Apologies to John Steinbeck...

A blurb today on yet another fine new book for the math novice or enthusiast: "The Grapes of Math" by Alex Bellos (oddly, the title is the same as an earlier math book for youngsters by Greg Tang).
I very much enjoyed Bellos' prior work, "Here's Looking At Euclid," (American title). Publicity for Bellos' latest offering, however, appeared to focus on what seemed some trivial/light matters, and so I had lower expectations for this particular volume. The first five chapters were a bit disjointed and indeed mundane in some parts, but better than I was expecting, with a nice extended treatment of Benford's/Zipf's Laws in chapter 2.  (The timing of the book's U.S. release, coinciding with Jordan Ellenberg's new book, may also have caused it to suffer slightly by comparison)…  BUT after that first half, the book takes off on a scintillating ride (starting with chapter 6, on the number e, onward). Even though the topics covered are fairly standard fare for a general audience presentation, Bellos is a particularly sharp/clear explicator. He goes into more detail and explanation than many writers do, yet without being heavy-handed or tedious, moving along neither too fast, nor too slow, with a nice mix of illuminating topics.

My favorite chapter is chapter 7, covering negative numbers, i, Euler's identity, complex numbers, quaternions, octonions, and finishing up with iteration and the Mandelbrot Set. It's not that these are favorite topics of mine, but I love the way the chapter flows along, Bellos seamlessly moving from one kind of number to the next with good explanations.
Following chapter 7, come excellent, thoughtful chapters touching on calculus, self-reference, proof, the Bourbaki group (which is still active), and ending with a long, great treatment of Conway's Game of Life. As I say, I think the last 5 chapters of this volume are particularly instructive and wonderful, but depending on your inclinations, you will certainly find parts to enjoy in the first 5 chapters as well. And at the book's conclusion come 35 pages of worthwhile glossary/appendices/notes.
This will be a fine addition to anyone's general math bookshelf, or a great gift to a young mathematician-to-be.

I'll end with just one of the specific examples I especially enjoyed from the volume (and which I don't recall reading elsewhere)… it's a fun little bit of math/probability that Bellos got from this more extensive 2009 "Knowing When To Stop" article in American Scientist:

http://www.americanscientist.org/issues/id.5783,y.2009,no.2,content.true,page.5,css.print/issue.aspx

I'll summarize and paraphrase a little game, as follows (my words, not Bellos):

Player 1 writes down two different numbers on two slips of paper. They can be anything: 3, 22222222222, 14 billion, 1/17, .0375623524, whatever. Two different numbers I'll call x and y that are placed face down on a table. My goal as Player 2 is to try and pick the largest number of the two, by picking up one piece of paper, looking at it, and deciding whether I wish to stick with it as probably being the largest, or switch to the other (sight-unseen) slip of paper.
If I select a piece of paper and it reads, "1,008,465,243,195" I must decide if I think the remaining face-down paper is a lower or higher number. And probabilistically I have no way of knowing, so my chance of guessing right is 50/50 (this assumes no Bayesian factors that might actually be involved by playing the game with the same person repeated times).
BUT what Bellos informs us is that if you play the game repeatedly many times, then there is a strategy that assures that (probabilistically-speaking) you can win over 50% of the time (even if only slightly over 50%). The strategy is as follows: When Player 1 is committing his/her two numbers to slips of paper, you also choose a number in your head, call it "k" -- any number of your choosing, although it seems to me, selecting an integer at least larger than say 2, may be of some benefit. You simply remember the number; no need to write it down or say aloud what it is.

Now, once you turn over one slip of paper and see the number written thereupon, your rules (to do better than 50/50) are as follows:

1) IF your number k is LESS than the number turned over, then assume the turned-number is the highest of the two slips of paper (and stick with it), but

2) IF your number k is HIGHER than the number shown, then assume the remaining (facedown) slip has the higher number and pick it.

This system insures that over many trials you will win over 50% of the time. I'll quote Bellos' explanation of why:

"…consider the value of k with respect to the two numbers on the pieces of paper. There are three possibilities: (i) k is less than both of them, (ii) k is higher than both of them, or (iii) k is between them.
"In the first scenario, whatever number I see, I stick with it. My chance of being right is 50/50. In the second scenario, whatever number I see, I choose the other one. My chance is again 50/50. The interesting situation is the third one, when I win 100 percent of the time. If I see the lower number, I switch, and if I see the higher number, I stick with it. When my random number serendipitously falls in the middle of the two numbers you wrote on the pieces of paper, I will always win!"

Bellos goes into a little more detail about the problem, but the basic point is that given many repetitions of the game over time, the third scenario yields at least a slightly better than 50/50 winning outcome. Just one more interesting probability thought exercise.

Bellos' entertaining book is another fine addition to the growing list of volumes that can be enjoyed by math fans of various levels. Indeed, it does my heart good to walk into my local Barnes and Noble and find TWO math books gracing the 'recent bestsellers' table (Ellenberg and Bellos)! This seems like a paradise age we live in for math appreciation, for such to be the case (not to mention all the wonderful internet math resources continually available). May it continue.

Headed Into The Weekend

Another week's mishmash of links:

1)  An excerpt from Alex Bellos' latest volume "The Grapes of Math":
http://tinyurl.com/ozffphx
(My own blurb about this fun volume will likely be up on Sunday.)

