Oliver Sacks... Story-teller

My inclination, upon hearing of Oliver Sacks' death, was to note it, but not attempt any further tribute, since so many will be penning better pieces than I can (plus, he doesn't fit that easily into a mathematics blog). But on reflection, as a small memorial, I've decided to re-run here at MathTango, the below entry that was originally posted at Math-Frolic over two years ago [...I've also now added G. Johnson's 2nd followup post-link to it].
[a couple of addendum links now added at bottom, as well]

---------------------------------------------
(from February, 2013):

If you are an Oliver Sacks fan you may well be familiar with the story of twin male autistic savants from his best-selling "The Man Who Mistook His Wife for a Hat" volume. Anyone captivated by prime numbers and savantism can't help but love the account, and George Johnson explores it in this blog post for Discover Magazine:

http://blogs.discovermagazine.com/fire-in-the-mind/?p=105#.USyQXhlHk1g

[...and then a week later Johnson did a follow-up post on the same subject:
http://blogs.discovermagazine.com/fire-in-the-mind/2013/03/04/idiot-savants-and-prime-numbers/#.VeNnys4sdo4 ]

Fascinating reads. There are further excerpts from the Sacks' chapter here:

http://empslocal.ex.ac.uk/people/staff/mrwatkin/isoc/twins.htm

The story tells of twin males who demonstrate great pleasure and joy in recognizing prime numbers… LARGE prime numbers, of the sort that normally only a computer might verify as prime in a short order of time, but that the twins appeared able to discern upon brief reflection. It is as if they had personal access to the so-called "Platonic" realm of numbers… the same might be said for other savant-like math knowledge or computational skills that are well-documented, but this is an even rarer facility.

There are dissenters who question Sacks' credibility or interpretation of this particular story which he only related about 20 years after its actual occurrence:

http://www.pepijnvanerp.nl/articles/oliver-sackss-twins-and-prime-numbers/

The above rebuttal also includes a YouTube video of the actual twins demonstrating their calendar-calculation skills (not their prime number skills).

Sacks' account is anecdotal and so the skepticism is understandable (by the time Sacks drew attention to the twins they had been separated and lost their special numerical skills)… but still... I admit… I want to believe it true ;-)

Here's a further followup to Sacks' story by another researcher:

http://goertzel.org/dynapsyc/yamaguchi.htm

And this research abstract indicates that the prime number recognition skill has indeed been reported for other savants:

http://www.ncbi.nlm.nih.gov/pubmed/8040161

Mind-blowing stuff!
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....It was a little over a year ago that Robin Williams tragically took his own life... perhaps this is not a bad time to remember both he and Dr. Sacks (who were friends) with this revised trailer to the movie "Awakenings":



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...and more:

ADDENDUM:  A reader sends me this interesting link from just a few days ago, coincidentally covering the same Sacks/savant story:
http://www.exploratorium.edu/blogs/tangents/prime-obsession
...and also this older blog post I didn't recall:
http://blog.computationalcomplexity.org/2009/09/possibly-recruits-for-polymath-primes.html

MathLinks Ahead...

...actually, several this week that are only tangential to math:

1)  More on Alex Bellos' new loop pool game:
http://www.bbc.com/news/magazine-34015430

2)  Madore mazes, hyperbolic surfaces, and Evelyn Lamb:
http://blogs.scientificamerican.com/roots-of-unity/an-epic-quest-on-an-8-812-holed-donut/

3)  A new "Math Teachers At Play" blog carnival is up here:
http://mrseteachesmath.blogspot.com/2015/08/math-teachers-at-play-89.html

4)  The math of chicken nugget numbers:
http://datagenetics.com/blog/august22015/index.html

5)  Last year's Brazilian Fields Medalist winner:
http://www.ozy.com/rising-stars/artur-vila-brazils-shining-math-star/61190

6)  The 5 latest "Mathgems" from Resourceaholic:
http://www.resourceaholic.com/2015/08/gems39.html

7)  Interesting piece on quantum cryptography:
http://www.pbs.org/newshour/updates/unbreakable-quantum-password/

8)  The phenomenal physics of friction and phone books:
https://theconversation.com/solved-the-mystery-of-why-its-impossible-to-pull-apart-interleaved-phone-books-46697

9)  Psychology, research, and replication, covered by:
FiveThirtyEight:
http://fivethirtyeight.com/datalab/psychology-is-starting-to-deal-with-its-replication-problem/

RetractionWatch:
http://retractionwatch.com/2015/08/27/yes-many-psychology-findings-may-be-too-good-to-be-true-now-what/

...and, The Atlantic:
http://tinyurl.com/ngdpf7e

10)  And pertaining to music, not math (but of course the two are intertwined): an interesting experiment in real-time "crowdsourcing" of a musical composition:
http://crowdsound.net/ 

11)  Among other things, Mike Lawler played with triangular numbers this week:
https://mikesmathpage.wordpress.com/2015/08/27/what-math-is-like-for-me-sometimes/

12)  A lot of talk these days about the importance of STEM jobs (including math-related ones) in the near future, but this "FiveThirtyEight" piece stresses the importance of interpersonal skills as well:
http://fivethirtyeight.com/features/the-best-jobs-now-require-you-to-be-a-people-person/


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

1)  I don't follow many Quora threads, but found some interesting, thoughtful ideas in this one on 'lessons that people learn too late in life':
http://www.quora.com/What-are-the-lessons-people-most-often-learn-too-late-in-life

2)  Science writer George Johnson muses about the "bubbles," science and otherwise, we live within, in the digital age:
http://tinyurl.com/qxc7u24

