...a companion blog to "Math-Frolic," specifically for interviews, book reviews, weekly-linkfests, and longer posts or commentary than usually found at the Math-Frolic site.

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." ---Bertrand Russell (1907) Rob Gluck

"I have come to believe, though very reluctantly, that it [mathematics] consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-legged animal is an animal." ---Bertrand Russell (1957)

******************************************************************** Rob Gluck

Thursday, December 17, 2015

Stayin' Alive... ;-)

Some end-of-year housekeeping:

1)  Sorry, am swamped with lots of year-end schtuff right now (are we all having fun yet!?) so, posting at MathTango will be light, if at all, 'til sometime into January!  Friday potpourris will be short or absent until then. (Math-Frolic will continue as normal through the month.)
Anyway, been a fantastic year for both blogs, and sincere thanks to all who've been in touch in any way, provided content or ideas, and helped keep these blogs, labors-of-love.

2)  Haven't done an interview here for awhile, so if you wish to suggest someone you'd like to see interviewed let me know (especially if you can provide an email address for the suggested person).
=> p.s.: I've attempted to interview every person suggested in the past, so if you previously recommended someone and it never happened it's either because they didn't respond to a request, or in some cases I simply couldn't find a current/working email for them.

3)  I've never taken 'guest posts' here, but might consider it in the next year (nothing spammy or merely selling a product)... if you have an interesting, provocative, or timely (mathy) subject you'd like to address, maybe shoot me an email about your idea.
Perhaps this being an election year (U.S.), that will offer new possibilities too.

Have happy and safe holidays everyone... and needless to say, "Don't drink and derive." ;-)

I'll leave you with this old Slinky/treadmill video (gotta be some math buried in there), that isn't Christmas music, but somehow always puts me in a Holiday mood ;-):

Friday, December 11, 2015

Friday Mathy Leftovers

More weekend reading:

1)  Starting with Escher, Keith Devlin highlights the use of games and media in math education:

  A 'trick' chess problem from Futility Closet:

...and a little algebra from Futility Closet as well:

Jo Boaler and "la revolution" in math teaching (h/t to Egan Chernoff):

4)  Another odd or surprising finding from Presh Talwalkar (once again involving probability... and Santa):

Peter Woit with a bit of update/commentary about Mochizuki's ever-complex "proof" of the ABC conjecture:

6)  From Quanta, a math "quartet" seeks mathematical breakthroughs:

7)   Ben Orlin offers a primer on teaching, across the years and across different levels:

8)  The mathematics of house keys... who knew!? (be sure to also read and follow the link in Mike Lawler's initial comment to the post):

9)  First review I've seen of the new Euler biography from Princeton U. Press:

10)  Futility Closet
entertains yet again with some peculiar polyhedra:

Siobhan Roberts returns to us with another mathy piece on a conjecture of Erdös, recently solved:

12)  Slightly technical, but an interesting statistical dissection of a biomed paper from Chris Harrow:

13)  Not exactly a math lesson, but certainly an interesting lesson of some sort from Simon Gregg (h/t to Nalini Joshi for this one):

Potpourri BONUS! (extra NON-mathematical links of interest):

Often I try to close out on an up beat note, but this week instead am just dropping in this classic, old Jacob Bronowski clip once again:

Friday, December 4, 2015

Weekly Math-mix

From the week....

Mathematically quantifying word "entropy" and humor (kind of a quoiky study ;-):

In her usually delicious manner Evelyn Lamb posted about the torus last week:

3)  John Allen Paulos expresses some regrets (in an excerpt from his latest book):

4)  Math Rising delves into some thoughts from David Mumford (about Platonism):

5)  Simple, lovely geometry from Futility Closet:

6)  Michael Harris responded in part to my recent brief comments about his wonderful book, "Mathematics Without Apologies," with this clarifying post:

7)  Short but interesting Princeton interview with NPR's 'Math Guy,' Keith Devlin:

You just know that when Ben Orlin passes out grades it'll make you smile:

9)  The NY Times once again on math education:

10)  Machine learning, pure and applied mathematics, via Quanta:

11)  Jason Rosenhouse fulminates on "specified complexity":

12)  And straying farther from math here, but a couple of pieces on consciousness (and "integrated information theory") this week from John Horgan and Margaret Wertheim:


13)  Some humor to close out with (h/t to Egan Chernoff for this one):

Potpourri BONUS! (extra NON-mathematical links of interest):

Fun read from Nautilus on jokes, how they bring us together... or keep us apart:

2)  Because EVERYbody loves penguins:

For a bit of calm, following yet another week of senseless, nerve-jangling violence, Pachelbel's Canon on acoustic guitar:

Sunday, November 29, 2015

The Year In Books

(via WikiMediaCommons)

Reviewing another great year in popular math! Your mileage may vary....
Which is always my way of warning that my picks for favorite reads of the year won't necessarily suit your own interests/tastes. With that said...

