Fun and Games (and oh yeah Math)

"The Innovation Factory" is promoting its "Magic Cube" product (a Rubik's Cube on steroids) with a contest to see who can be first to find the correct solution out of the 140,000,000,000,000,000,000,000+ possible solutions:

http://if-chicago.com/portfolio/the-magic-cube/

In exciting news from Keith Devlin, his company InnerTube Games is finally out with its "Wuzzit Trouble" app game for young people (currently available for iOS platforms as a free download). Great interview with Dr. Devlin in this Forbes article:

http://tinyurl.com/nhqkovr

This older American Scientist piece by Keith gives more of the principles behind 'Wuzzit' (with an analogy to music):

http://www.americanscientist.org/issues/pub/the-music-of-math-games/1

And finally, Keith also gives an introduction to the game in this video:

http://vimeo.com/73095116

More generally, one may also want to read about MMO games (if not already familiar with them) and their possible future in education:

http://en.wikipedia.org/wiki/Massively_multiplayer_online_game

And Dr. Devlin wrote a whole book on the general topic:

http://www.amazon.com/Mathematics-Education-New-Era-Learning/dp/1568814313

Nom Nom Nom...

In a couple of months "Math Munch" ("It's About Sharing Math") celebrates its 2-year anniversary (Hooray!). The internet is chock-full of math pages these days, including a large selection of sites geared toward primary/secondary students -- sometimes I think the 'Net will eventually have a glut of such math material, but for now it's still more like a very big smorgasbord. There aren't that many sites though that receive as much positive acclaim, and so quickly grow a following as Math Munch has done in its short two years. They also have a Facebook page here: https://www.facebook.com/MathMunch

Each week the Math Munch proprietors (Justin Lanier, Paul Salomon, and Anna Weitman, all New York-based) post "three great finds from around the mathematical internet." They look for "accessible, enticing" material that will give young people a fun, creative experience, and show kids that "math is a big tent and there's room for them."

It's sites like Math Munch that make me wish I grew up in today's world instead of 50+ years ago :-( They further note that Math Munch is a "jumping off point, not just a destination." And while the site is geared toward kids, hey, I've always believed that all math-lovers are essentially eternal kids-at-heart!

I do have one quibble with the site -- I've never liked the color scheme (with a background that one of my old college buddies would've called 'puke green' on 'dog-doo brown')… but, oh well (probably appealing to the young crowd).

If by any chance you're unfamiliar with Math Munch (or even if you are, but haven't seen the below clip) watch this 17-min. TED Talk intro to what they are all about -- last time I checked it only had ~1700 views and deserves a lot more:

Naughty and Nice...

Just passing along a couple of disparate items from my recent Twitter math feed:

If you follow science reports on the internet much you've probably noticed a recent study of relationships between effects of coffee consumption and age… it garnered lots of headlines. This post takes it down a notch (...or more) to a "useless study published in a peer-reviewed journal.":

http://tinyurl.com/p5ck343

And, changing moods, below, a very nice interview from 'Math Munch' with Aussie mathematician Nalini Joshi:

http://mathmunch.org/qa-with-nalini-joshi/

Tautologies At Work

From the 'Everyday math' Dept.:

Ever wonder how it is that every auto insurance company that contacts you claims they can save you $500/yr.? Presh Talwalkar wondered, and explains in his latest "Mind Your Decisions" post:

http://tinyurl.com/o9ls4ms

(...basically an insurer CAN save you $500 IF, by switching to them, you will save $500 ;-) otherwise known as 'selection bias' in advertising*)

* "advertising" -- otherwise known as propaganda

Sit Back and Relax…

You've most likely seen this before (and I've used it here myself before), but every now-and-then am just in the mood to chill-out and re-view this short, meditative math-and-Escher inspired film, entitled "Inspirations," from Cristobal Vila and Eterea Studios. ....Enjoy:

"the sexy job in the next 10 years…"

"The ability to take data, to be able to understand it, to process it, to extract values from it, to visualize it and to communicate it -- that is going to be a hugely important skill of the next decades, not only at the professional level but even at the education level."        -- Hal Varian of Google

Good news for all up-and-coming statistics geeks, "it is now OK to self-identify as a statistician"! Yes, yet another article touting that "big data," and thus statistics, is where it's at these days for those who wish to be part of the new sought-after job-seekers:

http://tinyurl.com/m4accko


[...in other matters, my latest post over at MathTango wonders about the authenticity of 'autistic savant' Daniel Tammet: http://mathtango.blogspot.com/2013/08/numbers-mnemonism-savantism-oh-my.html ]

"No Such Agency"

Regular readers here know I'm a huge fan of Keith Devlin, and have followed closely his vocal objections to the actions disclosed of the NSA for whom he once worked. Now another favorite science popularizer of mine (and a mathematician by academic training), Charles Seife, has gone public with an "open letter" on the NSA (for whom he worked as well) voicing his consternation (he notes early on that back in his day the super-secret agency was "nicknamed No Such Agency"):

http://tinyurl.com/l4sx7qz

And Seife essentially argues that more mathematicians should be publicly voicing concerns over disclosed NSA activities.

