This Week's Math Potpourri Serving

Things catching my attention this week:

1)  This is actually pretty fascinating from a mathematical standpoint (water-saving faucet); h/t Tim Skellett:
http://www.sciencealert.com/this-tap-saves-water-by-creating-incredible-patterns

2)  Congratulations in order for Ian Stewart and Steven Strogatz for sharing the 2015 Lewis Thomas Prize for Writing about Science:
http://giveandjoin.rockefeller.edu/events/lewis-thomas
(quite an honor for two mathematicians to win this!)

3)  And from the "p-values no longer get any respect" Dept.:
http://tinyurl.com/mb843zk

4)  Film review of "X + Y," about the International Math Olympiad:
http://tinyurl.com/m8lmwcy

5)  In honor of tomorrow ('Pi Day''), a simple question posed by Futility Closet, 'Does the binary expansion of pi contain more 1s or 0s?':
http://www.futilitycloset.com/2015/03/11/portions-of-pi/
Also an old Martin Gardner problem via Futility Closet this week:
http://www.futilitycloset.com/2015/03/07/time-and-distance/

6)  When it comes to area calculations, Ben Orlin points to a prevalence of rectangles:
http://mathwithbaddrawings.com/2015/03/11/the-secret-to-all-areas/

7)  The latest "Devlin's Angle" blog post is largely about that certain transcendental number in the news...:
http://devlinsangle.blogspot.com/2015/03/pi-day-cyclical-motion-and-great-video.html

8)  And Math Drudge was among the MANY others with Pi Day coverage:
http://experimentalmath.info/blog/2015/03/i-prefer-pi-background-for-big-pi-day-31415/

9)  Just around the corner (April 18) is the first (and FREE!) National Math Festival in Wash. D.C.:
http://www.mathfest.org/

10)  A blogger has put together a list of 8 FREE (yeah, I like that word) YouTube channels devoted to SAT test preparation (I'm not endorsing the channels myself, since I've not reviewed them, but looks worth checking out if SAT preparation is on your horizon):
http://moomoomath.blogspot.com/2015/03/8-youtube-channels-to-help-with-sat-math.html

11)  Mike Lawler's place on the Web:  https://mikesmathpage.wordpress.com/
I'm especially a sucker for nice geometry problems, and Mike worked through a couple two days ago:
https://mikesmathpage.wordpress.com/2015/03/11/geometry-problem-solving/

12)  Over at Math-Frolic this morning I've linked to a simply wonderful Erica Klarreich piece in Quanta Magazine, on deep connections in mathematics:
http://math-frolic.blogspot.com/2015/03/mathematicians-drunk-on-moonshine-so-to.html

13)  Them's fightin' words... "Are Physicists Saner Than Mathematicians?" from CosmosMagazine:
http://blog.cosmosmagazine.com/blog/2015/3/13/are-physicists-saner-than-mathematicians
[p.s.:  Happy Birthday to Albert Einstein tomorrow!!]

14)  And perhaps my favorite bit of humor from the week:
https://recursivelyrecursive.wordpress.com/2015/03/09/didnt-we-say-thered-be-no-more-self-referring-signs/


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

a)  To get you into a bit of a physics-y mood for an interview I may have up this Sunday, here's news of the approaching re-start of CERN's LHC near Geneva:
http://tinyurl.com/oxjvybw

b)  And will end again with another simple feel-good story that went viral, but ICYMI:
http://www.huffingtonpost.com/2015/03/06/dancing-man-found-bodyshamed-dance-party_n_6817794.html

Single Digits... and Much, Much More

"Single Digits: In Praise of Small Numbers"  by Marc Chamberland


Several books in recent times have been comprised of "biographical" sketches of numbers... listing interesting tidbits/stories/facts about various integers or other significant numbers. So when an advance review copy of Marc Chamberland's "Single Digits: In Praise of Small Numbers" appeared in my mailbox, I thought to myself, "...seen this approach, been done before... yawwwn."
Getting into the volume though I was very pleasantly surprised! This compact (slightly over 200 pgs.) volume offers up different problems, puzzles, theorems, findings, conjectures on virtually every page. It's a veritable carnival for math geeks!! Yes, its chapters take you through the digits 1 through 9, as a skeletal framework for the book, but the chockfull content goes well, well beyond such simplicity. Indeed, as you're reading the fascinating contents herein you quickly lose sight of whatever tie-in a given chapter has to any "single digit."

Much of the material is not new, and is often classic. But a surprising amount is lesser, or even rarely, known subject matter. I feel safe in saying that both amateur and professional mathematicians alike will find new items of interest here -- LOTS of mathematics grist for thought and play -- with a heavy emphasis on geometry and algebra, and just a smidgen of topology, trig, or other math fields. The last couple of chapters, "8" and "9," are some of the shorter, but also deepest and most difficult chapters in the book.
Alexander Bogomolny has written a quick review of the volume and indicates the surprising breadth of subject matter included (while still only touching on a small sampling of the topics):
http://www.cut-the-knot.org/books/Reviews/SingleDigits.shtml

Indeed, there is so much real math packed in here I can't really recommend this work for a general audience, but only to those who are already enamored of math or have some good background with it.  This book is not for tepid math folks, but for diving into exhilaratedly with both feet!  There are around 115 topics listed in the table of contents, and of course some of those topics entail further topics.
The title and cover of the book don't really do it justice, nor hint at, the amount, richness, or variety of that mathematical fare inside. In fact, I fear a lot of lay readers, may pick this book up expecting a simpler treatment than what is within, while other mathematicians may not recognize, from the deceptively lightweight look of the book, what a fantastic, useful volume it is!  In short, it's a book I thought might only deserve a passing glance, but in fact is a welcome, splendid, fruitful addition to my math bookshelf. Reading it has left me with a LONG list of interesting things I want to explore further on Google... and oddly, these days, I'm not sure you can pay a book any higher compliment than that!

On Amazon, "Single Digits" is listed as due for June 1 release -- something to anticipate, and can be pre-ordered.

