What I Been Readin’ Lately

1)  If you enjoy biographies, especially those of modern day mathematicians, then John Urschel’s autobiographical “Mind and Matter” is a must read. It’s breezy, relatively brief, and fascinating. All lives are unique, but Urschel’s account of a career weaving together his cerebral pursuit of advanced mathematics and his love of more brutish professional football is an especially surprising read. Urschel juxtaposes his two passions, chapter by chapter, in a manner that, if written as a novel, readers would never find believable… except of course it’s not a novel, it’s his real life! And he still has a long way to go in a math career that is just getting underway. Definitely inspiring to see how someone melded together two such disparate career interests/passions in one lifetime. Recommended.

2)  I missed the first two volumes of “The Mathematics of Various Entertaining Subjects” because they were out of my price range! But I had no doubt these volumes were excellent coming from Jennifer Beineke and Jason Rosenhouse (I’ve enjoyed all of Rosenhouse’s writing in the past) and Princeton University Press — the books are beautifully produced, but I’m still not sure the reason for the high price that limits their audience. Anyway, Volume 3 showed up in my mail as a review copy (hitting stores in August), and every chapter feels a little like opening a Christmas present in July! It’s like reading an all-new volume of Martin Gardner pieces, except these wonderfully diverse entries of course come, not from Martin, but from current, great math explicators. A back cover blurb says the book “focuses on four areas: puzzles and brainteasers, games, algebra and number theory, and geometry and topology” — I mean that alone should get you drooling for a copy!

By the way, the awkward, inelegant title of these volumes, stems from a conference each year called “Mathematics of Various Entertaining Subjects” (“MOVES” for short). I do think a far more enticing title is possible, but the entries come directly from that conference, and too late now to change it.

Of course the other thing I've been reading lately is a lighter version of "Mathematics of Various Entertaining Subjects" known as the "The Big Internet Math-Off" contest entries, and we are now down to the grand finale. Sameer Shah and Sophie Carr have fought their way to the end and will face-off this coming Tuesday for the undisputed crown. It's been a splendid, diverse run, and a shame that Christian (who runs it) couldn't bend the rules this year and have simply settled for a 4-way tie at the end! ;) Congrats to all involved. Recreational math is in good hands.

And this must be the Year-of-Calculus in the book trade! Yesterday in my local Barnes & Noble I saw Oscar Fernandez's "Calculus Simplified" newly in stock (this is Oscar's third popular calculus volume, by the way), and in a few months Ben Orlin's treatment of the subject should be out, all following the rousing success of Steven Strogatz's "Infinite Powers." In my lifetime I've seen an amazing evolution of calculus from a rarified subject primarily only for the most advanced, to mass-audience books in non-college bookstores introducing the subject on a regular basis.

Finally, while I'm passing along ways to wile away your time I'll mention this Sean Carroll hour+ "Mindscape" (podcast) episode from early July that I really enjoyed on "music and the brain" with Indre Viskontas (not much math, but fascinating stuff):
https://www.preposterousuniverse.com/podcast/2019/07/08/episode-54-indre-viskontas-on-music-and-the-brain/
If by any chance you're not already familiar with Dr. Carroll's podcast you should check out his list of prior wide-ranging episodes/guests.

Chi-i-i-i-i-i-ll Friday *

[ *  "Chill Friday" is Math-Frolic's meditative musical diversion, heading into each weekend]

A Little Bit of Smullyan...

Raymond Smullyan was famous for his “knight and knave” logic problems (knights ALWAYS tell the truth; knaves ALWAYS lie). Here’s a simple one for young persons (or, anyone); not too hard, but challenging enough to give a sense of satisfaction when solved:

There are two people, A and B, each of whom is either a knight or a knave. “A” makes the following statement: ‘At least one of us is a knave.' What are ‘A’ and ‘B’?

