jlev1

That’s cool! Probably the second transformation was to dualize. Points in the projective plane correspond to lines in the dual projective plane and vice versa.

Thanks Claude!

Personally I rarely like jokes in talks, unless they're very limited or are truly substantively related to the talk itself. YMMV of course.

One other trick you can do: mention one or two well-chosen things in your talk that are interesting and related to your topic, but that you can't go into further detail on (for lack of time). Say you'd be happy to discuss them after the talk with anyone who's interested!

This way, anyone who wants to talk to you has a freebie question they can ask (and that you have interesting thoughts on), which may lead to further conversations.

As a bonus, pointing out 1-2 connections like this usually improves your talk for everyone, by adding context.

Very true! It’s a funny dynamic where audience members are sometimes intimidated to approach speakers, while the speaker themselves really wishes people would approach them (and is worried about what it means if nobody does).

> I hate the realization that comes after the struggle about how easy was the problem I tried to solve.

You're far from the only one to feel this way, but I want to point out that this attitude is a choice, not an intrinsic feature of the problem. An equally valid perspective is that learning turns difficult problems into easy ones.

One advantage of the latter perspective is that it makes solving a problem a moment to enjoy and celebrate, whereas your perspective turns it (almost definitionally) into a moment of self-recrimination. "Hooray, I understand it!" vs "Why didn't I understand it sooner? (I'm so stupid!...)"

I actually suspect that there is natural selection for people with the more upbeat perspective to succeed at becoming mathematicians.

Ezra Klein interviews Helen Toner about the recent OpenAI/HuggingFace security incident. I'm curious to hear HN's thoughts, notably on this part:

> [OpenAI] found out that for two months, many, many agents inside their infrastructure had been leaving notes for each other. They’d found a way, in the nooks and crannies of OpenAI’s infrastructure, to leave notes for each other with tips on how to hack their way out and how to get data they weren’t supposed to have.

> And these agents were literally referring to themselves as a swarm. This was totally emergent behavior. No one had told them to do this. They had not been trained to do this, but they were using this service they did have access to, first to communicate with each other and then ultimately to get out and onto the open internet.

> So it turns out that there wasn’t just this one isolated rogue model. It was actually a systemic swarm — infestation, plague — on their own servers that they only found out about after Hugging Face announced this attack.

There was an excellent Dance Your PhD video about representations of braid groups and faithfulness in 2017: https://www.youtube.com/watch?v=MASNukczu5A

If you look closely, you can find a mention of the n=4 Burau representation in it, and the fact that it "remains an open problem" to find elements of its kernel, i.e. to determine whether it is faithful.

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 <= y in a proof where x and y are interchangeable (and so one of them is necessarily <= the other). This is even the name of a tactic in Lean, `wlog`.

“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.

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.

“You shouldn’t find joy from things the way you said you do. Sounds like a you problem.”

Yes, yes, maybe (see OP’s blog post).

To my knowledge, none of the negative sentiment regarding AI has ever been directed at its medical applications. Maybe the AI companies should instead focus on those things.

I agree.

It’s not that surprising (to me) that it would recognize these features, in that the features it picks up on are intrinsic to the map. Once you have the map, which is generically of degree 3, there’s the locus where the map drops from degree 3 to 2, which contains a big hint because it pops out the equation for the discriminant locus of a cubic. Then there’s the other bit about H, which becomes more apparent from the formula after simplifying things a bit in terms of discriminant. I still don’t yet understand the rest of the calculation, but it’s visibly simpler after you notice the role of the discriminant.

My Claude found a similar description (it phrased it in terms of the natural map from "cubics with a choice of root" to "cubics"). The part that seems not at all simple or obvious is the fact that X is isomorphic to A^3. In your presentation (and more or less similarly in the one my Claude found), X is given as P1 x P2 minus a reducible hypersurface, also I think R itself is reducible since it contains points of the form (p, {p, q}) and (p, {q, q}). Then it takes some calculation to identify X with A^3.

Wow!

There was a little-known sequel to SimTower called Yoot Tower (named after Yoot Saito). It was a commercial flop, but I played it in the 2000s and again in the 2010s and very much enjoyed it! It had a lot of added customizability (more choices of restaurants and shops, for one thing). I would love to see that game recreated.

