Elliptic Curves... Not So Simple

 A bit early for Halloween, but spooky nonetheless: elliptic curves, via the Simons Foundation:

https://www.simonsfoundation.org/2021/09/27/elliptic-curves-simple-equations-still-shrouded-in-mystery/

Math Meets Language... and Category Theory

Grant Sanderson in conversation (90+ mins.) with Tai-Danae Bradley:

https://www.youtube.com/watch?v=pvRY3r-b0QI

 

Lob's Theorem and Curry's Paradox

 Fitting coincidence that after yesterday's post this piece also on self-reference should come up:

https://inference-review.com/article/loebs-theorem-and-currys-paradox

Retro....

 Almost every year I find some excuse to run one of my favorite quotes ever from a math volume, a bit of linguistics and recursive philosophy from provocateur David Berlinski in "The King of Infinite Space" (about Euclid). Berlinski is nothing if not an artiste of wordplay, and recently finishing "Shape" by Jordan Ellenberg's (no slouch at wordsmithing himself; though a bit more fun), simply reminded me of it once again:

"Like any other mathematician, Euclid took a good deal for granted that he never noticed.  In order to say anything at all, we must suppose the world stable enough so that some things stay the same, even as other things change. This idea of general stability is self-referential. In order to express what it says, one must assume what it means.

"Euclid expressed himself in Greek; I am writing in English. Neither Euclid's Greek nor my English says of itself that it is Greek or English. It is hardly helpful to be told that a book is written in English if one must also be told that written in English is written in English. Whatever the language, its identification is a part of the background. This particular background must necessarily remain in the back, any effort to move it forward leading to an infinite regress, assurances requiring assurances in turn.

"These examples suggest what is at work in any attempt to describe once and for all the beliefs 'on which all men base their proofs.' It suggests something about the ever-receding landscape of demonstration and so ratifies the fact that even the most impeccable of proofs is an artifact."

Scientific American, Scott Aaronson, and Warning Against Indifference

 Scott Aaronson wonders aloud if Scientific American was Sokal’d in this posting:

https://www.scottaaronson.com/blog/?p=5850

…but perhaps my favorite part is this bit he adds in the comment section:

“Yeah, I’ve been bummed about it all day, and there’s a part of me that’s genuinely surprised how all my friends are just ignoring it and going about their day. It’s like, do they not understand what Scientific American used to be, in its 50s/60s/70s heyday? Can they not see that for Scientific American to print such self-parodying dreck is as shocking, in its way, as for the January 6 insurrectionists to gallavant all over the US Capitol waving Confederate flags? Or was no one else shocked by that either? I mean, if you support either ravaging of our culture’s main symbols of democracy and reason, then by all means say so, celebrate, cheer in the streets about this, but for God or Bertrand Russell’s sake don’t be indifferent about it! 🙂”

Cantor's Attic

 Just can't get enough of Georg Cantor?...want to explore his work/ideas further?... Is that what's buggin' you! In a tweet yesterday, Richard Elwes pointed out this site doing just that:

http://cantorsattic.info/Cantor%27s_Attic

Getting Into "Shape"....

 Recently finished Jordan Ellenberg’s latest, “Shape” (plenty of reviews online), a great followup to his fantastic “How Not To Be Wrong” volume. It’s 400+ pages of “the hidden geometry” of life, but this is not your daddy’s (or necessarily even your own) geometry, rather a bit more modern and diverse take than Euclid ever provided. Anyway, great read, though possibly a tad more pedagogical than his earlier best-selling work, if only because much of the subject matter is drier or just more pedagogical in nature (Ellenberg’s writing style always enlivens it though).

With all that said, at the end of the volume Jordan lists many of the topics he wanted or considered including in the book, but in the end left out… another great, varied list of subjects (that sound to me even more interesting than the topics he did include!), so hopefully, maybe, perhaps, Jordan is now hard-at-work on a third volume!?

Hou Yifan... Female Chess Champion

 The rise of a female chess champion (h/t to S. Strogatz):

https://www.newyorker.com/magazine/2021/08/02/hou-yifan-and-the-wait-for-chess-first-woman-world-champion

Jordan Ellenberg In BBC Podcast

 9 minutes of Jordan Ellenberg:

https://www.bbc.co.uk/sounds/play/p09w8sr2

A Few Health Numbers (by the book... or, buy the book)

 Recently finished, and much enjoyed, Dr. Robert Lustig’s latest volume on nutrition/health/food, “Metabolical,” a fairly searing take on the American diet and how it got to be this way. Toward the end of the volume comes this passage hinting at the insidious countervailing pressures at work:

“Which addictive substance is the cheapest to produce and procure, yet the most expensive burden to society? Nicotine used to be the cheapest. At its worst, lung cancer claimed 443,000 people a year and cost healthcare $14 billion annually. But it also made the U.S. government lots of money, because the median smoker died at age sixty-four, before they started collecting Social Security and Medicare….”

