Incidentally, while the Exponential Time Hypothesis was about sub-exponential time (in some sense) algorithms for 3-SAT (or k-SAT), it's a simple cute exercise to prove that there exist NP-complete problems that have sub-exponential time algorithms.
(Spoilers in screenshot)
ALT https://cs.stackexchange.com/a/9814
Not an expert, but my impression is complexity-theorists' intuitions have been towards hardness/separation, while old-schoolers (eg Knuth) have seemed naive/crank-like for saying “maybe there are algorithms we haven't thought of”. But this month has seen several such algorithms.
Here's a direct link to OpenAI's PDF claiming a refutation of ETH. In particular, it's claimed that 3SAT on n variables is in about exp(n/(log n)^{1/2+o(1)}) time
github.com/openai/math/blob/…
(FWIW I first posted a longer version on news.ycombinator.com/item?id… before I could fit into a tweet here. It turned out very popular; in hindsight exactly the kind of “midwit” comment that does well on HN: just superficial stuff; my only knowledge is from undergrad >15 years ago :D)
Shreevatsa R retweeted
My mathematician daughter was browsing in a used bookstore this weekend ... and found this:
writings.stephenwolfram.com/…
I recognize only three of these poems, and have none of them memorized. Really admire @rasaganga and his family.
A fun game of Antyākṣarī in Sanskrit with my father @rasagangadhara!
For more info on this classic game (also called Pratimālā), check out this article - prekshaa.in/article/pratim%C…
#antyakshari #sanskrit #sanskritverse #sanskritantyakshari #pratimala #antakshari
BTW it should not be a surprise, but current models (in this case GPT-6 Astra Max) can one-shot identify the verses: chatgpt.com/share/6add633b-b…
(Well, two-shot: as can guess from the prompt, on first attempt it couldn't fetch from X/YT, and also couldn't “listen” for some reason…)
Somehow the consensus about this movie is different from my opinion, but I find its chutzpah incredible: to make a movie about racism in 2004 and have it be full of racial stereotypes and insults and justifications for racism(!) and to get away with it!
Been 20+ years, but IIRC:
- IIRC there's also an Asian woman who is simply a bad driver (causes an accident or something) (and this is drawn attention to), with no redeeming features whatsoever.
Mathematicians' reactions as AI upends their field is giving me a better understanding of why so many people were upset at P. G. Wodehouse for taking WWII so lightly, in his perfectly innocuous broadcasts as a prisoner of the Nazis. (Apart from, you know, not having heard them.)
Many don't seem to understand that some people just take *everything* lightly. Such people are precious and must be protected.
A transcript of Wodehouse's broadcasts is here: wodehouse.ru/berlin.htm (and Orwell's essay: telelib.com/authors/O/Orwell…)
I imagine many paurāṇika stories reuse earlier character- and world-building (like fan fiction). E.g. Vālmīki developed the grand character of Rāvaṇa for the Rāmāyaṇa, and other stories (like Rāvaṇa attempting to lift Kailāsa, or his face-off with Kārtavīryārjuna) reuse this.
And this version, Sītā-parityāga, is more blunt/overt. Kālidāsa elevates it of course into something very moving—I remember when Prof. K. S. Kannan and Dr Meera presented it, both of them at points broke down in tears themselves (audio recording: archive.org/details/Raghuvam…)
Still.
Direct link to the relevant section of the Epic India article that touches on this “echo” theme: web.archive.org/web/20120217…
(If the Chrome section highlight doesn't work: from “Patterns In The Development Of The Folk-Myth” to “One folk-perception”)
The whole article is very good.