2)  A surprisingly involved puzzle from Presh Talwalkar last Monday:
http://mindyourdecisions.com/blog/2014/06/23/monday-puzzle-ratio-of-random-numbers/#.U6gHIqjrnKk

3)  Latest podcast guest with Sol Lederman is Sue VanHattum introducing her new volume (as editor), "Playing With Math":
http://wildaboutmath.com/2014/06/23/sue-vanhattum-inspired-by-math-38/
And here is a recent post from Sue about the book:
http://mathmamawrites.blogspot.com/2014/06/playing-with-math-can-we-keep-campaigns.html

4)  The dark side of 'big data,' from mathbabe:
http://mathbabe.org/2014/06/25/the-dark-matter-of-big-data/

5)  Dave Goldberg covers Emmy Noether:
http://io9.com/the-most-important-mathematician-youve-never-heard-of-1594835772/+dave_goldberg

6)  The awarding of the "Breakthrough" prize ($3 million) to five mathematicians earlier in week set off some debate over the appropriateness of such large award sums in science. Philip Ball of The Guardian weighed in here:
http://io9.com/the-most-important-mathematician-youve-never-heard-of-1594835772/+dave_goldberg

7)  Tangential to math, another fascinating physics piece from Natalie Wolchover, this time focused on pilot-wave theory:
http://www.simonsfoundation.org/quanta/20140624-fluid-tests-hint-at-concrete-quantum-reality/

8) Good, longish article on importance of computer or coding literacy for the future:
http://www.motherjones.com/media/2014/06/computer-science-programming-code-diversity-sexism-education

9)  And not so much math, but important reminder from Cathy O'Neil on what we, users of Google, really are:
http://mathbabe.org/2014/06/24/you-are-not-googles-customer/

Friday Wrap-Up

A varied mix of links that caught my interest in the week gone by:

1) Another interview with Jordan Ellenberg here (LA Times):
http://tinyurl.com/o63qxnx
For any who missed my review, last week, of Ellenberg's book "How Not To Be Wrong," it's here:
http://mathtango.blogspot.com/2014/06/how-not-to-go-wrong.html

2) A couple of quickie problems from Futility Closet:
http://www.futilitycloset.com/2014/06/15/milestones/
http://www.futilitycloset.com/2014/06/17/pointing-fingers/

3) A May talk (~1 hr.) by Marcus du Sautoy on the aesthetics of mathematics is now online:
http://www.gresham.ac.uk/lectures-and-events/the-secret-mathematicians

4) If you're interested in chess, a long, but interesting post about cheating in chess, and about Ken Regan (co-author of one of my favorite blogs, "Gödel's Lost Letter..."), who investigates such behavior (I'd never even considered the likelihood of cheating in professional chess!):
http://www.uschess.org/content/view/12677/763
...and R.J. Lipton takes up the same subject here (at the above blog):
http://rjlipton.wordpress.com/2014/06/18/the-problem-of-catching-chess-cheaters/

5) Another podcast interview from Sol Lederman, this time with Al Cuoco, author of "Learning Modern Algebra: From Early Attempts to Prove Fermat's Last Theorem," from MAA:
http://wildaboutmath.com/2014/06/14/al-cuoco-inspired-by-math-36/

6) A piece that isn't mathematical, but so interesting (provocative) about the superficiality of philosophy, I thought it ought be passed along (h/t Melody Dye):
http://tinyurl.com/nb6d3py
It's a long interview with philosopher Peter Unger about his new book "Empty Ideas." [There are some narrow aspects of philosophy that interest me, but otherwise I agree with much of what Unger says/implies here.]

7) And also speaking from a sort of quantitative-philosophical bent, the ever-interesting Scott Aaronson posts this very long, creative piece (h/t Cathy O'Neil) on "eigenmorality" (yeah, you read that right), a sort of crossing of philosophy, computer science, and complexity, involving Moses, Jesus, Rebecca Goldstein, Plato, Sergey Brin, Larry Page, et. al.:
http://www.scottaaronson.com/blog/?p=1820
[set aside some significant time to read and digest!]

8) Lastly, for the self-referentially-inclined:
First this:  https://twitter.com/michaelshermer/status/478681928703295488/photo/1
and then this (h/t John D. Cook): https://plus.google.com/u/0/+AnthonyScopatz/posts/cCAhUSkRgTR

How Not To GO Wrong...

…Buy THIS book: "How Not To Be Wrong" by Jordan Ellenberg


"The lessons of mathematics are simple ones and there are no numbers in them: that there is structure in the world; that we can hope to understand some of it and not just gape at what our senses present to us; that our intuition is stronger with a formal exoskeleton than without one. And that mathematical certainty is one thing, the softer convictions we find attached to us in everyday life another, and we should keep track of the difference if we can."  -- Jordan Ellenberg


To see it on a bookshelf Jordan Ellenberg's new volume looks like a slim, modest read… but, in fact, it's a dense, almost 450-page, surprisingly rich, entertaining, and jaunty math volume. And I'll cut to the chase to say that even though the year is only half over, I won't be surprised if this turns out to be my FAVORITE math book for all of 2014! It will certainly be in the top 2 or 3.