Will start with a few miscellaneous notes:

a) If you enjoy Tyler Vigen's humorous "Spurious Correlations" website (a sort of parody of statistical correlations) you can get a hardback version of it in his book of the same title.

b) Two books worth noting that I didn't read this year:

"Birth of a Theorem" by Fields Medalist Cedric Villani got some mixed reviews, some of which though were very positive.

"The Fascinating World of Graph Theory" (Benjamin, Chartrand, Zhang) -- a mini-popular-text on graph theory, probably for a narrower audience than other books here, but worth a mention.

I'll also note that Princeton University Press has just released the 700-page (and pricey) "Leonhard Euler: Mathematical Genius in the Enlightenment" by Ronald Calinger, and additionally from Princeton, this year's volume of "The Best Writing On Mathematics 2015" is due out in Jan. 2016.

c)  A 2014 book that came out in paperback this year, and I loved, was Gary Smith's "Standard Deviations," another in the growing genre of statistics treatments for the masses.

d)  Matthew Watkins' older trilogy on prime numbers was re-published this year by Liberalis Books; I'd still like to see these wonderful British volumes get WIDER circulation.

Now for my year's Top 10 list for a general audience, starting with numbers 4 through 10, without annotation:

4.  "The Proof and the Pudding" by Jim Henle

5. "Problem-solving Strategies In Mathematics" by Alfred Posamentier and Stephen Krulik

6. "Professor Stewart's Incredible Numbers" by Ian Stewart 

7.  "Numbers: Their Tales, Types, and Treasures"  Alfred Posamentier and Bernd Thaller

8. tie: "How To Bake Pi" (American title) by Eugenia Cheng
          "A Numerate Life" by John Allen Paulos

10. "The Magic of Math" by Arthur Benjamin

...and on to my favorite three:

I enjoy biographies but never expected a biography to ascend as my favorite popular math book in any given year... Siobhan Roberts proved me wrong. Her delicious account of John Conway, "Genius At Play," IS my favorite volume of 2015. Roberts' book follows a fascinating character, but also includes actual, interesting math along the way. Biographies of mathematicians of course, are rare, and Roberts paints an engaging portrait of her subject, while not shying away from his human warts and foibles (as I wrote at the time, "I didn't want this book about math, and one man's humanity and passion, to end"). Just a super read from beginning to end! (By the way, if you missed this recent Guardian podcast with Conway and Roberts, it's a great listen too.)

"Genius At Play" nudges out Michael Harris's eclectic, provocative, (almost oddball) "Mathematics Without Apologies," which I thought I'd relish more on a second reading, but actually fell slightly flatter on the re-read. Harris, more than any mathematician I've read, has a knack for saying things that sound interesting, but that are just vague or ambiguous enough to leave one uncertain of what his exact point is. That sounds like a criticism, but in some perverse way it makes his writing all the more thought-provoking and engaging... and good enough to just edge out my number 3 pick, Marc Chamberland's "Single Digits," a fabulous compendium of math examples, more geared to mathematicians than general readers. Three VERY different, very wonderful books for the math gourmet! They won't suit everyone's taste, but I really enjoyed ALL of these!

Left off of this personal list are dozens of other math books from the year that I either didn't look at or that simply didn't 'ring my chimes.' But if one of them did 'ring YOUR math chimes' feel free to give it a plug in the comments below as a possible stocking-stuffer in the weeks ahead.


Finally, if I combine my 3 favorite books from each of the last three years, and then throw in Strogatz's "The Joy of X" (my favorite from 2012), you have a nice eclectic 10-book-list for a mini-popular-math library. So in addition to the above three:

From 2014:

"How Not To Be Wrong" (Jordan Ellenberg)
"Things to Make and Do in the Fourth Dimension"  (Matt Parker)
"The Grapes of Math"  (Alex Bellos)

From 2013:

"The Outer Limits of Reason (Noson Yanofsky)
"Chaotic Fishponds and Mirror Universes (Richard Elwes)
"Love and Math"  (Ed Frenkel)


"The Joy of X"  (Steven Strogatz)

Anyway, to all the readers out there... bon appetit and happy holiday shopping for your math friends (everyone wants math books for Christmas, right ;-) Can't wait to see what 2016 has in (book)store(s) for us.

Friday, November 27, 2015

This Week's Leftovers...

Thankful for another week of mathy stuff...

For the advanced amongst you, Peter Woit posts about Langlands news:

Arthur Benjamin interviewed (podcast, 30-mins.) about his book, "The Magic of Math":

Once again sweet, amiable Doron Zeilberger considers possibly telling us how he really feels ;-):

Yet again someone tries explaining p-values:

Another interesting post from Michael Harris (but I won't even attempt to synopsize what it's about!?):

6)  And Jim Holt newly-reviews Harris's book "Mathematics Without Apologies" here (requires subscription for full access):

7)  Erica Klarreich, excellent as always (on "the Kadison-Singer problem"):

8)  Of sequences and EKGs (via Quanta):

9) Sean Carroll makes an excellent choice in giving thanks this year:

10)  "Retraction Watch" most often cites biomedical papers that are being retracted, but once in awhile a mathematics paper is retracted (due to honest errors):

11)  Hmmm... I'm wondering if even back in Civil War times kids asked, "When will I ever use this stuff?":

12)  And of course pick any day over at MikesMathPage and you'll likely find something of interest.