[ I'll note, lastly, that the author Marc Chamberland runs a YouTube site called "Tipping Point Math" here:  https://m.youtube.com/user/TippingPointMath? ]

Weekly Selections

Some of the stuff I've been reading this week:

ADDENDUM:  After posting all of the below this morning, discovered this new piece on Terry Tao  that is just too, too good to hold over 'til next week!:
http://www.smh.com.au/good-weekend/terence-tao-the-mozart-of-maths-20150306-13fwcv.html

1)  Cedric Villani and his new volume, "Birth of a Theorem," covered in The Guardian:
http://tinyurl.com/n7m57z4

2)  Something for the musically-inclined:
http://tinyurl.com/knz2tvr

3)  Yet another interesting interview with Ed Frenkel, this time on mathematics and our financial system (and crises):
http://www.thinkadvisor.com/2015/03/02/how-math-will-shape-wall-streets-future?page_all=1
And I learned from the piece that Dr. Frenkel now has his own website:
http://www.edwardfrenkel.com/

4)  Andrew Gelman voices a contrarian viewpoint because "A key part of science is to learn what we don’t know" and we ought "embrace" variation and uncertainty:
http://andrewgelman.com/2015/03/02/what-hypothesis-testing-is-all-about-hint-its-not-what-you-think/

5)  I got my undergraduate college alumni magazine in the mail this week and it included a brief piece by 'inspiringly stubborn' math professor Ami Radunskaya on "How To Become a Role Model For Women In Math":
http://magazine.pomona.edu/2015/spring/how-to-become-a-role-model-for-women-in-math/

6)  I just knew, with ~95% confidence level ;-), that Wm. Briggs would be beside himself with joy at recent news that the journal Basic and Applied Social Psychology was dropping p-values or the “null hypothesis significance testing procedure” from its articles: 
http://wmbriggs.com/post/15465/
Meanwhile, Deborah Mayo covered the same development here:
http://errorstatistics.com/2015/03/05/a-puzzle-about-the-latest-test-ban-or-dont-ask-dont-tell/

7)  Another review of Michael Harris's book, "Mathematics Without Apologies" (which I reviewed HERE) is in SIAM News:
http://sinews.siam.org/DetailsPage/tabid/607/ArticleID/415/Last-Bastion-of-Purity-in-a-Corrupt-World.aspx
...and Harris responds to it here at his own new blog:
https://mathematicswithoutapologies.wordpress.com/2015/03/03/how-to-read-a-bad-review/#respond
(h/t to Jordan Ellenberg for these)

8)  A new, packed "Math Teachers At Play" blog carnival here:
https://cavmaths.wordpress.com/2015/03/03/maths-teachers-at-play-83rd-edition/

9)  Fawn Nguyen as insightful/instructive as always with her 6th graders (where were the Fawn Nguyens when I was in 6th grade!):
http://fawnnguyen.com/reversing-the-question/

10)  Ian Stewart's latest book, "Professor Stewart's Incredible Numbers," should be showing up in bookstores any day now:
http://www.amazon.co.uk/Professor-Stewarts-Incredible-Numbers-Stewart/dp/1781254109/

11)  Just noticed (and haven't had a chance to listen myself) that the very latest (today) NPR TEDRadioHour is all math-related (looks good):
http://www.npr.org/programs/ted-radio-hour/388518439/solve-for-x

12)  And hey, it's March Madness time (in USA) so have to include this article (chance of a perfect bracket):
http://www.chicagotribune.com/sports/college/ct-march-madness-probability-met-20150303-story.html 

13)  Mike Lawler has been busy as always:  https://mikesmathpage.wordpress.com/


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

1)  First bonus from last week was just a great repeat segment from NPR's TEDRadioHour on "dirty jobs" -- about jobs and happiness (not what one might think):
http://www.npr.org/2013/11/01/240780579/are-people-with-dirty-jobs-the-most-successful

2)  And, off my usual beaten track, but for all the animal lovers out there (me included), this feel-good story from the week, to end with:
https://www.thedodo.com/puppy-and-kitten-rescued-1023829384.html

Richard Elwes.... Writing Maths For the Masses

 Math-Frolic Interview #28
               

"...it's time to slay some ghosts and kill some prejudices. Let's admit that any field of human endeavor worth investigating eventually gets to a level of technicality that becomes challenging, and it's fair to say that many people hit that ceiling earlier in mathematics before they do in other, perhaps more verbal, subjects. But before that level is reached, there is a whole accessible world of mathematics that can astonish with its diversity, captivate with its mystery, and enthrall with its beauty."

-- Richard Elwes from "Mathematics Without the Boring Bits" (American title)


Long time readers here know that one of my favorite math popularizers is Richard Elwes, a Brit who isn't well-enough known here in the States.

I've read four of Richard's books (below), and loved them all!. The first is an encyclopedic reference source of math terms/topics (I really know of no other book quite like it); the second is a super fleshing-out of 100+ key math concepts; the third is a wonderful introduction to a few dozen of math's most interesting (and non-boring), topics; and the fourth,"Chaotic Fishponds..." was among my favorite 2-3 math-reads of all last year:

1)  Mathematics 1001

2)  Math In 100 Key Breakthroughs

3)  Mathematics Without the Boring Bits

4)  Chaotic Fishponds and Mirror Universes
(note: the above are all U.S. titles, that may differ elsewhere) 
All Richard's books through Amazon are here:
http://tinyurl.com/o27s7g2   

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1)  For any who aren't familiar with you, tell us a little about your current position, and about your background/path to becoming a professional mathematician?

My path started off along the usual route for mathematicians: maths, maths, more maths, followed by yet more maths. I enjoyed the subject at school, and so went on to study it at university (Oxford). I enjoyed that too, so decided to do a PhD (in Leeds), and then went on to hold a postdoctoral position (in Freiburg in Germany). Then my career turned several corners. Firstly, I met a wonderful woman, and didn’t really fancy living on the other side of the world from her, which basically meant turning down my next postdoc opportunity. After a bit of dithering, I left academia to train as a high-school teacher. But just as I got qualified, I was offered the opportunity to write a book (Maths 1001). So I did that, and then went on to work as a full-time writer for a few years. Now I’m back inside the academic fold, but I’m still trying to find my niche there – a position which lets me balance the three things I love: teaching, researching, and writing.

2)  One of your main research interests is "Model Theory." Can you explain a bit about what that is, and what 'real world' applications it has?

If we’re going to use the old-fashioned terminology of ‘pure’ and ‘applied’, then model theory is about as pure as it gets! For model theorists, “applications” usually mean applications in number theory, group theory or some other area of (apparently utterly pure) maths. And maybe years down the line, those have applications in theoretical physics or computer science… or maybe they don’t. Who knows!

Having said which, there are some topics within model theory which have turned out to have genuine applications to real world, for example to neural networks. All of which only goes to show how flawed and fuzzy the old pure/applied distinction is.

Anyway, what is it? It’s an area of logic. Basically it works like this: you think of a mathematical structure, let’s pick the system of real numbers, but it could be anything. Then you write down all the rules they obey, in some highly formal logical language. And then you ask “what other systems can I find that obeys these same rules?” and then lo and behold, you’re confronted with a whole load of interesting structures no-one had ever thought of before! These are sometimes called “non-standard models” (of the real numbers, or whatever it is). What is more, studying these new structures can tell you a surprising amount about the original structure – which is probably the one you really care about.

Initially, model theory took place at a really high level of abstraction: while number-theorists study the natural numbers, and geometers study the real numbers, model-theorists worked with very general “structures”, which just means an object obeying some system of logical axioms. That stuff still happens, but more recently people have been working on the model theory of… various things: the model theory of groups, the model theory of graphs, the model theory of derivative maps,….

3)  Your writing is some of the best, clearest math explication I've seen... Have you always had a knack for good clear writing, or is that something you developed over time... or is a skilled editor very much involved?