The five parts of Ellenberg's book, are entitled:

Linearity
Inference
Expectation
Regression
Existence

You might infer from that, that it is a volume bent toward statistical, probabilistic, and 'big data' related topics. You'd be right. This is a math genre that has gained great currency in the last few years -- so much so that I'm a bit weary of reading popular (and somewhat redundant) treatments of these subjects. BUT... Ellenberg's text is amazingly fresh, current, and fun to read! So much so, that I initially wondered how much of the final product was Ellenberg's own voice, and how much possibly molded by an expert editor -- but Ellenberg has written a novel before and has a degree in creative writing… moreover, Cathy O'Neil (who wrote a great review of this book, and knows Ellenberg personally) assures us that the book "reads just like Jordan talks" -- so there you have it!

Having said all that, I'll caution that the book, while written for a general audience, does require some minimal interest in, and aptitude, for mathematical discussion if it is to be appreciated/enjoyed. I'll reiterate what I've said before that the only math book I've seen in recent years that I think can truly draw in the naive math-phobic or math-inept is Steven Strogatz's 2012 "The Joy of X." For anyone though who has 'graduated' from Strogatz's treatment, this is a great follow-up, and concentrated on very timely topics, while yet covering a surprising amount of ground.

Let me tell you just how fresh this book is: there is not one chapter, not one section, nor paragraph, or line or word about the Monty Hall problem! Don't get me wrong, I love the Monty Hall problem, and believe it is one of the most interesting, instructive math tales around, but it has become an obligatory, rite-of-passage entry into every popular math book around (especially any involving probability)… Ellenberg just skips it... and I think that's great!  In fact, even when Ellenberg touches upon subjects that are fairly routine in such volumes, he gives them his own engaging spin, his own re-creation, that makes them fresh again. It is a remarkable achievement in exposition. Coming across topics like Monty Hall in other books gives me a sort of yawning 'oh, here we go again' gut reaction… I NEVER had that response reading Ellenberg.

The very first example he uses in the book is a fascinating real-life one I was unfamiliar with, dealing with bullet holes in missing World War II planes: essentially, the question arose how to more efficiently aluminum-plate war-planes to resist being shot down -- too little plating and the planes were more vulnerable; too much and the added weight made them less fast and maneuverable. It was noted that returning planes had the most bullet holes in the fuselage and a smaller number in the engines… implying perhaps that the fuselage needed more protection… but NO, it took statistician Abraham Wald to deduce that the planes getting hit in the fuselage were actually able to return to base, and it was planes being hit in the engines that weren't even returning successfully (to be a part of the sample); i.e. it was the engine compartments that needed more shielding.
The book is full of such clever, sometimes counter-intuitive examples. And throughout, a major theme of Ellenberg's is that mathematics is not so much computation and mechanical procedures as it is the careful application of common sense to pattern and structure.

I'll just list some of the prominent popular subjects he touches upon through these pages:

-- the Laffer Curve (famous, laughable cornerstone of Reaganomics)
-- obesity research
-- prime numbers
-- "the Baltimore stockbroker" -- this is a famous tale (though I've never seen it given this name before) explaining a system for sending out 10 newsletters successfully predicting some stock market movement, and then (with your 100% batting ave.) sending out an 11th letter soliciting new customers for your prescient services.
-- a famous 2009 fMRI study of a dead salmon, that made the rounds (yes, a dead fish scanned by fMRI)
-- the "hot hand" notion in basketball
-- the "crisis" in scientific replication, and John Ioannidis' work
-- the "crappy algorithms" that are now part of business 'Big Data'
-- state lotteries
-- correlation vs. causation and the "slippery" slope between them
-- the nature of "genius" in mathematics
-- opinion polling and elections

And those are just some of the more interesting (popular) topics along the way, while in-between Ellenberg teaches a little calculus, statistics, Bayesian analysis, non-Euclidian geometry, game theory, and an excellent section on regression analysis (although this may also be, for many, the most boring or tedious part of the volume). Somehow Ellenberg manages to go into more depth than others often do, yet remain clear and not too technical. Also mixed in here, some reflective history as well, as Ellenberg relates how the "territoriality" of mathematics has expanded over time, from rather limited areas, to domains where it didn't even seem applicable at one time or another.

And beyond the more usual mathematicians, there is mention of a sundry cast of characters: Daniel Ellsberg, Thomas Picketty, B.F. Skinner, David Foster Wallace, Antonin Scalia, all make appearances in these pages.

Meanwhile, throughout, Ellenberg lobs in his droll humor along the way… rare (and wonderful) to find in a math book. For some reason the simple line that most cracked me up came when he was reporting on Bertrand Russell's famous communique to philosopher Gottlob Frege regarding the latter's magnum opus on math's logical foundations. Russell, almost casually, mentions a single paradox (now famously known as "Russell's Paradox") he has found in Frege's account of set theory , which essentially undid all Frege's hard work. Ellenberg writes, "Despite the respectful tone ('I have encountered a difficulty,' not 'Hi, I've just borked your life's work'), Frege understood at once what Russell's paradox meant for his version of set theory" -- something about even imagining the properly-British Lord Bertrand Russell writing, 'Hi, I've just borked your life's work,' sent me into a cascade of chuckles -- I'll just bet Ellenberg too formed a big Cheshire grin on his countenance when he wrote those words ;-) Anyway, there are many such grin-producing lines.

Another lovely aspect of the book are the hand-drawn illustrations throughout done by Ellenberg himself. In a day of easily-done, precisely-composed graphs and mathematical illustrations, Ellenberg's hand-crafted jottings add another surprisingly delightful element of 'freshness' to these pages (I've seen books where hand-drawn illustrations didn't work well at all, but here they do!).

