Dmitri Tymoczko pointed me to this article by John Baez explaining general relativity. I replied that this seems like some very important stuff, but I’m devoting all of that part of my brain to being confused by quantum mechanics. I have no room to be confused by gravity too!
Dmitri responded:
When I was 13, there were two things I wanted to understand more than anything else in the world: jazz and quantum mechanics.
Eventually I realized they are kind of similar. In both cases, you start with this fabulously complicated 19th-century language — Lagrangian and Hamiltonian mechanics in the one case, and romantic harmony in the other. Then you “twist” it. In the one case, you turn variables into operators, while in the other you add this scale-based improvisational component. But they are both difficult in kind of the same way because you have to learn this whole other language, and then apply this massive conceptual twist.
But quantum mechanics is genuinely mysterious — there’s some basic stuff we don’t know. General relativity is just straightforward geometry, no mysteries to solve.
All I can say regarding the connection between jazz and quantum mechanics is . . . wow. I wish I could play music, hold music in my mind, and read music. I guess that with a lot of effort I could make some progress in all three of these, but I can’t see myself putting in the time, so I’ll just be wistful about it, and I’ll continue to listen to lots of music and read a lot of music.
Here are some relevant posts (on music, not on quantum mechanics or jazz):
– Books by Charles Rosen and Jeremy Denk on piano playing and the nature of music
– Playing music, listening to music, background music, talking about music
– How Music Works by David Byrne, and Sweet Anticipation by David Huron
– Why do we prefer familiarity in music and surprise in stories?
– Luc Sante reviews books by Nick Hornby and Geoffrey O’Brien on pop music
– This guy is to music as I am to statistical graphics
– Why is modern poetry so hard to read? Adam Kirsch offers a clue.
And, finally:
A book about the cognitive and perceptual bases underlying some of the “rules” in music that you and Dmitri might find interesting is “Voice Leading: The Science Behind a Musical Art”, by David Huron.
Oof. That book is a bit of a sore subject for me. David Huron was a teacher of mine, and he drafted much of that book long before I entered the field. I then did a lot of work on voice leading (including two books: A Geometry of Music, and Tonality: an owner’s manual) both of which were, I believe, entirely relevant to the topics in David’s book.
David for whatever reason just dismissed this work, declaring that it was somehow concerned with a different topic, even though I think he and I were interested in the very same topic. At some level, I suspect he just didn’t think he could handle the math I was using (though I would have been happy to explain it to him). It is very frustrating, because it was a missed opportunity to think about connections between psychology and math.
Dmitri, I’m sure your familiar with his harmony thoughts in blog form, an example being [Baez mathstodon harmony blog](https://mathstodon.xyz/@johncarlosbaez/115780091005179545)
I’m surprised he hasn’t tried to make a connection of harmony symmetries with octonians.
Switching from David Huron to John Baez now! Yes, well, I find John worth reading on just about everything, whether it is something I don’t know at all or something I know well (like just intonation).
John Baez is a fun guy to read, I read his blog regularly. I hadn’t come across this paper and looks like a good read.
Speaking about art/literature and quantum mechanics I read recently Tokyo Express by Seicho Matsumoto. Written in the mid-1950s it is the founding rock of Japanese train detective stories and a delight to read. The story’s relation to quantum mechanics boils down to what I call time-table physics – you don’t know much about the journey, all you can do is read the timetable and look at the tickets. In rat-trap physics you catch a whole rat even though all you can only calculate is where it probably might go, but then, that’s statistics and physics for you.
Interesting; I recently finished Seicho Matsumoto’s “Inspector Imanishi Investigates” which I really enjoyed – I’ll look out for “Tokyo Express”.
The book is a police procedural similar in scope to the Martin Beck procedurals of Maj Sjöwall and Per Wahlöö (also great IMO). It gives a nice flavour of Japan/Tokyo in the 1960’s – it has a very minor music/physics component though I’m not sure I could conjure a quantum mechanics connection!
I think John is one of the great mathematics writers, kind of like a supercharged Martin Gardner — but with a lot more substance and detail.
This is an interesting comparison: both jazz and quantum mechanics tend to be learned and understood in a historical context, i.e., in relation to previous concepts. I wonder if this will change in the future, or is already changing to some extent? For example, I think many jazz players “discover” jazz for themselves without necessarily understanding it in relation to Western harmony as it developed up to the early 20th century. It’s possible to learn riffs and chords and how they operate without ever learning to read Western musical notation, just by listening and experimenting. Of course, to understand *why* the jazz style works the way it does requires historical context, but that’s separable from playing and listening. Similarly, I wonder whether future generations will have the option to learn quantum theory without learning about Maxwell.
