Colm Mulcahy... Let the Mathemagic Begin

Math-Frolic Interview #16 

"Follow your dreams while doing something worthwhile.  Share your toys. Cherish your family and friends..." -- Colm Mulcahy

For any who don't know of Colm Mulcahy I'll let him introduce himself to readers through the synopsis he sent along as part of this interview:

"Colm Mulcahy is a professor of mathematics at Spelman College, in Atlanta. Over the last decade, he has been at the forefront of publishing new 'mathemagical' principles and effects for cards, particularly in his long-running bi-monthly Card Colm for the Mathematical Association of America (MAA). He also blogs at the Aperiodical and the Huffington Post. Dr. Mulcahy has been a recipient of the MAA’s Allendoerfer Award for excellence in expository writing. His interests are broad, ranging from algebra and number theory to geometry. He earned a B.Sc. and M.Sc. in mathematical science from University College Dublin and a PhD from Cornell University for research in the algebraic theory of quadratic forms."

Here's a summary of places on the Web you can find Colm:

Twitter: @CardColm  https://twitter.com/cardcolm
author of "Mathematical Card Magic: Fifty-Two New Effects"
http://www.cardcolm.org
http://www.spelman.edu/academics/faculty/colm-mulcahy
http://www.maa.org/columns/colm/cardcolm.html ("Card Colm")
http://www.huffingtonpost.com/colm-mulcahy/
http://aperiodical.com/category/columns/maths-colm

One of the delights for me in interviewing Dr. Mulcahy, was that he was friends with Martin Gardner during the last decade of Martin's life, and so I took the liberty of inquiring a lot about Martin (almost like getting two interviews for the price of one! ;-) -- especially timely, since the annual "Celebration of Mind" (in tribute to Gardner) comes up next month. Hope you all enjoy these great responses as much as I did:

**************************************

1. You're both a magician and a mathematician… which interest came first, and have the two interests intertwined most of your life? Also, at what point did you know you wished to pursue math professionally?

I came to magic very late in life, in my early 40s.  Hence, combining that with my natural laziness, I’m a terrible magician.  Had I started at 14 like the rest of them, today I’d be good at double lifts, false counts, Charlier passes and the like.  So I have to resort to---gasp!--- mathematics, to entertain with a deck of cards.  What I do (and what’s in my book) is largely original creations. Forget clichés like dealing into three piles, basic addition or subtraction disguised, or casting out nines.  Those are hackeyed and pretty boring in my view!

As it happens, the only sleight-of-hand I can do is a perfect faro shuffle.  That took me a month to learn to get it right, after an intensive one-on-one tutorial from the ever-patient Mark Setteducati a decade back.  The only reason I stuck at that was because the mathematical possibilities fascinated me.

But what really fascinates me are the possibilities with a genuinely shuffled deck, or a slightly rigged deck, even after a riffle shuffle done by a spectator.  That’s what I’ve come to specialize in.  And none of my creations take advantage of perfect faro shuffles; that would put too much pressure on myself. Of course I take a dim view of crimps or other card marking.  I will include a little false shuffling, or tell a few white lies such as “I couldn’t possibly know what these cards are” for entertainment purposes, but the underlying principle of the magic I do has to be mathematical.

As regards my real career---the day job!--- when I started university as a teenager, I didn’t know that it was possible to focus just on mathematics, which was the only subject that made total sense to me then.  I had assumed I’d end up in science, like my brother before me, probably physics in my case.  But after six months I discovered that I could soon drop all yucky labs and do nothing but pure and applied mathematics coursework—what a revelation!   (This was in Ireland, where it was assumed that you already had picked up a decent liberal arts education in secondary school.) I went for it, hook, line and sinker, and never looked back.  I believe I’m still a student at heart, and a life-long learner.  The only real job I’ve ever had was the three years I served as department chair. For the past few decades I’ve actually been getting paid to study---I hope nobody finds out---and also to share the fun with others, they call that teaching, writing, publishing and presenting.

2. You're originally from Ireland… can you say what brought you to the States to begin with and do you get back to Ireland often?

I came over after doing my masters, back then it was impossible to get funded to do a PhD in Ireland.  I've been lucky to be able to get back often over the decades, at least twice a year these days.  Maths Week Ireland (www.mathsweek.ie) sometimes have me over, it's the largest mathematics outreach programme in the world (http://www.huffingtonpost.com/colm-mulcahy/math-weak-try-math-week_b_2008517.html), with over 130,000 kids getting involved last year. I spoke to 1000 of them myself, up and down the length of the country, in the course of my gruelling but fun 9 day "fall break".  The Maths in the Street activities are a hoot, because you get to engage curious people aged 8 to 80, who just go out to do their shopping and they get home with groceries AND a knowledge of the Towers of Hanoi, how to solve a maze, or a card trick they can do for the family.
[--We need more of that in the U.S.!]

3. You were a friend of Martin Gardner through the last decade of his life… are there any behind-the-scenes stories about Martin you can share that might interest my readers?

Martin was amazing. Humble, incredibly focussed and hardworking and productive.  So kind, and generous with his time and wisdom. We chatted on the phone and corresponded on and off from 2000 to 2006, when I finally visited him for the first time. By then he was in his 90s, and probably not as sharp as he’d been a decade or two earlier.  He was certainly a little forgetful: sometimes he didn’t remember that he’d already mastered something and written about it, but he could look it up quickly in his amazingly organized files, and it would come back to him right away.  And his less robust state didn’t stop him writing a half dozen books in his last five years, including the ace up his sleeve, his autobiography.

Back in 2000, I’d sent him about 50 Latexed pages of notes I’d made on mathematical card tricks---Latex is what most mathematicians use to typeset their work---largely stolen from assorted publications of his.  He responded with enthusiasm, and suggested I write a book on the topic.  I was flattered of course, but knew I’d have to come up with a lot more original material for that to be a reasonable proposition.  I set myself a personal goal of getting it published by 2006, the 50th anniversary of his landmark "Mathematics, Magic and Mystery," and found a willing (university) publisher.  I’m deadline driven: without one, a lot of things don’t get done.  With a deadline, they eventually get finished, although seven years late in this case, and with another publisher.  Along the way I decided to try to switch to the premier outlet for recreational mathematics, AK Peters (now part of CRC Press).  I was very happy that Klaus Peters offered me a contract and that I finally delivered the goods this year, before books become obsolete.

4. Gardner was surprisingly unpredictable in some of his viewpoints and interests… in your time with him was there any particular view he held or interest he had that most surprised you, or that the two of you debated over?

He tried to engage me in a debate once about whether I thought mathematics was discovered or invented, which is of course an old conundrum, and one he had definite views on.  Being the shallow person I am, I refused to be drawn in.  It never really interested me, though of course it should have. In more recent years, I have asked myself the same question in relation to mathemagical principles which I have stumbled on.  Did I create them out of nothing, or did I just get lucky and find them because I was kicking around in the leaves where nobody else before me had?  I still don’t know.  I probably should have paid more attention to Martin on this topic.

Following his death, many tributes assumed, as I myself had in earlier years, that he was either agnostic or atheist.  Not so.  I wouldn’t presume to speak on his behalf---we never discussed it and his views here are well documented in his own writings---but I believe he was a theist who did not believe in any organized religion.  That surprised me when I first realized it.
[-- Gardner covered this, and 'outed' himself as a "fideist," in one of my favorite volumes of his, "The Whys of a Philosophical Scrivener" -- a bit of an oddity among his works, and in some ways a dry read -- yet, made fascinating, by the chance to see how his mind worked on a very philosophical (less-empirical) level -- also, Gardner's high regard for Spanish philosopher/writer Miguel de Unamuno is made clear in this volume.]

One sweltering March day when I was visiting him, I spotted a curious object hanging up over the sliding door to the outside, and I asked him what it was.  It was a small musical saw. He confessed to playing it on rare occasion for relaxation.  Despite my gentle encouragement he made it clear that there would be no public or private performance, and I felt a little embarrassed, as if I had intruded on his privacy.

I never wanted to bother him unless I had something to share which I thought he’d really appreciate knowing about, but I did have a habit of phoning him now and then while waiting to board flights. The very last time I did this—about six months before his death---I ended the call as I often did by asking if he’d had any interesting visitors, and he replied in the negative, as usual.  After some prodding he perked up, and said he’d had one surprising visitor, which baffled him: Richard Dawkins.  He added something like, “I don’t know why somebody famous like that came to see me.”  I retorted, “Because YOU’re famous!” but he wasn’t having any of that.  I went on, pointing out that Dawkins had written much about theology and philosophy, just like he had.  He revealed that all they’d done was chat about life, and grandkids and baseball---Dawkins had just given a talk at the university nearby---until  his visitor stood up to leave because he had a plane to catch.  Then they both realized that there was a big topic they were supposed to discuss, and they sat down again and chatted intensely for 15 or 20 more minutes.  At this point I had a plane to catch myself---I was about to fly from Boston to Dublin---and I never got to hear the rest of the story.  Or, sadly, Martin’s voice again.  I'd grown very fond of him.  Such a sweet unassuming man, for such an intellectual giant.