Math Bits From the Week

Potpourri... incoming:

1)  "Math Rising" blog looked at the topic of consciousness in non-humans this week:
http://mathrising.com/?p=1313

2)  If you're interested in programming you'll probably want to read this piece from American Scientist about 'probabilistic programming language':
http://www.americanscientist.org/issues/pub/2015/5/programs-and-probability/99999

3)  Bill Gasarch tries to bring us up-to-date a bit on P vs. NP:
http://blog.computationalcomplexity.org/2015/08/have-we-made-progress-on-p-vs-np.html

4)  A GREAT, long piece on surreal numbers and more, passed along (tweeted out) this week by Jordan Ellenberg:
https://mathenchant.wordpress.com/2015/08/12/the-life-of-games/

...and, though I don't usually re-mention posts here that I've already linked to during the week, I'll make an exception for Scott Aaronson's long, mind-stretching post on "common knowledge":
http://www.scottaaronson.com/blog/?p=2410

5)  NY Times piece on skepticism around health studies:
http://tinyurl.com/osaxa8y

6)  Presh Talwalkar uses a joke police poster to lead into a discussion of game theory:
http://tinyurl.com/nwnhqwo

7)  Quantum computing... hard to fathom:
http://ideas.ted.com/the-jaw-dropping-promise-and-brain-twisting-challenge-of-quantum-computing/

8)  As if there haven't already been enough popular math books out this year, mathemagician Arthur Benjamin has a new one due in a couple of weeks:
http://basicbooks.tumblr.com/post/126918423579/qa-with-arthur-benjamin-mathemagician-and

9)  I don't think it's even possible for Ben Orlin to not be entertaining... and instructive... at the same time:
http://mathwithbaddrawings.com/2015/08/19/the-smartest-dumb-error-in-the-great-state-of-colorado/

10)  Algorithms are saying a lot about us... and lo-and-behold they ain't always accurate (nor accountable):
http://aeon.co/magazine/technology/judge-jury-and-executioner-the-unaccountable-algorithm/

11)  Related to the above, Kaiser Fung with a bit about management practices and big data:
http://junkcharts.typepad.com/numbersruleyourworld/2015/08/dumbing-by-numbers.html 

12)  I hope you already saw my review from last weekend of Gary Smith's take on statistical shenanigans, "Standard Deviations":
http://mathtango.blogspot.com/2015/08/still-legal-torturing-data.html

13)  Speaking of which... I've been saying for 40+ years that good science is extremely difficult to do, and finally others are making the same point:
http://fivethirtyeight.com/features/science-isnt-broken/

14)  Allen Downey tells us about something called "the inspection paradox":
http://allendowney.blogspot.co.uk/2015/08/the-inspection-paradox-is-everywhere.html

15)  And when he's not following Ultimate Frisbee games, Mike Lawler occasionally has math blog posts here:
https://mikesmathpage.wordpress.com/


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

1)  If you're an animal lover you won't want to miss Krista Tippett's interview last week with Katy Payne on her work with elephants and whales:
http://www.onbeing.org/program/katy-payne-in-the-presence-of-elephants-and-whales/241

2)  This is several months old, but if you've never heard Dave Isay's TEDTalk (23 min.) about his StoryCorps Project, well, you should make time for it:
https://www.ted.com/talks/dave_isay_everyone_around_you_has_a_story_the_world_needs_to_hear

Still Legal... Torturing Data

Review of "Standard Deviations" by Gary Smith

"Lying with statistics is a time-honored con. In Standard Deviations, economics professor Gary Smith walks us through the various tricks and traps people use to back up their own crackpot theories. Today, data is so plentiful that researchers spend precious little time distinguishing between goo, meaningful indicators, and total nonsense. Not only do others use data to fool us, we fool ourselves."
-- from the back cover of the book

This is one fun read! And a volume that hasn't received enough attention. It's 300 pages of easy-to-follow, enlightening, illustrative (and non-technical) material, that is actually very important, as a veritable romp through the mined landscape of troublesome statistics, be they from mass media, academia, or from scientists themselves!

Gary Smith's book came out in 2014 at a time when I felt overdosed on popular statistics treatments, so I didn't give it much attention. It's now out in paperback and had I read it earlier it would've been on my "best books" list of 2014. It adds to the growing arsenal of work critiquing our statistical naivete. The phrase "lies, damned lies, and statistics," coined well over a century ago, has never been truer than today.

Smith himself is an economist, but he draws examples for this statistics salad from every nook-and-cranny of life; sports, Wall Street and finance, gambling/lotteries, advertising, medicine, research, ESP, etc. The book offers example after example after example of statistical tomfoolery, shenanigans, trickiness, and plain honest mistakes. If you've read much in this genre, many of Smith's examples will be familiar, even time-worn, but still his firehose spray of cases is well organized, impressive, fun, AND educational.

Various important themes run through the book:

1)  One major theme is how humans are pre-wired to look for and find patterns in their observations... and how easily that can lead them astray. As he writes at one point, "data clusters are everywhere, even in random data." Patterns need to be mitigated by common sense... if a pattern just doesn't make sense, then don't believe it, but look for other confounding variables, or sheer coincidence. The use of 'common sense' and reason in tandem with data, permeates these pages. A theory without good data to back it up isn't worth much, but so too, provocative data without a good theory to explain it is dubious -- data and theory ought go together like hand and glove.

2)  Graphs and visual displays are often a source of bias or distortion -- always check the labeling and scaling/spacing of axes or other depictions. Don't assume that data are collected, analyzed, or reported accurately.

