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Leiden Declaration on Artificial Intelligence and Mathematics

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Re: Leiden Declaration on Artificial Intelligence and Mathematics

#81

Post by pfdietz »

Jblx2 wrote: post #77
pfdietz wrote: post #76

Earlier quoted context omitted.

The atomic bomb certainly had a cursory dependence on special relativity. E = mc^2, you know. Klystrons were used in WW2, and the beam current of a klystron scales as the beam voltage to the 3/2 power (due to space charge limits). Modern klystrons operate with relativistic electron beams, but I don't know if any of the WW2 ones did.

Is there any part of the theory or design or implementation of the atomic bomb that depends on E = m*c^2? Or is it: "if you could theoretically weigh the end-products, you would get a slightly smaller answer than the before-products". Seems like it would have been known that there was a lot of electrical potential energy stored in the nucleus (after the discovery of the proton).

Calculating the energy yield of a fission event is done by comparing the masses of the initial and final states. The difference is about 1/5th the mass of a nucleon.

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#82

Post by Jblx2 »

pfdietz wrote: post #81
Jblx2 wrote: post #77

Earlier quoted context omitted.

Is there any part of the theory or design or implementation of the atomic bomb that depends on E = m*c^2? Or is it: "if you could theoretically weigh the end-products, you would get a slightly smaller answer than the before-products". Seems like it would have been known that there was a lot of electrical potential energy stored in the nucleus (after the discovery of the proton).

Calculating the energy yield of a fission event is done by comparing the masses of the initial and final states. The difference is about 1/5th the mass of a nucleon.

I guess that seems legit. Thanks

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#83

Post by onetimeusename »

magimas wrote: post #75
onetimeusename wrote: post #45

Earlier quoted context omitted.

There is some of that but I wouldn't call it gatekeeping. Universities lately promote citations and publications so there's a sense that results are all that matters. Results matter, yes, but there's a human side too where we're kind of asking about human creativity and ability. To me an appropriate analogy is in climbing Mt. Everest. Proving something, or even writing a thesis, is like climbing Mt. Everest. A lot of…

I don't know, I don't think this "effort for effort's sake" is a very convincing argument. In particular, I think it's very much affected by recency bias in a way? What we perceive as "effort worth taking" instead of "dull occupational therapy" is very prone to change with technology. If you would argue that modern photographers need to take the time to physically develop their photos and use chemicals to get their e…

I'm not arguing that people should do things as hard of a way as possible, I think that's kind of a straw man. I am not saying we should tie stones around us, write things in Latin, and not use computers or something like that.

Math is not really about just piling up results in my opinion. Most people's day to day lives were not directly changed by the recent Erdős problem that was solved by AI. I think most people believe the result would have been more impressive if a human had found the counterexample. People do not list those problems because they need to be urgently solved but because they are hard and interesting and it impresses us when a human solves it.

But not only that, the person gains insight along the journey. I am not sure what insight AI can give us really. It basically maximizes text output over a massive dataset that includes mathematical research. So again, the journey itself is valuable not just because it's hard but because it gives us information.

There's also the problem that credibility for so many things is based on attribution of doing something difficult. A PhD has been a way we measure credibility in a field. It's a fence you hop to get in. If AI can write up a thesis in a tiny fraction of time and cost, it could break attribution if people print theirs with AI but also it breaks the credibility link. Is that important? For math, using PhDs as a measure of credibility in some ways is a bad way to do things, but it's effective and probably the best we have. (For other fields it could be catastrophic). So it destroys a signal about the author which may not be catastrophic here. Where this goes wrong is if getting a PhD is now obsolete. People who have experience and who can review AI output proofs exist right now but how will we ensure anyone is trained in proofs in the future? If we're going to outsource math to AI I think the reason people are right now getting PhDs could be completely obsolete unless we agree it's worth it for people to work through it on their own and gain that experience for themselves.

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#84

Post by ShinyLeftPad »

nh23423fefe wrote: post #79
palmotea wrote: post #72

Earlier quoted context omitted.

> That's the product of math from the point of view of mathematicians. But is it the point of view of those funding math? That's AI in a nutshell: the only point of view that matters is the point of view of people with a lot of money, and we've finally developed a technology that will allow all those other points of view to be squashed and discarded. The powerful won't need to be bothered with them anymore. For them,…

When did people with no power matter?

