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Is mathematics about to enter the conservatory?

mbmccoy.dev

131–140 of 145 posts

Re: Is mathematics about to enter the conservatory?

#131
post #21

Earlier quoted context omitted.

> Even the first-chair musicians and conductors have side gigs. A principal player (I don't think anyone beyond high school band calls them 'first-chair') in a major symphony orchestra in the United States makes $250k-400k a year. These are extremely competitive jobs and they are paid well. Certainly enough to live on if you wanted to. These people often teach, but not really because they need a "side-gig." If you as…

There are about twenty of these people, though. I said "approximately nobody". At a first approximation, no musician who does it for money makes a living out of it. Classical, pop, rock, whatever. Nobody in music, basically, makes real money. Fifty, maybe a hundred violinists in the entire world do earn a pure living. Perhaps another twenty five of each other instrument. A few international soloists in other instrume…

>Fifty, maybe a hundred violinists in the entire world do earn a pure living.

This has to be off by at least two orders of magnitude.

The Reykjavik symphonic orchestra in Iceland alone employs some 30 full time violinists. The nation's population is less than El Paso, tx - which also employs some 80 musicians in their symphonic orchestra.

Your main point might still have merit, but this forum is one where missing the numbers by so much will distract many readers. It distracted me, at least. :)

Pop musicians have fewer options and need to chase gigs, but the payoffs are also larger if they make it. One-hit wonders drive Ferraris.

Re: Is mathematics about to enter the conservatory?

#132

Earlier quoted context omitted.

You're overlooking the word "mostly" in the quote you trotted out. Ask yourself: what were the prompts that weren't encouragement and would you understand them if you looked them up?

Here's the transcript: https://www-cdn.anthropic.com/8a0d1add3c637b858a9a181e98c40e... Jarred is not a mathematician. He just heard about a problem and asked Claude to try solving it.

This is a very incomplete transcript : "The complete transcript of ONE autonomous Claude sub-agent, "E2", "

Re: Is mathematics about to enter the conservatory?

#133
post #89

Earlier quoted context omitted.

Looking a bit more into this, it doesn't seem your claim "most of the consequences of additional axioms have been worked out" holds up. Yes, metamathematics is well-developed, but I don't think that most of the consequences of any particular additional set of axioms have been worked out. Each such new set requires re-deriving all of this alternate mathematics from scratch. This is a lot of work! So I think my origina…

I don't see how you came to that conclusion, since I'm telling you the actual state of play. There's a big literature on what results require the Axiom of Choice, for example. (The book Handbook of Analysis and Its Foundations covers this thoroughly.) There are many results on what follows from the Continuum Hypothesis or other cardinal arithmetic axioms. There is a big literature on what follows from assuming the ex…

While the existing body of work on alternate axioms is tremendous, it's finite. The set of possible axiom systems is infinite. Does current the current body of work cover all consequences of all possible axiom systems?

Re: Is mathematics about to enter the conservatory?

#134

Earlier quoted context omitted.

Yes, but that sounds to me exactly the process vs. outcome distinction that the parent made, rather than a difference in the intent to communicate.

I think those two arguments converge into one- you can’t get the intent unless you have the process

The difference for most people against AI is that there is no world where someone with intent and skill can engage with AI to make anything approaching art. If your process includes AI, it is impossible to be an artist.

Even engaging with the nuance is beyond the pale.

Re: Is mathematics about to enter the conservatory?

#135
post #15
post #9

Earlier quoted context omitted.

Modern 'classical' music is a myth. In their day, classical composers were essentially pop performers. Women used to throw their undergarments at mozart... Today classical music is filled with people who want to pretend to be superior to pop musicians because they keep their repertoire confined to academically acceptable areas. And then the LARPers that want to make new music make complete and utter arhythmic and ato…

> Today classical music is filled with people who want to pretend to be superior to pop musicians because they keep their repertoire confined to academically acceptable areas. As somebody with classical training and a brother in the industry, it pains me to read this misinformed opinion of yours. Top-tier symphonies world round are doing crossover concerts with pop artists, play pop songs, modern and experimental mus…

> I know people who only listen to a single narrow genre or decade of pop music. How are they different?