[-- Wow, fascinating Dawkins story… easy to speculate that they could've had an 'intense' chat over the nature of religion or religious belief, but purely a guess; no doubt many possibilities. If any readers, perchance, know Dawkins well enough to ask him about it, I'd LOVE to hear what the "the rest of the story" is!
One of Gardner's most remarkable qualities (in my view) was his balancing act between being a strong skeptic and harsh critic on-the-one-hand, while also being humble/"sweet unassuming" on the other... opinionated, but not in a know-it-all kind of way; curious and uncertain of many things to the end.]

5. What are your own favorite aspects of mathematics to study or read about, and if you could only take say 3 or 4 math books with you to a desert island what might they be?

 I like surprises and counter-intuitive things which every graduate in all disciplines should know, such as not-so-obvious averages (http://www.huffingtonpost.com/colm-mulcahy/mean-questions-with-harmonious-answers_b_2469351.html) and non-Euclidean geometry. Most of us are smart enough to know that the earth isn’t flat, but is space flat?? I especially like things that teach us to distrust simple “numerical evidence”:  The false positive paradox. Simpson’s paradox. The Birthday Paradox.  Benford’s Law.  The Gilbreath Principle. There are probably five more of them out there that we all need to know about.  If anyone knows what they are, please tell me.

I really should have a good grasp of the basic history of mathematics. "Math Through the Ages" by Berlinghoff and Gouvêa is probably a great place to start.  I’m particularly interested in knowing about the contributions of all cultures around the globe, even if much of that was hidden until recently, or doesn’t “fit the mold.”

I’m woefully ignorant of topology, but if Pontryagin and Morin (both blind) could contribute so much to the subject, it wouldn’t kill me to learn a little.  I never really got quantum mechanics as a student all those years ago, it was the one topic I faked understanding, perhaps taking false comfort from the fact that Einstein didn’t buy it either.  I’m not that attracted to it, but if it was an undergraduate topic in the 70s, I should be able to handle it.

It’s time I understood the whole mathematics/music connection.  It might help if I actually knew something about music, but I’m strictly an avid consumer. 
[-- yes, I was surprised back in college days by how many music majors I ran into with math minors, or math majors with music minors! -- definitely an interesting connection]

Of course we should all study Diaconis and Graham’s "Magical Mathematics" daily.  If I could master half of the tricks in it, I’d die happy.

6. Do you have one mathematical-related achievement from your life that you're most proud of above others?

I suppose getting my first book out, twenty-five years after I first considered writing one, and after starting and abandoning two others!  The one just published bears no resemblance to anything I would have considered writing even fifteen years ago, and the people who trained me probably wouldn't recognize it as having much to do with mathematics, but it contains a lot of fresh creations. I hope it turns some youngsters on to the joys and possibilities of mathematics.

Starting in 2012, I've been blogging for the "general public", and not just for card magic aficionados as I do in Card Colm at maa.org.  I've written some things for the Huffington Post http://www.huffingtonpost.com/colm-mulcahy/ and also for The Aperiodical in the UK. http://aperiodical.com/category/columns/maths-colm  In recent times, both have taken a back seat due to the focus I needed to bring to getting my 380-page book manuscript to the printers, set up appearances and book signings and so on, but I plan to get back to that kind of blogging soon.

There's a big world out there that needs to have a better attitude about mathematics.  We've never had the best PR, and I aim to play a role in improving the image of the subject.  I've always had a big issue with the claim that people are either numbers or words people.  Many of us are both.  Some mathematics teachers are reluctant to correct basic spelling and grammar in their students' work, for instance, either on the basis that it's not their job, or it doesn't matter. Wrong!  It's all about communication, about being able to justify your position with a cogent argument using words AND numbers correctly. A string of numbers presented without accompanying text is hardly convincing, and may in fact mask the presenter's confusion or ignorance.  We all need to have a healthy skepticism of numbers and "experts" and learn to make informed decisions ourselves.  And be willing to change our minds in the light of compelling fresh evidence. Ironically, education is no inoculation against frauds and charlatans, whether they're peddling hokey stats or snake oil.  James Randi can confirm!

7. When you're not reading math or magic, what other types of reading do you like? And what other hobbies or activities do you enjoy?

Irish fiction. World history. Cookery books. Music, music, music.  I cook a lot and indulge in craft beers and chocolate more than is good for me.  I jog and am trying to bike more often, to atone for my sins.  Actually, I’ve always found that such outdoors exercise stimulates the mind.  Over the past ten years or so, some of my best ideas for new Card Colms have come to me while puffing and panting.  I am not alone in that regard (see http://www.huffingtonpost.com/colm-mulcahy/sports-and-mathematics_b_2475226.html ).

8. And back to Martin… You've been heavily involved with the "Gathering For Gardner" and "Celebration of Mind" (coming up soon in October) events which honor Martin Gardner's legacy.  Most Gardner fans are probably familiar with these events, but can you give a quick synopsis of them for anyone unfamiliar? And do you have a particularly memorable experience from one of these events that stands out for you over the years?

G4G is an insider and by-invitation-only conference held in Atlanta in March of even-numbered years.  They’ve being going on for 20 years.  They  attract very creative and interdisciplinary mathematicians, puzzlers and magicians as well as skeptics, illusionists, Alice afficionados, and so on.  Four or five days of extreme intellectual stimulation and networking.  You might meet some of your heroes, from Randi to Shortz, Conway to Penrose, Teller to Smullyan.   A few years back there, Erik Demaine announced that any two polygonal regions of the same area are hinge-dissection equivalent, meaning that the first can be cut into pieces and these swung around on hinges to form the second.  He got a standing ovation.  I was present when history was announced.  It was awesome.   I was able to tell my students at Spelman soon thereafter when I proved for them the much easier version ignoring hinges.  Who’d have thought it, a new math result proved in their college days that they could at least understand the statement of?

The 'Celebration of Mind' events were started in 2010, a few months after Martin died.  These are open to all, anywhere on the planet.  Anyone can host one or attend one---a few are strictly private but that’s not common.  They’ve happened on all continents and at both poles. They take place in and around October 21, which was Martin’s birthday.  We’d like this to go viral as well as global, especially with Martin’s centennial approaching in 2014.  There should be thousands of them each year, celebrating the triumphs of the human mind with cool stuff Martin made us think about:  recreational mathematics, brain teasers, logical loopholes, rationality, skepticism, optical illusions, puzzles mechanical and cerebral, the mathematics of M.C. Escher and Mandelbrot, origami, the list goes on.  The  www.celebrationofmind.org webpage has terrific resources, check out Vi Hart’s series of four hexaflexagon videos from last year to get some ideas of the fun and depth which lies just below the surface of innocent-sounding explorations.  Please also follow @WWMGT on Twitter!

There’s another celebration I’d like your readers to know about: the theme of the next Mathematics Awareness Month in the USA is “Mathematics, Magic and Mystery,” named after Martin’s groundbreaking book from 1956.  So in April 2014, American school children and students of all ages will be exposed to some cool stuff reflecting the amazing mathematical legacy Martin left behind.

9. Any parting words, not covered above, you'd want to pass along to a math-oriented audience?

Life can be short---just ask Steve Sigur or Kirsty MacColl---and it’s certainly finite.  Follow your dreams while doing something worthwhile.  Share your toys. Cherish your family and friends.  And as Nick Lowe said four decades ago, what’s so funny about peace, love and understanding?
Oh, you said a math-oriented audience… same advice, plus or minus epsilon.
[-- A splendid note to leave on!]

**************************************

Are those some wonderful responses or WHAT!!... THANKS so much for participating here Colm, and just like Martin Gardner may you keep contributing to us for many many years to come! ...or, as they say, 'Luck o' the Irish to you!'

Please do check out Colm's Webpages and book.

(p.s.: I haven't had a chance to check all the hyperlinks above, so do let me know if you find broken/misused ones.)


