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I know that my 17 non-bot followers will be devastated, but this site is officially so gross that I can't use it anymore. I've gone to BlueSky: @nathanielmath.bsky.social
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Nathaniel Johnston
53 posts
Nathaniel Johnston
@NathanielMath
Associate Professor of Mathematics at Mount Allison University I have moved over to BlueSky: @njohnston.ca
New Brunswick, Canada Katılım Kasım 2021
67 Takip Edilen92 Takipçiler
@aryehazan p=4 comes up in quantum information and tensor optimization stuff: arxiv.org/abs/1205.4484
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in what interesting mathematical settings have you encountered ℓₚ norms for p other than 1,2,∞?
I guess p=3,4 figures in some Khintchine and Paley-Zigmund-type derivations
& p=2/3 figures in distribution testing
& ofc p=0 figures in sparsity and compressed sensing
wht els?
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@VinceVatter Had something like this happen when ordering a test copy of my Game of Life book. The book arrived with all of the correct content, plus an extra 30 or so pages from some other book.
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Has anyone tried outsourcing their entire research program to MathOverflow? Seems a lot easier than actually doing research.
Anyway: mathoverflow.net/questions/4795…
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Hot take: squares are rectangles, which are parallelograms, which are trapezoids, and any textbooks saying otherwise should be burned.
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There's an entire section on the Wikipedia "trapezoid" page (#Inclusive_versus_exclusive_definition" target="_blank" rel="nofollow noopener">en.wikipedia.org/wiki/Trapezoid…) that discusses the apparent disagreement in the mathematical community re: whether parallelograms should be considered trapezoids. Is this actually a thing?
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Our paper about the new determinant formula is published! cambridge.org/core/journals/…
Really fun to write a paper with @robinhouston and @apgox, and really neat to write a paper that stemmed from Twitter, of all places (twitter.com/robinhouston/s…).
Robin Houston@robinhouston
The trick is that you can traverse the hexagon in either direction, so it's okay that we're missing a piece. We didn't define I = i(d-e) which would be the natural sixth thing. We didn't need to because each of the six is the negation of the sum of the other five.
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Over 15 years ago, I wrote a blog post with some formulas involving maximal self-avoiding walks (njohnston.ca/2009/05/on-max…). At the end of last month, @jpantone et al posted a paper that improves upon those results in ridiculously impressive ways (arxiv.org/abs/2407.18205).
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Fun fact for quantum information folks: if rho and sigma are separable density matrices (mixed quantum states) then their Hadamard product is separable as well. I somehow didn't notice this until today. Is this used anywhere?
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@cbounya @DrEugeniaCheng Just arrange it in a 1x17 rectangle -- easy!
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I made a prime number of things AGAIN.
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@JulietteBruce12 Singular value decomposition. So much of the rest of linear algebra (including rank-nullity) is a straightforward corollary of the SVD (as long as you’re OK with just working over R or C, and as long as you’re OK with “corollary” being logically backwards here).
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What do you think is the most OP theorem in math?
Personally, I’d go with the rank-nullity theorem but I think that says more about my tastes
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Minimal superpermutations are too hard. Solution: generalize and a problem that is easier!... in all cases except for the case we actually care about. New video: youtu.be/Uds_fgle37c
YouTube
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@VivaLaVegaaaa Their take is basically "horror movies without tons of gore shouldn't exist". But many PG-13 horror movies like The Ring would be made exactly 0% better by the addition of R-rated elements.
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Counterpoint, last few years:
M3GAN (unrated added nothing)
UNDERWATER
NO ONE WILL SAVE YOU
And in general, stuff like THE CONJURING, INSIDIOUS, DRAG ME TO HELL, EMILY ROSE… M. Night’s movies. They’re not outdated. Stuff like that can still work. It just has to be good.
Blair Bathory@blairbathory
Hot take: PG-13 horror films shouldn’t exist in 2024. We’re all desensitized at this point and need to take it up a notch to feel anything.
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@IAm_Not_APerson @no_earthquake It's honestly baffling to me that so many people contest the definition of 0^0, but then go on to use Taylor series or the binomial theorem without thinking twice about it.
0^0 = 1. If you need it to equal anything else or to be undefined, make that definition locally.
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“undefined” is mathematician speak for “we gave up out of laziness”
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A 1993 math paper that I'm reading mysteriously has lots of "w"s missing. Anyone have any insight onto why this might have happened? Is there some software that was commonly used back then that could've led to this problem, or is it likely just a find-and-replace mistake?
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@CmonMattTHINK We do. The “log identities” are the change of base formula and the facts that logs turn products into sums and exponents into products. The equation you posted follows from those.
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Sure, you've heard of verifying trig identities... but what about verifying "log identities"?
Why don't we do this?
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Why does every single graph on Twitter say something like “Source: A questionnaire by The Washington Post” on it with no URL or further information? Half a step away from writing “Source: Internet” but people do it completely unironically.
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It’s never too early to teach the kids about quantum computing.
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Dave Greene is doing an Ask-Me-Anything about Conway's Game of Life and our book: news.ycombinator.com/item?id=401315…
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