I play piano. Alkan is horrifically difficult. So hard, I don't even bother to play it. I do play Ravel and Balakirev's Islamey which is about as demanding as I want to handle. I have enough technique to play anything by Schumann, Chopin (except etude op. 10 no. 1), Beethoven, Brahms, Mozart, Bach, etc. without too much trouble. I like m…
I play piano. Alkan is horrifically difficult. So hard, I don't even bother to play it. I do play Ravel and Balakirev's Islamey which is about as demanding as I want to handle. I have enough technique to play anything by Schumann, Chopin (except etude op. 10 no. 1), Beethoven, Brahms, Mozart, Bach, etc. without too much trouble. I like music. The finger gymnastics and octave Olympics I'll leave to someone else.
You are a polymath. I would put Alkan right up there with Tesla and Einstein as, if geniuses at all, seriously flawed ones. My take on Einstein I inherited from my physicist bro in law who explained how the theory of relativity was already common knowledge in certain circles. Einstein, working in a patent office, just jumped first and hype by the tribal press did the rest.
I did Math Olympiad as a kid and learned Bach Inventions and the Well Tempered Clavier early on. It was mostly a case of having a strong interest and the right kind of perspective from the start. I got hooked on Bach from hearing it played at Church.
Regarding physics, it's just going to turn out how it's going to turn out. I have my own ideas where we might go. It's probably wrong but I might as well share them. Quantum field theory is a mess. We have a workable pile of heuristics and rules of thumb but nothing like a mathematically rigorous theory. There are Wightman axioms for QFT but it doesn't work for actual physics but it's mathematically interesting. In order to go further, I think we really need to understand QFT properly. We really are at that stage where an incomplete understanding of it will work anymore. These problems are present even in string theory which is a QFT that lives on a world sheet. It is often said that quantum gravity is the greatest problem. That may be but we really saw the limitations of quantum theory when applied to gravity. We need a way to go beyond perturbation theory and work with strong coupling.
The situation in physics is like that of Fourier analysis when it was first discovered. Fourier had a brilliant solution of the heat equation but it broke calculus. It took decades for men like Weierstrass, Cauchy, Abel, Riemann, Cantor, Dedekind and Dirichlet (I'm leaving people out) to detangle what was really going on. It took at long time to fix. Even then, integration was broken or incomplete at it had to be replaced with the Lebesgue integral and Measure theory was born. Fourier analysis really makes sense only with the Lebesgue integral, so we had to wait even longer. Functional analysis was born, Banach spaces, Hilbert Spaces etc. incidentally rigged Hilbert spaces and Self adjoint linear operators form the basis for ordinary QM as described in von Neumann's book. The moral of the story is we had a magic black box called Fourier series which seemed capable of solving differential equations and understanding physical phenomena like waves and radiation. It took a long time to figure out how that black box worked. Quantum field theory is another black box. It might very well be the case that 200 years from now in the rosiest of circumstances we might still be far off from complete understanding. Or maybe not. Our math is really not complete nor satisfactory to give a description of QFT. It might very well be that THIS is how a unified field theory is discovered, that once you understand the underlying theory properly, you immediately see the menu of particles and forces which are possible. Who knows? That's my opinion. We could hammer away at string theory forever and play with various symmetry groups and interesting geometries but it's really sailing a ship without a Compass and Navigation. I see signs that Alain Connes is headed in this direction with Non Commutative geometry. Life is short so I don't spend it on these problems. I like to finish things and move on to a different project even if the problems are more pedestrian. Still, these are my guesses for how things could proceed.
I am going to take some time to understand what you have written. It is clear, cogent and actually highly instructive even for an ignoramus like me. Thank you for sharing your thoughts so generously.
As for pedestrian problems, never forget that pedestrians invented the car, and a few other things besides. Pascal for instance, invented public transit and the computer.
I'm flexible. It's going to turn out how it's going to turn out. I often entertain strange gruesome ideas if they lead somewhere and look promising. If physics gets turned on its head, I'm fine with that but what replaces it has to be objectively better.