Thank you Shecky! I really appreciate the kind things you’ve said about my work over the years. I’ll answer the second question first: in my books, what you’re reading is pure Elwes. An editor might make suggestions about the broad structure, but they won’t usually tinker with the text, except to correct typos, etc.. (In some magazines it’s a totally different story – the first time around I was shocked that the editing process essentially amounts to wholesale rewriting. Of course you can get used to that too, so long as the editor’s someone you feel you can work with.)

As to whether I’ve always had a knack for it… maybe, but it’s something I didn’t really cotton on to until a few years ago. I’d done the occasional bit of (non-scientific) writing during my PhD days, just bits and pieces for my own amusement – but it was enough to convince myself that it was something I was reasonably good at, and enjoyed. Then in 2006 I entered the Plus Magazine New Writer’s competition – that was the first time I made a serious effort to write about maths for a general audience. I loved the process of taking something which looked horrifyingly complex, and drawing out the beautiful, simple ideas which underlie all those technicalities.

As an ambitious young researcher, you can miss the wood for the trees. When you’re presented with a theorem, your inclination is to dive straight into the proof, and start grappling with the toughest ideas in there. But when you’re addressing a general audience, you have to step back, pause, and ask “What is the point of this theorem? Where did it come from? Why should we care?” You’re forced to adopt a different perspective on the subject, and that’s refreshing. It’s also healthy to learn something about the social side of the subject – the people who made the breakthroughs. We usually think of mathematics as such a dry area, but there’s actually a lot of human interest in there. For instance, I’ve just read this great article by Alec Wilkinson about Tom Zhang’s proof of the bounded prime problem. When I first heard about that, like many people I was excited about the mathematics. But it turns out it’s also a wonderful human story: 
http://www.newyorker.com/magazine/2015/02/02/pursuit-beauty

Anyway, I won that competition, which was a huge encouragement for me to write more. You can read my article here: http://plus.maths.org/content/enormous-theorem-classification-finite-simple-groups

4)  Your books are often hard to find in the U.S. or appear here much later than in the UK. (and then often under a different title) -- I love your last book, "Chaotic Fishponds and Mirror Universes," but have never seen it in a bookstore here; instead I got a used copy online. Can you explain a bit of the whole publishing process involved, and why the books don't have better US distribution (also, why the occasional title changes)? And do you ever visit the states to lecture, study, or for book tours or conferences?

The answer to your first question is: not really, I’m afraid! The publishing side of things is mostly a mystery to me too. I am not involved in most of these decisions. All I can tell you is that publishers do a lot of wheeler-dealing with each other on different editions. So for instance when Maths 1001 was published in the UK by Quercus (who commissioned it), it also came out in the US via a different publisher, Firefly, under the title “Mathematics 1001”. I gather Chaotic Fishponds doesn’t currently have a proper US distribution. That’s disappointing. But I hope it may change – one thing I do know is that these things sometimes take time. (For instance, I’ve just heard that there is to be a Japanese edition of Maths 1001 -- five years after it first came out. I have Japanese family, so am extremely excited about this!)

The title changes are also largely beyond my control (in truth I wouldn’t have picked all of them myself!). One of my books “How to Build a Brain” has been sold under at least three titles, excluding foreign language editions.
[In the US the book is called, "Mathematics: Without the Boring Bits" and it is a GREAT introduction for general readers to a few dozen fun mathematical topics.]
 
On the US: I once went to a maths conference in Tucson, Arizona while I was a PhD student, otherwise I’ve only ever traveled to the US to see friends on holiday (and I’ve not done that for over 10 years). I’d love to come back if the opportunity arose, and if I could give a talk or two, or sign a few books, that would be fantastic. No immediate plans though.

5)  Do you fall clearly into one or the other of the math Platonist vs. non-Platonist categories? And why? (...or do you prefer a different philosophical handle?)

I would say that I was typical of most working mathematicians, firstly in that I don’t often think very deeply about this stuff, and secondly in that I am a Platonist for practical purposes, even if not necessarily by conviction. When I’m studying mathematical objects, it certainly feels as if you’re working with things which really exist, somehow or somewhere.

It’s funny how the type of maths you’re currently thinking about affects your thoughts though. I’ve written several times about the deep logical foundations of mathematics, and one’s really forced into grappling with these questions there. Can one really say that enormous mathematical objects called “large cardinals” truly exist? That seems a big call to make, because these things are completely unlike anything within our direct experience. All the same, certain large cardinals’ existence turns out to be logically equivalent to relatively simple statements about the natural numbers. So, if you held my feet to the fire, I’d be inclined to say “yes”… which I suppose must make me a Platonist of some sort.

6)  What are some of your own favorite math books to read for enjoyment?  Putting aside math, what other book-reads do you enjoy for pleasure or learning?

Two of my all-time favourite maths-related books are The Princeton Companion to Mathematics (edited by Tim Gowers) and Gödel, Escher, Bach by Douglas Hofstadter. Let me also throw in the works of the game-theorist Thomas Schelling (Micromotives and Macrobehaviour and Strategies of Conflict). I recently reread Longitude by Dava Sobel, which is a delightful (and short) book, which strongly makes the point that mathematical and scientific questions are not just interesting puzzles, but can be matters of life, death, and political power. (And that’s still true: see the recent fuss about the NSA and cryptography.

In broader science, and as he has been in many people’s thoughts recently, I would also like to mention the marvelous writer and neuroscientist and Oliver Sacks. I love several of his books, including the most famous: The Man Who Mistook His Wife For A Hat. I wrote a short review of another brilliant work, Musicophilia, on my website.

The human mind seems a perpetually good topic for books: I also enjoyed Thinking Fast and Slow by Daniel Kahneman, and the writing of evolutionary psychologist Stephen Pinker.

More generally I’m a fan of science fiction, particularly “hard science fiction” of which Greg Egan is the master. I also enjoy Philip K. Dick, Arthur C. Clarke, Iain M. Banks, etc.., and am rediscovering Ursula Le Guin – I adored the Earthsea cycle about 25 years ago, and have recently started exploring her other works.

In terms of guilty pleasures, I enjoy ghost stories and so-called weird fiction, MR James and Charles Dickens from UK and the US’s Edgar Allen Poe and HP Lovecraft are the classics of the genre. I’m currently reading the Castle of Otranto by Horace Walpole, which is supposedly the first gothic horror story. It’s not exactly a masterpiece, but it’s interesting to see where several of these gothic tropes – haunted castles and dark and stormy nights – started.

I’m also exploring Japanese literature. Shusako Endo is maybe my favourite Japanese novelist so far. The horror writer Edogawa Ranpo (quite a funny pseudonym – try saying it out loud) also ticks several boxes!

[Quite an array of book choices! Also, always interesting to me how many, diverse people include Hofstadter's "Gödel, Escher, Bach" on such a list -- his very first book (1979), written in his mid-30's, winning several awards, including the Pulitzer, and still classic to many of us.]

7)  Your "Mathematics 1001" volume is quite a tersely-rendered (and wonderful) encyclopedic overview of mathematics. How long did it take you to write it? And was it difficult to know when to stop or when you had included everything you wanted to cover?