ADDENDUM:  want to attach a voice to a name and learn still more about Dr. Mulcahy (with some nice detail on his card magic and book, and still more on Gardner)... Sol Lederman now has up a great podcast interview with Colm on his "Inspired By Math" series:

http://wildaboutmath.com/2013/09/21/colm-mulcahy-inspired-by-math-32/

Mathematics… Not Immune

Somewhat oddball topic today… just felt like airing it (bit of a rant on skepticism....):

I'm  sometimes amused by 'scientists' on the Web calling themselves "skeptics" only to find that they're aiming most of their fire at what I can only call "low hanging fruit": creationists who think the Earth is less than 10,000 years old, psychics who bend spoons, UFO abductees who've taken trips to the planet Kazaar (or some such), etc. etc. They often proudly call themselves "evidence-based" scientists… but don't seem to acknowledge that scientific "evidence" itself can be highly subjective, manipulated, and tainted fare... requiring skepticism itself.
What I've always wanted to see is more "skeptics" turning their keen eyes on the likes of the Journal of the American Medical Association, New England Journal of Medicine, CELL, Nature, Science, etc. Most "science" is so poorly done it doesn't even see the light of publication, but even research that does make its way into such 'premier' publications (let alone lesser ones) often escapes the scrutiny it deserves, receiving a sort of 'free ride' once published (the data, methods, underlying premises/assumptions, and of course conclusions, never being adequately challenged, nor replicated; and don't assume 3 peer reviewers have done their job either!). Most who have been heavily involved in research, IF they're honest about it, will admit that journal articles, as composed, often don't accurately reflect the actual work, as carried out. But with the digital age upon us, the needed sort of ongoing, ever-watchful skepticism is finally emerging.

Dr. Ivan Oransky has made a job of keeping track of journal "retractions" (often, but not always, for malfeasance) from research journals, with his wonderful, must-read "Retraction Watch" blog (sub headed: "Tracking retractions as a window into the scientific process"). And a recent 'Peer Review Congress' meeting in Chicago, well-tweeted (hashtag #pcr7) by Oransky and others, shined light on many of the important research issues that don't get voiced enough… and these are NOT new, but have been around for a long, long, long time, just finally getting the attention deserved. Anyone who has followed this area will be familiar with the name "John Ioannidis" as one of the most-vocal of those who've questioned the reliability/validity of much research. There are also now a number of twitterers (some better than others) focusing on biomedical/research skepticism, though 140 characters isn't always much to work with!
My sense is that a majority of the retractions that Oransky reports on involve the biomedical sciences, but even mathematics papers or journals occasionally appear among his subjects (sometimes almost laughably). So math, the 'queen of the sciences,' is not immune from sloppiness (or even fraud). Check these out:

  http://retractionwatch.wordpress.com/?s=mathematics

WHY the heck do I mention all of this now? Well, nothing earth-shattering, but in preparing the John Casti quote for the post that I did last Sunday on Math-Frolic (thought it would make a nice Sunday meditation), I came across information that disturbed me. Casti (who focuses on "complexity" theory) has long been one of my favorite science writers/thinkers; he is both a good explainer, and a thought-provoking one; I've read him for decades. So I was surprised/disappointed to learn from the internet that he'd been caught extensively plagiarizing material in the past -- multiple times... that doesn't make his material any less interesting or important to me (he plagiarizes from good people ;-), but it does throw a troubling ethical shroud over that material. Here are 3 web links that address Casti's sins:

http://www.nytimes.com/2002/03/09/books/connections-plagiarism-that-doesn-t-add-up.html
http://www.ams.org/notices/200206/commentary.pdf
http://onlinelibrary.wiley.com/doi/10.1002/cplx.20050/pdf

Last year, budding science-writer phenom Jonah Lehrer was disgraced and humiliated when he was found to have plagiarized, and even fabricated, passages in some of his best-selling books. His actions (and Casti's) are an affront to the many high-quality science communicators who choose to write books the old-fashioned way… by actually generating their own words ;-)  Casti's lapses may not be as grievous as Lehrer's, but it will now be difficult for me to read him with quite the same respect I did previously -- his repeated actions being such an unexpected/disheartening bit of chicanery to learn about.
Moreover, it harkened back to my prior MathTango post, wherein I wrote about learning that some observers suspect that Daniel Tammet (renowned autistic savant, and another person whose books I've enjoyed) may not be a genuine savant, but only a memory expert who uses his mental skills/tricks to portray himself as he does -- again, disappointing to learn that this is even a possibility. Sigh....  I consider myself a fairly critical reader, yet was caught unaware by these controversies around Casti and Tammet. (While I'm on this whole subject it may even be pertinent to note that the post prior to the Tammet post was a review of the new book, "Magnificent Mistakes In Mathematics," coincidentally, yet another focus on flaws-of-a-sort in science/math.)

On the Web, there are plenty of individuals, with or without some math credentials, who stake out math ideas that aren't credible (Mark Chu-Carroll of "Good Math, Bad Math" occasionally writes entertainingly about them, and their math "crackpottery"): http://scientopia.org/blogs/goodmath/?s=crankery ). But to discover shenanigans going on at a more professional level and/or in journals, is more disconcerting and unsettling… though I s'pose no field is immune from flim-flam artists of all sorts, math/science included.

Luckily, pure math really is probably more resistant to outright fraud, or even unchecked sloppiness, than most fields. In fact when I typed "math" plus "fraud" into Google most of the examples arising were, not too surprisingly, in regard to economics or finance. The other area that popped up, again not too surprising upon reflection, was statistics, which often gets used (though not necessarily deliberately) incorrectly to argue some point.

Anyway, I write all of this as a way of saying that real skepticism needs (unfortunately) to cut across all boundaries -- I'd dare say epidemiology can be critiqued almost as easily as astrology! Don't aim doubt and critical faculties at just the naive, the non-empirical, the 'low-hanging fruit'… but at the 'evidence-based,' the peer-reviewed, and occasionally even the mathematical as well. I applaud Oransky and others for bringing a critical eye to "the process of science" and trying to keep scientists not just skeptical, but honest as well. Science succeeds best through its vigilant, self-scrutinizing, self-correcting functions, which, for a variety of reasons, too often get left on the sidelines... occasionally even in mathematics.

In sum, Margaret Mead was famous for saying: "Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it's the only thing that ever has."
I'm tempted to parody that by saying, 'Never doubt that self-skepticism, close scrutiny, and doubt aren't key driving forces behind scientific progress… indeed, they always have been.'

Numbers, Mnemonism, Savantism, Oh My

Well, this is a bit disconcerting….

NPR recently ran an interview with author/autistic savant Daniel Tammet:

http://www.npr.org/2013/08/11/206660281/the-beauty-and-calm-of-thinking-in-numbers

I've enjoyed all three of Tammet's books. My favorite was his second one, "Embracing The Wide Sky," while the current one, "Thinking In Numbers," is a bit less consistent (from essay to essay), though still pleasant... couple of reviews here:

http://tinyurl.com/8llkr35
http://tinyurl.com/myz48jw

When I first became aware of Tammet, years ago, he struck me as a bit peculiar, especially his ability to introspectively and articulately describe his own mental processes (unusual for savants); he had an almost 'Uri Geller' style about himself, but, as he was studied by psychological experts in the field, I fully bought into his storyline. He has traveled widely and appeared extensively on television promoting his books, and there are plenty of examples of Tammet on YouTube as well:

 http://tinyurl.com/lx9oby6
(and even more of course on Google about him: http://tinyurl.com/mteo7sc )

...I've never read Joshua Foer's bestselling "Moonwalking With Einstein," but have always seen excellent reviews of it. So I was surprised to read in the comments to the above NPR piece that apparently in that volume Foer expressed doubt about Tammet's genuineness, believing he may just be a highly skilled mnemonist (memory expert) who passes himself off as a synaesthete and savant (turns out Tammet's real name is Daniel Corney though he had it legally changed over a decade ago, and Foer marshals evidence that Tammet isn't always candid about how he succeeds at what he does).

It's hard to know where the truth lies (especially since 'savantism' itself can be a bit hard to define), but the more I surfed around the Web the more suspicious Daniel's talents (or his personal portrayal of them) seemed. Even though many find Foer's skepticism unconvincing and continue to defend Tammet, others, with knowledge of memory training, do not. One of the most lengthy discussions comes at this forum site:

http://mnemotechnics.org/forums/daniel-tammet-840.html

The above has 6 pages (or 163 responses) of comments to sift through about Daniel Tammet (I haven't read them all myself, but they're not very encouraging for the authenticity of the standard Tammet-savant view). It's enough to make one a tad more leery of those neuroscience "experts" who study and report on savants (a bit reminiscent of scientists who studied and were taken in by Uri Geller decades ago) -- is the reality ever as incredible as portrayed by all the hype?

Still, savantism, including extraordinary mathematical abilities, remains a fascinating subject area, but perhaps one where a focus on Daniel Tammet is not entirely appropriate (of course the tricks of mnemonists are an interesting topic in their own right, just a different topic). Perhaps tellingly, Tammet himself, has long voiced a belief that his talents are not so rare or extraordinary, but rather are a function common to human brains, just not readily accessible to most people... that would indeed make sense if Foer's contention of extensive mnemonist training was the underlying mechanism.