3)  It's not always the data as presented that is a problem... it can also be the data that ISN'T presented -- either it was never collected, or it was collected, but for reasons not spelled out, then deleted from presentation. And what is missing may be more important than what is shown.

4)  "Regression to the mean" is the subject of another whole chapter, emphasizing that extreme or outlying data, performances, or events, often tend to revert to closer-to-the-mean values over time.

Of course sometimes a research study may actually be good, but the popular press reporting of it is flawed or oversimplified -- details and nuances being stripped away for the sake of time or space.

One reviewer faults Smith for being "relentlessly negative." That may be an overstatement, but even if true, I view it as a positive!... the book essentially says, 'Look here, and here, and over there, and at this here; at all these examples of the misuse of data leading us astray.' And THIS is a message we need to hear MORE, not less of, in today's data-saturated lives!

One thing I like about the book is that Smith doesn't mince his words. While he has positive things to say about such heavyweights as Daniel Kahneman and Dan Ariely, he doesn't hesitate to criticize other popular writers, including the authors of "Freakonomics," or a sociologist named David Phillips, or "The Motley Fool" writers, when they have erred. Some may find him too dismissive in a few instances where the issues aren't altogether settled, but I like his blunt, critical approach.
He also disparages some of the common arguments for the famous 'man with two children' probability paradox, which has a number of variations, and has been extensively debated (Smith gives the answer as 1/2 probability, not 1/3, as many do).

Each chapter ends with a short paragraph summary of the main points, and the final chapter of the book also summarizes the essence of each previous chapter. In short, and without being too redundant, Smith drives home the essential ideas he wants you to come away with from the plethora of examples provided.
Bottom-line, it isn't just difficult, but virtually impossible, to take into account all the 'confounding' factors that may affect a scientific study and its reportage, so a watchful, skeptical eye is in order.

One of my beefs with self-described 'skeptics' is how much time they spend on what I call 'low-hanging fruit'... astrology, ESP, UFOs, homeopathy, etc. while giving a light touch to articles in scientific journals that are weak, poorly-done, poorly reported, or even fraudulent. Excellent science is hard to do, but we ought at least be holding out for "good" science.  I HOPE a book like Smith's helps inculcate a greater wariness of assumed reputable scientific evidence. The "evidence" of "evidence-based science" (perhaps better-called 'publish-or-perish-science'!) is often incomplete or skewed, and considerably more subjective, biased, or based on ill assumptions, than acknowledged; it is rarely incontrovertible, and yet all-too-often escapes keen examination (especially via a broken peer-review process).
Professor John Ioannidis is famous for concluding that 'most research findings are false'. I'm more comfortable simply saying that most research findings are oversimplified, potentially-misleading, and ill-contrived, yet too-easily lapped-up by both uncritical skeptics and the public. The main defense against this state-of-affairs is an educated, on-guard citizenry (and more open-source peer review)... and Smith's book is a diligent effort toward that goal.
In the end, this isn't only a fun book; it's actually a highly important treatise!

Math of the Week

ICYM any of these:

1)  Dan Rockmore explains the Turing test on NPR:
http://tinyurl.com/p5c9vla

2)  The latest 'Math Gems' post from Resourceaholic:
http://www.resourceaholic.com/2015/08/gems36.html

3)  Yet one more summation of Twitter Math Camp I'll pass along, for those interested:
https://johnberray.wordpress.com/2015/08/08/tmc15/

4)  And as long as we're talking conferences, a couple of summaries of the recent Bridges Math Art conference:
http://blog.andreahawksley.com/bridges-math-art-2015/

http://www.ams.org/meetings/bridges-2015-conf

5)  ICYMI, this piece about David Wees and math-learning made the rounds:
http://ww2.kqed.org/mindshift/2015/08/04/seeing-struggling-math-learners-as-sense-makers-not-mistake-makers/

6)  Some simple geometric beauty from Futility Closet:
http://www.futilitycloset.com/2015/08/11/the-finsler-hadwiger-theorem/

7)  I blogged over a week ago about the newest pentagon found to tile a plane, and now Alex Bellos has covered it for The Guardian:
http://tinyurl.com/qjchkf4

...and plusMaths.org covers it here:
https://plus.maths.org/content/five-fits

8)  Meanwhile, Peter Cameron quickly reviews Bellos' "Alex Through the Looking Glass" (American version, "The Grapes of Math"):
https://cameroncounts.wordpress.com/2015/08/12/alex-through-the-looking-glass/

9)  More puzzle fun from the New York Times (thinking/outwitting others who are trying to think/outwit you):
http://tinyurl.com/nwo7sp6

...and John Allen Paulos' take on this sort of game:
http://abcnews.go.com/Technology/WhosCounting/story?id=97632

10)  I see Alfred Posamentier is out with yet another book (he must write them in his sleep!):
http://amzn.to/1J71RKK

11)  A few weeks back, Presh Talwalkar of "Mind Your Decisions" blog, began doing his own "This week in math" Friday wrap-ups, and you may wish to get in a habit of checking those posts out as well, if you're not already:
http://mindyourdecisions.com/blog/

12)  And for teachers, Crystal Kirch does a weekly linkfest as well:
http://flippingwithkirch.blogspot.com/2015/08/the-best-articles-resources-ive-found_9.html

13)  Finally, if the above isn't enough for ya, there be more links at the latest "Carnival of Math":
http://datagenetics.com/blog/august12015/index.html

p.s. -- I may(?) have a review of Gary Smith's "Standard Deviations" up here on Sunday or Monday morning; a book I loved and highly recommend.