Literally all the time in prior history, whenever people WITH power needed them to do smart stuff for them.

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#85

Post by pfdietz »

Jblx2 wrote: post #82
pfdietz wrote: post #81

Earlier quoted context omitted.

Calculating the energy yield of a fission event is done by comparing the masses of the initial and final states. The difference is about 1/5th the mass of a nucleon.

I guess that seems legit. Thanks

Another situation that occurs in nuclear weapons and in reactors is the scattering of energetic photons off materials. This process is inherently relativistic when the photons have energies comparable to or greater than the rest energy of an electron. (Differential) cross section computations are necessarily relativistic.

At Los Alamos, various techniques using energetic photons and electrons were used to diagnose implosion systems in development of the plutonium bomb.

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#86

Post by newsicanuse »

Spacecosmonaut wrote: post #51

Accelerationists may argue that the eroding of proper attribution and proof verification by humans is a meaningless short term struggle of a dying field. Mathematics seems to be entering an era where human + machine maximizes performance, much like chess in the 1990s. However, imagine a future where even talented mathematicians are nothing but noise in the machine (as is the case in chess now). A future where AI gene…

Keep dreaming

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#87

Post by wyan »

Jblx2 wrote: post #74
enugu wrote: post #32

Earlier quoted context omitted.

Power depends on understanding - Seeing a larger scale view of what is happening as opposed to an arbitrary sequence of manipulations. The foundations of the WW2 technologies you cite were dependent on previous theoretical efforts (ex:relativity) to develop a good understanding. Without understanding, you get brittle demos which fail as the environment or problem description changes.

Which WW2 technologies had even a cursory dependency on Special or General Relativity?

Not WW2, but GPS depends on General Relativity to calculate time differences between satellite signals and ground correctly.

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#88

Post by jonjacky »

Jblx2 wrote: post #74
enugu wrote: post #32

Earlier quoted context omitted.

Power depends on understanding - Seeing a larger scale view of what is happening as opposed to an arbitrary sequence of manipulations. The foundations of the WW2 technologies you cite were dependent on previous theoretical efforts (ex:relativity) to develop a good understanding. Without understanding, you get brittle demos which fail as the environment or problem description changes.

Which WW2 technologies had even a cursory dependency on Special or General Relativity?

Particles accelerating in a cyclotron at sufficiently high energy reach relativistic speeds. You have to account for their relativistic mass increase to get the cyclotron to work. Figuring this out was a big issue in cyclotron design in the 1930s. The remedy is to strengthen the magnetic field near the outer edge of the cyclotron where particles move fastest, by adding coils there to carry more current. I don't recall what the energy is where this becomes necessary - it is certainly needed at tens of MeV.

Plutonium was first synthesized in a cyclotron by Lawrence's group at Berkeley. I don't know what energy they used so I don't know if they needed the extra coils, but they did know of the effect and must have considered it.

Also, U235 was separated at Oak Ridge using machines called Calutrons invented by Lawrence that might have encountered the same problem -- at least they must have considered it.

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#89

Post by AndrewKemendo »

nh23423fefe wrote: post #79
palmotea wrote: post #72

Earlier quoted context omitted.

> That's the product of math from the point of view of mathematicians. But is it the point of view of those funding math? That's AI in a nutshell: the only point of view that matters is the point of view of people with a lot of money, and we've finally developed a technology that will allow all those other points of view to be squashed and discarded. The powerful won't need to be bothered with them anymore. For them,…

When did people with no power matter?

Never of course.

The only examples we have are when power is transferred or seized to someone previously without it.

But all you did was replace one figure head with another figure head in almost every single case and you just start the cycle over.

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#90

Post by bcjdjsndon »

Spacecosmonaut wrote: post #56
bcjdjsndon wrote: post #54

Earlier quoted context omitted.

> However, imagine a future where even talented mathematicians are nothing but noise in the machine (as is the case in chess now). Isn't chess more popular than ever? Ai dominating the game didnt seen to matter

Sure, but if we continue that analogy it does mean that there will be no human contributions to frontier mathematics.

If the output is better who cares?
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