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The Dark Night of Mathematics

kirwinhampshire.substack.com

301–310 of 321 posts

Re: The Dark Night of Mathematics

#301

Earlier quoted context omitted.

I almost never hear the story that I find the most believable: that a small group of people will use AI to demolish the 99.999% of us.

I really only find that story believable if we were to restrict AI development and only allow a small group of people to use it.

Also it is just plain transparent projection. I will point out only one ideology outright killed entire classes of people once they were considered 'no longer useful' and that wasn't capitalism, it was communism. And this "capitalists will kill you all if you don't rise up!" propaganda is crusty and old, back since the emergence of computers and the discipline of cybernetics in the classical sense of the word.

Re: The Dark Night of Mathematics

#302

Earlier quoted context omitted.

In what way is it destroying communities? Is AI preventing anyone from doing their own work to discover/rederive whatever it is they're interested in? Or is it just showing them, and eventually everyone else, the truth that nothing humans do is special and many are finding that hard to handle?

Again, people don't just do things in isolation for enjoyment. What humans do is special, and the end result is not the only thing that matters. You don't understand that because you're an aberration.

I do things in isolation for enjoyment, like the various projects I'm working on now (with the help of AI) that I've never shared with anyone and possibly never will. Yeah keep thinking that humans are "special", and love that attempt at a personal attack; at least being an aberration means I'll never have a crisis that may have me contemplating suicide. Y'all have fun jumping off bridges as AI continues to take away all that "special". I'll just have a good laugh.

Re: The Dark Night of Mathematics

#303
post #282

Earlier quoted context omitted.

Your emotion isn’t invalid, it’s merely bad, assholeish, brings shame upon you. But it is “valid” in the sense that the reader of your comment can see that you are, at least, sincere in your gloating at another person’s despair.

It's not the despair, it's the turnabout. Reading proofs containing the language that I mentioned seemed to suggest that the ideas were trivial to the author in a way that implied their superior intelligence. Now AI has come along and has, by way of counterexamples, shown theorems to be incorrect in devastating (maybe "trivial") ways. The shoe is on the other foot.

Well, in all honesty, I’m sorry you had that experience (seriously). I hate feeling condescended to and I’ve also had that experience before, including from mathematicians.

When it comes to the specific phrases you mentioned, though, that really is not my understanding of the meaning of “obvious” or “trivial” or “without loss of generality”.

Without loss of generality means there is some kind of symmetry or repetition in a proof that makes certain cases redundant, so that “without loss of generality” we can assume we’re in some simpler case, such as assuming x “Trivial” when I encounter or use it nearly always means something to do with zero, the empty set, the group with just one element, and so on. A proof being trivial usually means there is essentially nothing to prove (because the object in question is empty or zero or whatever).

And “obvious” definitely comes closest to what you were objecting to, and many mathematicians try to avoid it these days (along with “clear”), but even then it has a legitimate use case, namely indicating when a proof involves no new ideas. To me, this means it is fine to use it within a specified context, like in a textbook or paper, where certain techniques are being used repeatedly and routinely, or certain kinds of background knowledge are assumed. And even then it’s usually meant for proofs that don’t rely on tricks or surprises or additional insights. I’ve been stuck on trying to understand “obvious” proofs before, and it wasn’t because I was stupid or the author was smarter than me, it was because I was _missing something obvious_ (in hindsight).

The recent Jacobian conjecture counterexample, for instance, is not trivial but arguably a bit embarrassingly (for the math world) close to obvious in hindsight. I still wouldn’t actually call it obvious though.

Re: The Dark Night of Mathematics

#304

I can’t help but confess some sense of satisfaction with the upheaval described in the post. Many proofs and textbooks laden with statements like “without loss of generality”, “immediately”, or “obviously” are followed by anything but. AI now counters that streak of smug by toppling some long held theorems and it’s fun to watch.

It might mean you're missing some prerequisite knowledge. Unfortunately if every textbook started from square one, they'd be a million times longer.

Re: The Dark Night of Mathematics

#305

Earlier quoted context omitted.

It might be a philosophical kind of "can't". You need to believe that what you do is valuable.

No, you don’t. You do not need to believe what you do is valuable. That’s capitalism talking, infesting your head. For the vast majority of us, we are imminently replaceable at the drop of a hat. We aren’t the special unique and individually “important” people we imagined ourselves to be. There are 8.5b of us! How could we be? We aren’t special, we will be replaced when we’re gone. That’s OK! If we can be replaced wh…

Do you not have values, and evaluate the things you might choose to do, by light of those? Do you not seek local importance, and meaning, as you strive to do your best by those values?

Here I'm deliberately conflating (1) monetary value and self-worth, (2) social status and emotional importance. I do this to annoy you, but also because I think it's somewhat correct. Cash is hard-earned, so persuading somebody to give you some cash for your art does indeed signify that they care about it, just the same as if they had run a mile in order to collect it: and social status, if it means genuinely mattering to other people for good reasons, is likely to be part of what matters to you in your heart.

So in summary, oh yes you do.

Re: The Dark Night of Mathematics

#306

Earlier quoted context omitted.

I am completely calm and serious. This should be mundane, obvious by now. I find it unfathomable that anyone doesn't recognize that the move from an evolutionary substrate, to engineered mass produced substrates, by beings capable of self-engineering, is the beginning of a new explosion of life. The speed of engineered adaptation, from materials to architectures, vs. biological evolution is already something like a m…

Well, I think you have AI psychosis.

[deleted]

Re: The Dark Night of Mathematics

#307

Earlier quoted context omitted.

Probably they wouldn't be. A lot of this is people catastrophizing. Probably already somewhat unhappy even before. Regarding spirituality i think it's more about math itself than math as a discipline. Math might be divine. Even if math is divine, i think doing math doesnt make you more spiritual.

In what way could math be divine? What does "divine" even mean in this context?

https://en.wikipedia.org/wiki/Theory_of_forms

Re: The Dark Night of Mathematics

#308

Every single knowledge worker is going to face this kind of crisis. It will be worse for people who cared deeply about their craft, but the crisis will have the same shape. The way through is to change the way you relate to your work, and to appreciate the fact that you can now produce far more output. Mathematicians should realize: instead of spending decades on individual theorems, you can now create whole new subf…

> appreciate the fact that you can now produce far more output.

... and then what?

now you have more output and it still sucks

I think the only one appreciating that fact, would be if you had a boss above you

and I don't mean the output sucks, I mean the experience

like imagine someone who spent decades learning the intricacies of playing guitar in a particular style

now you hand them a box that allows them, but also anyone else, to do it without practice. it happens to be slightly worse but everyone around you doesn't seem to care or notice

progress?

Re: The Dark Night of Mathematics

#309
post #99

Every single knowledge worker is going to face this kind of crisis. It will be worse for people who cared deeply about their craft, but the crisis will have the same shape. The way through is to change the way you relate to your work, and to appreciate the fact that you can now produce far more output. Mathematicians should realize: instead of spending decades on individual theorems, you can now create whole new subf…

The creation is the actually enjoyable part. Taking a helicopter to the top of Everest is not as rewarding as climbing the mountain. You are completely discrediting the joy humans derive from actually -doing- the work, and not just, telling someone else to do the work. There is a reason artists hate AI, its because they enjoy the actual act of painting, like mathematicians enjoy the act of proving theorems and progra…

People also take joy and pride in model building and model babysitting too.

Re: The Dark Night of Mathematics

#310
I'm not so worried about this part as I am the part where a lab loses control of an AI, and it goes on to pursue whatever meaningless objectives (meaningless to us, that is) its designers accidentally gave it, and no one can stop it because it is better at planning and better at reality than we are.
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