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

1)  Just a mystery I found fascinating from NPR this week about the recent, sudden disappearance of 1000's of birds from a Florida nesting site (what could've happened?):
http://www.npr.org/2015/08/12/431807471/florida-gulf-coast-mystery-what-did-the-birds-on-seahorse-key-vanish

2)  And for your week's entertainment, I'll bet this post from "Flowing Data" blog got plenty of hits (I need more post titles like this at my blog):
http://flowingdata.com/2015/08/13/fitbit-during-sex/

...but the real fun comes with the comments to the original imgur posting:
http://imgur.com/gallery/GfRpoZb

More Math, Math, Math... & politics

End-of-week linkfest:

1)  Will start the weekly wrap-up off with a fun post (pigeon-pooping is fun, right?):
http://www.hopesandfears.com/hopes/now/math/215059-pigeon-poop-probability-nyc

2)  Keith Devlin on the increasing role of games in education (and a new book about it from Greg Toppo):
http://devlinsangle.blogspot.com/2015/08/hard-fun-video-games-creep-into-math.html

3)  Evelyn Lamb explores infinite earrings, and more:
http://blogs.scientificamerican.com/roots-of-unity/a-few-of-my-favorite-spaces-the-infinite-earring/

4)  A fun game from David Radcliffe ("Bojagi")
http://www.forbes.com/sites/kevinknudson/2015/08/02/a-simple-multiplication-game/

5)  Gary Smith's, "Standard Deviations," another popular treatment of statistics in the day-to-day world, is newly-out in paperback (good read):
http://amzn.to/1IdJ4vF

6)  James Tanton interviewed on teaching success:
http://scottbaldridge.net/2015/08/03/the-secrets-of-my-teaching-success-james-tanton/

7)  Another followup (out of a great many) to Twitter Math Camp:
http://mathcoachblog.com/2015/08/03/twitter-math-camp-a-scalable-model-for-pd/

8)  In a couple of postings, Steven Strogatz tells of his positive entry into the world of inquiry-based learning (h/t Egan Chernoff):
https://www.artofmathematics.org/blogs/cvonrenesse/steven-strogatz-reflection-part-1
https://www.artofmathematics.org/blogs/cvonrenesse/steven-strogatz-reflection-part-2

9)  Another fabulous post from Ben Orlin this week:
http://mathwithbaddrawings.com/2015/08/05/an-open-letter-to-benedict-carey/

10)  A half-hour of Marcus du Sautoy on "Flexagon Radio":
http://www.bbc.co.uk/programmes/b0640my1

11)  Interesting report on the Tor network and anonymity:
https://plus.maths.org/content/staying-anonymous

12)  Stretching on over to physics and some more fine reportage from Quanta Magazine (and Natalie Wolchover):
https://www.quantamagazine.org/20150803-physics-theories-map/

13)  So many links above already that I won't even bother to mention there's more mathiness over here ;-):
https://mikesmathpage.wordpress.com/

------------------------------------------------------
Potpourri BONUS!:

No bonus links this week, but punditry is too much fun, not to take part, so my take (easily skippable) on the Repub. debate last night, and what it holds for future:

1. Huckabee -- gained from the debate, final jibe at Hillary Clinton perhaps best moment for any GOP candidate; Huckabee cuts across a couple of elements of the Republican base; could end up winning the whole shebang by being everyone's 2nd or 3rd choice

2.  Kasich -- gained... but essentially had nowhere to go except up from previous standing... can he continue the 'momentum'? Likely, the most reasonable voice out there... but how many reasonable folks vote in Republican primaries???

3. Christie -- gained, but again mainly from starting off low; his style and temperament (while playing well in NJ) won't carry him through the primary process, and a lot of activists still mad at him

4. Trump -- lost a little ground, but still gave fans what they like... can carry this act on for awhile because there are enough sick-of-Washington, sick-of-politics-as-usual troglodytes in GOP to push him forward before eventually fading, to the relief of GOP establishment
(would he run as independent? probably only if mistreated enough that he wants to give GOP the finger)

5. Paul -- failed to gain or broaden his appeal, but held ground with the limited libertarian Republican wing; could emerge as a 'compromise' nominee only if more traditional Republicans eat all their own (...it could happen)

6. Rubio -- baby-faced, not-ready-for-prime-time (though prepping himself for 2020 or '24); eventually has to split the Florida vote with Jeb Bush (IF Bush is still in race by FL. primary!); don't see any clear road to the nomination, given the primary order and the competition, but most pundits seem to think he served himself well last night (I don't get it; seemed out-of-his-league)

7. Cruz -- didn't gain or do as well as I'd expected (he's a former award-winning Princeton debater), but ought do well enough through Super Tuesday 2016 (likely winning Texas) to stay in race for good while; somewhat dependent on Tea Party success, and moderate Repubs attacking each other

8. Walker -- slimy as always, with a thin message, but with a loyal, activist base; and Trump supporters may eventually turn to him when they leave the Donald; comes from same state that gave us Joe McCarthy ;-)

9. Bush -- floundering; even Republicans are weary (and leery) of the "Bush" name; and Jeb is either rusty at campaigning or just never had the skills needed to play beyond the anomalous state of Florida; weak enough that the money and machine-politicans backing him will dry up soon

10. Carson -- still no clue why he's running, or is a Republican; Fiorina likely to take his slot in another 10-person debate

This group almost makes one appreciate the days of Romney and McCain... ;-) (...I said 'almost').
And I honestly wonder if the eventual nominee will be ANY of the above (and how many ballots it will take)!?

