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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

#981

Post by dash2 »

class3shock wrote: post #713
dash2 wrote: post #465

Earlier quoted context omitted.

If it doesn't help average people, why do millions of them pay for it?

So if millions of people pay for something it must be helping average people but if 10s of millions of average people express concerns about a thing than what? I would assume since you were happy to go with the will of the people when it supported your argument, you would be in complete support of actually regulating ai and addressing the many concerns of society at large? https://www.reuters.com/world/us/americans-f…

I'm fine with regulating AI. I'd note that saying something in a poll is cheap talk whereas paying 20$ a month is not. But I can understand e.g. that people may derive value from their cars, whilst simultaneously being concerned about global warming and traffic jams.

Re: Ten advances in mathematics and theoretical computer science

#982

Post by sothatsit »

dennis_jeeves2 wrote: post #978
sothatsit wrote: post #971

Earlier quoted context omitted.

The distinction is between information flowing from people to power (elicitation), vs. it flowing from power to people (persuasion). These are not the same, even if they are closely related.

I guess I wasn't clear enough, _generally_ democracy = manufactured consent by manipulation of people by 'power'

Does AI make real opinion easier to hear, or fake opinion easier to spread? Even if you believe wholly in manufactured consent, how easy it is to manufacture matters.

Re: Ten advances in mathematics and theoretical computer science

#983

Post by fooker »

s4i wrote: post #492
fooker wrote: post #327

Earlier quoted context omitted.

There's a full fledged 'reasoning' step that basically expands your prompt. As long as you are not missing important information, how you word the prompt does not have any effect.

Isn’t that a huge simplification? Of course the way you phrase the prompt can carry semantic meaning, maybe subtly, but still. And sometimes that matters a little and sometimes a lot. I’ve stopped numerous agent sessions over the last few weeks to reword my initial prompt to get the agent off an unintended track.

> reword my initial prompt to get the agent off an unintended track.

The signal here is the action of stopping the agent “do something else, this is stupid”, not a tweak to the initial prompt.

Re: Ten advances in mathematics and theoretical computer science

#984

Post by dennis_jeeves2 »

sothatsit wrote: post #982
dennis_jeeves2 wrote: post #978

Earlier quoted context omitted.

I guess I wasn't clear enough, _generally_ democracy = manufactured consent by manipulation of people by 'power'

Does AI make real opinion easier to hear, or fake opinion easier to spread? Even if you believe wholly in manufactured consent, how easy it is to manufacture matters.

>Does AI make real opinion easier to hear, or fake opinion easier to spread?

The latter.

(caveat: we are talking about the vast majority of people, since you are on this forum your personal situation will be the opposite)

>Even if you believe wholly in manufactured consent, how easy it is to manufacture matters.

I believe it's easier.

(same caveat applies)

Re: Ten advances in mathematics and theoretical computer science

#985

Post by GPerson »

vlovich123 wrote: post #787
GPerson wrote: post #727

Earlier quoted context omitted.

In my opinion, after seein the Jacobian conjecture go, the Riemann hypothesis only has about a year left. I’m not sure if people just aren’t as aware, but the Jacobian conjecture practically was on par with those other great problems.

Whether or not it’s on par famously or difficulty level doesn’t predict whether the others will fall. They’re unique problems and math isn’t linear - the Jacobian it managed to find a counterexample and relied on other proofs that had been developed showing >3 case == 3 dimensional case. However, the Riemann may not fall in the same way because it may actually be true or the surrounding math isn’t quite ready to tack…

When I was in grad school we talked about the Jacobian conjecture as something that would never be solved, and not really even worth thinking about since it’s impossible. There’s been a lot more big open problems solved by AI than which reach the front page of news websites like this. Based on all of these problems getting solved fast I’m just saying I’d be surprised if the Riemann hypothesis lasts another year.

Re: Ten advances in mathematics and theoretical computer science

#986

Post by richardfey »

KajMagnus wrote: post #916
richardfey wrote: post #836

Earlier quoted context omitted.

> Part of this can be good (you talk about what they care about, where 90% of broadcast messaging might not apply) and part of it can be bad (manipulation.) Side note: it's manipulation either ways because you chose what to talk about, with a goal in mind.

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.

Re: Ten advances in mathematics and theoretical computer science

#987

Post by Kotlopou »

zahlman wrote: post #556
tuvix wrote: post #528

Earlier quoted context omitted.

I’m not talking about the actions we take or how we might perform at certain tasks, I’m talking about how our brains actually work. My point is that we have no idea how I’m able to imagine an apple and see it in my mind’s eye. It’s basically biological magic to us at this point. There are processes at work there that we don’t even have the language to describe.

Not only that, but we do it with a processor that is basically required to operate in a narrow temperature band below 40C, using a mere 86 billion neurons (although the equivalence with either machine-learning "neurons" or LLM parameters is not at all clear) operating on a few dozen watts; and with this we operate many other systems besides language processing. It's not clear that our reasoning process requires langu…

I recently read a blogpost from a human neuroscience student who came across this question (https://ccli.substack.com/p/the-biggest-mystery-in-neuroscie...), and she looked up the study behind this number (https://ora.ox.ac.uk/objects/uuid:1f559b3b-97fd-48c2-b2ac-29...), and it seems that the actual current state of knowledge is that the number is somewhere in the range 60-100 billion, with probably some of that variation being biological and some coming from uncertainty in the measurement techniques, hard to tell, because all the data comes from nine brains.

For now, caring about a topic (or having somebody you trust care for you) still gets you better information than asking an LLM.

Re: Ten advances in mathematics and theoretical computer science

#988

Post by Kotlopou »

Valakas_ wrote: post #829
5555watch wrote: post #499

Earlier quoted context omitted.

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. E…

I've seen this "everything is a remix" idea thrown around a lot, and always want to ask... so how did anything get started? What was the first cave-dwelling carver of a bone flute remixing? What was Alan Turing remixing to come up with the Turing machine? Where did Proto-Indo-European language come from?

Maybe there's some sense of "remix" that covers all of that, but then that meaning is not the standard one, or maybe you would concede that this happened in the past, but isn't happening now, but then where's the cutoff, or maybe something else...?

In your analogy, I would love to see some elaboration on the "reflective and spans outside of itself" part -- geometry doesn't work that way, do you have a more intuitive metaphor, or ideally a mechanism, or even better, some examples?

Re: Ten advances in mathematics and theoretical computer science

#989

Post by Kotlopou »

qnleigh wrote: post #299

Can anyone comment on the significance of any of these results for their respective fields? Or what impact they might have? Presumably none are quite at the level of the Jacobian conjecture, but some of the results on group theory and sphere packing sound pretty important at first glance.

Came here looking for this, sadly there's little engagement with the actual math in this thread. I hold out hope that Scott Aaronson might comment on the circuit bound eventually...

Re: Ten advances in mathematics and theoretical computer science

#990

Post by watutalkinbout »

hackinthebochs wrote: post #712
watutalkinbout wrote: post #603

Earlier quoted context omitted.

It's like Musks duplicitous argument about unlimited abundance. We have a lot of abundance now, we just keep accelerating it all into the hands of fewer and fewer people - whose response is only to want more, and more, and more.

Yeah, we really should just storm the facility where Musk is hoarding all the worlds bread and meat. Wealth in terms of capital doesn't represent material goods, it represents the system's confidence in your ability to direct capital efficiently. But eventually efficient capital bottoms out at consumable goods. Someone like Musk with a lot of capital under his control is contributing to the end goal of unlimited abun…

I agree.

The end goal is unlimited abundance (for a handful of people).

Let's not pretend that capital is actually directly efficiently, tulip.

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