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AI isn’t outthinking mathematicians, it’s out-remembering them

davidepiffer.com

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Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#511
post #489

Earlier quoted context omitted.

Same as the parallel comment: the situation of string theory is the same as with black holes and relativity. It is not it is not testable, it is that it is not testable yet. The situation is very similar of the situations of black holes and relativity at their own time. The fact that so many people, like you, just INVENT that it is not testable is quite worrying. Why? What's the point of doing that?

No one has "invented" that it's untestable. String theory literally doesn't give predictions that would allow it to be falsified. There are an astounding number of possible geometries that mean that any set of data could technically be "consistent with string theory". There are no specific energy bounds where it kicks in - if an experiement doesn't show existence of strings, it's "try again with more energy" instead…

First, it is incorrect to say that "any set of data is consistent with string theory". For example, string theory is death in water if we observe a single Majorana fermion with no partner at a comparable scale. This is an observation that fully falsifies string theory.

But more importantly, "falsifiable" means "observations reduce the landscape". It does not matter if the landscape never fully disappear, as long as the observations constrain the parameters of the theory, then the theory is falsifiable. This is the real condition for a theory to be unfalsifiable. Astrology is not falsifiable: whatever the observation, the full astrology theory remains exactly the same, nothing has been constrained.

Why is it the correct definition? Because your definition leads to illogical situations. For example, I can divide "string theory" into "string theory of region 1", "string theory of region 2", "string theory of region 3", ... which are all in different parameters space. In this case, suddenly, "string theory of region 1" can be fully excluded. But it is illogical to pretend that "string theory of region 1" is suddenly "good falsifiable science" just because you renamed it while the physics is 100% the same. Another example of illogical situation is "an observed theory suddenly qualifies as falsifiable" (cf. the example with the electromagnetism below).

Also, "try again with more energy" is very common in beyond standard model physics. It is the case for lepton compositeness, heavy bosons, fourth lepton generation, SUSY, all of Effective Field Theory, ... None of these theories are abandoned because "unfalsifiable". The argument that string theory is bad because unfalsifiable feels like a bad faith argument while plenty of other physicists activities have the same characteristics but people who are against string theory does not care when physicists work on those.

It's also the case with common theories like electromagnetism or weak force: we are happy with them because we have observed them, but theoretically (in their current formulation), their parameters are free: if the alpha constant was 10 to the power -100, electromagnetism would have been undetectable up to now (the world would be quite different, but still). And if in this parallel universe a physicist would have came up with the theory and tried to observe it and failed, they could have always said "well, it just means that the alpha constant is even smaller". So, do you agree that electromagnetism is a non falsifiable theory because the alpha constant is a free parameter and could have been arbitrarily small? Because if not, you are saying that exactly the exact same theory is sometimes falsifiable, sometimes unfalsifiable, depending on where the free parameters are: right now string theory is unfalsifiable, but if we observe cosmic superstrings, suddenly, the theory qualifies as falsifiable.

Finally, the more you eliminate part of the landscape, the more the credibility of the theory decreases. And even if some part of landscape remains, the theory is abandoned when it is virtually useless.

String theory necessitates observable objects to remain viable as an useful theory (for example, SUSY particles, specific inflationary signature, ...). If these are not observed, the theory is not 100% rejected, but it becomes "useless": it will prove that the reality needs another fix than the string theory to explain some of the problem we observe in the current standard model. In other term, "string theory" can always remain a possibility, but "string theory as the answer of the current problems" would be 100% rejected and physicists will start working on other theories.

The idea that you pretend that physicists will still work on string theory when all the "juice" would been removed due to constraints is just so surreal to me. The reason string theory is popular amongst physicists is because they want to understand the current problems and that, according to them, string theory is a good candidate to explain them. It is crazy to imagine that when we have demonstrated that string theory cannot explain these problems, people whose main motivation is to explain these problems would say "we know we will not get anything of what we want if we work on this subject, but, hey, it's theoretically not fully excluded, so, I have to continue for eternity before passing to a more promising subject".

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#512

Earlier quoted context omitted.

Check out NYC school district. Has high schools where entrance is 100% based on a single entrance exam score.

De Blasio tried to phase out G&T, and Mamdani has advocated for the same. There is an ideological push that views these accelerated tracks as fundamentally inequitable.

Yeah that sucks, as far as I found NYC is unique in having this truly merit based top end to their system (would love to hear of others if they exist). We have a tentative plan to move there if my kids need it.

Most other places water it down with lotteries, preference based on class or race, etc.

NYC is big enough that they can do what they do, which is have the very top end pure merit, then a tier lower that pulls people up from underrepresented groups. Best of both worlds. One of the top tier high school has numerous Nobel prize winners in the sciences. It's good for humanity to have these places.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#513
post #344

Earlier quoted context omitted.

You might benefit from (proper, not the multiple choice kind) aptitude testing.

What are the benefits? What would/could I do with the results?

Most people come in for educational or career guidance, but I think it's best used as a way of understanding how your mind works, especially in relation to others'. The on-the-flying reasoning isn't pitted against good memory (there also isn't a single "memory", but we have different strengths for remembering words, stories, ideas, shapes, faces, numbers, melodies, and rhythms), but against a more methodical and well-prepared presenter. The on-the-fly reasoners are also quicker to see patterns and make connections among disparate data. It's great for trial law, but not so great (or distracting at best) for tax law, where you can't just wing it.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#514

Earlier quoted context omitted.