13)  Last weekend I reviewed John Allen Paulos' new book, "A Numerate Life," and this coming Sunday I'll have up my wrap-up of popular math books for 2015.

Potpourri BONUS! (extra NON-mathematical links of interest):

1)  Daniel Kish's incredible, inspiring story (of using human sonar to aid blindness) never fails to astound me! It was re-told on a segment of TED Radio Hour last week:

 2)  Not that I have any time leftover for these, but a nice list of "best podcasts" collected here:

Sunday, November 22, 2015

A Life In Math

"What a wee little bit of a person's life are his acts and his words! His real life is led in his head, and is known to none but himself... Biographies are but the clothes and buttons of the man. The biography of the man himself cannot be written."
-- Mark Twain quoted in "A Numerate Life" by John Allen Paulos

A blurb today on John Allen Paulos' latest book (released in paperback), which he terms a memoir, "A Numerate Life." I expect this will be the last book I'll review this year, and it will be added to my list of 10 favorites for the year to be posted soon.

The volume is slightly reminiscent of Martin Gardner's autobiography, "Undiluted Hocus Pocus," with a similar light, off-handed, sometimes rambly, often nostalgic style reflecting on scattered matters that Paulos either deems important or simply remembers fondly from his varied but math-centered life. It is relatively short (under 200 pgs.), a bit quirky, and somewhat informal... you can almost imagine Paulos, like your grandfather, in a big ol' Lazy-Boy chair relating his life and thoughts on a Sunday afternoon.

I think it definitely helps to have read previous of Paulos works and already have a sense of his perspective, to accurately take in the recountings and musings in this volume. The same was true of Gardner's book, which was probably most appreciated by those who already felt they knew Gardner somewhat. If you know nothing about Paulos, and pick up this book, it may come off as self-indulgent or overly introspective, including matters that could strike uninitiated readers as trivial (like a paragraph on the logical approach to leaving the toilet seat up or down), but that Paulos recognizes exemplify his consistent, rather empirical, approach to life; he is if nothing else, always the teacher/explicator/analyzer.

Then too, Paulos tosses in puns all along the way, and given the frequency with which I see mathematicians use puns, I now wonder if there is some sort of neuronal connection between math aptitude and pun prowess (or wordplay in general)... whoever researches this for their PhD. dissertation can thank me later for the suggestion ;-)

There are bits of mathematics sprinkled throughout the book as well, moreso in the second half than the first half. Paulos touches on all the topics he's addressed in prior works: education, probability, coincidence, the stock market, religion, in addition to math.  Anecdotes and reflections abound here... a summing up as it were, as Paulos enters his seventh decade. Segments about his family are especially touching, and Paulos has a quirky ability to float back-and-forth between nostalgia and human musing, followed by terse, mathematical analysis of the same.
You also get the sense of Paulos' frustration with "innumeracy" in America (a term he coined for math illiteracy), and the difficulty of a remedy for it. There is also a sort of "meta" quality to the content, as the author often comments on what autobiographies are and are not capable of accomplishing.

I enjoyed the second half of the volume more than the first half, so be aware that if the early pages don't grab you the best is yet to come. This is a sit-back-relax-and-enjoy sort of volume, perhaps opening a window on what a typical (if there is such a thing) life of a professional mathematician is like... in some ways not much different from any other person's life... except, well, more numerate.

Friday, November 20, 2015

Math Potpourri

For your weekend reading/listening:

This Reddit thread mentions several math podcasts (several of which I include in my list on right-side of this page), and also pointed me to the Quanta Science podcast that I was unaware of:

A blurb from Mathbabe this week (linking in turn to THIS Nature article) on de-biasing science (...like THAT'LL ever happen ;-):

  In case you haven't read enough Bayesian vs. frequentist statistics pieces lately, here's another:

4)  A 97-year-old mathematician/space scientist awarded Presidential Medal of Freedom:

5)  A variety of upcoming "opportunities" with AMS (h/t to Katie Steckles for pointing it out):

6)  Ben Orlin's uncommon musings on Common Core:

7)  An (overdue) interview with Donald Knuth:

  Movie based on the life of Ramanujan now being shown... at least in Australia:

9)  The November "Carnival of Mathematics" was posted this week:

10)  Not new, but just learned of this site devoted to new books in mathematics:

11)  Futility Closet covers Gabriel's Horn... and more, today:

12)  A new, wonderful (30-min.) podcast with John Conway and Siobhan Roberts (via Ian Sample and The Guardian):

13 I'll end with a little miscellaneous science from the week:

a)  Physicist Sabine Hossenfelder defends scientific method (versus "self-optimization") here:

b)  Physicist Lisa Randall was Krista Tippett's guest on NPR's "On Being" last week:

c)  And lastly, a plug for Leonard Mlodinow's latest book, "The Upright Thinkers," a very good, accessible overview and history of science.