Anyway, sorry if this is all old news for some of you, and you were already aware of the so-called "debunking" of Tammet; it was news to me that, given my occasional interest in savantism, seemed important to share, especially since Tammet is currently getting attention here in the States where his "Thinking In Numbers" volume was only recently widely distributed (it was available through the UK a year ago). I still enjoy the volume... but with at least a bit more of a grain of salt. And I should add, Tammet remains an interesting fellow, whether it be as a true savant, OR as someone who has successfully pulled-the-wool over the eyes of trained specialists (getting a lot of free travel and attention in the process)!


...As long as I'm mentioning books, this might be a good time to point out that Edward Frenkel's "Love and Math: The Heart of Hidden Reality" is due for release in about a month, and I suspect it may possess some of the same deep, haunting joy of math that Tammet expresses, but coming from a true mathematician. From the Amazon description:

"In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we’ve never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space."

Some more about Frenkel here:

http://math.berkeley.edu/~frenkel/Frenkel-Love-for-Math.pdf

New Math Book, Full of Mistakes

…and delightfully so!!

-- Review of "Magnificent Mistakes In Mathematics" -- by Alfred Posamentier and Ingmar Lehmann

Any volume from Alfred Posamentier is to be looked forward to, and the latest one, "Magnificent Mistakes In Mathematics" is no exception (written again with Ingmar Lehmann); a fairly quick and entertaining read for typical math buffs, with a focus not often found in math books… on famous math errors.

The book endeavors to demonstrate that even the precise, empirical field of mathematics has its share of mistakes made by prominent, knowledgeable practitioners in the road to progress. And they note that the very need to examine and explain math 'flaws' is a good thing, often leading to whole new ideas/concepts.
 
The book starts right off putting the reader at ease by highlighting "noteworthy mistakes by famous mathematicians," including such accomplished figures as Pythagorus, Galileo, Fermat, Leibniz, Euler, Poincare, and several others. It's as if to say 'if the remarkable Euler blundered why should YOU dread making math mistakes.'  Many of these errors are well-known, but still interesting, or in some instances even humorous (for example a blackboard mistake by Enrico Fermi that ended up saved for posterity on an Italian postage stamp). Interestingly, at the end of the chapter it is mentioned that the also extraordinary Carl Friedrich Gauss was not known to have made mistakes in his published material.

Chapter 2 embarks on the progressive journey through mathematics with a look at mistakes in arithmetic. This may be the least interesting, or most mundane of the chapters, and is followed by chapters that delve, in order, into algebra, geometry, and probability and statistics errors; a seeming natural progression from the more abstract to the more applied or real-life-type examples. 
Geometry mistakes, of course are often a matter of misperception or interpretation (moreso perhaps than algebra, where mis-computation may be more frequent). In the geometry realm I was very surprised that the volume leaves out one of my very favorite 'mistakes,' which goes around the internet from time-to-time, demonstrating that pi=4: http://www.bestwtf.com/2010/11/explaining-why-pi-is-4.html The sort of error involved, "misleading limits," is documented in the book with other classic examples, but still, the circle-inscribed-in-a-square paradox is so good it ought not be missed.

Of course probability and statistics are perhaps the cause of more slippery mathematical mistakes than any other area, even among professional mathematicians. It is often famously told that even the great Paul Erdös initially had difficulty with the 'Monty Hall problem,' so it is a good chapter to end the book with. Many deceptive probability conundrums of recent times are now pretty much classic, and continue to elicit great debate when heard for the first time.

There are LOTS of types of examples used through the book, demonstrating how varied the sources of math mistakes can be. Having said that, there is also sometimes redundancy to the many examples employed for any one sort of error; but using multiple examples to make a point is not necessarily a bad thing.

For the professional or broadly-read mathematician this won't likely be a highly substantive or weighty math read. The bulk of examples in the volume are well-known, but what is new is bringing them altogether under one cover-to-cover format… an entire book focused contrarily not on what math does right, but on where it may go wrong. I think this somewhat unique approach makes the volume a worthwhile, entertaining addition to one's math bookshelf, and it may be particularly useful to secondary school teachers, providing a lot of grist for instructive, thoughtful examples in the classroom. As the authors repeatedly note, there is a LOT to learn from mathematical mistakes.

In short, a thumbs-up for this volume! Posamentier seems to produce a new book almost every year, and each one simply leaves me wondering what will he come up with next.

By the way, if you missed it, Posamentier did a great "Inspired By Math" podcast interview with Sol Lederman late last year here:

http://wildaboutmath.com/2012/12/16/alfred-posamentier-inspired-by-math-13/

A Book, A Cryptographer, and a Fun Guy

I'd normally post this over at Math-Frolic, but am so past-due to get a post up here... well, here goes:


1) If you're a fan of Mark Chu-Carroll's "Good Math, Bad Math" blog (one of the oldest and most popular general math blogs on the Web) you'll be happy to know his recent book  "Good Math: A Geek's Guide to the Beauty of Numbers, Logic, and Computation" is available through Amazon:

http://tinyurl.com/l6b5jkm 

Here's what Amazon begins by saying about it:

"Mathematics is beautiful--and it can be fun and exciting as well as practical. Good Math is your guide to some of the most intriguing topics from two thousand years of mathematics: from Egyptian fractions to Turing machines; from the real meaning of numbers to proof trees, group symmetry, and mechanical computation. If you've ever wondered what lay beyond the proofs you struggled to complete in high school geometry, or what limits the capabilities of computer on your desk, this is the book for you."

[Haven't read it myself, but assume from Mark's blog writing, it is good.]

2) I've previously mentioned my joy with "The New York Times Book of Mathematics" anthology, and its last chapter is composed entirely of wonderful profiles of accomplished mathematicians... mathematicians fascinate me as much as mathematics itself.  So I'll reach from there again today for this link to Gina Kolata's 1994 (and still hugely interesting) portrait of Leonard Adleman, the "A" in RSA encryption:

http://tinyurl.com/mmh8agy

It starts off thusly:

"There is nothing to look at in Dr. Leonard Adleman's office at the University of Southern California, no clue that the office is even occupied. There are no pictures of his wife or of his three daughters, no cartoons or mementos -- just a computer, two chairs, a desk and a blackboard. And that is fine with Dr. Adleman. For although he is an active faculty member at the university, although he is a devoted husband and father, his is a life of the mind.
"It is a life that is nourished by deep philosophical questions and the overarching beauty of mathematics. It is a life that involves days, weeks, months of pure thought, alone in his equally barren office at his home in Northridge, Calif., 30 miles from the campus. And it is a life that has led Dr. Adleman to play a central role in some of the most surprising, and provocative, discoveries in theoretical computer science."

...and just gets better and better from there.

3) Finally, a blast from the past… if you're ~55 or over a trip down memory lane….
Re-reading an old Jeremy Bernstein volume ("Cranks, Quarks, and the Cosmos") recently, I came across his chapter on Tom Lehrer (unfortunately I can't find a free full copy of it on the internet). Lehrer was a popular, clever, irreverent singer/satirist of the '50s, '60s and 70's before he largely retired from the scene (he was, by his own admission, a huge fan of Danny Kaye, whose style he very much emulated).
During his heyday, I honestly only found his material mildly amusing (there were LOTS of satirists around in those days), and it was only years later that I discovered his background (…which made him a far more interesting figure to me!)
So for any who don't know, Lehrer entered Harvard at the age of 15 and majored in mathematics, graduating at 19; a year later he got his Masters degree (and worked on, but never completed PhD. work). He taught for awhile at Harvard, MIT, and Wellesley. Joining the Army in 1955, Lehrer worked a couple years for some outfit called… drrrrrrumroll… the NSA!

If you're unaware of Lehrer you can still find his work on YouTube:

http://tinyurl.com/m3n43zv

(He's 85 now and his own website is here:  http://www.tomlehrer.org/ )

Anyway, Chu-Carroll and Adleman may well be fun guys as well for all I know, but Lehrer took math and fun to the level of turning it into a living. Nice work if you can get it (actually, a lot of his satire wasn't math-related).

Here's one sample of Lehrer's 'mathematical' work ("Lobachevsky"), to give you his flavor:

Keith Devlin… as you may not have heard him before….

Math-Frolic Interview #15 (...not the usual fare)

"As a naturalized American, I have an immigrant's reverence for those words of our National Anthem, 'Land of the free, home of the brave.' For many of my fellow citizens born here, I fear these are just words they learned to recite in elementary school. For the fact that 56% of Americans declare that they would give away fundamental freedoms to reduce the risk of terrorist attack indicates that we may become the 'land of the enslaved, home of the scared.' "  -- Dr. Keith Devlin in Huffington Post
                                            

I'm not sure there's anyone more generous with their time and energy than Keith Devlin….
Since Edward Snowden's NSA revelations (and subsequent controversy), I noticed Dr. Devlin expressing himself on the topic (as much as one can in 140 characters!) on Twitter (@ProfKeithDevlin) more than any other mathematician/scientist I follow. The passion of his opinions intrigued me and I asked if he'd do another Math-Frolic interview, but this time just on his views about this NSA controversy -- NO MATH (my prior math interview with Keith is HERE) -- I thought he deserved more time or space than available on Twitter or even Huffington Post, where he has a piece. So read up, Keith doesn't much mince his opinions!

