Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Ten advances in mathematics and theoretical computer science

openai.com

Post reply on HN
Print view View original

991–1000 of 1001 posts

Re: Ten advances in mathematics and theoretical computer science

#991

Post by Kotlopou »

deviation wrote: post #891

Genuine question, from someone with a non-math background - at what point does the constraint become the number of unsolved conjectures remaining, instead of the ability for LLMs to actually solve for one?

The oldest unanswered math problem known, based on (https://mathoverflow.net/questions/27075/what-is-the-oldest-...), is whether there are any odd perfect numbers (= numbers that are equal to the sum of their divisors). It's been open for 1900 years.

Math is very hit-or-miss; the complexity of a question does not give much of an indication about how complex the answer will be. Look up the formula for solving a degree-4 polynomial equation to get a purely visual idea how this can look (and then degree-5 suddenly forces you to use complicated new functions). And there are problems (like the Collatz conjecture or P vs. NP) that there doesn't seem to be any promising angle of attack for over at least decades.

I would wager that this is a fundamental part of the structure of math that has been a constant from ancient Greece till LLMs. There are even some formal results, similar to Gödel's theorems, that say that the maximum necessary length of a proof grows arbitrarily fast (e.g. more than exponentially, double-exponentially, or any function with a formula) with the length of the statement being proven.

Point is, math will most likely never suffer from this particular problem.

Re: Ten advances in mathematics and theoretical computer science

#992

Post by Delk »

naasking wrote: post #320
Delk wrote: post #260

Earlier quoted context omitted.

I just don't think linguistic (or other symbolic) representations alone can contain the information, in any sense of the word, of what e.g. human subjective experiences actually are like. The concepts we express with language get their meaning from our physical reality, even if quite indirectly in case of some abstract concepts. Hunger as a concept doesn't mean anything without the physical need. Politeness or bluntn…

> I can't see how the model could include the actual subjective human experience. People who say LLMs have subjective experience aren't saying they have human-type subjective experience. Nobody who sees an LLM express hunger when role playing as a hungry person thinks that the LLM is actually hungry. I too can role play as a hungry person despite not being hungry, so there is no reason in either case to conclude that…

Sure, but those internal states could then exist for just about any program, or at the very least for any ANN. Nobody in their right minds would have suggested that those might have been aware before the rise of generative models.

When people get the idea that a LLM (or some other generative model) might be aware, surely that impression is because of human-like output. I don't think there's any objective basis for that thinking.

Re: Ten advances in mathematics and theoretical computer science

#993

Post by Delk »

naasking wrote: post #217
Delk wrote: post #77

Earlier quoted context omitted.

I honestly don't think a language model is enough for self-awareness, regardless of the exact model of awareness. A language model (or an image model or whatever) cannot even be sentient, and I think sentience is a prerequisite for awareness. Even if we express a lot of our subjective experience with words, the language is just a symbolic representation of those experiences. The qualia themselves, even those that are…

> The qualia themselves, even those that are quite abstract, are rooted in our physical presence and evolution. There is no objective evidence of qualia. All evidence of qualia are vocal or other expressions of belief in qualia. Perceptions clearly exist and are observable, subjective experience and qualia, not so much. > I see no reason to believe that a neural network built entirely based on the symbolic level of l…

> There is no objective evidence of qualia.

You can argue there's no objective evidence for qualia in others than oneself, but I'm sure you know you have subjective experience just as I know I do.

> All of these appeals to differences with the brain never seem to acknowledge that fundamentally, the brain has the same explanatory gap with physics.

I don't claim that ANNs or other computational models are fundamentally different from brains in computational capacity (although AFAIK biological neurons are a lot more complex than those in ANNs, so drawing a parallel just because both are "neural networks" would be erroneous as well.) I'm claiming that language alone cannot represent qualia, so an ANN trained on the level of language alone cannot have subjective experience.

> This assumes a lot.

Perhaps, but so does the idea that "intelligence inherently develops a map of natural categories", including the rather elusive concept of intelligence itself. And that today's AI models could possess intelligence in whatever form that sentence requires.

If forming natural categories alone were enough for sentience, clustering algorithms could be sentient.

It has traditionally been assumed that only humans are sentient. Present understanding leans more and more towards many animals having some kind of sentience as well. Some of them are probably even self-aware. Language in animals is a lot more controversial, though.