Friday's Big Grab Bag

LOTSA links to ponder!:

1)  Fun Evelyn Lamb post that predicts your personality:
http://blogs.scientificamerican.com/roots-of-unity/kisrhombile-tiling-rorschach-test/
(next week, watch for her new horoscope column for Scientific American.... kidding!)

2)  A new "Math Teachers At Play" blog carnival here:
http://blog.ifem.co.uk/maths-teachers-at-play-88/

3)  Just a few of the many wrap-ups from last week's successful Twitter Math Camp in southern California:

http://samjshah.com/2015/07/27/my-thoughts-about-the-evolution-of-the-mtbos-2015-edition/
http://www.teachesmath.com/?p=795
https://www.youtube.com/watch?v=PlHf06upPDo

(p.s. -- from what I've read, Fawn Nguyen has earned a lifetime appointment as Keynote-Speaker-To-The-World-Of-Math-Teachers! -- I hear-tell that her address was Fun, Useful, Charismatic, and Knowledgeable -- uhh, just telling what I've been hearing folks...)

4)  Close enough to math to get a mention here... Peter Woit's positive review of physicist Frank Wilczek's new book, "A Beautiful Question":
http://www.math.columbia.edu/~woit/wordpress/?p=7881

5)  And a new Alex Bellos book is on the way in September:
http://www.amazon.co.uk/Snowflake-Seashell-Star-Adventures-Numberland/dp/1782117881

6)  Applying infinity to spiral optics:
http://skullsinthestars.com/2015/07/24/infinite-hotels-in-swirling-beams-of-light/

7)  From "Gödel's Lost Letter..." a (longish) bit on Raymond Smullyan, and chess-playing (human and otherwise):
https://rjlipton.wordpress.com/2015/07/28/playing-chess-with-the-devil/

8)  If you like mixing in some biology with your math/statistics, then some interesting commentary from Gelman here:
http://ow.ly/Qbnbj
(it all relates back to a highly-discussed 2-month-old Lior Pachter post HERE.)

9)  The latest Journal of Humanistic Mathematics edition is available online:
http://scholarship.claremont.edu/jhm/

10)  Ben Orlin explores infinite series some more:
http://mathwithbaddrawings.com/2015/07/29/where-the-laws-no-longer-hold/

11)  A puzzle via Terry Tao:
http://wordplay.blogs.nytimes.com/2015/07/27/tao/?_r=1

12)  And a somewhat classic Futility Closet problem:
http://www.futilitycloset.com/2015/07/29/knife-act/

13)  Not for beginners, but some Category Theory expounded here:
https://golem.ph.utexas.edu/category/2015/07/internal_languages_of_higher_c.html

14)  Richard Green with some observations on the Ulam Sequence:
https://plus.google.com/101584889282878921052/posts/KthXFvoHbyX

15)  Quanta Magazine with a probability conundrum for its latest splendid monthly puzzle:
https://www.quantamagazine.org/20150730-the-slippery-eel-of-probability/


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

1)  Half-hour interview with E.O. Wilson on Jim Al-Khalili's "The Life Scientific" podcast series:
http://www.bbc.co.uk/programmes/b0639kzv

Lastly, just to show how little times have changed, this 1950's quote from Adlai Stevenson:

"I will make a bargain with the Republicans. If they will stop telling lies about Democrats, we will stop telling the truth about them." ;-)

Another Friday Potpourri

ICYM any of these:

1)  The latest (124th) "Carnival of Mathematics":
http://gonitsora.com/carnival-of-mathematics-124/

2)  Rewriting (shortening) the proof of the classification of finite groups:
https://plus.maths.org/content/rewriting-enormous-theorem

3)  This NPR report from the World Rubik's Cube Championship:
http://www.npr.org/2015/07/20/424465069/for-the-rubiks-cube-world-champ-six-seconds-is-plenty-of-time

....and this fascinating, fun video on the world record:


4)  CONGRATS! For the first time in 21 years, the USA team won the International Mathematics Olympiad:
http://www.npr.org/2015/07/18/424122249/theyre-no-1-u-s-wins-math-olympiad-for-first-time-in-21-years
http://tinyurl.com/qfapvpt
...and The Atlantic magazine followed up here:
http://www.theatlantic.com/education/archive/2015/07/no-parade-for-us-math-olympians/399191/


5)  Gelman/Mayo on guess what... statistics (and a Government agency):
http://tinyurl.com/o4252gc

6)  Cathy O'Neil reports on an interesting tidbit about the Ulam Spiral and the number 17:
http://mathbabe.org/2015/07/22/the-17-armed-spiral-within-a-spiral/#comment-87548

7)  Using symmetry in math teaching:
http://ww2.kqed.org/mindshift/2015/07/21/how-teaching-with-symmetry-improves-math-understanding/

8)  Scott Aaronson on a 5-min. British podcast of "The Naked Scientists" talking about P vs. NP, with other sundry topics:
http://www.thenakedscientists.com/HTML/interviews/interview/1001376/

9)  Natalie Wolchover on Navier-Stokes equations in Quanta:
https://www.quantamagazine.org/20150721-famous-fluid-equations-are-incomplete/

10)  Nice little puzzle collection from Richard Wiseman here:
https://richardwiseman.wordpress.com/101-friday-puzzles/ 

11)  Interesting take on "statisticians" and "Big Data" (h/t Gary Davis):
http://blog.hackerrank.com/the-risky-eclipse-of-statisticians/ 

12)  Cathy O'Neil shares a recent 1-hr. David Kung talk on diversification in mathematics:
http://mathbabe.org/2015/07/24/gender-and-racial-achievement-gaps-in-math/

13)  ICYMI, my review of the delightful John Conway biography, "Genius At Play," earlier in the week:
http://mathtango.blogspot.com/2015/07/author-at-play-siobhan-roberts-reports.html

Lastly, just a cyber high-five to all the math-devotees attending (not me) "Twitter Math Camp" which is taking place now through the weekend on my old stomping grounds of the Claremont Colleges. Hooray! -- hope you're all able to get at least one shower in during the proceedings ;-) (...drought restrictions).


