not exactly what you're looking for but maybe useful
https://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EWD831.html
― 𝔠𝔞𝔢𝔨 (caek), Monday, 31 August 2020 16:31 (three years ago) link
Thanks, already went with your last suggestion.
― Two Little Hit Parades (James Redd and the Blecchs), Monday, 31 August 2020 18:07 (three years ago) link
HI DERE!
― Erdős-szám 69 (James Redd and the Blecchs), Saturday, 26 September 2020 22:55 (three years ago) link
Does anyone read the Cantor’s Paradise section of Medium?
― Here Comes a Slightly Irregular (James Redd and the Blecchs), Saturday, 17 October 2020 12:57 (three years ago) link
never heard of it before, but just read this nice post on concentration bounds https://medium.com/cantors-paradise/concentration-of-measure-the-glorious-chernoff-bound-1e96777cc29d
― flopson, Sunday, 18 October 2020 01:16 (three years ago) link
The few things I’ve read have been pretty good so far.
― Here Comes a Slightly Irregular (James Redd and the Blecchs), Sunday, 18 October 2020 01:21 (three years ago) link
Twitter programming language enthusiasts are the absolute worst promoters of category theory applicability.
― Allen (etaeoe), Sunday, 30 May 2021 21:10 (two years ago) link
Who's the picture at the top of this thread a picture of?
― Guayaquil (eephus!), Sunday, 30 May 2021 21:16 (two years ago) link
https://www.youtube.com/watch?v=sdlWiDgvjAY
― flopson, Sunday, 30 May 2021 21:21 (two years ago) link
sometimes things work out well:
I taught a course in computational algebraic geometry this summer.To high school students.Here's how it went.https://t.co/fCASlEoExx— Bill Shillito (@solidangles) August 3, 2021
― mark s, Wednesday, 4 August 2021 12:57 (two years ago) link
Good stuff, especially leading up to this:
In short, we need to stop conflating logical foundation with pedagogical foundation.
― Two Severins Clash (James Redd and the Blecchs), Wednesday, 4 August 2021 14:16 (two years ago) link
I think this is good but I also think it is super unclear to me that "pedagogical strategies that work well in a small group of student selected specifically as self-motivated high math achievers" has THAT much to say about what K-12 should be doing generally. And of course the idea that school math should involve playing around, discovery, "why do we do it this way? what if we did it this other way? if that doesn't work, what went wrong?" rather than "follow these rules to get the answer" is exactly the aspect of Common Core that was hated by legislators and parents and to be frank lots of kids (though I still can't help feeling there has to be a way to do it right.)
― Guayaquil (eephus!), Wednesday, 4 August 2021 14:35 (two years ago) link
Fair enough.I want to look at his divide by zero thing later.
― Two Severins Clash (James Redd and the Blecchs), Wednesday, 4 August 2021 14:40 (two years ago) link
never divide by zero, it always ends badly
― mark s, Wednesday, 4 August 2021 14:55 (two years ago) link
and yes, it absolutely depends on this being a schoolroom of the self-selectedly curious in a territory where the outcome stakes aren't especially high yet (in a bridge-will-fall-down car-will-catch-fire sense)
― mark s, Wednesday, 4 August 2021 14:58 (two years ago) link
― Two Severins Clash (James Redd and the Blecchs), Wednesday, 4 August 2021 15:00 (two years ago) link
trying to vibe at the pole of a reimann sphere, just not happening man
― mark s, Wednesday, 4 August 2021 15:50 (two years ago) link
I was trying to work out myself how to prove that pi is a constant, that all circles have the same ratio between diameter and circumference. I got stuck -- I couldn't figure out a way to prove that if there exists the same angle-side-angle values for two triangles, they are congruent. I looked it up in Euclid's Elements, but Euclid's proof only works when that applies for ANY given side. Is there a simple proof of this without going into the law of sines?
― adam t. (abanana), Friday, 3 September 2021 23:11 (two years ago) link
Found it, Book I Proposition 26 in Elements.
― adam t. (abanana), Saturday, 4 September 2021 00:27 (two years ago) link
To me the definition of a circle implies that all circles are similar to each other so pi has to be constant.
― Gwar ina Babyon (James Redd and the Blecchs), Saturday, 4 September 2021 20:14 (two years ago) link
I suppose using Euclidean methods you could use dilation and then superposition.
― adam t. (abanana), Saturday, 4 September 2021 21:17 (two years ago) link
here’s one way to prove it using integral calculus
take any circle x^2 + y^2 = r^2
circumference is the arc length of the curve, which is equal to 2r times an integral not involving t (as here https://math.stackexchange.com/a/1049390)
― flopson, Saturday, 4 September 2021 21:21 (two years ago) link
not involving r*
Okay, someone take the Terence Tao masterclass and tell me what he says.
― Tapioca Tumbril (James Redd and the Blecchs), Monday, 31 January 2022 16:29 (two years ago) link
I never heard the term The Martians before.
― Ferryboat Bill Jr. (James Redd and the Blecchs), Wednesday, 9 February 2022 12:20 (two years ago) link
I'm laughing so hard at this slide a friend sent me from one of Geoff Hinton's courses;"To deal with hyper-planes in a 14-dimensional space, visualize a 3-D space and say 'fourteen' to yourself very loudly. Everyone does it." pic.twitter.com/nTakZArbsD— Robbie Barrat (@videodrome) June 10, 2018
― 𝔠𝔞𝔢𝔨 (caek), Tuesday, 8 March 2022 22:02 (two years ago) link
Lol
― Mardi Gras Mambo Sun (James Redd and the Blecchs), Tuesday, 8 March 2022 23:03 (two years ago) link
Old enough to remember when the thing was to watch Tom Banchoff rotate a tesseract to help see the fourth dimension.