Thank you. The writing took about 6 months – and a very intense 6 months it was too -- followed by a lengthy editing process. In terms of content, there was an immovable limit, since I knew I had to include exactly 1001 things, and I knew how many words I was permitted! Because it was intended to be encyclopaedic there was an awful lot of stuff which I simply had to put in: you can’t imagine e.g. Fermat’s last theorem (FLT) being absent. But it was a good opportunity to fill in the gaps between the well-known highlights, and include material which doesn’t get aired so often. So, for instance, I was able to set FLT within a much broader context. Everyone knows that FLT is a long-standing and difficult puzzle, which a brilliant mathematician (Andrew Wiles) took a long time to solve. But it is just one of a whole class of problems called Diophantine equations, which have connections no numerous other topics, from logic (via Hilbert’s 10^th problem, which takes us to Turing machines) to algebraic geometry (via Diophantine geometry, which we can trace back to the study of Pythagorean triples) to complex analysis (via Modular forms, and elliptic curves), and so on. So it’s not just a free-standing puzzle, but one feature within a much broader landscape. These are the sort of connections I wanted to draw out. It was my first book, and probably still the one I’m proudest of.

8)  Are you currently working on a new book, and if so can you tell us about it?
 
I can tell you… that I am not currently working on a book. Currently my focus is on teaching and research – traditional academic stuff. But I promise I will write more, in future! I think I’d like to write something with a narrower focus – all of my books so far have been quite wide ranging with one chapter devoted to one topic and the next about something completely different. I’ve got a few ideas, but no firm plans yet.

9)  Lastly, since I really want my readers to be familiar with you, I'll just offer an open-ended chance to say anything additional you wish about yourself or your books that you would want them (as math enthusiasts) to know:
         
Since Chaotic Fishponds is not easily available in the US, perhaps I can say something about it here, and if there’s enough interest, maybe it might eventually pick up a proper distribution. It’s about how maths is used “in the real world”, meaning, for instance, within the modern technology of mobile phones, internet-search, space exploration, weather forecasting, robotics, computer graphics,… The impetus behind the book was that everyone knows that maths is important in all these areas, but if you then ask them how it is used, or what sort of maths is involved, most people have no idea. So, my book is an attempt to answer that question.
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Thanks for the in-depth answers Richard, and I do hope more folks on this side of the pond become familiar with your work. I think Richard's books can interest math enthusiasts at various levels, and are especially good for fostering the interest of young math up-and-comers.
(Seriously, some American publisher/distributor should be all over these books; moreso than seems to be the case!)

Richard's main website is: https://www.richardelwes.co.uk/blog 
And he can also be found at:
https://www.facebook.com/richard.okura.elwes
https://plus.google.com/u/0/+RichardElwes
https://twitter.com/RichardElwes
and recently even on Youtube:
https://www.youtube.com/channel/UCHpXTkb6ipS1B5JJ8ItYweg

This Week's Serving of Potpourri

Some things that caught my eye this week (when my power was on!):

1)  Evelyn Lamb with some wonderful math history in a few telling letters betwixt Gauss and Sophie Germain:
http://blogs.scientificamerican.com/roots-of-unity/2015/02/13/gauss-and-germain-on-pleasure-and-passion/

2)  Having some fun with Wolfram/Alpha:
http://tinyurl.com/jwqb52n
https://twitter.com/wacnt

3)  Entertaining podcast interview (40 mins.) with Jordan Ellenberg:
http://www.maureenanderson.com/images/stories/audio/013115hour1.mp3

4)  A bit of number-fun from Gary Davis and Ben Vitale:
http://www.blog.republicofmath.com/the-number-3608528850368400786036725/

5)   Andrew Gelman notes the problem of press releases and mathematical hype in this quick post:
http://andrewgelman.com/2015/02/22/academics-made-accountable-exaggerations-press-releases-work/

6)  Wow! I see from Princeton University Press's Spring catalogue that an 800+ page "comprehensive" biography of Euler (by Ronald Calinger) is on the way... for ~$50.
Now, how about a bio of Riemann next! ;-)

7)  Math podcasts are "burgeoning," and the key is to "tell a story"... read all about it:
http://blogs.ams.org/blogonmathblogs/2015/02/23/math-for-your-ears/#sthash.EOnYonKv.dpbs

8)  An interview with Ken Ono, mostly on his study of Ramanujan's work, with some update on the upcoming movie about Ramanujan's life:
http://gonitsora.com/in-conversation-with-prof-ken-ono/

9)  A research journal (in social psychology!) has banned the reporting of p-values (h/t to Jordan Ellenberg for this one):
http://www.tandfonline.com/doi/pdf/10.1080/01973533.2015.1012991

10)   This site has made an interactive version of Newcomb's Paradox (and is researching responses to the classic conundrum):
http://www.philosophyexperiments.com/newcomb/
(h/t to Colm Mulcahy for this one)

11)  A bunch of mathy links associated with the Cambridge Science Festival, given here:
http://plus.maths.org/content/maths-cambridge-science-festival

12)  Hannah Fry reviews Cedric Villani's "Birth of a Theorem" for The Guardian:
http://www.theguardian.com/books/2015/feb/25/birth-of-a-theorem-mathematical-adventure-cedric-villani-review

13)  Mike Lawlers' place on the Web:  https://mikesmathpage.wordpress.com/

....and on Sunday I'll have another new interview up here, so y'all come back now!

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

1)  Last week's NPR TEDRadioHour ("The Unknown Brain") started off with what may still be my all-time favorite TED Talk, neuroscientist Jill Bolte Taylor's remarkable viral 2008 story of experiencing her own stroke:
http://www.npr.org/programs/ted-radio-hour/384949524/the-unknown-brain
If somehow you've missed it, listen to at least her first segment on the show, but the whole hour is great.

2)  And a couple of interesting reads from Aeon magazine (also, neuroscience-related):
a)  the tendency of fiction to 'trump fact' on the Web:
http://aeon.co/magazine/culture/should-you-fact-check-your-grandmas-facebook-posts/
and,
b)  human brain elasticity:
http://aeon.co/magazine/psychology/can-i-make-my-brain-as-plastic-as-a-childs/

Ben Orlin... Math-blogging's Bill Watterson(?)

Math-Frolic Interview #27

 "We are all simultaneously experts and beginners, flaunting our talents while trying to cover our shortcomings the way an animal hides a wound. You could call this a 'math blog,' or a 'teaching blog,' but I would call it a blog about owning up to weakness and drawing strength from successes, however transient or trivial they may seem."
-- Ben Orlin (from his blog)


 I'm sure many readers here have been entertained by the fanciful cartoons that Ben Orlin uses to delve into mathematics and education at his blog, "Math With Bad Drawings" -- a blog that has established itself as one of the more distinctive, easily discernible sites in the burgeoning field of secondary math blogs. And because so many of us enjoy Ben's take on things, I wanted to learn more about him. Not unexpectedly, the humor evident on his blog comes through here as well:
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1)  First, some confusion: I see on the "about" page for your blog that you now teach in Birmingham, England. I always thought of you as a (Oakland) California teacher... When and why did the move happen, and is that temporary or likely permanent?