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answer:  A is a knight; B is a knave

‘nother update (#BigMathOff)

Just another Sunday update on the Big Internet Math-Off (by now you’re either interested in this contest or not)… My own quickie review of outcomes (and correct me if I have any of it wrong) is that Lucy Rycroft-Smith is the only contender with 3 victories under her belt thus far, which she has well-earned with some wonderful postings, while Carr, Haensch, Neale, Shah, and Warren, each have two matchup-wins apiece (if you didn’t notice, 5 of the 6 named are all females). As those following along know, Vicky Neale won her second match by default when Sunil Singh, had to drop out of the contest, due to some extraneous matters in his life — probably the biggest glitch in the proceedings thus far, and I’m not sure if it creates any future issues?
==> WHOA! (correction)... in looking back it appears Sameer Shah actually has 3 victories (not just 2) as well, and will face Rycroft-Smith in one of the semi-finals.

Overall, things have gone so well that I hear next year Christian (Master-of-Ceremonies of the event) is planning to copy the USA ‘March Madness’ NCAA Basketball Tournament format, and start the competition with 64 entrants… no, no, NO, just kidding; none of us want to see Christian’s head explode (…that would make for a verrrry messy day in the offices of The Aperiodical). 

Anyway, will be interesting to see what the competitors put out next — who offered up their best material early, and who is saving their best for last, and all permutations in-between? Can Lucy keep her streak going, or will someone lurch forward from the back of the pack? Will it be an all-woman finale? Could any of them truly defeat James Grime in a head-to-head match... or, in a smiling contest? And least important of all… when will we ever use any of this?

[Today's contest is between Alex Corner and Grant Sanderson... if you haven't already, go vote!]

Chi-i-i-i-i-i-ll Friday *

[ *  "Chill Friday" is Math-Frolic's meditative musical diversion, heading into each weekend]

#BigMathOff Well Underway...

Hope you are all following along with this summer’s Big Internet Math Off contest at the Aperiodical. Last year’s was fun, and with a new, more complex format, this year’s is even funner!! Christian Lawson-Perfect has taken last year’s experiment to a new level... which seems to be running with amazingly few glitches! 

Great also to get introduced to several expositors I was totally unfamiliar with. In fact, I’ve been blown away a bit by the quality of the presentations — it’s one thing to be able to find/pick out interesting nuggets of mathiness, it’s quite another to present them to a large-scale audience in both an effective visual and expository form; so far, many great examples. A little disappointing that there haven’t been more votes cast in several of the matchups, but no doubt a lot more folks are reading/enjoying these posts than are voting (I myself have sometimes been tempted not to vote, because it is so hard choosing!). The tournament is only about halfway over, so plenty more to look forward to. And so long as no one bribes Matt Parker (last year's runner-up) to sway his 85,000 Twitter followers to vote as a block I think all will be kosher... ;)

Anyway, once the contest is over it might be interesting for someone (I don’t have time) to look at many possible factors in the match-up results. It would be nice to believe that votes are based on nothing more than objective judgment of the quality of the posts, but of course there's much subjectivity involved and no telling what else enters into the equation:

1)  Is there a difference/advantage to being a first or second presenter in the matchups?

2)  How about more algebraic versus more geometrical presentations, or more visual or video-based presentations versus more textual? or, simply long versus short entries?

3)  Does day-of-the-week have any consistent effect on the voting, especially weekends versus weekdays (or the July 4th holiday)?

4)  Any pattern in the results of gender (male vs. female) match-ups? or, how about Brits vs. non-Brits?

5)  Would there be any advantage to having the posts be anonymous, simply labelled "Entrant A," "Entrant B," "Entrant C," etc. (could anonymity even be maintained through a multi-week contest)?

6)  And of course it would be great to know which astrological signs fared best in the contest? ;))

You can likely think of other factors to play with too…

The sample size from the contest is too small for any such analysis to mean much, but still might be interesting.  

And I’m not certain myself exactly how the scoring is being done to determine the semi-finalists/finalists; that may raise other questions as well.