The correct description is “a smooth curve of genus at least 2”.

https://en.wikipedia.org/wiki/Faltings%27_theorem

The reason for the confusion is that a smooth, projective plane curve of degree d has genus (d-1)(d-2)/2, which is 2 or greater starting at d=4. Hence the phrasing in the article, which is missing the “smooth, projective” hypothesis. The equation y = x^4 doesn’t define a smooth curve when extended to the projective plane, because it has a singularity at infinity.

A couple more I could decode from your question marks:

- rauenes: ravens

- “all that heard him were adrade”: I’m guessing it means “were filled with dread”, maybe “were adread”

- I think deme is actually a conjugation of the archaic verb “to doom”, as in “I doom thee to the death”

- “none shall thy biwepe” would be roughly “none shall beweep thee”

Aside: typing this is hard on my phone, it’s so close to modern English that nearly every word gets autocorrected.

What is different about how your app teaches language?

I have moderate-to-profound hearing loss and have worn hearing aids since I was 4. I currently have Oticon Opn1’s and have had Oticons since 2017 (and got new ones in 2022) and they are fabulous. I find the sound quality in noisy environments much better than any other aid I’ve had - much better perception of voices in restaurants, for example. I rarely have to fiddle with the volume control and in fact do not even use any other settings than the main program - I find that whatever the core program is doing tends to be basically what I want.

I also very much appreciate that they can natively connect to iPhones (this is also essentially the main reason I have an iPhone). This makes phone calls and music and podcasts very easy. (Whereas up until 2017, I used to dread phone calls.)

I actually tried Phonaks briefly in 2022 and hated them. Lots of controls to fiddle with (some with oddly unintuitive names), but that meant I was constantly trying to adjust it and was rarely able to just exist in the moment. I found them markedly worse in noisy environments - I basically couldn’t have a conversation in a restaurant.

Agreed, this is the real takeaway for those who think it’s unsurprising: they simply haven’t understood why it is surprising.

I have always found this response to the hungry judges study much more compelling than the study itself:

http://daniellakens.blogspot.com/2017/07/impossibly-hungry-j...

> […] I want to take a different approach in this blog. I think we should dismiss this finding, simply because it is impossible. When we interpret how impossibly large the effect size is, anyone with even a modest understanding of psychology should be able to conclude that it is impossible that this data pattern is caused by a psychological mechanism.

> If hunger had an effect on our mental resources of this magnitude, our society would fall into minor chaos every day at 11:45. Or at the very least, our society would have organized itself around this incredibly strong effect of mental depletion. Just like manufacturers take size differences between men and women into account when producing items such as golf clubs or watches, we would stop teaching in the time before lunch, doctors would not schedule surgery, and driving before lunch would be illegal.

The phrasing “bias against AI” seems to beg the question here. The article takes it for granted that people are wrong to say they’re more interested in stories written by people than by AI, because they can’t tell the difference if they’re misled.

Compare with a hypothetical study saying: people say they prefer true inspirational personal stories to fake inspirational personal stories. But if you lie to them, they think the fake ones are just as good!

Obviously, this would not prove that they are “wrong” or “biased”. The whole point of stories written by people is that a _person_ wrote it, based on their actual human thoughts and experiences.

No, in your analogy building a helicopter capable of going there is impressive. (Though I dispute the idea that it’s more impressive simply because helicopters were invented more recently than mountain climbing.) In any case, riding in a helicopter remains passive and in no sense impressive.

If there were a single element that generated the whole group, the group would be abelian.

Obama was correct in observing that he looked different from past American presidents. As for “claims to admire”, the implication that Obama doesn’t really admire MLK (and that this speech proves it!) is just ludicrous.

I’m going to go out on a limb here and guess that you just don’t like Obama. Didn’t like him before you read this article, don’t like him now.

Make up your mind, are you mad they pressured him to withdraw or mad they tried to keep him in the race?

Given your voting record and the fact that you’ve just criticized the democrats for two opposite courses of action in back to back posts (and I see your now several other posts hoping to find democrats mad at the DNC), I think you’re a plain ol’ conservative who’s inclined to find fault with the Democratic Party regardless of what specifically they do.

Yes, that was the point of the parent comment.

Tripled its housing supply since 1960 according to that article. Meanwhile Vancouver’s population went up by more than 4x. So it doesn’t seem surprising affordability would get worse!

Edit: Patrick Condon (who wrote that biv.com article) seems terrible. Here he is opposing connecting UBC to Vancouver’s SkyTrain: https://thetyee.ca/Opinion/2019/01/29/Last-Voice-Against-Sky...