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

1)  NPR's RadioLab has done many touching stories over the years. And they did one last week:
http://www.radiolab.org/story/grays-donation/

2)  There actually is a bit of math involved in this surprising story about the latest victory of possibly the world's greatest Scrabble player:
http://www.theguardian.com/lifeandstyle/2015/jul/21/new-french-scrabble-champion-nigel-richards-doesnt-speak-french

Author-At-Play... Siobhan Roberts Reports on Life with John Conway

REVIEW:  Genius At Play: The Curious Mind of John Horton Conway

"Above all he loves knowledge, and he seeks to know everything about the universe... For his own part, he calls himself a professional nonunderstander. The pursuit is what counts, and chasing after Conway's promiscuous curiosity and probing his ebullient intellect is this book's modus operandi."
(...from the Prologue to the book)


I can't imagine spending 6+ years of my life, off-and-on, following another individual around, taping and interviewing them, plowing them with questions. But luckily for us, Siobhan Roberts could.

Her book "Genius At Play" is an astounding accomplishment (a total 8 years in-the-making), rich in its portrayal of a man's life, and his mathematics. John Horton Conway is routinely described with adjectives like, "brilliant," "versatile," "creative," "charismatic," "genius," but also, "zany," "eccentric," "juvenile," and even "confused." Or perhaps best characterized at one point as, “Archimedes, Mick Jagger, Salvador Dali and Richard Feynman all rolled into one" -- how could such a biography not be fabulous! Atticus Finch, eat your heart out!

Mathematicians, more than most (I believe), see the entire Universe as a playground, and few typify this more than Conway, who has admitted at times, to never working a day in his life (because he's an eternal child, just having fun).  I think I once saw Conway referred to as "a mathematician's mathematician"...I'm not even certain exactly what that means, but Conway is definitely the sort of character that mathematics needs as an 'ambassador' for a subject so often viewed by the public as dry and sterile. In these pages one man's love and enthusiasm for numbers is made palpable, if not infectious. At 77-years-young, Conway has been contributing to mathematics well-passed the 40-or-so-year-old cutoff that some declare for productive mathematicians. By the way, the "acknowledgements" section at the end of this book reads like a Who's Who of interesting, fun, modern mathematicians/thinkers.

 The volume looks dense and imposing (400+ pages), but is chock-full of marvelous stories, anecdotes, vignettes... I couldn't pick out 2 or 3 favorites, without wanting to mention 10 or 15 others just as entertaining, so I'll let you read the book and latch on to your own top tales.  Also, a surprising amount of the volume is in Conway's own words; frequent and sometimes lengthy passages from the man himself, that really lend the flavor of the character that he is. Roberts' own writing is splendid, but I did especially enjoy these monologues, imagining Conway settled in a big ol' lounge chair, staring at the ceiling, explaining deep thoughts to the uninitiated, in his gruff voice.
At times in the narrative, one wonders if Conway is more showman and performance-artist than the frumpy, messy, absent-minded professor he portrays himself as... but it never takes long to be re-convinced that the latter is indeed the true Conway.

The book touches upon (as it must) a remarkable array of math topics that would be hard to come by in a bio about any other living mathematician. But Conway has been active and productive in number theory, group theory, game theory, recreational mathematics, sequences, topology, lattices, combinatorics, symmetry, infinity, and perhaps most notably, "surreal numbers" that Conway invented (...worth noting it was Donald Knuth who really made "Surreal Numbers" famous in a novel of the same title). "The Game of Life," that Conway is best known for, gets its due here, but not an inordinate amount, as it is a topic Conway himself is largely sick of. Indeed Conway invented a great many games (almost ceaselessly) throughout his life (Hackenbush, Dots and Boxes, Phutball, Sprouts, and a programming language "Fractran," to name a few...).

Beyond games, Conway ranged all over the place: tiling, "partizan" theory, knots, groups, sphere-packing, symmetry, lexicographic codes, mental calendar calculation, the "Thrackle" problem, even a "Free Will Theorem," almost always for fun, with little concern about application. And bits of it all shine here. His most well-known book, by the way, was "On Numbers and Games."

Roberts has a lovely way of explaining the deep ideas she was faced with, hanging out with Conway. When I interviewed her at MathTango and specifically asked her how it was to hear and try to comprehend such weighty, abstract notions, she responded:

"I ask a lot of (ostensibly stupid) questions. And many of the questions I ask many, many, many times. I circle around things until I’ve got a semi-coherent intuitive understanding. At least that is how it feels to me. Then I go back and fact-check, and correct all the nuances that I inevitably got wrong."

And I could really sense that 'circling around' throughout this book.
The only small weakness I find in the volume is that Roberts may not have adequately explained the importance of "symmetry" or the "Monster" group (and its connection to "modular functions") for lay readers -- the "Monster" group is hard enough for even mathematicians to comprehend! -- and it does get plenty of mention in these pages, as Conway himself admits he wishes he could understand it before he dies.