A remarkable thought and certainly not what passes for Science these days which seems to be superstition and aping things little understood. That kind of 'Science' deserves the definite article the lugenpresse has given it - The Science indeed!
I play piano. Alkan is horrifically difficult. So hard, I don't even bother to play it. I do play Ravel and Balakirev's Islamey which is about as demanding as I want to handle. I have enough technique to play anything by Schumann, Chopin (except etude op. 10 no. 1), Beethoven, Brahms, Mozart, Bach, etc. without too much trouble. I like music. The finger gymnastics and octave Olympics I'll leave to someone else.
You are a polymath. I would put Alkan right up there with Tesla and Einstein as, if geniuses at all, seriously flawed ones. My take on Einstein I inherited from my physicist bro in law who explained how the theory of relativity was already common knowledge in certain circles. Einstein, working in a patent office, just jumped first and hype by the tribal press did the rest.
I did Math Olympiad as a kid and learned Bach Inventions and the Well Tempered Clavier early on. It was mostly a case of having a strong interest and the right kind of perspective from the start. I got hooked on Bach from hearing it played at Church.
Regarding physics, it's just going to turn out how it's going to turn out. I have my own ideas where we might go. It's probably wrong but I might as well share them. Quantum field theory is a mess. We have a workable pile of heuristics and rules of thumb but nothing like a mathematically rigorous theory. There are Wightman axioms for QFT but it doesn't work for actual physics but it's mathematically interesting. In order to go further, I think we really need to understand QFT properly. We really are at that stage where an incomplete understanding of it will work anymore. These problems are present even in string theory which is a QFT that lives on a world sheet. It is often said that quantum gravity is the greatest problem. That may be but we really saw the limitations of quantum theory when applied to gravity. We need a way to go beyond perturbation theory and work with strong coupling.
The situation in physics is like that of Fourier analysis when it was first discovered. Fourier had a brilliant solution of the heat equation but it broke calculus. It took decades for men like Weierstrass, Cauchy, Abel, Riemann, Cantor, Dedekind and Dirichlet (I'm leaving people out) to detangle what was really going on. It took at long time to fix. Even then, integration was broken or incomplete at it had to be replaced with the Lebesgue integral and Measure theory was born. Fourier analysis really makes sense only with the Lebesgue integral, so we had to wait even longer. Functional analysis was born, Banach spaces, Hilbert Spaces etc. incidentally rigged Hilbert spaces and Self adjoint linear operators form the basis for ordinary QM as described in von Neumann's book. The moral of the story is we had a magic black box called Fourier series which seemed capable of solving differential equations and understanding physical phenomena like waves and radiation. It took a long time to figure out how that black box worked. Quantum field theory is another black box. It might very well be the case that 200 years from now in the rosiest of circumstances we might still be far off from complete understanding. Or maybe not. Our math is really not complete nor satisfactory to give a description of QFT. It might very well be that THIS is how a unified field theory is discovered, that once you understand the underlying theory properly, you immediately see the menu of particles and forces which are possible. Who knows? That's my opinion. We could hammer away at string theory forever and play with various symmetry groups and interesting geometries but it's really sailing a ship without a Compass and Navigation. I see signs that Alain Connes is headed in this direction with Non Commutative geometry. Life is short so I don't spend it on these problems. I like to finish things and move on to a different project even if the problems are more pedestrian. Still, these are my guesses for how things could proceed.
I am going to take some time to understand what you have written. It is clear, cogent and actually highly instructive even for an ignoramus like me. Thank you for sharing your thoughts so generously.
As for pedestrian problems, never forget that pedestrians invented the car, and a few other things besides. Pascal for instance, invented public transit and the computer.
I'm flexible. It's going to turn out how it's going to turn out. I often entertain strange gruesome ideas if they lead somewhere and look promising. If physics gets turned on its head, I'm fine with that but what replaces it has to be objectively better.
A remarkable thought and certainly not what passes for Science these days which seems to be superstition and aping things little understood. That kind of 'Science' deserves the definite article the lugenpresse has given it - The Science indeed!