Speaking of books, I'll be perusing John Allen Paulos' latest, "A Numerate Life" on Sunday right here at MathTango.

Potpourri BONUS! (extra NON-mathematical links of interest):

1)  A fascinating segment from last week's TED Radio Hour on the linkage between speech, stuttering, and singing:

2)  Listening to Dave Isay talk about his StoryCorps Project never fails to put a smile on my face! Yesterday he was on Diane Rehm's show, explaining among other things, his upcoming project for the Thanksgiving holiday involving a downloaded app. If you missed it, and are having a Thanksgiving gathering, hope you find time to listen:


Friday, November 13, 2015

Friday Math Wrap-up

Math from the week...

Evelyn Lamb covered the topologist winner of the Breakthrough Prize award this week:

 ...and long, interesting Michael Harris post on the Breakthrough Prizes here:

  From fivethirtyeight blog a cautionary tale on scientific method:

3)  For M.C. Escher fans:

For those who like a little cosmology in their potpourri, this piece on Bayesian probability and the Anthropic Principle:

5)  A very simple introduction to statistical inference:

6)  ICYMI, Mathaloger explored various curves, cardiods, and more on YouTube this week:

7)  This one's a couple weeks' old, but I just learned of this wonderful Colm Mulcahy piece on another recreational math problem:

8)  The big news in complexity theory:

...and great write-up by Jeremy Kun:
9)  Math is so useless, it's useful... as Ben Orlin explains:

Not new, but I don't think I've linked to these math podcasts before:

11)  Hey!, I love Bob Ross's old painting show too (403 episodes), but I still think maybe this guy had a wee bit too much time on his hands ;-):

12) This month's puzzle from Quanta Magazine:

13)  H/T to John Golden for pointing out this interesting Dan Meyer post and series of comments (on "understanding" and "explaining" math):

14)  Lastly, in case some of you have never heard this one, Futility Closet crossed over into the math-humor business last week:

Potpourri BONUS! (extra NON-mathematical links of interest):

1)  A fascinating Nautilus read on first (or native) languages:

2)  This Oatmeal comic made quite a few rounds this week, as well it should... but in case you missed it:

Friday, November 6, 2015

That Was the Math Week That Was

So much math, so little time....

1)  Jordan Ellenberg with another of those viral-type math probability problems (which he relates back to the 'hot-hand' controversy):

And another problem, this time geometric, making some waves:

...and still some more monthly puzzles here:

3)  Evelyn Lamb gathered together a few of her scariest posts for Halloween last week:

4)  "Mathematics Rising" blog once again on some of Gregory Chaitin's and David Deutsch's work:

Peter Smith has put up a "gentle introduction" to category theory (160-pg. pdf):

6)  Most articles I read these days about MOOCs are about their lack of success... so, nice to read something more favorable for a change:

7)  There were plenty of tributes to George Boole this week, on the occasion of his 200th birthday, including Colm Mulcahy's:

8)  New 6-min. overview of Ramanujan's life on YouTube:

9)  Among his many entries for the week Mike Lawler covered a fun construction problem introduced by Patrick Honner:


Ben Orlin's commentary of the week:

11)  BBC Radio discussion (podcast) of P vs. NP (starts at ~2:00 mark):

...also related to P vs. NP, major rumored (and highly technical) news of the week reported by Scott Aaronson and Godel's Lost Letter :

12)  And because we can never read too much about Ramanujan:

13)  The ever-entertaining Matt Parker explains the British lottery (via YouTube):
A quick note that Martin Gardner's autobiography, "Undiluted Hocus Pocus," is newly-out in paperback this week.
And finally, if you missed any of the Math-Frolic links this week (Mon., Tues., Thur., and today!) you should check them out for some further reads.

Potpourri BONUS! (extra NON-mathematical links of interest):

1)  Cosmologist Martin Rees argues that if we make contact with advanced extraterrestrials they will likely be machine-like rather than organic:

2)  A fascinating bit on Steve Jobs and Wozniak, pre-Apple, as 'phone phreaks,' hacking the phone system (ohh those younguns!):

Friday, October 30, 2015

Spooky Potpourri

...well, not really, just another big, diverse mix this week:

1)  "Skewes Number" is reviewed by James Grime of Numberphile:

2)  Evelyn Lamb on the Fano plane, "the smallest interesting space":

3)  In a brief post, one sixth-grade teacher bemoans an experience I suspect many face as a result of the furor over Common Core:

4)  Speaking of Common Core, another piece (via Medium) here:

5)  Meanwhile, an elementary teacher utilizes McDonald's in the classroom:

6)  Specifically for chess fans, this interesting post from Jason Rosenhouse:

7)  Mathematics in neuroscience (neuro-geometry? ;-) ..."Clique topology" applied to neuronal activity:
and http://arxiv.org/abs/1502.06172