I especially enjoyed the fleshing out of some of Conway's connections to other sharp thinkers. His relationship with Martin Gardner is well-known, but I learned in the book more about his connection, such as it was, to Stephen Wolfram, whose tome, "A New Kind of Science" is largely an AI focus on Conway-esque "cellular automata."  More interesting, was his relationship with Douglas Hofstadter, who wanted to glean more from Conway about their overlapping cognitive interests (...but didn't). And there was also Conway's connection to the yearly "Gathering For Gardner" get-togethers with a host of top-notch mathematicians/magicians/recreationalists (in honor of Martin Gardner). And Conway's love for the ladies (almost as great as his love for numbers) gets covered a bit as well.

The book, especially the second half, is also peppered with a surprising number of guffaw-inducing moments, sometimes about Conway, but often just from his own droll commentary.

For lay readers unfamiliar with Conway, I'd recommend viewing some of the Numberphile videos featuring him, to gain a sense of what you're dealing with here, before reading the book. And just to make my high school English teachers cringe, I'll say that though we're all unique human beings, Conway is uniquer! ;-))

Toward the end of this volume, fuzzy associations between John Conway and Georg Cantor drifted into my thoughts: both with single syllable first names followed by 6-letter, 2-syllable last names beginning with "C;" both quite enamored of infinity. Cantor though was driven insane by the same obsessive pursuit of numbers that innervates Conway; and Cantor was often rebuked by his peers, while Conway is fully-appreciated in his own time.
Occasionally, reading about the likes of a Conway or Cantor, or Erdös or others, and their driving passion for numbers, such geniuses seem transcendent, attaining salivating peeks of a realm inaccessible to the rest of us. A famous phrase invoked following the Space Shuttle Challenger tragedy referenced 'slipping the surly bonds of Earth to touch the face of God' -- and sometimes, in this book, I almost fancied Conway doing just that, merely through the power of thought!

One of the few downer notes in the volume is the telling of Conway's suicide attempt in the 1990s; a reminder of how ubiquitous and stealthy clinical depression is. Another sad note is Martin Gardner passing away shortly before Siobhan and Conway were to pay him a visit. Overall though, the book gets better and better (and more joyous) as it rolls along. I especially liked the final two chapters: Chapter 16, recounting Conway at a MathCamp for youngsters in 2003 (when "he was 65 going on 16"). And Chapter 17 covering Conway's "Free Will Theorem," which deduces that the Universe is neither deterministic nor random, but governed by a third state of 'free will' (and I was also happy to see him label as nonsense the philosophical attempt to reconcile determinism and free will known as "compatibilism"). The chapter ends with Conway submitting to neuroscientific MRI studies of his own brain.

Finally, I'm not ashamed to say that when I finished the "Epilogue" to this touching biography I had a tear in my eye! (unusual, no, for a math-related book)... I didn't want this book about math, and one man's humanity and passion, to end... a very flattering, but also very human, portrait ("warts and all") of... a child at play! Thank you Siobhan Roberts and Bloomsbury Press for bringing it to us.

Elsewhere on the Web, I especially enjoyed Colm Mulcahy's review of the book:
http://www.huffingtonpost.com/colm-mulcahy/john-h-conway-genius-at-p_b_7749796.html

...and 2 more reviews here:
http://www.buffalonews.com/city-region/review-genius-at-play-the-curious-mind-of-john-horton-conway-20150712

http://aperiodical.com/2015/07/review-genius-at-play-the-curious-mind-of-john-horton-conway-by-siobhan-roberts/

Grab Bag From the Week

The week gone by:

1)  enjoyed this tweet from last weekend:

What would you do??  pic.twitter.com/tkt7gQvCXA

— Chris Volinsky (@statpumpkin) July 10, 2015

...and Presh Talwalkar tackled the above problem here:
http://tinyurl.com/o9e7z9g

2)  A profile of 6 Indians following in the "footsteps" of Ramanujan:
http://mintonsunday.livemint.com/news/meet-the-heirs-to-ramanujan%E2%80%99s-genius/2.3.3593071363.html

3)  During the week, Fawn Nguyen found this nice problem-solving site for young people:
http://www.1001mathproblems.com/

...and here, another interesting-looking puzzle site that popped up on Twitter:
http://dave.uktv.co.uk/shows/dara-o-briain-school-of-hard-sums/seeall/2194/

4)  Evelyn Lamb on prepping for the International Mathematical Olympiad:
http://tinyurl.com/q6tqtxd

5)  Using math to untangle "controlled chaos":
http://blog.cosmosmagazine.com/blog/2015/7/14/mathematician-devises-equations-to-untangle-controlled-chaos

6)  Colm Mulcahy's wonderful review of the new John Conway biography:
http://www.huffingtonpost.com/colm-mulcahy/john-h-conway-genius-at-p_b_7749796.html

7)  Ben Orlin on the harmonic series, 9's... and, the DMV:
http://mathwithbaddrawings.com/2015/07/15/the-strange-music-of-the-harmonic-series/

8)  Of network complexity and "explosive percolation, via Quanta Magazine:
https://www.quantamagazine.org/20150714-explosive-percolation-networks/

9)  Interview with Ben Goldacre on statistics here:
http://tinyurl.com/ps724n8

10)  Some interesting references/links (on Grothendieck, and some French mathematical unification) included in the latest post from Peter Woit:
http://www.math.columbia.edu/~woit/wordpress/?p=7854

11)  A bright future ahead likely for applied math jobs built upon internships (via American Scientist):
http://www.americanscientist.org/blog/pub/internships-connect-math-students-to-new-career-paths

12)  I haven't honestly explored these enough to even understand them, but looks like something several readers might find interesting:
http://themathkid.tumblr.com/post/124195368919/theres-some-fascinating-research-happening-now

13)  And more than a little math goin' on here:
https://mikesmathpage.wordpress.com/


