...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

Sunday, August 30, 2015

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:


[...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:


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:


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:


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


Mind-blowing stuff!

....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":

...and more:

:  A reader sends me this interesting link from just a few days ago, coincidentally covering the same Sacks/savant story:
...and also this older blog post I didn't recall:

Friday, August 28, 2015

MathLinks Ahead...

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

1)  More on Alex Bellos' new loop pool game:

2)  Madore mazes, hyperbolic surfaces, and Evelyn Lamb:

3)  A new "Math Teachers At Play" blog carnival is up here:

4)  The math of chicken nugget numbers:

  Last year's Brazilian Fields Medalist winner:

6)  The 5 latest "Mathgems" from Resourceaholic:

7)  Interesting piece on quantum cryptography:

8)  The phenomenal physics of friction and phone books:

9)  Psychology, research, and replication, covered by:


...and, The Atlantic:

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:

11)  Among other things, Mike Lawler played with triangular numbers this week:

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:

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':

2)  Science writer George Johnson muses about the "bubbles," science and otherwise, we live within, in the digital age:

Friday, August 21, 2015

Math Bits From the Week

Potpourri... incoming:

1)  "Math Rising" blog looked at the topic of consciousness in non-humans this week:

If you're interested in programming you'll probably want to read this piece from American Scientist about 'probabilistic programming language':

Bill Gasarch tries to bring us up-to-date a bit on P vs. NP:

4)  A GREAT, long piece on surreal numbers and more, passed along (tweeted out) this week by Jordan Ellenberg:

...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":

5)  NY Times
piece on skepticism around health studies:

Presh Talwalkar uses a joke police poster to lead into a discussion of game theory:

Quantum computing... hard to fathom:

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:

9)  I don't think it's even possible for Ben Orlin to not be entertaining... and instructive... at the same time:

10)  Algorithms are saying a lot about us... and lo-and-behold they ain't always accurate (nor accountable):

11)  Related to the above, Kaiser Fung with a bit about management practices and big data:

  I hope you already saw my review from last weekend of Gary Smith's take on statistical shenanigans, "Standard Deviations":

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:

14)  Allen Downey tells us about something called "the inspection paradox":

15)  And when he's not following Ultimate Frisbee games, Mike Lawler occasionally has math blog posts here:

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:

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:

Sunday, August 16, 2015

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!

Friday, August 14, 2015

Math of the Week

ICYM any of these:

1)  Dan Rockmore explains the Turing test on NPR:

The latest 'Math Gems' post from Resourceaholic:

  Yet one more summation of Twitter Math Camp I'll pass along, for those interested:

And as long as we're talking conferences, a couple of summaries of the recent Bridges Math Art conference:


  ICYMI, this piece about David Wees and math-learning made the rounds:

6)  Some simple geometric beauty from Futility Closet:

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:

...and plusMaths.org covers it here:

8)  Meanwhile, Peter Cameron quickly reviews Bellos' "Alex Through the Looking Glass" (American version, "The Grapes of Math"):

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

...and John Allen Paulos' take on this sort of game:

10)  I see Alfred Posamentier is out with yet another book (he must write them in his sleep!):

11A 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:

And for teachers, Crystal Kirch does a weekly linkfest as well:

Finally, if the above isn't enough for ya, there be more links at the latest "Carnival of Math":

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?):

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):

...but the real fun comes with the comments to the original imgur posting:

Friday, August 7, 2015

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?):

2)  Keith Devlin on the increasing role of games in education (and a new book about it from Greg Toppo):

  Evelyn Lamb explores infinite earrings, and more:

4)  A fun game from David Radcliffe ("Bojagi")

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

6)  James Tanton interviewed on teaching success:

  Another followup (out of a great many) to Twitter Math Camp:

8)  In a couple of postings, Steven Strogatz tells of his positive entry into the world of inquiry-based learning (h/t Egan Chernoff):

  Another fabulous post from Ben Orlin this week:

  A half-hour of Marcus du Sautoy on "Flexagon Radio":

11)  Interesting report on the Tor network and anonymity:

12)  Stretching on over to physics and some more fine reportage from Quanta Magazine (and Natalie Wolchover):

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

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)!?