8)  A little history of Galois and group theory from plus Magazine:

9)  I'm sick, sick, sick of the topic... but, since others are not... a couple more pieces on "the hot hand" this week (psssst... it exists):

http://tinyurl.com/o6a8zmh  (J. Ellenberg)
http://tinyurl.com/ousspq8  (NY Times)

The latest (91st) "Math Teachers At Play" blog carnival posted here:

Another piece on Asian rote math learning vs. Australian non-rote approach:

The latest book from Jo Boaler, "Mathematical Mindsets," is newly available:

13)  Richard Elwes paid tribute to British mathematician Barry Cooper, who passed away this week:

14)  Another great tribute piece to Martin Gardner (who would've turned 101 this month) and some of his problems, from Colm Mulcahy:

15)  Gregory Chaitin on epistemology and metabiology:

16)  Algorithmic flexibility, universal computing, natural/artificial sciences:

17)  Lastly, some math comic-relief, from Paul Rudnick of the New Yorker:

Potpourri BONUS! (extra NON-mathematical links of interest):

1)  Latest podcast from the always quirky, unpredictable, entertaining Futility Closet (who you can support through Patreon):

2)  Michelle Feynman interviewed (podcast, ~20 mins.) about her new book, "The Quotable Feynman," on her famous father:

Friday, October 23, 2015

That Was the Week That Was... in Math

The math mix:

1)  Latest "Carnival of Math" blog here:

2)  A Carl Zimmer piece giving a nice little statistical history lesson:

3)  George Johnson's NY Times piece on the "hot-hand fallacy":
...and my own take at MathTango was here:

Samantha Oestreicher on the attraction of recreational mathematics (including mention of one my favorite books from the year, Jim Henle's "The Proof and the Pudding"):

The NY Times "Numberplay" puzzle this week highlights Ed Frenkel (and Gödel):

William Briggs peddles his somewhat interesting, somewhat oddball, prospective statistics book/text to any publishers interested:

Another Futility Closet geometry puzzler:

This David Mumford post that I already connected to through Math-Frolic is worth a re-mention, it's such a fun read (on math tribes):

One of many recent articles on the NSA's ability to "break" digital encryption due to the re-use of "a handful" of large prime numbers:

Recent episode from "Scam School"... put on your thinking caps:

11)   If you read Evelyn Lamb's "Roots of Unity" blog (as I hope most readers here do), an online (15 min.) research survey is interested in getting your responses:

12)  New from Siobhan Roberts, in Nautilus, on Neil Sloane and his remarkable OEIS:

Just one of Mike Lawler's several posts this week, that covers a lot of ground:

Lastly, from the bizarro dept., a man who got seizures working on Sudoku puzzles:

Potpourri BONUS! (extra NON-mathematical links of interest):

1)  As someone who never much cared for science fiction/fantasy (nor fiction in general) I enjoyed this piece reporting on a study showing children's preference for TRUE stories over fictional stories.  
The real world is so utterly fascinating unto itself (be it the evolution of flowers, the life cycle of praying mantises, the creation of stars/planets, the behavior of bonobos, and on and on and on) that I've never understood the preference for fiction and escapism! And maybe I'm not so alone in that predilection after all:

2)  A guest post over at Mathbabe this week I particularly enjoyed (because I agree "we have no fucking clue..."), on 'cargo cult' brain science:

Sunday, October 18, 2015

Hot Hand... You Betcha!

via Reisio/WikimediaCommons
"Gödel's Lost Letter" tackled the "hot-hand fallacy" recently:


 I have to confess to tiring a bit of this whole debate: there IS such a thing as being 'in the groove' or 'in the zone' or 'on your game' or 'HAVING A HOT HAND' (IMHO) and everyone who has ever played basketball or tennis or golf or bowling or any number of other sports KNOWS it (there are times we ought not downplay people's personal experience in favor of slapping dry stats and randomness onto situations that are exceedingly difficult to analyze, and where uncontrolled variables abound -- reminds me of what is routinely done in epidemiology... don't get me started).

A lot depends on simply how you define "hot hand" and what units of time are considered... i.e., does someone have a hot-hand for a game, or for a 13-min. stretch of a game. And in the case of the basketball "hot-hand" the stats often look at 2-4 shots in a row to predict the next shot, when larger samples, probably 5-10 shots minimum, need to be considered, because the variables are so-o-o many -- also, if you make 4-5 layups in a row it probably means nothing; but if you repeatedly put in shots from the far corner, the 3-point-range, and while being double-teamed (i.e, lower-percentage shots) that begins to mean something, yet I've never seen "shot-type" or shot-circumstances taken into consideration.