a couple of excerpts:

"...we all knew that the math was sexy. This might sound bizarre to a non-mathematician, but certain mathematical problems just exude a certain something—a feeling of importance, of gravity, along with a sense that the solution is not far outside of your grasp. It's big, and it can be yours if you just think a little bit harder. When I signed up, I knew that the NSA was doing interesting math, but I had no idea what I was in for. Within a week of arriving at the NSA, I was presented with an amazing smorgasbord of the most alluring mathematics problems I had ever seen, any of which could possibly yield to a smart undergraduate. I hadn't seen anything like it—and I never will again."

...but then this:

"The agency insisted, over and over, that the weapons we were building—and weapons they are, even if they're weapons of information—would never be turned on our own people, but would only be used upon our enemies.
"What do we do now that we have to face the fact that the Agency broke its word?"….

"I can only guess how much more horrified the ex-NSAers I know—you, my former colleagues, my friends, my professors, and my mentors—must be. Unlike me, you have spent much of your working lives helping the NSA build its power, only to see your years of work used in a way it was never supposed to be used. You could speak out now in a way that violates neither your secrecy agreement nor your honor. It's hard to believe that the professors I know at universities around the country would remain silent as the NSA abuses their trust and misuses their work.
Or would you?"

The NSA is known to be the largest employer of mathematicians in the country... one can't help but wonder what, if any, effect all this public disillusionment will have on its ability to recruit the nation's most able mathematicians going forward?

A Garden of Math

The Web is such an endless supplier of delight… just came across yet another math blog I was previously unfamiliar with and want to pass along:

http://mathgardenblog.blogspot.com

It's titled "Math Garden" (subheaded "Math for the curious") and appears to only post a few entries each month but they are wonderful little gems of textbook-like explication.
The author writes that "This is a math blog written with the intention to stimulate math curiosity in young school children. The author, Dongvu Tonien, won a silver medal in the 35th International Mathematical Olympiad in 1994 and obtained his PhD in Computer Science in 2005."
Well, I don't think you need to be a 'young school child' to enjoy these posts, just curious and young-at-heart maybe.

Posts cover a number of different mathematical topics, as indicated in the right-hand column. Here's a nice geometry example, on "the power of a point with respect to a circle":

http://mathgardenblog.blogspot.com/2013/07/power-of-a-point.html

If Only I'd Had Robin Williams As a Teacher…

just a quirky little post I came across that linked together math, teaching, and one of my favorite Robin Williams' movies, "Dead Poets Society":

http://casualcalculations.wordpress.com/2013/08/21/dead-mathematicians-society/

Watch the scene in the above post and then, if you've seen the movie, re-live the ending, that still tugs at me (but not specific to math and probably only meaningful if you've seen the film):

A Few Links

Stumbled across this interesting math problem while surfing around recently:

http://wordpress.mrreid.org/2013/07/22/mathematics-as-the-language-of-physics/

It comes from the blog of a physics teacher, "Mr. Reid," which I don't recall seeing before (though he's been around quite awhile on the Web); seems to have some more interesting math posts here (check him out):

http://wordpress.mrreid.org/tag/mathematics/
 
And on a separate note, my review of Alfred Posamentier's latest volume, "Magnificent Mistakes In Mathematics" is up at MathTango now:

http://mathtango.blogspot.com/2013/08/new-math-book-full-of-mistakes.html

Math As Science

Waxing a bit philosophical today....

The debate over whether or not mathematics is a science goes back a long while. I won't address that argument specifically (since I think the underlying question of what is "a science" is unresolved and unresolvable -- the author below believes there exist "standard" operating definitions for science that work -- I don't believe those definitions can be used consistently, precisely, or unambiguously (and that has nothing to do with 'post-modernism' per se, as the writer would imply, but simply with the imprecise nature of language and limits/uncertainties of human cognition -- some biology IS science, some ISN'T; same for physics, geology, psychology, medicine, etc.).

But with that said, I did enjoy the approach and content of this 2008 piece on the subject, which touches upon several topics:

http://www.arachnoid.com/is_math_a_science/

In the end the author concludes:

"Nature is innately mathematical, and she speaks to us in mathematics. We only have to listen.
"Because nature is mathematical, any science that intends to describe nature is completely dependent on mathematics. It is impossible to overemphasize this point, and it is why Carl Friedrich Gauss called mathematics 'the queen of the sciences'."

 I have no qualms calling math 'the queen of the sciences' -- am just not sure that that means anything more than that math is the most logically precise/rigorous and least ambiguous of the large, continuous (not discrete) gradient of human thought processes.

