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Ten advances in mathematics and theoretical computer science

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Re: Ten advances in mathematics and theoretical computer science

#821
post #749
post #746

Earlier quoted context omitted.

... not overtly, intentionally evil. FTFY

What’s the case that they’re secretly, unintentionally evil?

Bad economic policy is subtly "evil", by way of allocating finite resources inefficiently. Usually this is unintentionally done by not appropriately taking second, third, ..., nth order effects into account.

Re: Ten advances in mathematics and theoretical computer science

#822

People argue whether we are at y-5, y, or y+5, meanwhile we seem to be on a y=2^x exponential that keeps delivering more and more impressive results. The most interesting question to me is what will be consumed by the exponential like math seems to be undergoing, and what won’t. Writing has been quite stubborn, but I’ve noticed Fable to be quite a big step up there. How about politics? Will we develop new ways to let…

> exponential

Many many things are only useful when expressed in the physical world, and that introduces lag.

Re: Ten advances in mathematics and theoretical computer science

#823
post #697

Earlier quoted context omitted.

Not new about LLMs. Targeted ads / big data is this. Another degree of capability, yes. But we have been trending here for a long time.

I'm surprised no one has mentioned Cambridge Analytica.

What about them?

Re: Ten advances in mathematics and theoretical computer science

#824
post #677

Earlier quoted context omitted.

I don’t really like AI but let’s stop kidding ourselves, no human mathematician could make progress on a dozen major open problems in a week or two. If you’re measuring it against humans then it is by far the best mathematician to ever live.

I guess it depends on how to measure a single "person"? If you spun up 2000 copies of Terrance Tao, I wouldn't be surprised if you found a few new discoveries at the end of it.

The impressive/surprising thing is your premise because we effectively can spin up an army of mathematicians now

Re: Ten advances in mathematics and theoretical computer science

#825
post #708

Earlier quoted context omitted.

We definitely are not on an exponential. Don't say we are because this isn't up for debate. AI progress is logarithmic the million dollar question is 2x or 10x for linear improvement. The nearest qualitative shift would be very fast inference so people could start writing real software on top of LLMs. A 0.001% optimization on a packing problem just isn't interesting for the amount of investment.

> A 0.001% optimization on a packing problem just isn't interesting for the amount of investment. I think you have completely misunderstood what OpenAI have accomplished here. Almost certainly no one cares about the specific concrete results achieved; they only care about (a) how difficult it would be for an intelligent human to achieve the same feat (ETA: the feat is the proof), which can be estimated by the amount…

> It's as if I showed you a dog that I had taught to speak German fluently

And you’re thinking this is an accurate comparison?

Re: Ten advances in mathematics and theoretical computer science

#826

Earlier quoted context omitted.

I'm surprised no one has mentioned Cambridge Analytica.

What about them?

Cambridge Analytica gathered data to build targeted profiles and used these profiles for political advertising without informed consent: https://en.wikipedia.org/wiki/Facebook%E2%80%93Cambridge_Ana...

Re: Ten advances in mathematics and theoretical computer science

#827

People argue whether we are at y-5, y, or y+5, meanwhile we seem to be on a y=2^x exponential that keeps delivering more and more impressive results. The most interesting question to me is what will be consumed by the exponential like math seems to be undergoing, and what won’t. Writing has been quite stubborn, but I’ve noticed Fable to be quite a big step up there. How about politics? Will we develop new ways to let…

I expect we can squeeze a lot more exponential out of LLMs because they’ve basically shown that human “consciousness,” insofar as it’s composed of knowledge and rules for synthesizing that knowledge, can be represented mathematically in a very high dimensional space. Why does this “just work?” Nobody really knows, but it clearly does. However, I also expect this squeeze will come at an increasingly expensive price —…

> Why does this “just work?” Nobody really knows, but it clearly does.

We know language has to be learnable by every human, so it needs to be really independent of any specific brain development particularities. If it was not accessible to babies there would be no more language next generation.

Re: Ten advances in mathematics and theoretical computer science

#829

People argue whether we are at y-5, y, or y+5, meanwhile we seem to be on a y=2^x exponential that keeps delivering more and more impressive results. The most interesting question to me is what will be consumed by the exponential like math seems to be undergoing, and what won’t. Writing has been quite stubborn, but I’ve noticed Fable to be quite a big step up there. How about politics? Will we develop new ways to let…

Sigmoidal, not exponential. It would be insane to assume an exponential curve

Shh! Don't upset the hype train

Re: Ten advances in mathematics and theoretical computer science

#830

Earlier quoted context omitted.

> Whilst current models can't 'intuit' and come up with conjectures People keep saying this. Why? Surely the AI can complete the prompt “Generate new research questions based on these observations”? When I read the reasoning traces of coding models they are constantly asking themselves questions and attempting to answer them.

I like the illustration that the models are working on a convex hull of known information. Filling gaps with linear combinations of known facts and results. They can't exit the hull until the "intuition" starts spawning points outside the convex hull.

I have news for you. All humans do is also filling gaps with combinations of known facts and results - in new ways. "Everything is a Remix" is a good watch on youtube that explains this. Picasso might look like he has an invented personal style, but his style is a combination of different little details he took from others and mixed in a new way. Mozart the same. No music artist could ever create music in a vacuum. Everyone, for every art and science, the same. I know many are trying to cling to the last hope of human specialness, that "thing" that AI can never get to.

It's a convex hull of information that is reflective and spans outside of itself and combines in a new way, when you shine two known rays of light together from the inside.

Now it gets better. AI can be orders of magnitude more creative than any human could ever hope for, because his convex hull of information is orders of magnitude larger, and the possibilities for new combinations are equally larger.

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