Temporary! Back to America in 2017, after my wife's postdoc here ends.

In late 2013, she was finishing her PhD and applying for 50-100 postdocs across the US. I'm a Boston kid, and I loved the Bay Area, but I agreed to move elsewhere (like Missouri or Wisconsin) if the job was good for her. The less exciting the location, the better the job had to be.

One day she says, "There's a great research fit for me at University of Birmingham."

My future flashed before my eyes: mosquitoes, high school football, Confederate flags. I said, "Well... is it a GREAT fit? Because, I mean, Alabama isn't what I was--"

"No, not Alabama!" she said. "England!"

We moved out here in August, and it's been great. (My apologies to Alabamans; I'm sure your state is lovely.)

2)  Please tell readers a little about your math background... When did your math interest begin? When did you decide to pursue it professionally? And what are your main specific academic interests within mathematics?

My academic interests run a mile wide and three feet deep. There are parallel universes where I majored in Econ/Biology/Philosophy/English/Spanish. The way some people fear romantic commitment, that's how I fear intellectual commitment.

So why math? Because I got pulled in by great teachers and great classes. (And because I knew it was a marketable degree.)

As for interests within math... well, I'm a dilettante there, too. I love probability. I got a huge kick out of Galois theory and fractal geometry. Years of talking to my wife about her research have turned me into a bit of an analyst, too.

I know a little about a lot, and a lot about nothing. Very liberal arts, I guess.

3)  These days there are a multitude of blogs from math educators.  You almost have to have a gimmick to break out from the crowd. How did your blog start, and how did the amateurishly endearing cartoons you use come about (had you already done cartoons in the past)?

I wanted to write about math. But I knew math is really hard to read. The ideas are so dense, you need to surround them with fluff: pictures, jokes, stories, asides.

My original plan was to ask friends to draw illustrations for me. But who wants to sketch out somebody else's ideas, for a blog nobody will probably read, for no payment?

I've always been terrible at drawing. But I'd been writing about the value of learning new things, and seeing your gaps not as weaknesses but as chances to grow. So I figured I ought to practice what I preach.

Hence, the drawings. And the title.

Also, math intimidates people. I hoped the images, so manifestly incompetent, would put people at ease. They'd send a clear message: "Even if you feel like you're bad at something, you shouldn't be afraid to try it."

And it seems to have worked. While my drawings still safely qualify as "bad," they've gotten a lot better!

4) Your blogposts seem to range from silly to semi-serious, often ending, it seems to me, with some sort of moral to the (mathematical) story -- is that a fair characterization of your postings, or how would you describe them?

Sounds right! I don't think there's much of a unifying principle for the blog, other than bad drawings.

And how do the posts evolve before we see the final result on the blog -- do you start with a message you want to get across, and then work backwards to figure out how to tell a storyline producing that message, or does the story enter your mind first, and then you figure out what lesson it can be used to teach?

The posts tend to evolve over a long period. I've got a big folder of half-baked ideas, most of which will never see the light of day. Each follows its own trajectory, but here's a frequent evolutionary path:

(a) I come up with a message/moral I want to share. In its initial form, it's overstated and overconfident.

(b) Thirty minutes into writing, I recognize my own hubris, and start asking, "Where did I get this conviction? How am I so sure about this?"

(c) I think back to the experience(s) that led me to this conclusion: little moments, year-long adventures, single lessons, whatever.

(d) I write that story instead, trying to limit my conclusions to what that story can justify.

(e) It comes out overly general and hubristic anyway. And that's okay.

5) Do certain of your blogposts stand out as personal favorites or ones that were the most fun to work on? And from the other side, which posts seem to have been most popular or attention-getting from your readers?

Yeah! My favorites:

I "filmed" the gifs for The Math Aficionado's Guide to High Fives in my old school, along with a bunch of friends and my (amazing) high school math teacher.

I accosted conference-goers at the 2014 Joint Maths Meetings and had them draw pictures for 39 Ways to Love Math.

I woke up one morning and wrote A Fight with Euclid before lunch.

The Kaufman Decimals came out of a fun conversation with a friend.

A Ray of Light is one of the my more honest pieces of writing.

The Church of the Right Answer is a recent soap-box tirade that was good to get off of my chest.

And as for most popular, I've had four big hits. What It Feels Like to Be Bad at Math is still my proudest. Also, two of my humor pieces "went viral," Math Experts Split the Check and Headlines from a Mathematically Literate World.

But my most popular post, by leaps and bounds, is Ultimate Tic-Tac-Toe. It's been viewed something like 800,000 times, and has spawned a whole mini-industry of mobile apps. Nothing I write will ever again reach such a wide audience. It turns out that people LOVE tic-tac-toe.

6)  How, if at all, do you utilize online math resources in your own classroom? And do you employ your blog or any social media, as teaching tools, in your classroom as well?

I'm awful about this. My 2015 new year's resolution is to steal more stuff. I have the bad habit of writing all my own materials, which is a lousy, time-destroying instinct. There's so much great stuff out there: nRich, Dan Meyer's three-act lessons...

I don't use my own blog, except occasionally to copy and paste an image.

7)  You've written for some other outlets, notably Slate and The Atlantic magazine... how did those opportunities arise, and would you like to freelance more in the future?

I have a friend who works at Slate, who very kindly passed "What It Feels Like to Be Bad at Math" along to an editor there. Aside from that, I just pitched them stories via email.

I may pitch pieces again in the future, although being back in the classroom (after a year off) is keeping me plenty busy!

8)  When you're not teaching math or cartooning around what are some of your other main interests/hobbies/activities?

I live in Europe now! So I have two main hobbies:

(1) Exploring new places (and being stupidly fascinated by trivial differences, like the signage fonts and the retail brands)

(2) Skyping home! Speaking of which, I'm going to check if my family is awake now.

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Thanks Ben for rounding yourself out a bit here. I think the personality that concocts those whacky caricatures shines through.  And regarding those cartoons, just one small piece of advice: ...hold onto your day job! ;-)

If by any remote chance you've missed Ben's blog introduce yourself to it with some of the links above (caution, you'll soon be hooked).
Ben tweets at: @benorlin
and has a Facebook page here:  https://www.facebook.com/MathWithBadDrawings

[p.s. -- I believe??? all the broken interview links on the Math-Frolic interviews-listed page have now been fixed. And for next weekend I've got one of my very favorite math writers lined up!]

Another Week's-worth of Schtuff...