The mathematical jousting continues almost daily through the end of the month when a winner is crowned. Good luck to all!

Octonions, C. Elegans, Mystery, and More...

Replacing the usual meditative musical interlude this Friday with a lovely (meditative in its own way) 13-minute clip that Cliff Pickover passed along on Twitter last weekend, of Eric Weinstein 'explaining' octonions to Joe Rogan. Enjoy:



[this clip actually comes from a recent 3-and-1/2 hr. Rogan episode]

Danica McKellar…. Wonder (Years) Woman

Math-Frolic "profile" #10 is for all the middle-aged male mathematicians who came-of-age in the generation following behind my own esteemed, fab generation (that brought you the Beatles and Tiny Tim)... i.e., those of you who's first heart-throb was Winnie Cooper!

For all who didn’t experience the 1960s first-hand, “The Wonder Years” was an award-winning, memorable TV show from 1988 to 1993 that captured some of the 60's essence, with retro plot-lines and music, and child stars Fred Savage and Danica McKellar (winning 22 awards and 54 other nominations in the process!). I don’t know what's become of Fred, but Danica, bless her heart, became a book-authoring mathematician or a mathematical actress or an icon of American nostalgia... take your pick!

After beating out her very own sister for the role of 'Winnie Cooper' and eventually ending a very successful run, McKellar continued her acting as an adult while also enrolling at UCLA where she graduated summa cum laude with a math degree in 1998 (at which point she no doubt realized, to her dismay, that she could've attended Pomona College, right down the road). She originally planned to be a film major, but says “I kept finding myself taking math classes for fun, 'cause I missed them from high school!” (That's right folks, "FOR FUN"!)

While the baby boomer male generation may still crush on Chelsea Handler, a younger generation probably has never forgotten Winnie Cooper’s first kiss on national TV. And perhaps they even remember one of her personal favorite episodes where she outscores co-star Savage (as “Kevin Arnold”) on the math SAT -- a very rude thing to do back in the day!... luckily times have changed. Jimmy Fallon, who named his first-born girl “Winnie,” once remarked that Winnie Cooper was “the coolest girl in any TV show ever.” Of course he’s too baby-faced-young to remember Mouseketeer Annette Funicello… but, I digress.

Born a Capricorn in 1975, Danica was destined for success, just like Elvis Presley, Stephen Hawking, and uhhh, Howard Stern. Looking her up for this report, several things surprised me. As someone not very tuned into TV or movies I had no idea that since her childhood success, McKellar has been in over 30 films, and has 50+ TV appearances to her credit, as well as several voice-overs. She guested in diverse hits ranging from "The Big Bang Theory" and "Dancing With the Stars," to a recurring role on "The West Wing" as a White House assistant, even though no White House assistants or staff in the last 2+ years has had an IQ even close to Danica’s (although rumor has it that Sarah Sanders did once sit in on a math class). And she was invited to be on Donald Trump’s crowning intellectual masterpiece (cough, cough) “The Apprentice” but wisely turned it down (probably because of that small-print clause in the contract that permitted/promoted groping by the show's main protagonist). McKellar still acts today, while also being a mom and author.

To date she has written 6 math books (or, in base 2, 110 books), usually with catchy titles intended to get the attention of young people, especially girls:

Math Doesn’t Suck: How to survive middle school math without losing your mind or    
     breaking a nail

Kiss My Math

Hot X: Algebra Exposed

Girls Get Curves: Geometry Takes Shape

Do Not Open This Math Book

Goodnight Numbers

She is dedicated to seeing more middle school girls pursue their interests and talents in mathematics, and not be nudged away from it early on for social reasons. She says at one point:

“My main concern with the condition of mathematics in high school is that there's a lot of fear involved! Math is not, generally speaking, presented in a fun way. The concepts, as I see them, ARE fun, and that's the way I'd like to convey them myself.”