This book (and its author) is getting widespread coverage right now (#19 on one bestseller list), and sometimes when that happens there's a lot of hype and PR involved… in this instance it's all well-deserved. Cathy O'Neil writes of Jordan having "an infectious positivity," and that is indeed one of the unexpected benefits and appeals of this volume.
Just a splendid book (Fields Medalist Timothy Gowers says of it "destined to be a classic"), especially for the first time out-of-the-box… can't imagine what Jordan will do for an encore… or, if he even needs an encore after this bravura performance!

[Additionally, an excellent review of Ellenberg's book from Alex Bellos here:
http://tinyurl.com/pbsrxl2 ]

Friday Potpourri

 First, a note that Sunday morning, here, I'll have up my review of Jordan Ellenberg's new volume, "How Not To Be Wrong" -- hint: (like everyone else) I loved it.

 Now, some recent math links:


1) Math professor Dan Rockmore argues the case for banning laptops from the classroom:
http://tinyurl.com/obtfzzv

2) I'm often taken by surprise by which tweets I do get significantly re-tweeted. This week one by Cliff Pickover, regarding pi, was popular:
https://twitter.com/pickover/status/444533534284189696/photo/1

3) New podcast from Sol Lederman, with David Reimer, interesting author of "Count Like An Egyptian":
http://wildaboutmath.com/2014/06/07/david-reimer-inspired-by-math-35/

4) The 111th Carnival of Mathematics appeared last week full of its usual variety:
http://boolesrings.org/krautzberger/2014/06/08/carnival-of-mathematics-111/

5)  Oftentimes, mathematical puzzles have ramifications in other fields, as in this news report about the four-color theorem and crystal structure:
http://phys.org/news/2014-06-four-color-theorem-linked-crystal-magnetic.html

6) A bounded gaps update and other polymath projects:
http://cp4space.wordpress.com/2014/06/01/bounded-gaps-one-year-on/

7)  Alex Bellos' latest book, "The Grapes of Math" is newly-available in US:
http://tinyurl.com/nutompp

8) From xkcd (channeling Fermat):
http://xkcd.com/1381/

9) Lastly, my own latest rant about "truth-in-labeling," courtesy of Coca-Cola:

http://math-frolic.blogspot.com/2014/06/pomegranate-blueberry-juice-not.html

Much Ado About Turing Tests (ho-hum)

When I was much younger the first thing I read from Kurt Gödel was his "proof" of the existence of God. It seemed so weak and shallow I couldn't imagine there was any point in reading anything else generated by such a mind. So it was decades before I returned to Gödel to discover the delicious, insightful and logical profundity of which he was capable.

In a similar vein, and not to take anything away from his other accomplishments, I never could see much significance in the "Turing test" of Alan Turing. As others have occasionally written, passing a Turing test probably says more about the gullibility, subjectivity, and naivete of humans (and the ambiguity/imprecision of language), than it does about actual artificial intelligence (AI); or put more simply, Turing tests likely say more about the human interrogators than about the machines being tested.
I fully expect in the not-too-distant future a program will be written that can fool well over half of any judges interacting with it into believing they are communicating with a human being (and once one program does it, there will be a flood of others)… to which I'll yawn and quizzically mumble 'soooo?' I see it as akin to (while admitting it's different from) IBM's "Deep Blue" supercomputer beating chess grandmaster Gary Kasparov… interesting, noteworthy, even fun, but neither truly profound nor necessarily cognitively meaningful.
Of course the big news yesterday in some circles was that a program (or "Chatbot algorithm"), purporting to be a 13-year-old non-native-English-speaking boy named Eugene Goostman, for the first time passed the Turing test (by persuading 1/3 of a sample of judges that they were conversing in brief keyboarding sessions with a live human).  io9.com was one of the many outlets covering this story of human judges falling for some mimicry or simulation, if somehow you missed it:
http://io9.com/a-chatbot-has-passed-the-turing-test-for-the-first-ti-1587834715
also, this skeptical approach from Buzzfeed:
http://www.buzzfeed.com/kellyoakes/no-a-computer-did-not-just-pass-the-turing-test

One mathematician, critical of all the hype the story produced, tweeted: "isn’t it a wacky coincidence that the result came on the anniversary of Turing’s death? What were the CHANCES?!" And followed that with: "It’s almost as if the University of Reading is doing a Turing Test to see if journalists can tell the difference between ‘science’ and ‘PR’. I expect there will be more skeptical takes on the story in ensuing days, and will add links here as I see fit* (and I'm hoping certain bloggers will cover the story more fully and critically). Already, some are questioning the number of judges, the 5-minute conversations, the 30% benchmark, and other general circumstances of the test.

The Turing test is, I s'pose, better than nothing… which is part of the problem: that AI enthusiasts have so few benchmarks for measuring true AI, and perhaps one might even assert that a successful Turing test is a necessary, though insufficient, prerequisite for AI.  In the longer run, I suspect Turing tests (and certainly this particular one) will be seen as interesting curiosities that didn't deserve the ballyhoo they attracted. Anyway, here's a longish article from 2006 giving voice to some of the cynicism around "Turing tests":
http://www.thenewatlantis.com/publications/the-trouble-with-the-turing-test

The article ends on this simple note with which I'd concur: "It may be uncomfortable to live with uncertainty, but it’s far better than insisting, against all evidence, that we have accomplished a task that we have in fact scarcely begun."