Any athlete will have experienced that rare feeling when their health/nutrition/sleep/physiology/physical prowess/movement/mood/psychology/whatever all seem to coalesce to yield an excellent performance, where they can be depended upon, more than other teammates, for crucial plays. Not every instance that looks like a "hot-hand" of course, to the outside observer, may be one, but I'm a believer ;-) that it does exist on occasion (and am old enough to recall Wilt Chamberlain's 100-point effort in 1962, including a phenomenal 28 out of 32 free throws! And a 'hot' Michael Jordan's winning shot for the 1982 NCAA championship, or Christian Laettner's 1992 championship shot, and on and on).
I s'pose next the statisticians will try to tell me that Reggie Jackson was NOT really ever "Mr. October" for the NY Yankees! ;-)  DON'T even go there!!

Sports performance is clearly in part a function of skill and experience (and psychology), which can vary from day-to-day (even moment-to-moment) for a given individual. A 'hot-hand-like fallacy' is more likely to hold sway in something like gambling where outcomes are more strictly governed by "chance," not skill, and a perceived "streak" may not be real (even in gambling though, it is possible that tiny, almost imperceptible clues, trends, properties, signals, are picked up by the experienced gambler at times that raise his/her performance on certain games).

Anyway, while I'm merely banking on common sense here (admittedly, a dangerous medium), there are statisticians who have also found technical flaws with the 'hot-hand fallacy' argument (see Gelman, for example, here), and therefore speak of the 'fallacy of the hot-hand fallacy' to which, of course, their detractors can respond with the fallacy of the fallacy of the hot-hand fallacy... but then, I find their arguments fallacious.

Now, excuse me while I go shoot some baskets, while I'm feeling kinda hot (...under the collar).


ADDENDUM ==> the above post was written a few days back and pre-scheduled for Sunday-posting. Lo-and-behold, just yesterday, science writer George Johnson had a piece in the NY Times on, of all things, the hot-hand fallacy!:


As indicated above I consider the "hot-hand fallacy" and "gambler's fallacy" two very different subjects and levels of complexity; referencing them together is mixing apples and oranges a bit (though I understand why both show up in such discussion).
Like most articles, this one fails to take into account the intrinsic oversimplifications of hot-hand analyses, and again treats the hot-hand as something spectators observe, rather than something an athlete 'feels' or experiences.
I wish this whole area would just move along now as not worthy of further exploration (...but am sure it won't).

Friday, October 16, 2015

Some Stuff From the Week In Math

The weekly mix:

1)  Quanta Magazine's latest monthly puzzle column:

2)  Mathemagic fun from Futility Closet:

3) ...and mathematicians via 3 Quarks Daily (h/t John Allen Paulos):

  A little tidbit on the art of translation from Brian Hayes:

5)  ICYMI, "The Importance of Recreational Math" from the NY Times:

6)  The Social Security number and identification:

Andrew Gelman, once more on p-values:

8)  Ben Orlin's little round-faced friends question the meaning of counting:

9)  "Denominator blindness"... I'd not heard the term before, but I like it... h/t to Cathy O'Neil for this Bloomberg article:

10)  Chaos, ecology, dynamic modeling:

11)  Some upcoming awards, math, and other links via Peter Woit:

12)  Reminders that there is always good stuff at Mike's Math Page:
....and later on Friday afternoon, Presh Talwalkar does his own linkfest of picks from the week:

[p.s., on Sunday here at MathTango, I'll rant about the "hot-hand fallacy."]

Potpourri BONUS! (extra NON-mathematical links of interest):

1)  I always enjoy reading John Brockman's anthologies of science essays centered around some single question. His latest, "What To Think About Machines That Think" is no exception, with close to 200 contributors (I think it's his longest volume in the series):

2)  With Halloween around the corner, perhaps a fine time to check in with Henri Le Chat:

Tuesday, October 13, 2015

Of Myths and Madness (...and Math)

In a wonderful post last weekend  Peter Rowlett talks about popular math myths and inaccuracies:

My favorite, of those cited, is the idea of Cantor being driven mad by the Continuum Hypothesis, which is followed up on by Richard Zach here:

While I'd certainly agree that the Continuum Hypothesis, by itself, didn't drive Cantor mad, it's easy to imagine his obsessive-grappling with the entire mind-blowing subject of infinity as an ingredient in the process.
Zach actually touches on the broader issue of whether contemplating deep logical paradoxes perhaps leads to mental breakdowns, with other examples besides Cantor. The matter sometimes seems reminiscent of the Bible's tale of the Tower of Babel, where God thwarts the tower-builders from entering his domain by bestowing them with different languages, frustrating communication.
So too several mathematicians who thought they were approaching the 'mind of God' with their exploration of deep logical quandaries, instead were thwarted and unable to complete the task at-hand. The human brain, both its capabilities and limits, is endlessly fascinating.

Such ideas even bleed over into the whole Platonist/non-Platonist debate in math. Is our brain simply creating as we go along, the mathematics that seems to work in our particular universe... or are we discovering the immutable essence of all there is (as Max Tegmark argues, is the universe composed entirely of nothing-but mathematics).  And if our brains are indeed approaching that latter Platonic realm, then is there ultimately a price paid for doing so? If we stare at the sun... we go blind. What happens when we contemplate the deepest, most profound reaches of mathematics (or are we merely manipulating tautologies in our brain)? Like the statement, "This sentence is false," does the recursion of mathematically-thinking about mathematics, at the highest levels, eventually result in an endless loop of no escape? Are language and logic, impediments (instead of facilitators), to endless breakthroughs?

[Worth noting that the vast majority of working mathematicians do NOT end up in asylums, nor under psychiatric care, even if some of the most interesting and famous genius-level mathematicians of the past do fall into that category.]

Anyway, go read the other diverse myths/legends Rowlett serves up for debunking.

Friday, October 9, 2015

Friday Potpourri Served Up

Again, plenty to choose from....

1)  David Brooks (no, not THAT David Brooks) continues his search for interesting sequence-generating integers:


2)  Chess fans, fabulous post from Jason Rosenhouse reviewing the new Bobby Fischer docu-drama ("Pawn Sacrifice"), and including other Fischer anecdotes, as well:

3)  Interesting post on password algorithms from DataGenetics:

4)  Max Tegmark expounds on his 'mathematical universe' for Aeon:

5)  Making pi, the Futility Closet way:

6)  Deborah Mayo re-blogs about 'evidence' and 'junk science':

7)  Alex Bellos writes about James Stewart of calculus fame (and riches):

Interesting "rich tasks" from Cavmaths:

9)  I was never one of those to say "I can't do math," but am not ashamed to say I've never heard of, nor comprehend, most of the proposals made here for future Polymath projects! :-(:

h/t to Evelyn Lamb for calling attention to this relatively new blog from a CUNY math grad student:

 ...and a second doff-of-the-cap to Dr. Lamb for this explication of calculus's fundamental (if not terribly popular) treatment of limits:

11)  Shinichi Mochizuki's "impenetrable proof" ('abc conjecture')... will it be resolved?:

12) Latest issue of Chalkdust Magazine with good stuff:

13)  Lastly, for visual delight (or confusion), a few days back Cliff Pickover tweeted out this older story about a janitor's awesome maze-drawing:

Potpourri BONUS! (extra NON-mathematical links of interest):

1)  As always, another wonderful edition of NPR's "RadioLab" last week, this time on conversing with animals, in 3 segments of which the second (18-min.) was probably my favorite (related to John Lilly's dolphin research):

2)  And sticking with NPR, this week's episode of "This American Life" included an old segment (17-min.), for those who are old enough to enjoy some nostalgia from The Ed Sullivan Show:

Friday, October 2, 2015

Math From the Week

Math here and there:

1)  RJ Lipton reviews "The Curious Incident of the Dog in the Night-Time" (the play, about an autistic math savant):

2)  Terry Tao's latest math-splash (Erdös proof) via Scientific American:

...and Erica Klarreich explains Tao's work for Quanta Magazine readers:

3)  Nice little review of the four-color theorem (h/t Egan Chernoff) :

4)  Robert Talbert writes about his evolution as a teacher, and how thinks about himself and his students.
(I suspect this is the sort of introspective analysis that all teachers can benefit from doing on occasion, and all will both share and differ from certain aspects of Robert's experience):

5)  Geometry from Futility Closet this week:

Deborah Mayo posting about a prior NY Times piece on use of statistics in research (Bayesian vs. frequentist):

...far worse, as Jason Rosenhouse points out, are statistics from the "pathological" party:

A classroom brainteaser from Sarah Hagan:

This, from the 'Blow Your Mind Dept.!': Solving Rubik's Cube... in 26 seconds... blindfolded (h/t Egan Chernoff):

Terry Tao teaches probability theory (h/t Lior Pachter):

10)  Brit Christian Lawson-Perfect visits the National Museum of Math in NY while on vacation, and gives a review:

11)  Marilyn Burns promotes Ken-Ken for the classroom:

12)  Odd connection between pi and Mandelbrot Set in latest Numberphile video:

13)  Patrick Honner tweets that he often thinks that "nothing in mathematics is more beautiful than Varignon's Theorem." If you don't recognize that name, check it out (especially for geometry fans):

14)  Okay, not strictly math, but have to note that "The Quotable Feynman" (edited by daughter Michelle Feynman) is now out in bookstores:
...as Sean Carroll blurbs, "All evidence indicates that Richard Feynman was the most quotable physicist of all time. This collection is a vivid demonstration of his wit, wisdom, and unquenchable passion for finding things out."