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

1)  TEDRadioHour replayed a fascinating old segment on Luis Von Ahn and his "Captcha" and "duolingo" collaborative projects:
http://www.npr.org/2013/10/04/191620023/can-you-crowdsource-without-even-knowing-it

2)  Richard Elwes posts his thoughts on learning from babies:
http://richardelwes.co.uk/2015/07/16/learning-to-learn-from-babies/

The Math Potpourri

Some of the math I didn't report at Math-Frolic this week:

1)  The 87th "Math Teachers At Play" blog carnival:
https://cavmaths.wordpress.com/2015/07/04/maths-teachers-at-play-87/

2)  An interesting old SAT problem gets covered by Presh Talwalkar:
http://tinyurl.com/qbcp4b8

...and here, Presh explains in a video why a certain fraction automatically generates the Fibonacci numbers (for awhile):
https://youtu.be/i2rDbfhRHok 

3)  An excerpt from John Allen Paulos' forthcoming book, "A Numerate Life":
http://www.theatlantic.com/technology/archive/2015/07/how-math-can-defeat-bullies/397061/

4)  Another wonderful post from Ben Orlin, this time on the (false) allure of linearity:
http://tinyurl.com/px9hexw

5)  One blogger's thoughts on memorization:
https://fivetwelvethirteen.wordpress.com/2015/07/07/memorization-good-or-evil/

6)  Evelyn Lamb briefly reviews Cedric Villani's "Birth of a Theorem":
http://blogs.scientificamerican.com/roots-of-unity/what-it-feels-like-to-be-cedric-villani/
(I haven't read Villani's book, partly because I've seen such oddly-mixed, contradictory reviews of it, but Lamb's take encourages me to reconsider it before year's end.)

7)  Hey, c'mon folks, does ANYone who's ever played basketball truly doubt that the "hot hand" exists (no matter what some quant-ish types might try to tell you)? Andrew Gelman takes on the topic here (arguing in favor of hot hands):
http://andrewgelman.com/2015/07/09/hey-guess-what-there-really-is-a-hot-hand/

8)  Not math, but some of the consistently best science-reporting on the Web these days comes from Ivan Oransky and his "Retraction Watch" group. In a podcast he talks about the current 'boom' in bad science (and catching the bad science red-handed, often does involve math):
http://mendelspod.com/podcasts/ivan-oransky-todays-retraction-boom/


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

1)  This week NPR's RadioLab re-ran a segment with Dr. Elizabeth Loftus on the malleability of memories (including the backlash she faced for casting doubt on the memories of children):
http://www.radiolab.org/story/91573-adding-memory/

2) The bizarre NY Times story of identical twins mixed up as fraternal twins:
http://tinyurl.com/p9tv3u2

 

Math Bits of the Week

Here and there:

1)  First, a fun little (economics) paradox over at Math-Frolic this morning:
http://math-frolic.blogspot.com/2015/07/gladly-paying-110-for-dollar-bill.html

2)  Conway.... J-J-John  Conway!:

ICYMI, last Monday I got to talk with Siobhan Roberts about her upcoming biography of John Conway:
http://mathtango.blogspot.com/2015/06/siobhan-roberts-playing-with-geniuses.html

...and in Nautilus this week Siobhan gives a taste of Conway in an excerpt from her book:
http://nautil.us/blog/this-early-computer-was-based-on-a-urinal-flush-mechanism

...finally, new from the Numberphile folks, more on "the brain of John Conway":
https://www.youtube.com/watch?v=y5ARAxW2k_4

3)  Video of Ed Frenkel's talk this week on AI, Gödel, algorithms, pain, reality & more, at the Aspen Institute:
https://www.youtube.com/watch?v=lbLI9aX5eVg

4)  Mark Chu-Carroll explaining "judgements" and type theory:
http://www.goodmath.org/blog/2015/06/26/truth-in-type-theory/

5)  A nice bit of Escher retrospective from Joselle Keyhoe here:
http://mathrising.com/?p=1293

6)  Some fun (and variation on an old probability quandary) from Andrew Gelman:
http://andrewgelman.com/2015/06/29/god-is-in-every-leaf-of-every-probability-puzzle/

7)  IF you're interested in the foundations of math, check out this recent post from Peter Cameron:
https://cameroncounts.wordpress.com/2015/06/29/on-foundations/
(if you're not interested in foundations, probably skip it)

8)  A podcast interview with Katie Steckles on Sam Hansen's "Strongly Connected Connections":
http://www.acmescience.com/2015/07/scc-62-katie-steckles/

9)  Matt Parker gives a little tutorial on factorials:
http://aperiodical.com/2015/07/how-many-ways-to-shuffle-a-pack-of-cards/

10) This Steven Strogatz piece on IBL is almost a month old, but just came across it this week (h/t to Gary Davis):
https://www.artofmathematics.org/blogs/cvonrenesse/steven-strogatz-reflection-part-1

11)  I haven't found time to swing by Mike's Math Page this week... but am sure there's some good stuff THERE!

sidenote (heads-up!):  apparently Jordan Ellenberg, Jo Boaler, and Steve Strogatz will be on TODAY'S edition of NPR's "Science Friday."


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

1)  Some fascinating, paradoxical science (physics) from the always fascinating Natalie Wolchover:
https://www.quantamagazine.org/20150702-paradoxical-crystal-baffles-physicists/

2)  And another fun re-run segment from RadioLab last week on the magic of an old Australian radio show:
http://www.radiolab.org/story/you-are-judge/
 (actually, the entire hour-long "Black Box"episode of RadioLab is good)