...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

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:
https://www.youtube.com/watch?v=Lihh_lMmcDw&feature=youtu.be

2)  Evelyn Lamb on the Fano plane, "the smallest interesting space":
http://blogs.scientificamerican.com/roots-of-unity/a-few-of-my-favorite-spaces-the-fano-plane/

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:
http://nathankraft.blogspot.com/2015/10/why-common-core-why.html

4)  Speaking of Common Core, another piece (via Medium) here:
https://medium.com/i-math/common-core-math-is-not-the-enemy-c05b68f46b3e#.45noae4t6

5)  Meanwhile, an elementary teacher utilizes McDonald's in the classroom:
http://exit10a.blogspot.com/2015/10/this-ones-for-robert.html

6)  Specifically for chess fans, this interesting post from Jason Rosenhouse:
http://scienceblogs.com/evolutionblog/2015/10/26/sunday-chess-problem-51/

7)  Mathematics in neuroscience (neuro-geometry? ;-) ..."Clique topology" applied to neuronal activity:
http://www.sciencedaily.com/releases/2015/10/151019183005.htm
and http://arxiv.org/abs/1502.06172

8)  A little history of Galois and group theory from plus Magazine:
https://plus.maths.org/content/stubborn-equations

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)

10) 
The latest (91st) "Math Teachers At Play" blog carnival posted here:
http://mathmamawrites.blogspot.com/2015/10/math-teachers-at-play-91.html

11) 
Another piece on Asian rote math learning vs. Australian non-rote approach:
https://theconversation.com/what-is-the-secret-to-being-good-at-maths-49222

12) 
The latest book from Jo Boaler, "Mathematical Mindsets," is newly available:
http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470894520.html

13)  Richard Elwes paid tribute to British mathematician Barry Cooper, who passed away this week:
http://richardelwes.co.uk/2015/10/28/barry-cooper-1943-2015/

14)  Another great tribute piece to Martin Gardner (who would've turned 101 this month) and some of his problems, from Colm Mulcahy:
http://blogs.scientificamerican.com/guest-blog/martin-gardner-at-101-it-s-as-not-so-easy-as-3-4-5/

15)  Gregory Chaitin on epistemology and metabiology:
http://inference-review.com/article/an-algorithmic-god

16)  Algorithmic flexibility, universal computing, natural/artificial sciences:
https://www.quantamagazine.org/20151027-the-physical-origin-of-universal-computing/

17)  Lastly, some math comic-relief, from Paul Rudnick of the New Yorker:
http://www.newyorker.com/magazine/2015/10/26/diagnostic-exam-do-you-have-math-anxiety


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):
http://www.futilitycloset.com/2015/10/25/podcast-episode-79-one-square-inch-of-the-yukon/

2)  Michelle Feynman interviewed (podcast, ~20 mins.) about her new book, "The Quotable Feynman," on her famous father:
http://ia601506.us.archive.org/26/items/groks705/groks102115.mp3


Friday, October 23, 2015

That Was the Week That Was... in Math


The math mix:

1)  Latest "Carnival of Math" blog here:
http://blog.ifem.co.uk/carnival-of-mathematics-127/

2)  A Carl Zimmer piece giving a nice little statistical history lesson:
http://nautil.us/issue/16/nothingness/why-we-cant-rule-out-bigfoot

3)  George Johnson's NY Times piece on the "hot-hand fallacy":
http://tinyurl.com/ndstbp8
...and my own take at MathTango was here:
http://mathtango.blogspot.com/2015/10/hot-hand-you-betcha.html

4) 
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"):
http://socialmathematics.net/2015/10/19/recreational-math/

5) 
The NY Times "Numberplay" puzzle this week highlights Ed Frenkel (and Gödel):
http://wordplay.blogs.nytimes.com/2015/10/19/frenkel-age-of-a-child/?_r=1

6) 
William Briggs peddles his somewhat interesting, somewhat oddball, prospective statistics book/text to any publishers interested:
http://wmbriggs.com/post/17112/

7) 
Another Futility Closet geometry puzzler:
http://www.futilitycloset.com/2015/10/22/whats-the-angle/