See which of these you've missed...:

1)  A Marcus du Sautoy "In Our Time" podcast on the work of Kurt Gödel:
https://soundcloud.com/marcusdusautoy/in-our-time-godels-incompleteness-theorem

2)  "Medical research is in bad shape" -- that's the first line in this interesting retrospective of John Ioannidis' crusading work since he first noted 10 years ago that "...most published research findings are false":
http://www.vox.com/2015/2/16/8034143/john-ioannidis-interview

3)  Alex Bellos profiles Fields Medalist Cedric Villani and his work here (H/T to Egan Chernoff for this one):
https://cosmosmagazine.com/mathematics/seduced-calculus

4)  Patrick Honner carried on a Google+ conversation this week over the question of why there is so much more editorial criticism of K-12 math education in the U.S. than there is of college math education (several viewpoints expressed):
https://plus.google.com/u/0/+PatrickHonner/posts/8akbT2M9jec

5)  Interesting history and tribute to R.A. Fisher ("father of modern statistics") here:
http://errorstatistics.com/2015/02/17/r-a-fisher-how-an-outsider-revolutionized-statistics-aris-spanos/

6)  Keith Devlin on R.L. Moore and the "Moore Method" of teaching (better known today as "inquiry-based learning" or IBL):
http://devlinsangle.blogspot.com/2015/02/the-greatest-math-teacher-ever.html

7)  Cathy O'Neil summarizing some of the problems in the "practices of 'big data'":
http://mathbabe.org/2015/02/18/aapor-big-data-report/

8)  A brief summary from MAA of the annual joint math meetings held in San Antonio last month:
http://www.maa.org/news/feasting-on-mathematics-at-the-joint-meetings

9)  New "Wild Cool Math" from James Tanton:
http://tinyurl.com/pzml7pw

10)  The latest "opinion" from Doron Zeilberger relates to the future of mathematical proofs:
http://www.math.rutgers.edu/~zeilberg/Opinion141.html

11)  "Ask A Mathematician..." site offers a nice tutorial on quaternions, octonions, and beyond:
http://www.askamathematician.com/2015/02/q-quaternions-and-octonions-what/

12)  Nautilus Magazine has been putting out consistently GREAT stuff of late, including now, this fabulous interview (both video and transcribed) with computer scientist Scott Aaronson (of the blog "Shtetl-Optimized"):
http://nautil.us/issue/21/information/ingenious-scott-aaronson

13)  Over at AMS blogs Evelyn Lamb introduces us to a blog, "Social Mathematics," that looks good, that I'm ashamed to say I was unfamiliar with even though it's been around since 2007! Check out Evelyn's post and the blog itself:
http://blogs.ams.org/blogonmathblogs/#sthash.cVfAVMKr.WDIxxyjX.dpbs
http://socialmathematics.net/

14)  Keep an eye on what Mike Lawler is up to:  https://mikesmathpage.wordpress.com/

15)  Not mathematics, but a fascinating geeky, historical piece from Amanda Gefter for Nautilus about William Pitts (previously unknown to me and apparently many other readers):
http://m.nautil.us/issue/21/information/the-man-who-tried-to-redeem-the-world-with-logic

16)  Finally, last Sunday, over at MathTango, I reviewed the new book from Michael Harris, "Mathematics Without Apologies" (...I kinda liked it):
http://mathtango.blogspot.com/2015/02/a-review-without-apologies.html

Meanwhile, THIS Sunday MathTango will have a new interview with another delightful instructor from the math blogosphere. Stay tuned....
[p.s. -- I think I've now repaired links to ALL the other interviews as well, in case anyone had tried those recently only to find several broken.]

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

1)   Another incredible podcast from NPR's RadioLab last week... amazing segments on surviving rabies, and on what major medical procedures DOCTORS choose to have carried out on THEMSELVES (almost none) toward the end of life:
http://www.radiolab.org/story/dead-reckoning/

2)  Speaking of end-of-life, ICYMI, in this NY Times piece Oliver Sacks, who has entertained and enlightened people for so long with his writings and talks, faces the same subject with his usual thoughtful perspective:
http://tinyurl.com/or8e39y

A Review Without Apologies

 "Mathematics Without Apologies" by Michael Harris....



 "Insofar as the present book is about anything, it is about how it feels to live a mathematician's double life: one life within this framework of professional autonomy, answerable only to our colleagues, and the other life in the world at large."
-- Michael Harris

"...the only way somebody can be a scientist is that somehow their personality gets frozen at an early age... at the playful stage."
 -- Andrei Kolmogorov (as quoted in Harris's book)


For starters, I'll say that this will be among my favorite math volumes for all of 2015... to which I'll add, your mileage may vary! (it won't suit everyone's taste). This is a volume that almost defies adequate review, so vast, variegated, and tangled is its content.  It is as odd, eclectic, even intractable a piece of mathematical writing as I have ever come across. Peculiar, dense, trenchant, hopscotchy, sometimes turgid, verbose, hard-to-follow, even inscrutable... but also interesting, rich, quirky, creative, original, a tad enigmatic, unpredictable, curious, cerebral and thought-provoking, sprawling across the landscape of ideas and interests. Gregory Chaitin, in his blurb for the book, writes, "Mathematical high culture collides with pop culture and all hell breaks loose! Harris takes us on a wild ride -- never a dull moment!" I couldn't agree more (and how often can you say 'all hell breaks loose' in a math book!). A press release for it states that it is for "intellectually curious readers" -- that is a colossal understatement! The same press release calls the volume "post-post-modern" -- I understand where the description comes from, but as someone who isn't a fan of post-modernism I prefer to avoid that terminology (even though it clearly fits some passages in the book); but, if not post-modern, it's certainly post-1950s! ;-)

The author says at some point that this is a book he always felt needed to be written... and only when no one else did it, did he take the task upon himself. And he writes: "My original aim in writing this book was to suggest new and more plausible answers to the 'why' question; but since it's pointless to say why one does something without saying what that something is, much of the book is devoted to the 'what' question [what is mathematics]."
I'll say up front that much of the technical math in this book (which is not the bulk of the content, but it does exist) is beyond my ability to even judge, though given the author's credentials I certainly assume it credible and valid. I'll be dealing here more with the style/approach/presentation than with the technical aspects.

There is a lot of focus in these pages on Galois, Grothendieck, and Robert Langlands as initiators of grand, sweeping programs in mathematics. I mention that just to indicate the level of mathematics that is often addressed in these pages, even though the discussion is more general, and intended for a broader audience. This is not the typical popular math book written at the level of high school or early college math.  Even without including a lot of technical, computational mathematics, Harris's subjects are deep and abstract and, depending on your background, may be difficult for a lay reader to follow. I like that sort of challenge, but some may find it off-putting, if they get lost in Harris's commentary or occasional technical jargon.

The book ranges all over the place: math, literature, science, psychology, history, music, culture, film... it's all here in bites. I'm sure the author had some idea how it was organized in his own mind, but I can't offer a clue! And that's not said as a criticism, just a warning to readers, and for me it gave the book a rollicking, unpredictable style that made it spirited. The writing is sometimes less-than-scintillating... because the subject matter is sometimes less-than-scintillating. It is a strange mix of dense, heavy, at times convoluted or rambly stuff, that is yet made scintillating and engaging by its very originality.
So even though I sometimes found myself lost reading these pages, it was lost in an exciting, challenging way... not in a dark, foreboding forest, so much as in a sunny, expansive, amusement-filled park!