 ***********************************

1) The recent NSA revelations have generated a broad range of opinion across the spectrum (from outrage, to 'ho-hum, nothing new here'). Of the many math/science persons I follow on Twitter you've been among the most harshly outspoken. Can you explain a little more deeply where that sense of betrayal stems from… as a 'naturalized' citizen do you perhaps appreciate American democratic ideals even more than a lifelong born-citizen who just takes them for granted… and how much does your British background (another country with a strong democratic history) come into play? Or, is it mostly just a straightforward legal/Constitutional issue for you, unrelated to background?

Appreciating the iconic ideals of US Democracy as enshrined in the Constitution is part of my outrage at the way the US (the nation, not just the government) has allowed those ideals to slide. I certainly am under no illusions as to the many deficiencies in the US, for instance, its third-world levels of poverty and infant mortality and its medieval prison system. But those words of the Founding Fathers are one of Humanity's greatest achievements. It's surely worth remembering that the US owes its existence to the fact that those Founding Fathers were traitors. So far, everything I have seen of Edward Snowden puts him into the same camp as the Nation's founders. Certainly, his public statements and actions so far qualify him as a greater American than the current President who complicitly -- and secretly -- allowed the slide away from the founding ideals to continue.

The personal twist in my case is that, twice in my life, I've found myself as the "suspected outcast". I'll describe the first. As a young assistant professor in Germany in the 1970s, when Germany was struggling with massive student unrest and genuine internal terrorism (Bader-Meinhoff, etc.), security forces surveillance of some of my students brought me into their radar, and for a few weeks I was followed around and my mail was regularly intercepted. The fact that I was very aware of this indicated that the intention was probably to scare me as much as to find any incriminating evidence against me, and my wife and I actually regarded the whole affair with amusement. I was clearly low level, peripheral fish in their surveillance sweep, and after a few weeks they were (as far as I know) out of my life. Still, it made me realize how easy it is for a totally innocent individual to find him or herself on a government security list, simply by virtue of the people they interact with. (To this day I have no idea if any of my students were active in the political unrest of the time, or indeed if any engaged in illegal activities.)

The second time was in the UK, and contributed to my leaving my homeland for the US, but the one example I have described should be enough to indicate why I simply don't buy the frequently touted idea that "If you have done nothing wrong, you have nothing to fear." In the age of big data, just as we can easily find ourselves with a wrecked credit rating that can take years to sort out, so too we can find ourselves on a government "person of suspicion" list. In my case, I had the psychological strength to shrug it off -- albeit I did emigrate from the UK to the USA. Had I a different psychology, the ending could have been tragically different, as it was for Aaron Swartz, who was unable to sustain the inhuman persecution by US attorney Carmen Ortiz and Massachusetts assistant US attorney Stephen Heymann, who clearly viewed him as a mere pawn to advance their careers.

2) Related to the above, you actually worked for the NSA at one time in your life (contractor???). I suspect you can't say a lot about that work, but can you say, in a more general way, if that specific experience with NSA, contributes to your strong feelings? And are there any details from your own NSA experience you can tell us about which are pertinent to this ongoing story?

In the early post-9/11 era, I did work on a large, non-classified (albeit not publicized) project to improve the quality of the actionable intelligence that could be obtained from massive amounts of data. I was glad to play my small role, though when that project came to an end, I held the same view I did at the start: absent a significant HUMINT lead (human intelligence), trawling through massive amounts of data is a waste of time. There is no chance you will be able to prevent a terrorist attack. I know that a number of intelligence leaders have made statements of late that claim otherwise, but all I can say is that after working hard on the problem for five years, I reached a very different conclusion. To be sure, I do not know the computing capabilities the NSA has, but based on my understanding of the problem, without a good HUMINT lead, it won't be enough. Mathematically, the problem is known as combinatorial explosion. (With a HUMINT lead, on the other hand, you don't need to trawl the data, you just have to search for confirming evidence, starting from that one lead.)

3) Author Kurt Eichenwald wrote a book a few years ago, "500 Days," apparently divulging info similar to what Ed Snowden has revealed. Have you by any chance read this volume? He claims on Twitter (as do others) that there is nothing new in the current revelations, and that in fact some of the details, as covered by the press, are simply wrong or misleading. To those who would say, there's no real news here, and moreover, private companies (Google, Facebook etc.) snoop on individual lives FAR MORE than the Gov't., what would you say?

I've written elsewhere (Huffington Post) that the Snowden revelations were akin to Lance Armstrong's appearance on Oprah. In both cases, we learned nothing we did not already strongly suspect. But making it public knowledge, as opposed to widely believed suspicion, changes the debate. In the Armstrong case, within days, he had lost all his multi-million dollar sponsorship deals. After Snowden, the intelligence chefs could not respond to questions by saying there was no wrong doing, they had to provide actual details, in at least one case revealing a clear-cut case of perjury before Congress. Maybe heads will roll -- they should -- but maybe not. (In fairness to those involved, the nature of intelligence does put people in a difficult position with regard to being truthful. Few of us have the courage of Edward Snowden.) In any event, even ordinary citizens had a pretty good idea of what the NSA was doing, so for sure our enemies did. Statements that the Snowden revelations damaged national security are clearly absurd. The security lies in the data, not the knowledge that is exists. The only damage from the Snowden revelations is the embarrassment of people in power. (It surely cannot be international relations, except on the surface, since all the other countries harbored the same suspicions as we all did, and for sure the many countries with the technological capabilities knew for sure what we were up to!)

4) Personally, while the massive net for "metadata" concerns me, what troubles me even more (and doesn't get much coverage) is the potential for NSA individuals to target specific politicians/leaders for scrutiny and use that info for strictly partisan purposes… possessing knowledge about the personal lives of political opponents is an even greater danger to democracy than knowledge of the general citizenry. Any thoughts?

This is the real worry. Right now, we have President Obama saying "Trust me, this immense security apparatus is being used for your safety." As it happens, I am inclined to give him that trust, though in so doing I am making a leap based on no first-hand knowledge. But that's not the point. Who knows who will hold the reins in the future? It was not long ago that J Edgar Hoover was in charge of the FBI. We've had despots in positions of power before, it can happen again. When I was living and working in West Germany, I traveled occasionally to East Berlin to consult with university colleagues, and learned enough about the STASI to never want to live in a state with such a powerful and intrusive security apparatus.

5) Some people view Snowden (thus far) as a highly-intelligent, sincere, courageous, deeply-patriotic  individual, and others label him narcissistic, self-aggrandizing, delusional (some have even said, why can't he be ALL of the above!). Care to say, how you would characterize him?

I already did. I think history will portray him as a twenty-first century "Founding Father", who initiated a return to the principles by which the country was founded. Assuming, that is, that we do indeed step back from the abyss. The current attempts to discredit him are as predictable as they are transparent. His personal character actually makes little difference. He did the US a great service (that's the part history will remember) by performing a heroic act, clearly at high risk to himself. Exactly the same can be said of the Founding Fathers. Acts can endure, personalities are replaced by stories.

6) One of the interesting major disagreements is between those who say that the sort of massive "dragnet" surveillance that is going on is outright illegal and not authorized by Patriot Act measures, versus those who say there is NO "surveillance" but only the collection of large-scale metadata (which does not constitute surveillance), and only when a 'pattern' of interest is found in the data can the Gov't. then seek a court order to do further actual surveillance. I know you are interested in the uses of language and meaning, and clearly that is what we have here… Any comments?

It is clearly illegal, being against the Constitution. It's also immoral. Period.

7) Do you feel very disillusioned (as some do) by the Obama presidency over the various issues of transparency/secrecy that have arisen, or are your issues more with the intelligence community than with the White House?

We live in a democratic republic. The intelligence community do their job, and implicit in that is to collect as much information as they can. The elected government are the ones setting the limits and calling the shots. If there has been a breakdown in that line of command, it is the government that has the responsibility to put things right. If ever we were at a juncture where a president should offer real leadership, now is that time. I understand Obama would like to go down in history as another Lincoln. Now is his chance. I wonder if he has it in him.

8) Supposedly Glenn Greenwald/Guardian have several more disclosures to make from the information Snowden provided. Care to make any predictions (and I know you think that predictions, especially about the future, are difficult ;-) about what may happen over the course of say the next year? …Will Snowden be extradited and prosecuted here in the U.S.? Will the Patriot Act be revisited and revised by Congress? Will the stand politicians' take on this affair (with or against Snowden/NSA) have a major effect on the 2014 mid-term elections?….