8) 
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):
http://www.dam.brown.edu/people/mumford/blog/2015/MathBeautyBrain.html

9) 
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:
http://bgr.com/2015/10/20/nsa-encryption-flaw-spy/

10) 
Recent episode from "Scam School"... put on your thinking caps:
https://www.youtube.com/watch?v=CY10Sm19rss

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:
http://lsu.qualtrics.com/jfe/form/SV_0dIyegEdCzOFNxr

12)  New from Siobhan Roberts, in Nautilus, on Neil Sloane and his remarkable OEIS:
http://nautil.us/issue/29/scaling/how-to-build-a-search-engine-for-mathematics

13) 
Just one of Mike Lawler's several posts this week, that covers a lot of ground:
https://mikesmathpage.wordpress.com/2015/10/21/a-really-intersting-twitter-conversation-sparked-by-kate-nowak/

14) 
Lastly, from the bizarro dept., a man who got seizures working on Sudoku puzzles:
http://time.com/4078049/seizure-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:
http://tinyurl.com/pucaxo4

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:
http://mathbabe.org/2015/10/20/guest-post-dirty-rant-about-the-human-brain-project/


Sunday, October 18, 2015

Hot Hand... You Betcha!


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

https://rjlipton.wordpress.com/2015/10/12/is-the-hot-hand-fallacy-a-fallacy/

 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!:

http://tinyurl.com/ndstbp8

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:
https://www.quantamagazine.org/20151008-symmetry-math-curves-puzzle/

2)  Mathemagic fun from Futility Closet:
www.futilitycloset.com/2015/10/11/remainders/

3) ...and mathematicians via 3 Quarks Daily (h/t John Allen Paulos):
http://tinyurl.com/p6upg6t

4)
  A little tidbit on the art of translation from Brian Hayes:
http://bit-player.org/2015/lost-in-translation

5)  ICYMI, "The Importance of Recreational Math" from the NY Times:
http://www.nytimes.com/2015/10/12/opinion/the-importance-of-recreational-math.html

6)  The Social Security number and identification:
http://fivethirtyeight.com/datalab/the-way-we-use-social-security-numbers-is-absurd/


7) 
Andrew Gelman, once more on p-values:
http://andrewgelman.com/2015/10/13/what-do-you-learn-from-p-05-this-example-from-carl-morris-will-blow-your-mind/

8)  Ben Orlin's little round-faced friends question the meaning of counting:
http://mathwithbaddrawings.com/2015/10/14/counting-to-five-is-harder-than-you-think/

9)  "Denominator blindness"... I'd not heard the term before, but I like it... h/t to Cathy O'Neil for this Bloomberg article:
http://www.bloombergview.com/articles/2015-10-14/don-t-be-blinded-by-big-scary-numbers

10)  Chaos, ecology, dynamic modeling:
https://www.quantamagazine.org/20151013-chaos-theory-and-ecology/

11)  Some upcoming awards, math, and other links via Peter Woit:
http://www.math.columbia.edu/~woit/wordpress/?p=8040

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

[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):
http://edge.org/annual-question/what-do-you-think-about-machines-that-think

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:
http://aperiodical.com/2015/10/mathematical-myths-legends-and-inaccuracies-some-examples/

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:
https://www.ucalgary.ca/rzach/blog/2009/09/logic-and-madness.html

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:
http://aperiodical.com/2015/10/guest-post-sequence-numbers/

http://sequencenumbers.blogspot.co.uk/

2)  Chess fans, fabulous post from Jason Rosenhouse reviewing the new Bobby Fischer docu-drama ("Pawn Sacrifice"), and including other Fischer anecdotes, as well:
http://scienceblogs.com/evolutionblog/2015/10/03/the-big-bobby-fischer-movie/

3)  Interesting post on password algorithms from DataGenetics:
http://datagenetics.com/blog/november22012/


4)  Max Tegmark expounds on his 'mathematical universe' for Aeon:
http://nautil.us/issue/29/scaling/life-is-a-braid-in-spacetime-rp

5)  Making pi, the Futility Closet way:
http://www.futilitycloset.com/2015/10/04/easy-pi/