Along the way, the author intersperses conversations between an imagined "performing artist" and a "number theorist" to make various points -- it is reminiscent of a technique used by Douglas Hofstadter in the past. I think Harris does an even better (less tedious) job of it than Hofstadter did, and doesn't overdue it as Hofstadter may have.

If you like puzzles, equations, computations, proofs, etc., this is NOT the math book for you. It's hard to describe WHO this book IS for!... certainly someone more interested in the contemplation of, and philosophy underlying, math, and its role in society, more than in doing or learning mathematics.  On the other hand, only those with an already deep background in math will fully appreciate the ideas Harris eagerly romps about in.

I've tried to think of any other book I've read with a similar feel to this volume. Perhaps William Byers' "How Mathematicians Think," but only very slightly so. Harris references Jeremy Gray a number of times, so I wonder if Gray's volume, "Plato's Ghost," might bear some similarity, but I've not read it and can't say. The writing style reminds me a tad of David Foster Wallace (who also gets an occasional nod in the volume), but that too is a stretch. The author cites Thomas Pynchon from time to time, and mentions Pynchon's "non-linear" writing style -- again, I've not read Pynchon myself, but "non-linear" or "Pynchon-esque" just may be an apt descriptor for Harris's prose. Finally, there's a slight similarity here to Ed Frenkel's "Love and Math," but only in so much as both volumes turn some attention to the Langlands program, and both touch on subjects well outside the perimeter of mathematics, but Harris scampers MUCH farther afield than Frenkel. Essentially, I'm doubtful this work can be readily compared to any other math volume.

And I'd love to have been a fly-on-the-wall for the editorial sessions that produced this book! I could be completely wrong, but I imagine much give-and-take, with the editor requesting lots of changes, and the author unwilling to assent to them. To my ear, the writing just seems less edited, less clean, more disjointed, than what's customary in a popular math book -- it's more like the unvarnished author coming through. I also imagine the author making changes/additions right up to the very last moment, as this volume could never really be finished. ...But these are all just idle (and perhaps wrong) impressions on my part. Again, not intended as criticism, but rather a sign of the uniqueness of this multifaceted effort.

I'll only touch upon a few highlights from the volume:

Early on, somewhat oddly, the author discusses "charisma" (and competition) in mathematics --  both in the field of math study, as well as in the practitioners who do math. The discussion revolves around the "sociology" of mathematics, which, unlike either the logic, philosophy, or computations of math, doesn't usually get wide play. Harris also ends up touching on the Elsevier boycott that was spearheaded by Fields Medalist Timothy Gowers, and the "fascinating questions about the possibility of reconciling the goals of science with the material organization of society."

Chapter 4 presents an interesting treatment of the 2008 financial collapse, the Black-Scholes equation, and failures of mathematicians... there's a good reason that economics has been called "the dismal science" and this chapter exposes it.

Chapter 6 on the "mind-body problem" covers a lot of mostly non-mathematical ground. Harris spends some significant time discussing Ed Frenkel's independent film "Rites of Love and Math." Though both men work on the Langlands program, Harris actually spends more time considering, not Frenkel's mathematical work, but rather his popular short film that replaces the geeky mathematician stereotype with a loving (even nude!) mathematician in an uncompromising search for truth. The chapter feels like something written by a devotee of the humanities, moreso than the product of an academic mathematician.

There are a couple of chapters focused on number theory (Harris's main field), parts of which may be hard to follow without a firm grounding in that subject, but I think I found chapters 7 and 8 the most difficult to follow of the more general chapters. One interesting segment in chapter 7 though, recounts the use of drugs by many who were successful mathematicians (Erdös and his amphetamines being a classic case). And then, Harris writes, "Pharmaceutical enhancement may be redundant if mathematics is itself the drug." Next he quotes several mathematicians who make reference to how doing mathematics is like being on a drug. It's an interesting notion that helps explain the addictive quality that math has for so many practitioners, that non-mathematicians often find inexplicable.
In chapter 8 he looks at "tricks" in mathematics, but these aren't the simple or quick tricks you might learn in a YouTube mathy presentation, but much higher-level or abstract tricks that may not be easily grasped. Later in the chapter the always-interesting relationship between math and music is discussed.

Chapter 10 is on the "math-is-beauty" and "math's-unreasonable-effectiveness-in-science" themes.  Even in dealing with such oft-treated matter, Harris's presentation is fresh and thoughtful. And it is also in this chapter that he comes full circle back to G.H. Hardy's "A Mathematician's Apology," in order to reiterate that he makes NO apologies for the beauty and usefulness of pure mathematics in our lives.

I've barely scratched the surface here of this volume's contents -- I won't apologize for that or for the large chunks that fell beyond my comprehension. Nor can I fully communicate the oddity and freshness of this uncommon effort. Along with a regular index, at the end there is a separate "Index of Mathematicians" of those mentioned by name in the text -- this index includes well over 250 individuals within a book body of 325 pages!  And as for others (non-mathematicians) who get more than a passing mention in the book, here are some of those names: Aquinas, Goethe, Huizinga, Kant, Kuhn, Mehrtens, Pynchon, Wittgenstein... to give a sense of the breadth of material here (what the publisher, Princeton University Press, calls "a ridiculously diverse assortment of... sources"). Indeed! Additionally, there are ~70 pages of 'notes,' and a wide-ranging 20+ page bibliography -- much of it technical (indeed, I was surprised that several "popular" math works I looked for weren't even included).

I've read through this book once... which doesn't do it justice -- it's the sort of volume you can pick up, randomly turn to any page, begin reading, and gain more insight than was bestowed by the first read-through. The professional mathematician will no doubt get more from these pages than the lay reader can... and, probably find more to disagree with as well. Having said that, I also suspect people will, Rorschach-like, read into many of Harris's passages what they think or want him to mean, rather than what he intended. Doug Hofstadter has written in the past, that despite the praise (and awards) lavished upon his first book, "Gödel, Escher, Bach," most reviewers got the book wrong. The same may happen for much of Harris's content.

Still, I love that this volume reveals a mathematician who breaks out of the nerdy math stereotype to talk philosophy, humanities, arts, culture, literature, and other subjects too often missing from the public's image of the professional mathematician. I can appreciate Harris's discussion... even when I don't fully comprehend it, because I value seeing the inner mathematician turned loose for public consumption. I don't recommend you all read this book once... I recommend you read it, indeed savor it, 2-3 times. It will certainly be re-appearing on the Christmas list I compile at the end of the year for readers. It stands, perhaps, in a category of its own.