Since I don't know what information Snowden has, I don't see how anyone can make predictions. Whatever he has clearly already exists in multiple copies, held by different people, so it will likely eventually come out. So in practical terms, the best option for the US is to simply leave Snowden alone in Hong Kong. Public interest being as it is, "the Snowden story" will soon go away -- though I hope that real reforms result. Trying to have him extradited to the US, in contrast, will not only keep the story on the front pages for months and more likely years, but if the attempt succeeds, we will have a martyr on our hands. And martyrs are dangerous. Do we want to turn Snowden into another Nelson Mandella? How do we respond if, for instance, an imprisoned Edward Snowden is awarded the Nobel Peace Prize? (Those Scandinavians have a strong sense of social justice and are not easily pressured, so that could very well happen!) Better not to go that route. There is a slew of downsides, but the only "upside" is revenge, and there is no way the US could come out with dignity and respect if we throw our immense power going after one of our own citizens so it would prove to be a hollow upside.

9) And one last crystal ball inquiry… many have contended for a long while now that in the future there simply will be NO privacy… some think current young generations have ALREADY forfeited any significant concern over privacy. I truly wonder if, a century from now, "privacy" won't be just a quaint little term in historical footnotes. You and I might not wish to live in that world, but is not the near-complete loss of privacy inevitably coming? :-(

I think that here in the US we have a choice. In 1789, a bunch of traitors to the ruling authority formulated the First and Fourth Amendments as they set the new nation on its course.  Like him or hate him, Edward Snowden has put the questions of public information and personal privacy on the table once again. As a result, we have an opportunity to correct our course. Because of the Founding Fathers, we are currently able to debate this issue freely and openly. If we don't live up to those two-hundred-years ideals now, that great episode of human society (great for all its flaws, which lie in the execution, not the ideals) will have come to an end. We will be the "Land of the enslaved, home of the scared."

***********************************

....I don't completely agree with everything Keith says here, but I surely love the man's passion... as he demonstrates in everything he takes an interest in or speaks about. And further, as someone who has experienced unwarranted governmental suspicion/surveillance elsewhere -- albeit by his admission short term and low level -- his views deserve close attention. THANKS again for taking the time to respond Dr. Devlin.

I'll close out (...for some comic relief) with this "Good Will Hunting" scene that I've already used over at Math-Frolic, and most of you have likely seen:

Waxing Platonic…

The Platonic divide in math....

Ramanujan

The book I've highlighted recently, "The New York Times Book of Mathematics," ends with a chapter of readings on various notable mathematicians… Erdos, Ramanujan, Conway, Gödel, Wiles, etc. I suspect most (if not all) of the brilliant figures profiled were/are Platonists (mathematics is discovered, not merely created). Yet many other recent math figures (Reuben Hersh, William Byers, Keith Devlin, Jim Holt, and more) have forcefully argued that mathematics is indeed a mental creation that might even differ considerably in a different Universe than ours -- indeed some almost seem to find the notion of mathematical Platonism so wrong-headed as to be silly (while Martin Gardner found the non-Platonist view almost silly). And occasionally such writers cause me to sway toward their non-Platonist stance though I always seem to float back toward Platonism.

One thing that so many of the greatest, most productive mathematicians seem to share is an uncanny, almost inexplicable ability to tap into a realm of intuition or mental landscape not readily accessible to most of us. Ramanujan is certainly the unparalleled, most inexplicable, example of this; producing amazing mathematical results that are still today being explored and proven. Reading James Gleick's portrait of Ramanujan in the Times volume it really hit me… was Ramanujan, who routinely produced such results/theorems without ever showing the steps that led to the outcome, in direct access of the "Platonic realm?" He himself claimed his insights came in dreams and trances directly from the Indian Goddess Namagiri... Who are we to argue (and where did she reside)?!!

In many ways, Ramanujan's extraordinary talents are reminiscent of the incredible abilities of various mathematical savants and prodigies who usually can't explain how they do what they do. Their brains seem clearly to operate, or even be wired, differently from those of 'ordinary' people.

My point in all this is simply that such rare, yet nonetheless real, individuals DO give an appearance of tapping into a realm… call it perhaps the Platonist realm… that the rest of us lack ready access to, where numbers and math really DO exist apart from our day-to-day world.  Naysaying non-Platonists will simply argue that however Ramanujan and the rest gain their special knowledge, it ultimately still arises via the firing of neurons within a physical human brain situated between two ears… i.e. it is still a human creation. I can't prove that reductive view wrong, but the notion that there are worlds out there that only some of us can easily tap into, and only some of the time, through means we don't even comprehend… is so much more appealing! As Shakespeare put it long long ago, “There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy.”

I think Martin Gardner might well relate to this idea too… For all his empirical skepticism, Gardner also described himself as a "Mysterian," a philosophical view which holds that ultimately consciousness cannot be explained by any human brain. In the famous words of computer scientist Emerson Pugh, "If the human brain were so simple that we could understand it, than we would be so simple that we couldn't."  Is it possible that humans are able to draw upon a Platonic world, and can recognize 'consciousness,' yet perhaps never, with our limited minds, fully grasp either? Does the 'Platonic world' exist, but like the Continuum Hypothesis, fall into a nether land of things that simply can't be proved true or false by human logic?
Speaking of certain mathematical proofs, Paul Erdos would famously say, "This one is from The Book!" I'm not so sure he was speaking in metaphor... perhaps The Book, in some (Platonic) manifestation, exists. Is the alluring beauty of math only in our heads, or is it an integral part of all creation? MIT physicist Max Tegmark has argued for some time now that the entire physical universe, as we perceive it, is nothing more than mathematics, or a mathematical structure (called the MUH, or "mathematical universe hypothesis").

Anyway, read Gleick's beautiful 1987 portrait of Ramanujan and just imagine the Indian mystic-mathematician dreaming and dipping into a realm where numbers are as 'real' as rocks and chairs are to most of us:

http://www.nytimes.com/1987/07/14/science/an-isolated-genius-is-given-his-due.html?

a couple of brief lines from therein:

" 'When he [Ramanujan] pulled extraordinary objects out of the air, they weren't just curiosities but they were the right things,' said Jonathan M. Borwein of Dalhousie University in Halifax, Nova Scotia...
" 'He seems to have functioned in a way unlike anybody else we know of,' Dr. Borwein said. 'He had such a feel for things that they just flowed out of his brain. Perhaps he didn't see them in any way that's translatable.' "

It's probably also worth noting that the very first entry in the entire NY Times anthology is a 1998 George Johnson piece also addressing the subject of Platonism:

"Useful Invention or Absolute Truth: What Is Math?" by George Johnson

At the end of the piece, Johnson cites a 1995 book, "Conversations on Mind, Matter and Mathematics" that covered a debate between French mathematician Alain Connes and French neurobiologist Jean-Pierre Changeux over the subject of math Platonism. An interesting and rich review of that book here (even makes brief reference to Ramanujan):
 
http://www.timeshighereducation.co.uk/161513.article 

Connes and Changeux didn't resolve the debate... and we won't here... but still, nourishing food-for-thought.

Math via The New York Times

Non-technical math anthologies are rare critters… when one comes along my instinct is to pounce on it. "The New York Times Book of Mathematics," edited by Gina Kolata, was worth the pounce!

This volume covers a wide and interesting array of topics. Here are the 7 chapter headings (though they don't fully hint at the range of material touched on):

1) What Is Mathematics?

2) Statistics, Coincidences and Surprising Facts
 
3) Famous Problems, Solved and As Yet Unsolved
 
4) Chaos, Catastrophe and Randomness
 
5) Cryptography and the Emergence of Truly Unbreakable Codes
 
6) Computers Enter the World of Mathematics
 
7) Mathematicians and Their World

That should give you a sense of the breadth of topics on display here. The pieces are vibrant, terse treatments (no doubt only intended to fit within a certain column length). The writing is so good that the pithiness leaves one reaching the end of most pieces wanting more... just one more page pl-e-e-ease.

I think Gina Kolata sets the tone and 'feel' of this engaging volume very aptly when she writes in her Introduction:

"A mathematician once dismissed the very idea that people outside his circle could ever understand the true essence of the field. Mathematics is an art form, like music or painting. Translating math into the English language, he said, is harder than translating Chinese poetry. The beauty is lost, the elegance, and a proof that is a thing of ineffable iridescence becomes reduced to a baffling or mundane-sounding bottom line....

"But even if the rest of us cannot appreciate mathematics as an art form, are we really shut out? Articles in the New York Times may not give the details of proofs, but they reveal a rich world that can be exciting, surprising, and can even tug at the heartstrings."