[Danica has taken heat from some quarters for the approach she takes in her books, but her attitude (as I understand it) is that girls should be allowed to maintain “girly” interests while succeeding in math/science, and moreover you have to approach people where they (or society) are at, not where you might like them ideally to be, in order to bring about change.]

In all honesty, I’m not directly very familiar with McKeller's books (perhaps having something to do with the fact that I was never a pre-teen girl in my current lifetime — though in this era of gender fluidity, who knows!), but they have won wide praise and several awards (including the 2014 JPBM Communications Award, which places her in very luminous company... even if you include Matt Parker).

She promotes her approach to math at her website:

http://mckellarmath.com

Danica admits there are two different sides to her personality, the half that loves logic and math and puzzles, and the half that loves acting and entertaining (…there’s probably also a half that gets sick of talking about/answering questions about "The Wonder Years," but, realistically, she’ll still be doing that when she’s 94 and a whole new generation of cable subscribers discover her). Even though 3 halves can't be right...

In 1998, with another student and her UCLA professor she proved/published a new math/physics theorem, the Chayes-McKellar-Winn Theorem:

 “Percolation and Gibbs states multiplicity for ferromagnetic Ashkin–Teller models on Z2” 

You can read the paper here: 

http://www.danicamckellar.com/pdf/percolation.pdf

It deals with magnetism in two dimensions, and I would gladly take time to explain it in more detail for you all… except that that would require me to learn some math… and science… and big words, myself.  I believe this paper earned her an Erdös Number of 4, but who’s counting (certainly not Paul, he’s long gone to meet the Supreme Fascist in the sky... as he would say -- but hey, just maybe her proof made it into "The Book" so he is aware of her).

Danica is also into palindromes, though that may only be the result of eating too much ‘UFO tofu’… and then wondering aloud ‘do geese see God.’ She has enjoyed posting questions on her Twitter account that have palindromic answers. I've noticed that quite a few math buffs enjoy palindromes; I’m not sure why that is, but Wow!

You can follow Danica on social media (in the event that you're one of the dwindling number of needy folks who still think social media have any pertinence in polite, civil society):

http://www.facebook.com/danicamckellar

https://twitter.com/danicamckellar

Here’s an old (2007) transcribed interview with Danica, when she was coming out with her first book:

https://web.archive.org/web/20151016195125/http://scienceblogs.com/aetiology/2007/07/25/interview-with-math-whiz-autho/

And here she is answering a few questions for nostalgia buffs (…in which she reveals that her childhood crush was not on Fred Savage, nor even Terry Tao, but on Michael J. Fox!... but then who hasn't had a crush on Michael J. Fox at one time or another...or... perhaps I've said too much):

…side-note: Tao was actually one of McKellar’s instructors at UCLA, and wrote glowingly about her once in this long post on his own blog:

https://terrytao.wordpress.com/2007/08/20/math-doesnt-suck-and-the-chayes-mckellar-winn-theorem/

Here’s hoping Danica will keep encouraging young girls to outshine the boys, and pursue math and STEM fields to their hearts-content; so that just maybe one day, in a world Donald Trump can’t even fathom (and for which Ivanka is dismally unqualified), women will rule (...and, I don't mean Theresa May).

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Prior math profiles have been of: 

Matt 

Evelyn 

David 

Sean

Cathy

Al

Tadashi

Holly

Erik

(read 'em all, if you dare)

Chi-i-i-i-i-i-ll Friday *

[ *  "Chill Friday" is Math-Frolic's meditative musical diversion, heading into each weekend]

[looks like I should have another math "profile" ready-to-go Sunday morning]

Where's The Gold?

Just a re-run post of a simple logic problem — a good one to try on young folks:

3 sealed boxes face you on a table. You are told one contains gold while the other two are empty. Each box has printed on it a written clue regarding its contents, HOWEVER only one statement is accurate, while the other two are false. Which box has the gold?

1) No gold in here     2) No gold in here   3)  The gold is in box 2

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answer: Box 1 contains the gold