No one mistakes a pop artist or afficianado for some great connoisseur of culture.

Re: Is mathematics about to enter the conservatory?

#136
post #19
post #9

Earlier quoted context omitted.

Modern 'classical' music is a myth. In their day, classical composers were essentially pop performers. Women used to throw their undergarments at mozart... Today classical music is filled with people who want to pretend to be superior to pop musicians because they keep their repertoire confined to academically acceptable areas. And then the LARPers that want to make new music make complete and utter arhythmic and ato…

The idea that classical composers (before about Liszt) were the "pop music" of their day is uninformed. Consider 1) the size of the venues that Mozart or Haydn's secular music was performed in, and 2) the fact that the bulk of the population was peasantry who wouldn't be admitted to such venues in a time of strict class distinctions. Outside church settings, classical music of the Baroque, Classical and early Romanti…

Pop music is also mostly trash too, but no one pretends otherwise. At least they have the decency to use auto tune.

Re: Is mathematics about to enter the conservatory?

#137
post #9

Earlier quoted context omitted.

Modern 'classical' music is a myth. In their day, classical composers were essentially pop performers. Women used to throw their undergarments at mozart... Today classical music is filled with people who want to pretend to be superior to pop musicians because they keep their repertoire confined to academically acceptable areas. And then the LARPers that want to make new music make complete and utter arhythmic and ato…

> Today classical music is filled with people who want to pretend to be superior to pop musicians because they keep their repertoire confined to academically acceptable areas. What an incredibly cynical take. I’ve done several chamber music collaborations with a violist who also plays pop music gigs on keyboards. There are arrogant pricks in classical music. And in software engineering and every other discipline. Per…

> while you yourself do the same about modern composers.

I literally gave several examples of modern genres in which classical composers still produce good work. I just said they're unlikely to be found in academia

Re: Is mathematics about to enter the conservatory?

#138

> Consider classical music. Our society does not support classical musicians in the same way that we support ‘popular’ musicians “Society” is a leaky abstraction here. If you reify society as a thing that is capable of “supporting” or “not supporting” something you mean essentially the government. In that case, “society” probably provides more support to classical music than pop music, through grant programs, public…

[deleted]

Re: Is mathematics about to enter the conservatory?

#139
post #98

> I haven’t fully verified the proof; I worked through it with Claude Fable and it passes the sniff test, but fully digesting it will take a bit more energy than I have right now. This is overlooked but really important. Nobody wants to watch robots play chess against each other - we watch human chess even though bots are better. Nobody needs math that has not been verified by humans. Human understanding and communic…

> Nobody wants to watch robots play chess against each other - we watch human chess even though bots are better Many humans have studied robots play chess and learned from them. For example the concept of a "thorn pawn" was popularized after Leela played it with great success. > Nobody needs math that has not been verified by humans. There already are proofs that are understood by a handful of humans; without underst…

> Many humans have studied robots play chess and learned from them.

Yes, robot chess is very useful for chess players. It's a great technology.

People don't want to watch robot chess. They want to watch humans, even those who used AI to train. The human part of chess is what matters.

> There already are proofs that are understood by a handful of humans

Yes, exactly.

Re: Is mathematics about to enter the conservatory?

#140
post #98

> I haven’t fully verified the proof; I worked through it with Claude Fable and it passes the sniff test, but fully digesting it will take a bit more energy than I have right now. This is overlooked but really important. Nobody wants to watch robots play chess against each other - we watch human chess even though bots are better. Nobody needs math that has not been verified by humans. Human understanding and communic…

Mathematics is not chess, it is about reality. There is a huge value in P=NP for example, if such result is ever rigorously proved, regardless of the proof. Less so perhaps for P!=NP, but it would be a definite answer to a long standing question. This is why I think "Leiden program" and similar proposals will eventually fail. It is true that the questions to be solved would have to be interesting to humans, though. B…

For sure LLMs will be used more and more.
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