Yet several reviews I've seen of the volume are rather ho-hum about it, but these are usually from professional mathematicians -- for the working mathematician there may not be that much here to excite -- although I think any math lover will find at least a few pieces that strike a chord. But for lay folks with an interest in math (my core readership!!) this may be the BEST anthology I've ever come across! There is no technical material or equations to weigh down your enjoyment, nor slow your consumption. It is all about math and mathematicians... without doing math.

One downside is that because this is limited to NY Times' writers, many excellent popular math writers are absent.  Indeed, I'd normally be skeptical of an "anthology" that was restricted to the number of writers this one is -- it is very heavy on pieces from Gina Kolata and James Gleick -- but these writers are SO good at their craft that skepticism quickly fades away. While Kolata and Gleick's pieces are perhaps the best, there are numerous fine contributions as well from George Johnson, John Markoff, Dennis Overbye, and others. Oddly, there are no entries from Steven Strogatz here (author of some of the most popular math pieces the Times has carried in recent years), but perhaps his offerings simply didn't make the 2010 cutoff for the volume. The one other thing that may be missing from the collection, it seems to me, are more articles which relate math to the other sciences, particularly physics and biology (I believe the Times has run several such pieces).

Most of the entries come from the last 3 decades or so, but some go back as far as the late 1800s. I wasn't particularly enamored of several of the older entries that were probably included more for the sense of history or progression they illustrate than for the math covered. Still, overall the mix is appealing.
 
Chapter 5, focusing on cryptography, would have been interesting in its own right, but became even more-so, in light of current events, as almost every article makes mention of the NSA and its relationship with mathematicians (by most accounts, by the way, NSA is the largest employer of mathematicians in the world). But there isn't a bad chapter in the volume.

In short, I love this compendium, even more than I expected to. If it wasn't such a thick, heavy volume I would almost recommend it, at this time of year, as a 'beach-read'… for the mathematically-inclined. In the distressed world of print journalism, the NY Times has been cutting back on science journalism, so it is wonderful to have this hard-copy of delicious math-related essays to keep on one's shelf as a permanent source of popular math writing stretching across decades. Hats off to Ms. Kolata on a job well-done!

Flipped Classrooms, MOOCs, and Having a Blast

Timing is everything....

Well, this was great… I was planning to write a post musing a bit more about math education in regards to both "flipped classrooms" and MOOCs… but then discovered Keith Devlin has just put up a new (longish) post on his MOOC blog saying most of what I wanted to say, and with more authority than I could say it. So please read it:

http://mooctalk.org/2013/06/03/the-mooc-will-soon-die-long-live-the-moor/

Do note that I think his title may be a bit misleading so follow carefully all he has to say. I was afraid his long lapse in blogposts might mean that the 2nd rendition of his 'mathematical thinking' MOOC hadn't proceeded well (though his insanely busy schedule could also account for it), and luckily it doesn't sound like that was the case… though he does still write with caution about MOOCs, and will have more to say in the future about this last go-around.

Here are a few of the most trenchant comments he makes (I've added some emphasis):

"the vast majority of people under twenty now interact far more using social media than in person.
We could, of course, spend (I would say “waste”) our time debating whether or not this transition from physical space to cyberspace is a good thing. Personally, however, I think it is more productive to take steps to make sure it is – or at least ends up – a good thing. That means we need to take good education online, and we need to do so for the same reason that it’s important to embed good learning into video games…
"The media of any age are the ones through which we must pass on our culture and our cumulative learning."

"Something else that digital technologies and the Web make possible is rapid iteration guided by huge amounts of user feedback data – data obtained with great ease in almost real time."

The one place where I think Keith sounds a little too negative is when he writes:

"Experimentation and rapid prototyping are fine in their place, but only when we all have more experience with them and have hard evidence of their efficacy (assuming they have such), should we start to think about giving them any critical significance in an educational system which (when executed properly) has served humankind well for several hundred years. Anyone who claims otherwise is probably trying to sell you something."

Actually, I think "experimentation and rapid prototyping" may now be an integral part of our quickly evolving world and education system… more than ever before change can happen with such speed that we may try 4 failed experiments and still succeed at #5 in an acceptable/practical amount of time (even before the "hard evidence of efficacy" is fully in or agreed upon. Just the speed with which the MOOC movement has grown is a testament to that, and as Keith implies, the time is ripe for us to "make sure" they [MOOCs] work in some form.

So much for MOOCs…
What actually got me thinking again about education was a recent Twitter tweet that led me to this blog I was previously unfamiliar with:

http://flippingwithkirch.blogspot.co.uk/

Despite the uk URL appendage it's from a California high school math teacher (Crystal Kirch) focused on the "flipped classroom" concept. Just scanning over it, it looks interesting and impressive to me, but as someone not in the loop of secondary education I don't want to assume too much. What definitely caught my attention though (and those of you in secondary education likely already knew this) was the sheer number of other blogs with a similar focus on flipped instruction (as well as a network of teachers with this interest) that Mrs. Kirch links to. The "flipped classroom" has been around long enough that LOTS of teachers are trying it, tweaking it, playing/experimenting with it, blogging about it, and just generally sharing their experiences (good and bad) with their peers. What a great collaborative endeavor!!… and not brought on by some agency-directed-commissioned group-on-high, but by the spontaneous interest of those who share similar goals. Again, before the internet this sort of rapid cross-communication effort wasn't possible.

The term "flipped classroom" came about, so far as I'm aware, from early uses of Khan Academy videos (and Khan Academy still has many vocal critics), but of course there are now MANY internet resources available to choose from, and Khan itself constantly evolves. (Some have noted that the 'idea' of the flipped classroom, though not the term itself, actually long precedes Khan Academy.)

It is fascinating to me how both "flipped classrooms" and MOOCs, which in some ways share little in common, and operate on different levels of education, have simultaneously sprouted up like mushrooms in the cyber landscape, both controversial and rapidly-evolving, yet giving tremendous promise.

As Keith writes so aptly at the end:

"Those of us in education are fortunate to be living in a time where there is so much potential for change. The last time anything happened on this scale in the world of education was the invention of the printing press in the Fifteenth Century. As you can probably tell, I am having a blast."

And some of us are just having a blast... watching those of you who are in the trenches having a blast.
To Keith, and Mrs. Kirch, and all others doing the nitty-gritty work that will shape the education of future generations... THANK YOU!

Vickie Kearn... She Reads 'em Before You Ever Hear of 'em

 Math-Frolic Interview #14

"Appreciating the power of math and what it has and can do for us is really important. It isn’t just a lot of numbers, it is about people and applications and improving everything we care about." -- Vickie Kearn


You're likely not as familiar with the name 'Vickie Kearn' as most of the other names I've interviewed here... but it's a joy for me to bring her forth from behind the professional curtain where she hangs out. As an editor for Princeton University Press (a favorite of mine) she shepherds a great many of the books and authors we come to love, to our bookstores for us to read. It's fun to gain a better sense of how that whole behind-the-scenes process works. Read on (I've emphasized a few bits with bold):

********************************

1) To start, can you tell readers a little about your background or anything else pertinent to your math interest and your editorial position with Princeton University Press?

I have always loved math and had teachers who encouraged this love. When I was 10 my parents moved to Venezuela so when I was 16 I had to come back to the States to go to boarding school since there were no English schools where we lived. I went to a very small school and had the same math teacher (Elsie Nunn) for three years. She was wonderful and we had math club every day. Now you might think that was a bit much but she was so exciting and told terrific stories about the people behind the math. She could do all sorts of things with simple tools like sting and cardboard. I remember that she was double jointed and could draw a perfect circle.

When I went to college the women took classes on one side of the lake and the men on the other. Lucky for me, the advanced math classes were all taught on the men’s side of the lake. I went to a Baptist school and men and women could only talk to one another on certain days of the week. Because of my math connection, I got to talk to them every day of the week. Perhaps not a reason to major in math, but a really neat benefit.

After college I taught school for eight years (elementary and middle school math) and then moved to New York City to begin a career in publishing. I had pretty much had it with the books I was given to use in my classrooms and thought that I could make a difference if I could find a way to get more interesting and useful books published, especially in math. I started my career at Academic Press as a developmental editor. I had to read all of the math textbooks, work all the problems (to make sure all of the needed information was there and that the problems could actually be worked) and write the solutions manuals. After three years I did not think I could work out one more calculus problem and really wanted to get on with finding those books I so sought. I moved to Marcel Dekker where I was an acquiring editor. I actually got to look for authors who could write the next great math text. I didn’t know if when I was hired as the math editor that I would end up also working on statistics, electrical engineering, quality control, and food science. Although I got a lot of experience, I was not making much progress with my math hunt. I then went to the Society for Industrial and Applied Mathematics which was heaven because it was all math. I worked on books and journals as well as conferences and membership drives. This was exactly what I was looking for.  This was a great job but I found that there were some titles that I longed to find but which were not good fits for the society. I wanted to reach out to other disciplines to show how math could be used not just in the sciences but also the humanities and the social sciences. I wanted to bring more math to general readers—the math lovers and the math haters and math phobics. It was difficult for a math society to reach all of these different audiences without publishing books in all of these areas.

