where is the energy? It's relative. It's all quite tricky. 🙂
Last edited:
Heaviside was self taught. Quite a remarkable character IMV
https://en.m.wikipedia.org/wiki/Oliver_Heaviside
I have a copy somewhere of Maxwell’s original book/paper and the equations are indeed nebulous. Apparently Heaviside was criticised by mathematicians of the day for his ‘lack of rigour’ but he dismissed their concerns saying his mathematics produced the right result.
A proper engineer 👍
https://en.m.wikipedia.org/wiki/Oliver_Heaviside
I have a copy somewhere of Maxwell’s original book/paper and the equations are indeed nebulous. Apparently Heaviside was criticised by mathematicians of the day for his ‘lack of rigour’ but he dismissed their concerns saying his mathematics produced the right result.
A proper engineer 👍
My understanding of electromagnetism is 2 equations in 4 variables:
https://en.wikipedia.org/wiki/Electromagnetic_four-potential
Cue the 4D tesseract:
It gets worse. Beyond the Reals (R), and the complex (C), the Quaternions (Q) and the Octonions (O) lie the Sedenions (S):
https://en.wikipedia.org/wiki/Sedenion
This is Mathematics way beyond my ability! 🙁
https://en.wikipedia.org/wiki/Electromagnetic_four-potential
Cue the 4D tesseract:
It gets worse. Beyond the Reals (R), and the complex (C), the Quaternions (Q) and the Octonions (O) lie the Sedenions (S):
https://en.wikipedia.org/wiki/Sedenion
This is Mathematics way beyond my ability! 🙁
Whereas Maxwell's equations are 20 equations in 20 variables (or four equations in two variables thanks to Heaviside).
The electromagnetic four-potential you mention is an alternative mathematical description of the electromagnetic field which involves gauge freedom.
https://en.wikipedia.org/wiki/Gauge_fixing#Gauge_freedom
I can only stare slack-jawed at the mathematics! 😵
I read elsewhere that in the simplest case the electromagnetic four-potential represents the amplitude for finding the intermediary particle associated with the electromagnetic gauge field. This particle has zero mass and is called the photon.
Aren't Sedenions alien invaders from the 16th dimension?
Their appearances are similar to various types of sea creatures, suggesting their home dimension is full of water!
Explorations of the Universe are ongoing, and I allude to that fine Harry Nilsson kid's film "The Point".
This is a Conics joke, of course. How Euclid would have laughed!
I have discovered today that most Physicists of the last century would not touch General Relativity with a bargepole.
Thought the whole thing was a waste of time. (A lot of folks thought Quaternions stunk too... but whatever.)
The obvious interpretation is it's a 4 dimensional problem. But it seems Paul Dirac liked the Quaternion idea.
Cue John Baez:
https://math.ucr.edu/home/baez/octonions/conway_smith/
See, whenever I see a factor of 8 Pi or the sum of 4 squares, I am thinking 4 dimensions and not worrying about the odd negative sign on the time or space components of Spacetime:
I'll stop there. This post is already way too long. 😛
This is a Conics joke, of course. How Euclid would have laughed!
I have discovered today that most Physicists of the last century would not touch General Relativity with a bargepole.
Thought the whole thing was a waste of time. (A lot of folks thought Quaternions stunk too... but whatever.)
The obvious interpretation is it's a 4 dimensional problem. But it seems Paul Dirac liked the Quaternion idea.
Cue John Baez:
https://math.ucr.edu/home/baez/octonions/conway_smith/
See, whenever I see a factor of 8 Pi or the sum of 4 squares, I am thinking 4 dimensions and not worrying about the odd negative sign on the time or space components of Spacetime:
I'll stop there. This post is already way too long. 😛
Last edited:
You seem to have some spooky Mathematical intuition there, @Galu.
This is EXACTLY the problem I am working on right now!
All good Number Theorists are aware that any whole integer can be written as the sum of 4 squares of positive integers...
https://en.wikipedia.org/wiki/Lagrange's_four-square_theorem
You will find that this problem is also related to what are quaintly known as "Kissing Circles".
Top people like Fermat, Dirac and Heaviside and Noether were well aware of this problem. It's 4 dimensional (Q) in some sense, though in Weyl Spinors you might look at it as the product of two 2D (C) complex numbers..
I just ran the (-1,2,2,3) case up the flagpole, and darned if it doesn't get a salute.
I got 6^2 = 36 = 2 x 18. (Watch out for the minus sign on 1)
Apart from the obvious relation to Special Relativity and Lorentz Quadruples, I see a similarity to the mysterious Koide Formula:
Very happy with my current investigations. Bit more work to do, of course. But how hard can it be?
This is EXACTLY the problem I am working on right now!
All good Number Theorists are aware that any whole integer can be written as the sum of 4 squares of positive integers...
https://en.wikipedia.org/wiki/Lagrange's_four-square_theorem
You will find that this problem is also related to what are quaintly known as "Kissing Circles".
Top people like Fermat, Dirac and Heaviside and Noether were well aware of this problem. It's 4 dimensional (Q) in some sense, though in Weyl Spinors you might look at it as the product of two 2D (C) complex numbers..
I just ran the (-1,2,2,3) case up the flagpole, and darned if it doesn't get a salute.
I got 6^2 = 36 = 2 x 18. (Watch out for the minus sign on 1)
Apart from the obvious relation to Special Relativity and Lorentz Quadruples, I see a similarity to the mysterious Koide Formula:
Very happy with my current investigations. Bit more work to do, of course. But how hard can it be?
Last edited:
You could use this to recursively calculate the area of a circle. I suspect the area of any shape is amenable to this approach.
Dylan was asked in Poets Society San Francisco 1965 if he played folk music. He said, no. Then what kind of music do you play? Mathematical music.
The Apollonian circle packing you mention produces an Apollonian gasket, which is apparently one of the earliest fractals described in print.
I could see a "sum of 4 squares" in this link: https://en.wikipedia.org/wiki/Apollonian_gasket
Then there is Apollonian sphere packing which can generate some pretty images: