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.
The Dark Night of Mathematics
301–310 of 321 posts
Re: The Dark Night of Mathematics
#302Earlier 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.
Re: The Dark Night of Mathematics
#303Earlier 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.
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
#304I 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.
Re: The Dark Night of Mathematics
#305Earlier 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…
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
#306Earlier 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.
Re: The Dark Night of Mathematics
#307Earlier 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?
Re: The Dark Night of Mathematics
#308Every 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…
... 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
#309Every 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…