(Admittedly, though, we cynics of the TT are probably in the minority, and the arguments pro/con are a lot more nuanced than I have the time/space for here.)


* ADDENDUM:  Martin Robbins now has a critical post up on the story (h/t Ed Yong):
http://www.vice.com/en_uk/read/eugene-goostman-alan-turing-test-kevin-warwick 

I was hoping that perhaps Scott Aaronson might have something to say on this matter... and now he has:  http://www.scottaaronson.com/blog/?p=1858 

And another view here, from a Turing judge, giving matters more context:
http://tinyurl.com/ogm8vol

Finally, Ian Sample/Alex Hern coverage here:
http://tinyurl.com/knm7dl8 

Friday Linkages...

Some links from the week gone by:

1) Mistakes made using statistics:
http://www.ma.utexas.edu/users/mks/statmistakes/TOC.html

2) This pretty amazing thread showed up on Reddit last week in response to a mother's desire to encourage her young child's interest in math:
http://tinyurl.com/lq3ybwk

3) "Silicon Valley… is a place of endless failures" …Keith Devlin again addressing the vital importance of failure:
http://tinyurl.com/k8rtbro

4) Evelyn Lamb's review of Jordan Ellenberg's new volume, "How Not To Be Wrong":
http://tinyurl.com/oly4l38

5) And wonderful (7-min.) NPR interview with Ellenberg here:
http://tinyurl.com/obl3nfh
(I'll probably write some sort of review of his book myself at some point, once I've completed it… so far, luvin' it.)

6) Presh Talwalkar explaining a simple continued fraction:
http://mindyourdecisions.com/blog/2014/06/02/monday-puzzle-infinite-fraction/

7) "Gyre and Gimble" on math as pattern recognition:
http://www.abstractmath.org/Word%20Press/?p=9285

8) Ben Orlin argues the SAT scoring system is gibberish here:
http://mathwithbaddrawings.com/2014/06/02/the-sats-scoring-system-is-gibberish/

9) And if you don't have enough going on to fill up your weekend, have a crack at "The 10 hardest logic/number puzzles" (h/t to C. Pickover):
http://www.calcudoku.org/hardest_logic_number_puzzles/

10) Finally, let's see, young people are stuck with student loans they can't pay off, slightly older folks are now gun-shy of the housing market, and banks have cracked down on lending anyway, so why should anyone be surprised that the housing market is in the dumps, and will remain so for the foreseeable future (...thank you George Bush):
http://tinyurl.com/nzsx8lg
 

Friday Links

Some links from the week gone by:

1) new issue of "The Mathematical Intelligencier":
http://link.springer.com/journal/283/36/2?wt_mc=alerts.TOCjournals

2) Video from "MinutePhysics" in which Max Tegmark once again explains his view that the Universe is entirely a mathematical construction:
https://www.youtube.com/watch?v=HGG4HmlotJE&list=UUUHW94eEFW7hkUMVaZz4eDg

3) MIT's George Luzstig was awarded the Shaw Prize in mathematics for "weaving together" algebra, algebraic geometry, and representation theory "to solve old problems and reveal beautiful new connections":
http://www.shawprize.org/en/shaw.php?tmp=3&twoid=96&threeid=234&fourid=410

4) Exciting news from Sue VanHattum… a volume she has shepherded for math teachers everywhere, "Playing With Math," is near completion. She has had three recent posts about it:
http://mathmamawrites.blogspot.com/2014/05/playing-with-math-rave-reviews-from.html
http://mathmamawrites.blogspot.com/2014/05/playing-with-math-table-of-contents.html
http://mathmamawrites.blogspot.com/2014/05/playing-with-math-authors-and-artists.html

5) Spreading outward a bit from mathematics, interesting to find two heavyweights of the blogging world, in different areas, Sean Carroll and Scott Aaronson, working together (on the topic of complexity) here:
http://www.scottaaronson.com/blog/?p=1818

6) Robert Talbert on adding "coding" to the early education regimen:
http://tinyurl.com/n6vunyx

7) Sol Lederman has posted a transcribed interview with Director of MATHCOUNTS Foundation, Lou DiGioia, here:
http://wildaboutmath.com/wp-content/uploads/2014/05/MathCounts.pdf
He introduces the interview here:
http://wildaboutmath.com/2014/05/12/lou-digioia-on-largest-human-pascals-triangles-and-more/

8) Wonderful review from Cathy O'Neil of Jordan Ellenberg's brand new book, "How Not To Be Wrong":
 wp.me/p1CO0X-2fP

Friday Potpourri

Some links from the last 10 days or so (many of which I've tweeted, but not blog-posted about):

1)  The inimitable John Conway in conversation at Numberphile (at the end speaking almost reverentially of "the Monster group"):
https://www.youtube.com/watch?v=xOCe5HUObD4&feature=youtu.be

And Numberphile's own attempt to explain the Monster group here: 
https://www.youtube.com/watch?v=jsSeoGpiWsw&feature=youtu.be

2) Robert Talbert continued his series about skepticism over "flipped" classrooms here:
http://tinyurl.com/lz8uqp2

3) Joselle Kehoe of "Mathematics Rising" on some of the details of the Jason Padgett "acquired savant" syndrome story:
http://mathrising.com/?p=1155

