one foot through the looking glass
Joined December 2018
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the key identity used to disprove ETH is from a guy from the 18th century named Carl Degen
![From the ETH proof. Lemma (Eight-square identity [CS03, AM99]). There is a function σ : {0, 1}3 × {0, 1}3 → {−1, 1} such that for all x, y, u, v ∈ {0, 1}3, with ⊕ the bitwise exclusive or, (12) 2 [x = v] [y = u] = [x ⊕ y ⊕ u ⊕ v = 0] (σ(x, y) σ(v, u) + σ(x, u) σ(v, y)). Proof. Let σ(p, q) = (−1)ϕ(p,q) with ϕ(p, q) = ∑ k≤k′ pkqk′ + q1p2p3 + p1q2p3 + p1p2q3. Equa- tion (12) is a statement about 12 bits, and it can be checked at all 4096 settings. (§4 and Appendix F prove it by hand.) ■ The identity is two centuries old: Degen found it in 1818, and Graves found it again in 1843 by showing that the norm of the octonions is multiplicative [Bae02, Section 1].](https://pbs.twimg.com/media/HVvWXQXWIAA-hLM.jpg?name=orig)
ALT From the ETH proof. Lemma (Eight-square identity [CS03, AM99]). There is a function σ : {0, 1}3 × {0, 1}3 → {−1, 1} such that for all x, y, u, v ∈ {0, 1}3, with ⊕ the bitwise exclusive or, (12) 2 [x = v] [y = u] = [x ⊕ y ⊕ u ⊕ v = 0] (σ(x, y) σ(v, u) + σ(x, u) σ(v, y)). Proof. Let σ(p, q) = (−1)ϕ(p,q) with ϕ(p, q) = ∑ k≤k′ pkqk′ + q1p2p3 + p1q2p3 + p1p2q3. Equa- tion (12) is a statement about 12 bits, and it can be checked at all 4096 settings. (§4 and Appendix F prove it by hand.) ■ The identity is two centuries old: Degen found it in 1818, and Graves found it again in 1843 by showing that the norm of the octonions is multiplicative [Bae02, Section 1].
checked in on the pretty new zealand girl who messaged me on last fm when i was 17 saying she liked my music taste . she's happily engaged to a woman.. i've seen enough im gonna throw up
the margaret hamilton photo would never happen to me because i'm tall and write only skinny papers of staggering beauty
"the exponent is so bad i guess the universe is inherently ugly" are you dumb?? that is not the actual tight answer. it's a work in progress. you'd pass on the house of your dreams if you didn't like the color the walls were painted
oh noo, your area was cleared out? your big problems all got solved? im sooo sorry. i mean, the problems ive worked on are all still standing. but i get it, we can't all work on hard problems
fun fact: when a college in a tiny town tries to hire a prof who’s single, some ppl will address the dating issue explicitly: “you can find a wife here. many have before. we have lots of eligible profs. and it’s not encouraged but grad students in other depts are not off limits”
put a whole soup dumpling into my mouth and my mom said, no, you’re supposed to eat them like kissing: you bite and then suck. and while i furrowed my brows she laughed
neppy retweeted
if u write a research paper, five ppl tell u "nice work" and four of them havent read it and the fifth secretly hates u bc u have shit methodology. if instead u write gay fanfic where John Wick tells u "You have to be brave" you improve the lives of hundreds of undiscerning teens
i’ve seen enough. i’m done making myself useful. i’m deleting every pdf and tex file from my computer. then i’m joining a lindy hop club, polycule, and the dsa