Princeton University Press has been a perfect fit for me. We publish in almost every discipline you can imagine. We have sales reps who visit bookstores and publicists who visit major media outlets for print, TV, and radio. The Press and our editorial board are willing to try new things like books of puzzles and graphic novels.

2) Prior to this point, I've been interviewing individuals who are direct math communicators, bloggers and/or authors. You're sort of a layer back as a gatekeeper of the very sorts of other folks I normally interview. That makes it interesting, because many readers won't know your name and yet you are probably more personally familiar, than those readers, with the very names they are so familiar with! Can you say a little of what it's like to work with distinguished math authors as you mentor their idea or first draft from proposal to publication? And do you build personal friendships with many of these writers as you collaborate with them over time, or is it more of a strictly arms-length business relationship?

Many of my closest friends are mathematicians.  In a way I have grown up with them and my son is the same age of many of their children. In addition to our love of math and great books, we share this common bond of raising kids, sending them to college, and watching them find their way. When I began my career in publishing in 1977 I did not know anyone. There was a lot more competition than there is now and there were many seasoned editors who had built a core of authors who always published with them. I decided that the best thing to do was to contact the people at the top of their careers (all the big prize winners) and ask them about their brightest students. These are the people I contacted and talked to about what books they needed or would have been helpful when they were studying math.  Since these were the rising stars they were soon in a position to write books and they remembered me when they were considering a publisher for their book. Now they are the prize winners and I am still publishing them and they are now recommending their students. Every book I have published has been special in one way or another. I have had the privilege to meet the most honored and famous mathematicians of our time. I also have had the honor to meet some of the greatest teachers around the world. You don’t have to win a lot of prizes to write a good book. You do have to be creative and be passionate about your subject. The trick to publishing great books is finding these people. Sometimes an author comes to me with a completed manuscript that is almost ready to go. The books that are the most fun, however, are the ones that we design together from the seed of an idea to a finished product that is widely read. This can take several years which is plenty of time to establish a lasting friendship.

 [....Sounds like a dream job!! ;-)]

3) Princeton University Press puts out some of the most consistently excellent, interesting, well-designed math books of any publisher! So I'm curious how that selection process works so successfully. Can you describe a little of how things proceed from the time a writer approaches PUP to the time a book is accepted for publication and finally produced, and what is your role along the way?

Princeton University Press cares a great deal about its authors and the books it publishes. Each book is carefully selected to ensure that it is accurate, fits a specific audience and is pleasant to look at and read. Sometimes authors come to me with an idea and sometimes I think of a topic I think will be great for a book and seek an author who would be perfect to write it. This can take a long time so you have to be patient. I have given up on a topic at times when I can’t find the right author. The first step in our process is to put together a proposal for a book. I then present it to my colleagues who help me decide if the topic fits our list and if we can promote the book effectively. If so, I have the proposal reviewed and if the readers are positive, we offer a contract. We might work on the development of the project over many years or it might come together quickly. Once the final manuscript is complete, it is sent out for a final review. If the book is for the general reader or an undergraduate textbook, I read though it as well and give the author advice on changes to consider. If the reader reports suggest more work, then the author revises and we send it back to the readers. If the suggestions are minor, I take the book to our editorial board for final approval. The board consists of five Princeton University professors across all disciplines who approve books for publication based on my recommendation and those of the readers. They ensure that the book reflects the mission of the University as well as the Press.

The production process is a careful one. We copyedit all of our books and redraw art where necessary. We have designers who look at the book to make sure that the manuscript will be laid out it the most user friendly way. They also are responsible for designing a cover that is attractive and reflects the content of the book. During production, our publicity, marketing, and sales departments are all preparing materials and contacting people to make sure that our newly published books will be as noticeable as possible and will get into the hands of readers.  During this time I am solving any problems that arise and working on getting endorsements which will go on the cover of the book. I no longer have to write solution’s manuals but I make sure that the authors are. I also help authors come up with ideas for ancillary material that they might want to put on the webpage for their book. We are also developing Facebook and Twitter accounts for each book during this time.

[Very interesting to hear about the whole process! Needless to say I think PUP achieves its goals well -- your math books are always very readable, informative, AND very attractive to look at!]

4) Roughly speaking, of proposals you get for math fare, what percentage might PUP generally end up publishing? And is it possible to generalize about what the most common reason for rejecting a proposal is?

The sciences are different from the humanities and social sciences where it is imperative to write a book or two in order to get tenure. The editors in these areas are deluged with proposals. In math, the opposite is true. They are writing and publishing research papers to get tenure. Most of the proposals I get are from direct recommendations from someone I know, an author I have already published, or someone I have approached so I don’t get a lot of unsolicited proposals. I do get a few and look at each one carefully before deciding what to do. Many are rejected for various reasons and others get published. The most common reason for rejecting a proposal is that it is totally wacky or not prepared properly. Sending an editor a proposal with hand drawn figures and no coherent description of the book or who you are writing for is a good sign the book will not be worth publishing. Just as you would never think about sending in a resume that is loaded with typos for a job application, you should check your proposal carefully to make sure it states what the book is about, why it is important, who it is for, what the reader will gain from reading the book,  and what the competition includes. Oh yes, and check for typos!

I publish a very small percentage of the unsolicited proposal I receive. However, there is a very high publication rate of those that are recommended to me or that I go looking for.

5) Obviously, any book you choose to publish, you believe is well-done and will have an audience, but are there any examples of Princeton math books that especially surprised you with the volume of their sales?

As I said, each book I work on is special in some way. It may be that it sells only 600 copies but the readers use the information inside to solve some great problem or advance a new area of math in some way. Others might sell tens of thousands and get high school students excited about math. All are important in my mind. Some books get great reviews and just don’t live up to expectations. Others get little notice in the media but find their way and outsell our expectations.

6) On the other side of the coin, have you ever been involved in rejecting a book for Princeton, only to see it become a major seller for another publisher, and thought, 'ohhh man, why did we let that one slip away!'…?

On several occasions I have rejected books that I know will sell well but which didn’t meet our mission in one way or another. Every publisher wants their books to sell as many copies as possible but not at the risk of getting negative reviews and possibly damaging a reputation that has long been established. I actually can’t think of a book that I was sorry I rejected for these reasons.

7) Can you tell us anything about some of the math titles/topics/authors we have to look forward to coming down the pike shortly? 

I just presented my fall 2013 list to our sales reps and there are some great books on that list. They include:

Undiluted Hocus Pocus: The Autobiography of Martin Gardner -- This is one of the last things that he wrote before he died. He was a very private person and even his closest friends have learned a lot from reading the manuscript.   

Beautiful Geometry by Eli Maor and Eugen Jost is an illustrated guide to some of the major ideas in geometry. It includes proofs, history and art designed just for this book.  

Wizards, Aliens, and Starships by Charles Adler is all about the math and physics in fantasy and science fiction. Which cool things could actually happen and which are impossible?  

Will You be Alive Ten Years From Now is a book of probability puzzlers by Paul Nahin who is a perennial favorite. He has published many books with us and has a very loyal following. 

 [Ohhh Wow, these sound FANTASTIC!!! And an autobiography from Martin Gardner... I'm almost drooling over the keyboard thinking about it... who knew there would be yet more Martin to enjoy 3 years after his demise. I'm not familiar with Adler, but Maor and Nahin are other favorites. THANKS so much for letting us know about these ahead-of-time!]

8) When you're not editing math books, what are some of your other main interests/hobbies/activities?  

I like to tutor kids who are struggling with math and I volunteer for a pet rescue. I also like to read and solve logic problems.

9) Any parting words, not covered above, you'd want to pass along to an audience of math readers and enthusiasts?

Every day I try to find someone who does not like math (or thinks they don’t) or thinks it is hard and convince them that math is fun and is not really that hard (at least on some level). Appreciating the power of math and what it has and can do for us is really important. It isn’t just a lot of numbers, it is about people and applications and improving everything we care about. From sports to medicine to ensuring we are safe, math plays a large part. If every reader could convert another person every day, we soon would have a hard time finding people who don’t like math.

...A great thought to end with!

THANKS, Vickie, for giving us an inside look at how the books we enjoy so much end up in our hands.

*******************************
And if you want to hear her voice, Vickie was also interviewed last year as part of Sol Lederman's podcast series here:

http://wildaboutmath.com/2012/06/03/vickie-kearn-inspired-by-math-8/