Peter Woit reviewed the volume here:
http://www.math.columbia.edu/~woit/wordpress/?p=7479

...and there is an interview with the author here:
http://blog.press.princeton.edu/2015/02/04/qa-with-michael-harris/

'nother Week's Cornucopia of Math

A non-spooky Friday-the-13th! edition of potpourri:

1)  A summary of some recent math events from "Math Drudge":
http://experimentalmath.info/blog/2015/02/is-the-nature-of-mathematical-proof-changing/

2)  Peter Woit gives this interview with Ed Witten a big thumbs-up (covers some thoughts on number theory, Langlands program, dualities, and other recent advances at the interface of math and physics):
http://www.ipmu.jp/webfm_send/1053

3)  A bit about thinking 'fast and slow' in this post on the "cognitive reflection test" and creativity:
https://fivetwelvethirteen.wordpress.com/2015/02/07/cognitive-reflection-test/

4)  Analyzing the long-and-the-short of crossword puzzles... an interesting (as always) tidbit from "Futility Closet":
http://www.futilitycloset.com/2015/02/09/cross-purposes-3/

By the way, on a side-note, if you've never seen what some consider the cleverest NYT crossword puzzle of all time ('predicting' the 1996 U.S. Presidential election) you should check that out:

http://www.dailydot.com/lol/clinton-1996-election-nyt-crossword-gif/

5)  A longread:  in this, a further year of Alan Turing remembrances, Neil Gershenfeld reminds us why Claude Shannon also deserves much recognition:
http://edge.org/conversation/neil_gershenfeld-digital-reality

6)  The latest incarnation of Keith Devlin's "Introduction to Mathematical Thinking" course starts up this weekend:
https://www.coursera.org/course/maththink

7)  The newest "Carnival of Mathematics" up here:
http://www.whitegroupmaths.com/2015/02/119th-carnival-of-mathematics.html

8)  Khan Academy is launching "LearnStorm" a new initiative in math skills learning/competition, initially for 3rd through 12th graders in some California counties (to be broadened out if successful):
http://edsource.org/2015/khan-academy-launches-ambitious-math-challenge/74454#.VNpyqcZDTLV

9)  Game theory via Freeman Dyson and William Press in Quanta Magazine:
https://www.quantamagazine.org/20150212-game-theory-calls-cooperation-into-question/

10)  H/T to John Golden for pointing out this Boston Globe opinion piece by a math teacher weighing in on the education debates:
http://tinyurl.com/mohz59n

11)  Pick-and-choose from MikesMathPage here :
http://mikesmathpage.wordpress.com/

12)  And with tomorrow being Valentine's Day, MathMunch offers an appropriate posting:
http://mathmunch.org/2013/02/11/the-sierpinski-valentine-cardioids-and-mobius-hearts/

...and for Math-Frolic, I once had a semi-Valentine's tradition of referencing this old Jennifer Ouellette post... I'll do so again:
http://blogs.scientificamerican.com/cocktail-party-physics/2011/09/29/love-among-the-equations/


P.S. --  Sunday, here at MathTango, I'll be reviewing Michael Harris's remarkable new book "Mathematics Without Apologies."

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Potpourri BONUS (just extra NON-math links for your enjoyment) :

1)  If you love the poetry of Mary Oliver you'll want to hear last week's podcast episode of Krista Tippett's "On Being" in which she interviews Mary for an hour (...and if you don't love the poetry of Mary Oliver, well, what... is... friggin' WRONG... with you!? ;-):
http://onbeing.org/program/mary-oliver-listening-to-the-world/7267

2)  And from NPR another fantastic "Invisibilia" episode this week on the encroachment of computers in our lives, cool or creepy?:
http://www.npr.org/programs/invisibilia/385792677/our-computers-ourselves


[...please let me know ASAP of any broken/bad links]

Another Week in the Math Blogosphere & Beyond

ICYM any of these:

1)  Having fun teaching calculus to non-calculus people:
https://napmath.wordpress.com/2015/02/01/delicious-lessons-in-calculus/

2)  Evelyn Lamb covered the current measles outbreak this week with emphasis on a key number:
http://tinyurl.com/qffnzyk

3)  Cathy O'Neil on math and medals:
http://horizonsaftermath.blogspot.com/2015/02/i-love-math-and-i-hate-fields-medal.html

4)  "Futility Closet" offers up a paradox very reminiscent of Aristotle's "wheel paradox":
http://www.futilitycloset.com/2015/02/01/the-coin-paradox/

5)  If you're into some of the critical names and issues surrounding applied statistics (especially in the social sciences) then this longish Deborah Mayo post is sure to entertain:
http://errorstatistics.com/2015/01/31/2015-saturday-night-brainstorming-and-task-forces-1st-draft/
...also at Deborah's blog this week a guest post from Stephen Senn on statistically pooled data:
http://errorstatistics.com/2015/02/05/stephen-senn-is-pooling-fooling-guest-post/

6)  And a piece from the Washington Post also outlining two big issues for science: 1) explaining its findings to the public and 2) reproducibility:
http://tinyurl.com/n2sc3ek

7)  I suspect these logic tasks/puzzles (Wason Selection Task) are familiar to most readers here, but if they're not, you should work through them, or perhaps try them out on some friends:
http://www.philosophyexperiments.com/wason/Default.aspx
...and many more conundrums from this site listed here:
http://www.philosophyexperiments.com/

8)  Not math, but just some nutty, ongoing fun from Andrew Gelman this week:
http://andrewgelman.com/2015/01/15/picking-ideal-seminar-speaker-ultimate-bracket/
http://andrewgelman.com/2015/02/02/deciding-ultimate-seminar-speaker-rules/

9)  H/T to John Allen Paulos for pointing me to this interview ("The Stuff of Proof") with philosopher/writer Penelope Maddy on foundational aspects of mathematics; it's pretty 'meta' and philosophical, but if you like that sort of thing, quite interesting:
http://www.3ammagazine.com/3am/the-stuff-of-proof/

10)  An intro to some topology ideas from "ThatsMaths":
http://thatsmaths.com/2015/02/05/perelmans-theorem-who-wants-to-be-a-millionaire/

11)  A quick note that Max Tegmark's "Our Mathematical Universe" and Nate Silver's "The Signal and the Noise" are both newly-out in paperback.

12)  pick and choose from MikesMathPage weekly entries:
http://mikesmathpage.wordpress.com/
...By the way, at the end of a number theory post today, Mike especially recommends the following 3-min. video of award-winner Manjul Bhargava, for young people interested in math:
https://www.quantamagazine.org/20140812-the-musical-magical-number-theorist/ 


The Potpourri BONUS (just extra NON-math links for your enjoyment) :

FOUR-for-the-price-of-1... I love bird nestcam websites of which there are now a large selection on the internet... a few current favorites:

a.  Two Great Horned Owl sites:
http://www.ustream.tv/recorded/57878544
http://cams.allaboutbirds.org/channel/46/Great_Horned_Owls/

b.  California hummingbird nestcam:
http://www.bellahummingbird.com/

c.  Albatross nestcam (Hawaii):
http://cams.allaboutbirds.org/channel/41/Laysan_Albatross/

(CAUTION: these live webcams can prove hopelessly addictive, rendering the viewer incapable of proceeding with work or other activities!)