4) Monkeys, hypercubes, quaternions, and Vi Hart from Evelyn Lamb:
http://tinyurl.com/lrfqd6m

5) Some fun and interesting math history here:
http://mathematigal.com/home/2014/5/20/a-mathematical-history-tour

6) 3 camps of math students... "Muddling along," "completely lost," and "completely comfortable":
http://mathmisery.com/wp/2014/05/20/some-cute-integrals-intermission/

7) Some possible variations on the traditional "I (heart) Math" bumper sticker:
http://visualizingmath.tumblr.com/post/86363962441/i-mathematics

8) Commentary from Dan Meyer on futurists as "adaptive learning" enthusiasts:
http://tinyurl.com/odqt32y

9) Interesting post on the Friday get-togethers one university math dept. came up with to "inspire" and "hook" their math majors:
http://maamathedmatters.blogspot.com/2014/05/hooking-student_22.html

10) Lastly, a couple of probability conundrums from "Futility Closet" this week:
http://www.futilitycloset.com/2014/05/21/two-olive-problems/

Fawn Nguyen... Passion Personified

Math-Frolic Interview  #24

"Mathematics is my passion, and kids are my love – one fuels my head, the other expands my heart. That’s grace." -- Fawn Nguyen

This week, another opportunity to get to know one of my fellow math bloggers better.  I'm tempted to say Fawn Nguyen needs no introduction… even though I don't follow education blogs regularly, early on I kept seeing her name pop up in various places in the math blogosphere; she clearly had a large, loyal following. And reading her varied, instructive, heartfelt, creative posts I understand why. Now that I know more about her whole history I'm even more impressed! If you're not already a Fawn fan you will be after reading her words below...:
(I've added bold to a few lines)

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1) For starters, maybe just give us a bit of bio about your path from being a youngster in Viet Nam to being a math educator in Southern California…?

When Saigon fell in 1975, my family made a failed attempt to flee the country by sea. The following year, my older brothers planned another escape for our family, but this time my father did not want to have anything to do with it. The experience from the first attempt scared him, and I supposed it also scarred him. His decision to stay back only meant that my mother and two sisters also had to stay.
So my three brothers, along with my oldest brother’s wife, another sister, and I escaped again in June of 1976. After four days at sea, we were rescued by Thai fishermen who helped us ashore. We stayed in a refugee camp in Songkhla, Thailand, for three months before we were flown to St. Cloud, Minnesota. With the help of a Catholic church in St. Cloud, my sister-in-law’s aunt had sponsored us over.
I had an ESL (English as a Second Language) teacher – all to myself :) – for an hour each day for the first two years. Because of this one-on-one attention and the fact that none of my teachers spoke Vietnamese, I picked up English more urgently for survival. Watching television helped; my two favorite shows were Happy Days and The Price is Right. The game show was all about numbers, so I didn’t need to know a lot of English to understand; and the sitcom had The Fonz – and I’m Fawnzie to my family and friends, so that’s where that link is.
One day I realized I was thinking in English. It was really weird. My thoughts were parading in my head with English labels all over them.
Minnesota was too cold, so we moved to Oregon after 3 years.
In college I majored in Biology, made a half-ass attempt at Pre-Med too. I got my teaching credential during my 5th year and was hired to teach science at a middle school where I did my student teaching. After my first year of teaching, I married a medical student whom I’d known for 7 years. When he finished med school, we had our first child, Nicolai. Then Gabriel arrived a couple years later, and then Sabrina was born in 1996.
I married again in 2002. (This was after the dissolution of the first, of course.) We moved to California because my husband got a job here. I took advantage of the location change across state borders to apply for math positions instead. Without a degree in mathematics, I had to pass a few subject tests to become certified. But I’ve always loved math – my father was a math teacher his whole life – so I continued to take post-baccalaureate courses in mathematics. Teaching math seems like the most natural thing for me – I don’t mean natural as in easy because teaching is anything but easy, I just mean natural as in my calling.

[Wow! Remarkable life-story... and both your English and math seem impeccable!
Moreover, as a fan of Happy Days, you'll henceforth always be "Fawnzie" to me ;-)]

2) You have a very popular presence on the Web, where there are 100s of math-education blogs to choose from. So tell us a little about how/when you came to be a blogger, and to what do you attribute the popularity of your work that allows you to break out from the crowd so-to-speak?

I started my blog in late November 2011 wanting to write mostly about food. My first post was about a Thanksgiving dinner that I’d prepared.
I’ve been reading other people’s blogs for a very long time. Not until 4 years ago, I was the only math teacher at my school, so I definitely felt isolated. Scouring the internet for lesson ideas makes me feel connected and current. I steal well.
I write many of my lessons as narratives, and I suppose there weren’t too many of these posts around. That structure is simplest to me because I don’t have to make anything up, I’m just scribing what I see and hear from the lesson. Stuff kids say – or don’t say – helps guide my instruction, so writing them down forces me to reflect. That’s also why many of my lesson posts are normally up the day after we do the lesson. My short-term memory is getting shorter. And the urgency to tell that story – that lesson – keeps me honest. This is probably why I write mostly in present tense, whether it was about the latest lesson or something long ago. The story-telling way that I write lets my voice come through in ways that I hope people can relate to. Or not relate to, but it’s there, and it’s me.