[he goes on to dispatch with alcohol in a similar vein, before coming to his conclusion that “By far and away, the most expensive burden to society is sugar,” which he has spent much of the book detailing].

Not terribly mathematical (though plenty of facts and figures), but a good, if scathing, read on processed food in America.

Probability and Randomness via Twitter

 Oh, just another interesting Twitter thread:

https://twitter.com/svpino/status/1437793433255620633

"Dimension" -- What Is It?

 "Dimension"... like many intuitive ideas, not so easily defined and grasped:

https://www.quantamagazine.org/a-mathematicians-guided-tour-through-high-dimensions-20210913/

What's Been Happenin'

 Another round-up of monthly mathy news from The Aperiodical:

https://aperiodical.com/2021/09/aperiodical-news-roundup-august-and-half-of-september-2021/

Mathematics & Category Theory

 Emily Riehl covering category theory for the uninitiated:

https://www.scientificamerican.com/article/infinity-category-theory-offers-a-birds-eye-view-of-mathematics/

Math... High School Requirement or Not?

 An interesting Twitter thread on secondary math education:

https://twitter.com/mikeandallie/status/1437527668115791873

Teaching "Mathematical Habits of Mind"

 From Sam Shah:

https://samjshah.com/2021/09/12/mathematical-habits-of-mind/

Two Great Ones Discuss Progress In Science

 A fascinating interview (via AMS Notices) with Steve Smale and Lee Hartwell:

https://www.ams.org/journals/notices/202109/rnoti-p1578.pdf

A Little Weekend Reading (via Stephen Wolfram)

  Stephen Wolfram continues with his computational paradigm:

https://writings.stephenwolfram.com/2021/09/even-beyond-physics-introducing-multicomputation-as-a-fourth-general-paradigm-for-theoretical-science/

Podcast With Donald Knuth

 Wow, 2+ hours of Donald Knuth talking with Lex Fridman:

https://www.youtube.com/watch?v=EE1R8FYUJm0

Multiplying With John....

On your marks, get set... multiply!:

https://www.johndcook.com/blog/2021/09/09/double-triple-quadruple/

Solvable.... Yes

 A tricky one from Futility Closet today:

https://www.futilitycloset.com/2021/09/08/exam-week/

Dilbert Espouses...

 An oldie-but-goodie:

Dilbert.com

Just Another ASMR Video

Shaving cream....

Have the Mice Had Their Coffee Yet... ;)

 Mouse studies... time-of-day may matter!:

https://www.scientificamerican.com/article/many-mouse-studies-happen-at-the-wrong-time-of-day/

A Tweet For Folks Who Love Big Numbers

 5^(69^96) ... have at it:

https://twitter.com/johncarlosbaez/status/1433800220383584256

4, 6, 8, 12, 20... Points On a Sphere You Ask

 An apocryphal story via John Cook:

https://www.johndcook.com/blog/2021/09/02/spreading-out-points-on-a-sphere/

Jo Boaler with Lex Fridman

 Math educator Jo Boaler recently spent 90 minutes with Lex Fridman on his podcast:

https://www.youtube.com/watch?v=KZnGSVwIpeU

Just For Fun & Amazement (illusions)

This is old (…well around 5 years old), but Cliff Pickover retweeted one of my favorite static illusions yesterday, the “Scintillating Grid Illusion” by gamer Will Kerslake. The grid contains 12 black dots at intersections but you can’t see them all at the same time! Be befuddled:

Here’s one piece on it:

https://www.sciencealert.com/here-s-why-you-can-t-see-all-12-black-dots-in-this-crazy-optical-illusion

...shortly after preparing the above post yesterday, I then came across this Tweet introducing me to the Ames Window motion illusion, which was possibly new to me (and definitely worth checking out if you're unfamiliar with it):

https://twitter.com/gunsnrosesgirl3/status/1432793383760764938

And here is Veritasium's great take on it:

https://www.youtube.com/watch?v=dBap_Lp-0oc