To that last question, I wonder what other concepts in history were initially understood only in relation to some older concept, but then came to stand “on their own” later? For example, modern science can be understood in contrast to alchemy, but we don’t teach physics by first teaching about phlogiston. But perhaps that was not always the case?
I am a physicist and modern classical mechanics is not understood in a historical context. It is just said to be invented whole cloth by Newton using Galileo and Kepler’s concepts (which had no precursors, supposedly) and then generalized by Euler/Lagrange. Math is taught in even less of a historical way. It’s just taught that you have these axioms and you can derive these theorems from them. From what little I know and from what books I have skimmed, statistics seems to be taught like math. (What would be the need for Bob Carpenter to make posts (https://statmodeling.stat.columbia.edu/2026/05/16/why-are-there-squares-everywhere-in-statistics-normal-variance/) about the least squares concept otherwise?)
Even for quantum mechanics you only get some slight historical tidbits when you are learning it. Some vague statements about the failure of classical mechanics to account for black body radiation. Griffiths, one of the most popular textbooks, does not even do this much.
Maybe this is also the difference between teaching and doing. The original inventors of quantum mechanics understood the context of their work and what they were improving on. But they did not teach it this way, at least not in their textbooks. You can see Dirac’s textbook for an example.
This is why I have always loved M. S. Longair’s “Theoretical Concepts in Physics.”
That seems like a very interesting book! Will check it out.
Math is not taught in a historical way since it would take much longer and would be much harder. Our modern definitions are clean and precise and get you to the theorems faster. However, they are not appropriate for elementary or high school, which is a main reason school math is so bad. There are many good books on the history of math.
Bebop jazz I get: those guys were writing classical music in real time: scalar lines, arpegios, enclosures, octave displacements, etc. etc. were all the tricks of the trade Bach and Mozart were using back in the day.
QM is similarly simple. Feynman explained it just fine in 1963:
“Things on a very small scale behave like nothing that you have any direct experience
about. They do not behave like waves, they do not behave like particles, they do not
behave like clouds, or billiard balls, or weights on springs, or like anything that
you have ever seen.”
Like bebop, it’s not magic, it’s repeatable rules that can be explicated by experiment. In particular, subatomic objects are probabilities, have infininte extent in space, and appear at a point when their wave function collapses.
But these rules drive physicists mad: completely insanely mad. They were trained and promissed that physics was the most basic of the sciences, that it predicted everything. But in reality it’s just random wackiness.
Feynman was wrong. They behave like particles guided by waves, since that is what they are.
Interesting analogy. QM being 19th century CM with a twist is something I can get behind. Many people, including physicists, seem to think it’s far more different than this, and I think that is not correct.
But I was confused by this: “But they are both difficult in kind of the same way because you have to learn this whole other language, and then apply this massive conceptual twist.”
“Other” with respect to what? The “other” language is the default, at least in physics, because you learn CM before QM in school.
Right, well, when I was in high school I wanted to learn QM and hear all about complementarity and half-dead cats, and so I called up physics professor at the local college and said I wanted to take QM, and he said I had to take this other course about pendulums linked by springs, which really didn’t interest me very much. So that “other” subject felt quite different from the thing I was interested in.
Since half-dead cats don’t exist, you saved yourself some time. There are good books on quantum mechanics you can read without having to first read a book on classical mechanics. E.g., Bell’s book or Bricmont’s books.
I read John Baez as Joan Baez, who would have probably introduced even more musical connections
Joan is his cousin.
That’s not unusual, it’s just that the moon is full.
as Andrew said above, “but I’m devoting all of that part of my brain to being confused by quantum mechanics”, I have to say me too. Way more a part of my brain than should be. I just read “The Book of Tea” by Okakura Kakuzo, tr. Bruce Richardson, which was a delight. You have to read “Flowers” and if that doesn’t make you laugh…
That said, in the same time frame I read Part N.4 of Tony Zee’s “Quantum Field Theory in a Nutshell”, 2ed., “Is Einstein Gravity Secretly the Square of Yang-Mills Theory?”. This kinda brings Baez and Zee together maybe, just sayin’. Maybe you square Baez and get Zee? It’s a thought.