3) You obviously love teaching (I believe you've been at it well over 20 yrs.), in a day when so many teachers are burnt-out quickly. What keeps you motivated and drawing satisfaction from the profession, and do you teach year-round or do something else in the summers? Also, you seem to be very close to your students... do you stay in touch with some of them long after they've moved on from your classroom?

And here I was just about to reveal to the world that I’ve had enough of this damn teaching: the ungrateful kids and their difficult parents, the lousy pay, the long hours, the nonexistent lunch time, the sleep deprivation. Ha! I’m kidding. Not really. Because that’s all true to some extent you know. Right, I think this is year 23 for me. I started teaching when I was 15.
With three kids currently in college, I’m quite motivated to stay employed.
I honestly believe I have the best job, and the only reason I can say that is because of my students. Mathematics is my passion, and kids are my love – one fuels my head, the other expands my heart. That’s grace.
My school feels like home, sans bathrobe and slippers. I have to give my colleagues and administrators credit for that too. At the core of this extended family unit is our deep respect for one another. (Don’t get me wrong, though, I LOVE my weekends – away from school! I guess it’s not unlike loving your children with all your heart, but having a quiet dinner every now and then without them is pretty damn fantastic too.)
Year-round school?? Kill me now, Shecky. All teachers need a more prolonged period to recharge because teaching is draining. It’s tough tough tough. I love this tough work because doing anything easy isn’t worth doing. But it takes its toll. I have yet to learn to eat and exercise properly from September through June – it’s very sad, and I need help.
Yes, I’m still in touch with a few of my former students. It’s weird when the “older” ones start calling me Fawn. Can you believe that my students from my first year of teaching are now 40?! I’m not even that old.

4) Education possibilities evolve incredibly rapidly these days… What online resources do you incorporate into the classroom now that weren't even around say 5-10 years ago? And where does "social media" fit in (do you use it in the classroom at all, or just with your teaching peers)? Finally, how much do you "experiment" with new methods/approaches/resources in a typical year?

Desmos!! Desmos has been the biggest addition to my classroom in the last two years. Other resources we consistently use are Geometer’s Sketchpad and Excel. I just use Remind101 to text parents and students homework for the evening.
I haven’t tried too many new anything this year because we went from two periods of math in the last couple of years to just one period this year. If anything, there are a bunch of solid lessons I’d done previously that I still haven’t had time to squeeze them in this year. I have a set of criteria that a new resource or method has to stand up to before I implement it. (C’mon now, I have some standards, y’all.) Whatever I choose, the math has to be a big component: simple for kids to dive into, yet rich in mathematics content.

5) Which of your blog posts have been the most enjoyable or rewarding for you to work on?

 You are a girl. Female.

[...but have a tissue handy if you're going to read this, folks!]

6)  Math education seems forever controversial!… do you ever foresee a day when there will be wide consensus, rather than strongly-held, competing views of how best to do it? […because personally, I don't! :-(  ]

Consensus in education – that’s like finding tofu in bouillabaisse. I don’t think so. I know we adults talk and make decisions because that’s what adults are supposed to do. But when grown-ups talk, it’s very quick for all the noise to gather around and next thing you know, we can’t hear each other so we’re shouting wanting to be heard. Social media amplifies this noise in magnitudes that were not around 10 years ago. I’m willing to bet that there’s a direct correlation between how fast we receive information now and how fast we react to such information. This instantaneous feedback loop makes us less critical of the information itself yet more critical of the humans with different views than our own. I just don’t like the disrespect, the putdowns, the ill-informed-yet-quick-to-judge, the meanness.
We no longer jump on the bandwagon, we jump on the Ferrari.

7) If you had to give some words of advice to new math teachers, that maybe you wish you'd heard when you first started out, what might you say?

Get help. No, I don’t mean seek psychological help – which maybe I could use. I mean reach out to colleagues, on site and online. What we do is way more honorable than it is heroic. We don’t have to be alone. And misery loves company. MTBos rocks my socks.

8) Finally, when you're not thinking/teaching/doing/dreaming/writing about math ;-) what do you like to do in your spare time?

This is a mean question, Shecky :)
I love reading, eating, gardening, watching foreign movies.

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Thanks Fawn; your passion for your work shines through and is inspiring... and I'm blown away a bit learning about your life-story -- our luck to have you here! hope even your long-time fans gained some insight about you as well.

Cathy O'Neil interviewed Fawn, btw, for her views on Common Core awhile back here:
http://mathbabe.org/2014/04/23/interview-with-a-high-school-math-teacher-on-the-common-core/

And if you want to see Fawn operating in the flesh she covers several of the same topics from this interview, in a recent brief video (which I also linked to on Friday):
https://www.youtube.com/watch?v=u1P6AA_IEd4&feature=youtu.be

Happy Math Links... and... Mother's Day!