Potpourri BONUS! (extra NON-mathematical links of interest):

1)  I especially enjoyed Futility Closet's 'lateral thinking puzzle' this week... beginning at about the 22-minute point of their podcast:

2)  And perhaps my favorite cartoon from the week ;-):


Friday, September 25, 2015

Math, Math... and More Math

Bursting at the seams this week:

1)  John Pavlus tries to explain, very briefly, why P vs. NP is such a big deal:

2)  Another recreational math book to look forward to (but unfortunately not due out 'til January 2016, not in time for the holiday season):

3)  Keith Devlin has recommended the following site for some online math:
(I don't have any experience with it except that Dr. Devlin recommends it)

4)  Speaking of Keith, another Devlin podcast interview (38-min.), this time with Hemant Mehta:

5)  An interesting little problem, you may have missed, from DataGenetics this week:

6)  "Mathematics Rising" blog considers the thoughts of Vladimir Voevodsky, homotypy theory, and the future of mathematics:

7)  Tim Gowers wrote about Terry Tao's recent solution to the Erdős discrepancy problem:

....and "Gödel's Last Letter..." covers it well here:

8)  Venturing over to physics briefly, Peter Woit posts about Nima Arkani-Hamed and the future of physics:

9)  Guardian review of latest Alex Bellos effort, a coloring book not just for kids:

....and Aperiodical reviews it here:

10)  Using "Which one doesn't belong" in the classroom:
11)  Do you enjoy Ben Orlin's writing, drawing, perspectives?... then you'll enjoy hearing him in this 15-min. podcast:

12)  More math education discussion/debate in NY Times:

13)  The world of Web algorithms:

...and Marcus du Sautoy on the same subject:
14)  A link from Math-Frolic earlier in week that I think worth reiterating -- Lior Pachter's post on possible problems for Common Core:

Potpourri BONUS! (extra NON-mathematical links of interest):

1)  Don't know how many of you have already seen this video that went semi-viral a couple weeks back, of an (extinct) pterosaur flying over Idaho! -- I just saw it this week and thought it was fun (despite its flaws)... most are presuming it's CGI (or some think it's a kite), but I'd find it more interesting if it's a drone dressed up in pterosaur garb:
(if anyone has learned an official, definite explanation let us know; I've seen plenty of speculation)

2)  More monkeying with the copyright law:

==> per usual, please let me know of any broken/incorrect links ASAP

Sunday, September 20, 2015

Two More Books

Just mentioning a couple of volumes today for your consideration (both currently available in paperback, BTW)....

Won't have time to write a full review, but will recommend Alfred Posamentier's (with Bernd Thaller) latest book, Numbers: Their Tales, Types, and Treasures."  It's a typical Posamentier offering... clearly written and organized, without oversimplifying or dumbing-down the wide-ranging material; some interesting and fun things mixed in with historical and classic material.
I enjoyed the second half of the book, and especially the last few chapters, more than the first half with its focus on history (for whatever reason, math history, pre-1800 has never much held my interest). Again it is a great refresher for some adult math enthusiasts and an especially good read for the young person already inclined toward mathematics.
The final chapter of the book focuses on foundations and philosophy of mathematics, although near the end the authors seem to favorably quote Steven Weinberg's portrayal of philosophy as something that does not "provide... any useful guidance" to scientists. They even cite another philosopher as saying that philosophy is a "waste of time... from the point of view of the working mathematician." (Most of the book is definitely more mathematical than philosophical.)

Anyway, if you want to get a greater sense of the volume's overall content, here's a longer review from the Web:

    A book I'm currently perusing (haven't finished, but willing to recommend) is "Professor Povey's
Perplexing Problems" by Thomas Povey, who will be familiar to many from his "Perplexing Problems" website:

The book is a nice compendium of amusing problems with varying difficulty;  a little more challenging mix than often found in standard puzzlebooks. However, only about a quarter of the problems are strictly mathematical. The remainder are more physics-related (though often, of course, still requiring math), so for someone with little interest in physics this may not be a good book choice. Luckily, most math fans probably enjoy physics as well, and young, budding physicists should definitely enjoy.

In the last chapter Povey tells the story of Larry Walters who took flight from his backyard in 1995, in a lawnchair powered by helium balloons, just one of the typically entertaining segments of the book. You can read more about Larry here if you like:

You can even view news of Larry's oddball flight on YouTube here:

And here's a couple of lines that cracked me up for some reason, from chapter 2 of the volume:
"Over dinner once I was told what I believe is a true story about the principal of a Cambridge college taking out a calculator to multiply a number by 100.  In a rare moment of lucidity I quipped, 'was it a difficult number that was being multiplied?' Only the scientists got the joke."
Anyway, you get the idea, in-between the puzzles are some entertaining bits.
To finish out, I'll adapt one of the simpler math problems from the volume for inclusion here (I'm telling it less entertainingly than Povey's rendition):

Captain Fishmonger goes on a treasure-hunting voyage.  He arrives at the deserted island for which he has a treasure map showing just two trees and the instructions, "Walk 50 paces from one tree AND also 50 from the other. There lies the treasure."
But as Fishmonger peruses the island he finds that in the time since the treasure was buried and the map drawn, now 14 more trees have grown up. There are now 16 trees all less than 100 paces from one another.
In the WORST CASE scenario, what is the MAXIMUM number of spots the Captain will need to dig to find his treasure?
.answer below
. answer:  240  ...drawing 50-pace circles around any two tree-pairs gives you TWO possible digging (intersecting) points, and combinatorics can be used to calculate the total number of possible tree pairings (120).  2 x 120 = 240 as maximum number of digs required.