Yeah, publishing in ML can be annoying because of that. What's wrong with "I thought this problem was interesting"?

Because your institution's PR department and the journal you're publishing in want the publicity of "scientist cures cancer". And you probably wrote "I'm curing cancer" in your grant application, team charter, or whatnot.

Comic: "The Science News Cycle" - https://phdcomics.com/comics/archive.php?comicid=1174

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#515

I suspect that a lot about what we call being very intelligent is ultimately out-remembering people around us. I think of all the times in my software career when I did something that others considered very high performance, it either came down to either having more energy than others at tackling a problem they thought was more trouble than it was worth, or just bringing back random knowledge from previous jobs or se…

So what do you teach the kids

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#516
post #505

Earlier quoted context omitted.

You are taking the approach of Brian Greene, in this debate: "Why string theory isn't real physics | Roger Penrose, Brian Greene, and Eric Weinstein" - https://youtu.be/5GGGhI9ablQ It did not work out....

The argument that I'm making was not at all discussed in the video. Can you point to the exact time in the video this argument is made? It looks like you just took a video with someone defending string theory and simply concluded that we have the same arguments. My point is that you could build a similar panel (with some eminent physicists pro and con investing in the theory) about more or less all cutting-edge theor…

>> The argument that I'm making was not at all discussed in the video. Can you point to the exact time in the video this argument is made?

03:56 - https://youtu.be/5GGGhI9ablQ?t=235

Conceptually is the same. For a moment I though you were him.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#517
post #505

Earlier quoted context omitted.

The argument that I'm making was not at all discussed in the video. Can you point to the exact time in the video this argument is made? It looks like you just took a video with someone defending string theory and simply concluded that we have the same arguments. My point is that you could build a similar panel (with some eminent physicists pro and con investing in the theory) about more or less all cutting-edge theor…

>> The argument that I'm making was not at all discussed in the video. Can you point to the exact time in the video this argument is made? 03:56 - https://youtu.be/5GGGhI9ablQ?t=235 Conceptually is the same. For a moment I though you were him.

What are you talking about? This is not my argument, this is a different argument.

His intervention (which is not even really an argument) is that "physicists chose what to work on and some of them think string theory is interesting" (and I think his interlocutor failed to provide any rebuttal to that. Weinstein counter-argument is "their choices have side effect so they should make the choice I prefer" which does not really hold water).

My point is that this specific debate that we observe around string theory happens in plenty of cutting edge physics and string theory is not "special".

In the section you mention, Greene does not even mention or make any reference of the situation in any other field than string theory. How is that even barely related?

When people discuss what to do after LHC, some people say "let's prepare for building a Future Circular Collider", to which some physicists are saying "no, that's a bad idea and a waste of money and time". Other people say "let's focus on other ways to probe particles with different kind of detectors", to which some physicists are saying "no, that's a stupid bad and a waste of money and time". Other people say "let's not continue to explore particle physics", to which some physicists are saying "no, that's a bad idea and a waste of money and time".

Whatever you say about what to do after LHC, they will always have people saying it's a bad idea. Maybe you have a personal opinion of what would be best, in which case, you are exactly in the same position as Greene: there will be people who will say "no, I don't like that".

("what to do after LHC" is just an example. There are plenty of other topics: do exotic physics or precision measurement, approach the problem top-down or bottom-up, cold fusion, modified gravity, supersymmetry, ...)

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#518

I suspect that a lot about what we call being very intelligent is ultimately out-remembering people around us. I think of all the times in my software career when I did something that others considered very high performance, it either came down to either having more energy than others at tackling a problem they thought was more trouble than it was worth, or just bringing back random knowledge from previous jobs or se…

So what do you teach the kids

A better question: why do you teach the kids? We're not there yet, but as AI advances, we are replacing human brains. And if we do that, there's no more need for education.

It becomes a hobby, like lifting weights.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#519
post #153

Aka - it’s a stochastic parrot with a good memory, for anyone still struggling to understand this. It should be obvious, imo, but some people seem to have trouble with the concept.

I don’t understand why this is such big news. OpenAI has essentially made a bunch of marketing copy by gussying up an algorithm being given a near unlimited budget to stochastically permute through its lossy memory. I think the real scandal is that we are almost 3-4 years into this (I think the release of GPT 3.5 is a good marker of when this public frenzy started) and all we’ve seen is OpenAI and the other major AI…

[flagged]

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#520

One thing about human mathematicians is that they only publish positive results. Professors etc might have file drawers full of "negative results", but the incentives and bandwidth of human mathematicians makes publishing these useful results impossible. But AI agents have no such limitations and can publish and re-use negative traces easily. There have been some recent projects ( https://www.theoremdb.org ) aimed at…

What is a "negative result" in maths? "I tried something and it didn't work" isn't really a result. It's experience maybe. But it's not like science where finding only evidence for the null hypothesis is considered boring. Even unsurprising results are published and even celebrated in mathematics, like Fermat's last theorem.

it might be something explaining that a certain path towards a solution didn't work or provide anything useful. the result itself might not be useful but it could prevent future mathmaticians from going down the same road and wasting effort.
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