― Mardi Gras Mambo Sun (James Redd and the Blecchs), Tuesday, 8 March 2022 23:06 (two years ago) link
https://www.youtube.com/watch?v=90olwwLdEYg
― Mardi Gras Mambo Sun (James Redd and the Blecchs), Tuesday, 8 March 2022 23:09 (two years ago) link
Hinton's a real one
― Guayaquil (eephus!), Tuesday, 8 March 2022 23:33 (two years ago) link
who knows how to visualize a complex or even quaternionic one
Anyway I see what he is saying.
― Mardi Gras Mambo Sun (James Redd and the Blecchs), Wednesday, 9 March 2022 00:33 (two years ago) link
Category theorists are always wilding out on my timeline
― Allen (etaeoe), Monday, 11 April 2022 13:14 (two years ago) link
I have just learned that it may not be related to category theory and is likely a byproduct of Twitter’s new recommendation features (I assume it’s inferring an interest based on following math people and following computer science people).
― Allen (etaeoe), Monday, 11 April 2022 17:13 (two years ago) link
pic.twitter.com/maySTJd1wA— depths of wikipedia (@depthsofwiki) April 18, 2022
― mark s, Monday, 18 April 2022 14:22 (two years ago) link
What does Snopes have to say?
― jmm, Monday, 18 April 2022 15:10 (two years ago) link
Surely there is a Medium article or two addressing this. I believe I may have gotten an email alert about one this morning iirc.
― Ramones Leave the Capitol (James Redd and the Blecchs), Monday, 18 April 2022 15:15 (two years ago) link
https://www.newyorker.com/magazine/2022/05/16/the-mysterious-disappearance-of-a-revolutionary-mathematician
― Don't Renege On (Our Dub) (James Redd and the Blecchs), Friday, 13 May 2022 19:50 (two years ago) link
https://www.youtube.com/watch?v=uqwC41RDPyg
― The Crazy World of Encyclopedia Brown (James Redd and the Blecchs), Monday, 13 June 2022 02:01 (one year ago) link
a tweet linking to an essay i can't now find: explaining how, yes, in 4D a klein bottle does not intersect itself but NO, in 4D a klein bottle does NOT have "only one side"
bcz "sides" don't really exist in 4D
(viz -- i believe -- bcz the concept of side is topologically incoherent in 4D: as eg the concept of edge is topologically incoherent in 3D)
anyway i've probably explained the stuff in brackets wrong or used the wrong terms or something lol and i can't find the piece that explained it but it was a good ACTUALLY so i did remember it to post here, eventually)
― mark s, Wednesday, 7 September 2022 11:11 (one year ago) link
I don't know how to search for this thread so I didn't post this at the time that it appeared on redactle:
The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with its imaginary part equal to zero.
Isn't this trivially true, since every real root is also a complex root (with imaginary part equal to zero)?
― ledge, Wednesday, 7 September 2022 12:58 (one year ago) link
he concept of edge is topologically incoherent in 3D
doesn't a mobius strip have only one edge?
― ledge, Wednesday, 7 September 2022 13:08 (one year ago) link
It’s talking about the the coefficients, not the roots, the roots may still be complex.
― Jean Arthur Rank (James Redd and the Blecchs), Wednesday, 7 September 2022 13:14 (one year ago) link
but (let's say) if a polynomial (with complex coefficients) were to have one single real root, it would therefore have 'at least one complex root'?
― ledge, Wednesday, 7 September 2022 13:18 (one year ago) link
It's trivially true but not for the reason you're saying - it's saying that every polynomial with real coefficients is automatically a polynomial with complex coefficients. Real roots are a red herring.
― toby, Wednesday, 7 September 2022 13:26 (one year ago) link
i found the relevant thread and (as i kind of knew) i got the argument wrong lol (nothing to do with edges as analogy):
It's common to hear the following facts about Klein bottles:1) To avoid self-intersections, it must live in at least 4-dimensional space.2) Like a Möbius band, it's a one-sided surface.The problem is, a Klein bottle living in 4-dimensional space is NOT one-sided! Why not? 1/13 pic.twitter.com/ertVreTkRx— Dave Richeson (@divbyzero) August 23, 2022
― mark s, Wednesday, 7 September 2022 13:31 (one year ago) link
xp ok, well i get what you're saying - i don't really get why that wikipedia sentence isn't talking meaningfully about the roots but whether that's down to me or the article, either way i'll let it pass.
― ledge, Wednesday, 7 September 2022 13:31 (one year ago) link
Toby otm
― Jean Arthur Rank (James Redd and the Blecchs), Wednesday, 7 September 2022 15:52 (one year ago) link
TIL John Truss is Liz Truss’ father.
― Allen (etaeoe), Sunday, 2 October 2022 14:24 (one year ago) link
Meanwhile, what are people working on?
I realize I haven’t written since I moved from academia to industry. I’ve been working with a colleague on a paper about the use of transformers for root-finding. It’s been remarkable to see the learning capability of these models. We started simply by learning the root-finding method numerically (i.e., from coefficients) but we’re starting to encode symbols (i.e., the parse tree of a polynomial). It’s way too hypothetical to discuss elsewhere but I think it’s possible we’ll be able to use these transformers to discover entirely new and useful generalized functions.
― Allen (etaeoe), Sunday, 2 October 2022 14:30 (one year ago) link