6)  Deborah Mayo re-blogs about 'evidence' and 'junk science':
http://errorstatistics.com/2015/10/04/will-the-real-junk-science-please-stand-up/

7)  Alex Bellos writes about James Stewart of calculus fame (and riches):
http://tinyurl.com/obsp4ol

8) 
Interesting "rich tasks" from Cavmaths:
https://cavmaths.wordpress.com/2015/10/05/playing-with-jigsaws-is-the-way-forward/


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! :-(:
http://mathoverflow.net/questions/219638/proposals-for-polymath-projects

10) 
h/t to Evelyn Lamb for calling attention to this relatively new blog from a CUNY math grad student:
http://www.math3ma.com/


 ...and a second doff-of-the-cap to Dr. Lamb for this explication of calculus's fundamental (if not terribly popular) treatment of limits:
http://blogs.scientificamerican.com/roots-of-unity/the-subterfuge-of-epsilon-and-delta/


11)  Shinichi Mochizuki's "impenetrable proof" ('abc conjecture')... will it be resolved?:
http://www.nature.com/news/the-biggest-mystery-in-mathematics-shinichi-mochizuki-and-the-impenetrable-proof-1.18509

12) Latest issue of Chalkdust Magazine with good stuff:
http://chalkdustmagazine.com/

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:
http://tinyurl.com/ou3mmdf


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):
https://www.wnyc.org/radio/#/ondemand/535162


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:
http://www.thisamericanlife.org/radio-archives/episode/568/human-spectacle-2015?act=3#play


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):
https://rjlipton.wordpress.com/2015/09/28/a-curious-inversion/

2)  Terry Tao's latest math-splash (Erdös proof) via Scientific American:
http://www.scientificamerican.com/article/maths-whizz-solves-a-master-s-riddle/

...and Erica Klarreich explains Tao's work for Quanta Magazine readers:
https://www.quantamagazine.org/20151001-tao-erdos-discrepancy-problem/

3)  Nice little review of the four-color theorem (h/t Egan Chernoff) :
https://cosmosmagazine.com/mathematics/maths-problem-colouring-set

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):
http://rtalbert.org/blog/2015/four-behaviors/

5)  Geometry from Futility Closet this week:
http://www.futilitycloset.com/2015/09/29/a-new-angle/

6) 
Deborah Mayo posting about a prior NY Times piece on use of statistics in research (Bayesian vs. frequentist):
http://tinyurl.com/qbpv5gn

...far worse, as Jason Rosenhouse points out, are statistics from the "pathological" party:
http://scienceblogs.com/evolutionblog/2015/10/01/how-to-lie-with-statistics/

7) 
A classroom brainteaser from Sarah Hagan:
http://mathequalslove.blogspot.com/2015/09/make-it-even-brain-teaser.html

8) 
This, from the 'Blow Your Mind Dept.!': Solving Rubik's Cube... in 26 seconds... blindfolded (h/t Egan Chernoff):
http://tinyurl.com/q9sk8pl

9) 
Terry Tao teaches probability theory (h/t Lior Pachter):
https://terrytao.wordpress.com/2015/09/29/275a-notes-0-foundations-of-probability-theory/#more-8428

10)  Brit Christian Lawson-Perfect visits the National Museum of Math in NY while on vacation, and gives a review:
http://aperiodical.com/2015/10/what-i-did-on-my-summer-holidays/

11)  Marilyn Burns promotes Ken-Ken for the classroom:
http://marilynburnsmathblog.com/wordpress/can-you-kenken/ 

12)  Odd connection between pi and Mandelbrot Set in latest Numberphile video:
https://www.youtube.com/watch?v=d0vY0CKYhPY&feature=youtu.be

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):
https://en.wikipedia.org/wiki/Varignon's_theorem

14)  Okay, not strictly math, but have to note that "The Quotable Feynman" (edited by daughter Michelle Feynman) is now out in bookstores:
http://amzn.to/1QMYTMH
...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:
http://tinyurl.com/o77j4xc

2)  And perhaps my favorite cartoon from the week ;-):
http://bizarro.com/comics/october-1-2015/