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Comment by pfdietz | Hacker News Reader

That's the product of math from the point of view of mathematicians. But is it the point of view of those funding math?

I suggest if one looks at the history of funding for mathematics and science, the product of these efforts is not understanding, but rather power. Funding went way up after WW2 when the war demonstrated that power flows from them. Math not only contributed to the scientific weapons of the way, but was directly used in operation planning (the birth of the field of Operations Research) as well as in cryptography.

The reason this matters is that AI is also a quintessential power-oriented technology. From the point of those providing the monetary lifeblood on which modern mathematical practice depends, the current math-AI discussion presents no issue worthy of concern.

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> 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, math is an instrument. Disagree? Fuck you, you don't matter anymore. Be excited about the future!

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.

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.

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?

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.

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.

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

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.

The debate on the funds of scholarship and education has been between democratic vision of "an informed citizenry" versus the technocratic vision of education for jobs and technical progress. Both of those might be "power" (Foucault said "everything is power" and if so, it tells us nothing). Thus I don't think your particular framing is useful.

For many who pursue mathematics, it is a refuge from ordinary life (or normal "power"). Within mathematics, there has historically been a tension between the "Babylonian" model of pure calculation and the "Greek" model of advancement through understanding. If current AI models subsume mathematics entirely, the Babylonian model will have "won" and the possibility of an informed citizenry will be in doubt.

There is more to math, than input (money) and output (power). Sure, there is some relation between applied sciences and how knowlegde can assist effecting world events.

But for the most part, math discovery relied more on human curiosity than on resources to "do math". Conversely, if people allocate lots of money to developing AI, that doesn't mean mathematicians have an obligation to take the money provide ROI to investors.

I mean, in real life it's a combination of both. Some money is for math as an exploration of our world that will never pay off. Some money is learning things that may pay off long after we're dead (planting trees so our great grandchildren have shade). Some money is for solving problems right now.

Getting funding can be quite difficult at times, so you'll see some portion of researchers (or mathematicians in this case) take the dollars they can get.

> That's the product of math from the point of view of mathematicians. But is it the point of view of those funding math?

Yes, and your examples are exactly examples of what the GP quote is talking about.

Of course people paying money want applications, which includes "power" in your kind of reductive framing (applications to war being only one of many types of applications, or we could redefine any gradient provided by expanded understanding as "power", in which case the choice of word just seems melodramatic).

What we've also learned over the centuries, a lot more clearly in the last few, is that seemingly pointless or applicationless understanding can very quickly become useful. This is why it's clearly worth still funding pure math.

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