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

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

#341

Post by chongli »

a2ff6eeb0 wrote: post #339
chongli wrote: post #309

Earlier quoted context omitted.

If I told you "don't use spin locks, call futex instead", do you think have gained an understanding of the Linux scheduler? Yes, because I already knew what schedulers are, what spinlocks are, and if I want to know what futex is I can go look it up. Comprehension is within my grasp. Your original claim, which you’ve repeatedly distanced yourself from (by trying to use comprehensible examples) but won’t admit to, was…

Bullshit. Human comprehension will not continue, it will reduced to "when the AI tells us to add Bismuth, strontium, and copper together in this way, we get a superconductor", but that doesn't mean we understand high temperature superconductivity. For what it's worth, we've known about BSCCO for nearly 40 years, and we still don't have a great physical understanding of how it works, thought we made decent progress in…

That’s still comprehensible. Incomprehensible chemistry instructions simply could not be followed by any human. They would be of no use to anyone.

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

#342

Post by awesome_dude »

scarmig wrote: post #147
runarberg wrote: post #84

Earlier quoted context omitted.

In other words: Thousand monkeys with a thousand typewriters... https://news.ycombinator.com/item?id=48231974

Take something like (1+x*y)^3*z+y^2*(1+x*y)*(4+3*x*y);y+3*x*(1+x*y)^2*z+3*x*y^2*(4+3*x*y);2*x-3*x^2*y-x^3*z|0,0,-1/4|1,-3/2,13/2 If a thousand monkeys typed at a character per second, on a keyboard with the 23 relevant characters, it would take roughly 10^136 years for them to come up with this counterexample. Though, to be fair to monkey scenario, there's a large family of them known now, so it's not quite this bad:…

Just FTR - 1 character per second is glacially slow - it's 12 wpm - fine for (slow) transcription, but the monkey typing exercise doesn't require them to know what they are typing out

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

#343

Post by calf »

chongli wrote: post #191
a2ff6eeb0 wrote: post #174

Earlier quoted context omitted.

You may have missed the present tense. I didn't say it's over, but that it will be. Please pay attention and don't make straw men. Again, do you believe that there are documents, of any value, that humans don't understand? Maybe an LLM could help you notice what I was saying, since it's clearly beyond at least one human's comprehension!

Again, do you believe that there are documents, of any value, that humans don't understand? There is no value in an undeciphered document until understanding is achieved, just as a lode of gold ore in some asteroid orbiting a distant star has no value until we can fly there and extract it. If an LLM can help us understanding something then it was not incomprehensible, by definition.

But this is just arguing over word tenses. You think "cannot", they think "could". Somewhere between there is the actual crux of disagreement.

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

#344

Post by cwnyth »

pwython wrote: post #296
jermaustin1 wrote: post #260

Earlier quoted context omitted.

Same. I have bad "factual" memory, but very good "conceptual" memory. I might not remember exactly what someone told me, but I probably gathered a keyword, and a feeling and idea of what they told me. Almost like it takes what they said then compresses it into my mind in a nice little multi-key lookup table.

Yes. "Weak detail recall but strong fluid reasoning, conceptual/gist memory, and adaptive problem-solving" is how GPT sums up what I feel. And "high fluid intelligence" is a label it gave that I won't be using anytime soon... But I like the sound of it.

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

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

#345

Post by Fr0styMatt88 »

yladiz wrote: post #340
Fr0styMatt88 wrote: post #329

I often think “what will ‘maintainable’ code look like in the future?” given this kind of thing. Much of ‘good coding’ is about optimising the codebase for workability for a human intellect with human working memory. Though having said that, from the studies I’ve come across it seems like LLMs tend to generate more verbose code but perform better over the long-term when the code is maintained and not allowed to spraw…

Is this assuming or studying human maintenance?

I’ll dig up the references but I believe they were studying what happened to LLM performance as the complexity and verbosity of the code went up (ie- just letting the LLM rip without doing explicit code cleanup and simplifying).

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

#346

Post by itsalwaysgood »

hibikir wrote: post #198

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…

There is an ability to hold ideas in the mind simultaneously. Some can hold a great deal more than others. It can be exercised, but is definitely bound by genetics.

If you want an example of someone at the near peak of human ability, check out Jon Von Neumann.

Then there is an ability to peer deeply into complex problems and somehow find the simplest truths that make sense of it all. Think of Einstein.

Both are incredibly intelligent, but in different ways. I'd say Von Neumann's memory was far greater than Einstein's though.

One can flawlessly ponder anything known to man, and the other could ponder completely original ideas (to an extent)

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

#347

Post by calf »

okamiueru wrote: post #190
tossandthrow wrote: post #171

Earlier quoted context omitted.

> That sentiment makes me cringe. If you understand how LLMs work, you'd know > But not in the "I'd love to learn more" kind I hope you are able to see the problem in your own communication here. Computation classes are interesting because they say something about fundamental capabilities. Two machine that are Turing complete are in theory able to carry out the same computations. They are isomorph mediums of computat…

The thing about discussing or explaining constraints, is that it rarely is useful or productive if the other side does not accept (or understand) the reality of them. Turing completeness is not exactly a high bar, and it's genuinely confusing as to why you bring it up. Your C++ precompiler is exactly as intelligent as whatever is your favorite agentic workflow with whatever harness you're referring to. Both might be…

I'll bite, I think Turing completeness is relevant in that it has to be used to informally argue via the Church-Turing thesis that biological intelligence cannot exceed the power or expressivity of formal neural network models. It thus is a good counterargument to stochastic parrot dismissals of neural net based AI such as LLMs, which really are still black boxes. The issue is not simply "So you think that humans are as powerful as LaTeX (or vice versa), ha ha how absurd!"

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

#348

Post by a2ff6eeb0 »

chongli wrote: post #341
a2ff6eeb0 wrote: post #339

Earlier quoted context omitted.

Bullshit. Human comprehension will not continue, it will reduced to "when the AI tells us to add Bismuth, strontium, and copper together in this way, we get a superconductor", but that doesn't mean we understand high temperature superconductivity. For what it's worth, we've known about BSCCO for nearly 40 years, and we still don't have a great physical understanding of how it works, thought we made decent progress in…

That’s still comprehensible. Incomprehensible chemistry instructions simply could not be followed by any human. They would be of no use to anyone.

You're using a very bad definition of incomprehensible. We don't understand the chemistry behind how these things work, it's that simple. If you're going to argue it's comprehensible, you'd better show how it works and go collect your Nobel prize.

All we know is that if we melt the right rocks together, we get a superconductor that works in some mysterious way that we can't explain. We know it's not Cooper pairs.

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

#350

Post by fragmede »

andybak wrote: post #248
estetlinus wrote: post #232

Earlier quoted context omitted.

A smart kid can be anything from not eating rocks anymore to multiplying numbers at an early age. Most of us turn out like the rescued exotic bird which turns out to be a seagull covered in curry.

Sometimes I wish there was a Hacker News comment hall of fame.

https://news.ycombinator.com/highlights

but you can also favorite comments for your own hall of fame, eg https://news.ycombinator.com/favorites?id=andybak&comments=t

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