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.
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 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.
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.
> […] 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.
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.
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!
Relevant context: it’s very hard to learn from research-level math talks, because the material is almost absurdly complicated even when presented well. This advice is for grad students who are often totally at sea as to how to get anything useful or real out of attending a math talk.