Nobody knows how (or even why) sentience emerges. But since it seems to exist in other animals as well, including those that probably don't have language or abstract concepts, it would seem to be a product of something else than language. It might even be some kind of a spectrum, with different animals having different levels of sentience and, ultimately, even awareness.

Re: Ten advances in mathematics and theoretical computer science

#994

Post by cure_42 »

samatman wrote: post #671
cure_42 wrote: post #25

Earlier quoted context omitted.

I'd say the creator is the one who created the 3d model, not the one who pushed the print button.

True story: I have a moisture issue in my furnace, such that it needs vacuuming out. This involved detaching a length of tubing, but that puts stress on said tubing, sometimes knocks other things out of alignment, and involves completing the seal between the wetvac and the tubing with my hand. I also have a 3D printer. I also have a ChatGPT subscription, and some OpenSCAD chops. I came up with a part which would go i…

Would have said cool story but you're an ass, so.

Cool story bro

Re: Ten advances in mathematics and theoretical computer science

#995

Post by cure_42 »

dgellow wrote: post #58
cure_42 wrote: post #25

Earlier quoted context omitted.

I'd say the creator is the one who created the 3d model, not the one who pushed the print button.

I would say „I made this gadget with my 3d printer, but the designer is someone else (I found the model online)“. The intent, the drive, the action comes from the human

The action came from the machine. The drive could have come from anywhere, maybe it was you maybe it was someone else. The intent seems largely irrelevant to who made it.

If I commission an artwork, the intent came from me but I sure as heck didn't make it.

Re: Ten advances in mathematics and theoretical computer science

#996

Post by [deleted] »

richardfey wrote: post #986
KajMagnus wrote: post #916

Earlier quoted context omitted.

Actually, no. "Manipulation" is a negatively loaded word, and you wouldn't use that word if f.ex. someone helpfully & truthfully helps others see they've misunderstood sth.

I disagree. Whether something is manipulation depends on whether you are trying to change someone’s opinion or behavior, not on whether the manipulator has “good” or “bad” intentions, since those judgments are not objectively universal.

[deleted]

Re: Ten advances in mathematics and theoretical computer science

#997

Post by KajMagnus »

richardfey wrote: post #986
KajMagnus wrote: post #916

Earlier quoted context omitted.

Actually, no. "Manipulation" is a negatively loaded word, and you wouldn't use that word if f.ex. someone helpfully & truthfully helps others see they've misunderstood sth.

I disagree. Whether something is manipulation depends on whether you are trying to change someone’s opinion or behavior, not on whether the manipulator has “good” or “bad” intentions, since those judgments are not objectively universal.

You can look up the word in a dictionary, instead of arguing. Bye & have a nice day.

Re: Ten advances in mathematics and theoretical computer science

#998

Post by [deleted] »

MinimalAction wrote: post #969
dash2 wrote: post #855

Earlier quoted context omitted.

Really? "The benefit to all of humanity from advances in mathematics outweighs the lost jobs of research mathematicians". That's an insane take?

It is the very humanity that is absent in all of this. The power is still in the hands of a very few. I feel you're dismissing this with a grandeur vision of AI developement.

[deleted]

Re: Ten advances in mathematics and theoretical computer science

#999

Post by watutalkinbout »

aswegs8 wrote: post #852
watutalkinbout wrote: post #655

Earlier quoted context omitted.

It isn't an implementation for neurons, unless you believe in a designing god. Matrices are an implementation detail in reconstructing the surface of human knowledge. It's a complex surface, but it's a regurgitation.

What's the argument here? It's not about the implementation method, it is about the behavior that emerges from it. You could calculate the next token by hand on paper if you had enough time.

Yep, it's a facsimile of a filtered subset of all human behaviour.

Re: Ten advances in mathematics and theoretical computer science

#1000

Post by strbean »

danparsonson wrote: post #925
strbean wrote: post #550

Earlier quoted context omitted.

> When rapid progress is made in a poorly-understood field, then how can our definitions and requirements for success not change? It's in how they change, not the fact that they change. The skeptics seem to have secret definitions for intelligence, sentience, consciousness, creativity, etc. that amounts to "a thing only humans have". Often that thing is equivalent to a soul. When yesterday's challenge (LLMs don't hav…

OK, I see, thanks. That applies to some skeptics, though - I'm in the AI skeptic camp but only in the sense that I believe we should make sober assessments of what these things are actually capable of.

> That applies to some skeptics, though

Totally! Arguments like yours often get lost in the noise of the less interesting / nuanced arguments unfortunately :(

Post reply on HN