A host of links to catch up on, if missed:

1) New books!!
Some philosophy websites are recommending: "Philosophy of Mathematics in the Twentieth Century" by Charles Parsons:
http://www.hup.harvard.edu/catalog.php?isbn=9780674728066&content=toc

New, slender volume from Oscar Fernandez entitled "Everyday Calculus" (Princeton University Press), looks good:
http://tinyurl.com/n5s8nhq
(link includes 1 hour interview with the author)

And also from Princeton U.P.  notice of a new paperback version of "The Recursive Mind: The Origins of Human Language, Thought, and Civilization" (more philosophy/psychology than math) by Michael Corbaliss:
http://press.princeton.edu/titles/10297.html

2) A 6-minute interview with math professor/educator Jo Boaler:
http://tinyurl.com/kut2amh

3) In the category of "some-things-never-change," this (re: math education):
http://thescamdog.wordpress.com/2014/05/06/letter-to-a-science-journal/

4) Nice Nautilus piece on Penrose tiles and quasicrystals:
 go.nautil.us/penrosetriumphs

5) Peter Woit reports a bit on the work of mathematician Daniel Quillen, bordering math and physics:
http://www.math.columbia.edu/~woit/wordpress/?p=6861

If Peter calls Quillen's stuff "pretty mind-blowing" (and he does) then I suspect others will find it so.

6) From Scientific American, another piece on the neuroscience of mathematics and beauty:
http://tinyurl.com/myqhxq6

7) New (36-min.) "MathEd" podcast with Canadian Egan Chernoff (aka MatthewMaddux):
http://mathed.podomatic.com/entry/2014-05-03T05_37_31-07_00

If, like me, you've missed most of these podcasts you may want to go back and check out some of the prior offerings (they look GOOD!):
http://mathed.podomatic.com/

8)  Really nice graphical representation of different math-related paradoxes broken into categories (h/t to Gary Davis):
http://wikibrains.com/map/53621d86e4b017c9fdee45c2

9) Dan and Katherine at "Math For Love" have produced a new board game called "Primo" based on arithmetic use of prime numbers:

http://mathforlove.com/2014/05/primo-the-beautiful-colorful-mathematical-board-game/

They need help via Kickstarter to put the game into production, so check it out.

10) If you're in the mood to have your mind stretched, then h/t to Patrick Honner for pointing out this Numberphile video explaining "Ricci Flow":
https://www.youtube.com/watch?v=hwOCqA9Xw6A 

11) I hope to interview popular teacher/blogger Fawn Nguyen in the near future for this blog, so am hesitant to even link to this wonderful 5-min. clip of her (a bit PG-rated), because it answers several of the questions I had posed to her... BUT, it's too delicious not to pass along!:
https://www.youtube.com/watch?v=u1P6AA_IEd4&feature=youtu.be

12) So MUCH rich stuff here --> the interviews of Martin Gardner collected online:
http://martin-gardner.org/Interviews.html 

13) And when you're finished with my link offerings, you can go savor the diverse collection of the (110th) "Carnival of Math" freshly-up at "Flying Colours Math" blog:
http://www.flyingcoloursmaths.co.uk/carnival-mathematics-110/

14) Finally, after causing some to fear for her sanity with videos of microwave countdowns, Vi Hart is back demonstrating again why people anxiously anticipate her videos, with a doodling explanation (her inimitable style), of "net neutrality" and the evils of Comcast, Verizon, etc. (uhhh, Comcast merging with Time-Warner??... is somebody in the Government NUTS!!!):



....enjoy the weekend! (...and let me know ASAP of any broken links)

Friday Catch-up

This week's potpourri batch of links:

1) The below is a 2+ years-old post, but I only came across it last week when no less than Terry Tao referenced it in a comment left over at "Mathbabe" blog:
http://m-phi.blogspot.com/2011/10/inconsistency-of-pa-and-consensus-in.html

For the philosophically and foundationally-minded, it's an interesting discussion of consensus in mathematics (and how that may differ from consensus in other fields).

2)  Another oldie-but-goodie: Steve Mirsky re-tweeted this old Scientific American podcast (27-mins.) that shouldn't be missed… Douglas Hofstadter talking about Martin Gardner, following his death in 2010:
http://www.scientificamerican.com/podcast/episode/remembering-martin-gardner-with-dou-10-05-24/

3) Thoughtful post on flipped classrooms from Robert Talbert (a good one if you're contemplating or doing a flipped classroom):
http://tinyurl.com/mmy5y96

4) Fascinating piece on algebraic numbers, Ken Ono, and Ramanujan here:
http://esciencecommons.blogspot.com/2014/04/mathematicians-trace-source-of-rogers.html

5) Revisiting Ramsey Theory and tiling planes (h/t to Jennifer Ouellette for this one):
http://tinyurl.com/mcovoyg

6) And uh-ohhh, supporters of Common Core may have finally gone too far… it's one thing to draw the ire of Diane Ravitch, but now (and if you follow math news you couldn't have missed this, it got such wide coverage) they've upset Louis CK!:
http://www.businessinsider.com/louis-ck-math-homework-2014-4
(and Louis has continued the cynical tweets since the above were recorded)

7) The week wouldn't be complete without some statistics-bashing… this guide fills the bill:
http://www.statisticsdonewrong.com/

8) A couple of Colm Mulcahy wrap-ups to Math Awareness Month (April) here:
http://www.huffingtonpost.com/colm-mulcahy/mathematics-awareness-month_b_5239135.html
http://cardcolm-maa.blogspot.com/2014/04/foregone-outset.html

9)  Fibonacci as the precursor of Steve Jobs... courtesy of Keith Devlin:
http://devlinsangle.blogspot.com/2014/05/deja-vu-all-over-again-fibonacci-and.html

And if you missed my interview with blogger Mike Lawler last Sunday, catch up on that right before this post (in a few more years maybe I'll interview his kids!).

.... A great weekend to all.