Kids These Days ;-)

Video was an offshoot of this conversation between Patrick Honner and Grant Wiggins:

http://grantwiggins.wordpress.com/2013/08/14/a-dialogue-with-patrick-honner-on-rigor/

Tweetfest

Haven't had time of late to write anything up, but will pass along a number of miscellaneous links (in no particular order) I've been tweeting in the last week that may be of interest if you've missed them:

1) A little math history synopsis from LiveScience:

http://www.livescience.com/38936-mathematics.html

2) "Matroid Theory" and Rota's Conjecture:

http://tinyurl.com/n45h5xz

3) Ingrid Wickelgren at Scientific American promotes John Mighton's "JUMP math" program:

http://tinyurl.com/pn5kjeu

4) A quick look at 'category theory' from AMS blogs with links for more info (also links back to this post at "Mathematics Rising" on the interweaving of math and physics: http://mathrising.com/?p=1055 ):

http://tinyurl.com/lyxt8sh

5) A letter from the reclusive genius Alexander Grothendieck:

http://sbseminar.wordpress.com/2010/02/09/grothendiecks-letter/

(by the way, I recently read Amir Aczel's "The Artist and the Mathematician," which is focused on "Nicolas Bourbaki," and while I only thought the volume was so-so overall, I did especially enjoy the sections at beginning and toward end on Grothendieck.)

6) Another nice little post on infinity here:

http://ieet.org/index.php/IEET/more/dvorsky20130813

7) A post from the always-good Richard Elwes on the "Perko Pair" and knot theory:

http://richardelwes.co.uk/2013/08/14/the-revenge-of-the-perko-pair/

8) And last but not least... rigorous, a discussion from Patrick Honner and Grant Wiggins on "rigor" in mathematics:

http://mrhonner.com/2013/08/14/a-conversation-about-rigor-with-grant-wiggins-part-1/


Hope everyone will find at least one thing of interest from the above for their weekend time and perusal....

NSA Critic/Curmudgeon To Again Teach MOOC Course

;-)

The 3rd edition of Keith Devlin's MOOC course "Introduction To Mathematical Thinking" is coming up beginning Sept. 2 (...I understand it will include a special added section this go-around on whistleblowing and NSA thought control…. er, no, nevermind, just kidding, not on the syllabus).

Seriously though, anyone contemplating joining the 13,000 already signed up for the course should read what must be Keith's best intro yet to what the course IS and ISN'T (I suspect a LOT of people sign up for the course with a mistaken notion of what it will be like!):

http://mooctalk.org/2013/08/13/evaluation-rubrics-the-good-the-bad-and-the-ugly/

Early on, Keith states,

"With the primary focus on helping students develop an new way of thinking, the course was always very light on “content” but high on internal reflection. A typical assignment question might require four or five minutes to write out the answer; but getting to the point where that is possible might take the student several hours of thought, sometimes days."

It is a long post that covers a lot of general ground, and should be read by anyone thinking of taking Keith's course, but may well be of value to anybody thinking of taking… OR, offering… any MOOC.

...Oh, and lucky Princetonites! Dr. Devlin (who is based at Stanford) divulges in the post that he will be spending a term at Princeton early next year teaching in the undergraduate classroom (something he hasn't done for years).

Meanwhile, in other news, the new (101st) 'Carnival of Mathematics' is up-and-running here:

http://aperiodical.com/2013/08/carnival-of-mathematics-101-prime-numbered-special-edition/

and the 65th 'Math Teachers At Play' carnival is here:

http://mathandmultimedia.com/2013/08/14/math-teachers-at-play-65/

Monday Memo...

What do Mark Chu-Carroll, Leonard Adleman, and Tom Lehrer have in common? …not necessarily a whole lot, except all 3 are mentioned in my latest post over at MathTango:

http://mathtango.blogspot.com/2013/08/a-book-cryptographer-and-fun-guy.html

Speaking of which, if anyone (math writer/blogger/professional) is willing to submit to an interview in the next few weeks for MathTango please let me know: SheckyR@gmail.com )

Alfred Posamentier (with Ingmar Lehmann) has a new book due for release this week, "Magnificient Mistakes In Mathematics." Looks good:

http://tinyurl.com/mh9n7qw

Quote… Unquote

just a few quotes to end the week, drawn from miscellaneous things I've read lately….


“Poetry and prime numbers have this in common, both are as unpredictable, difficult to define, and multiple-meaning as a life.”
-- Daniel Tammet

"Mathematicians are explorers of many miniature mathematical worlds. Explorers often find the objects or phenomena that they discover novel and surprising and they do not always describe them accurately. Indeed, just because they are novel and surprising, early explorers may mis-describe them, misunderstand them, and give most misleading reports.
"It is only after much further study that the 'true nature' of the kangaroo, or the manatee, or carnivorous plants are determined. The same is true of mathematicians exploring their miniature worlds."
-- David Wells

“Our whole problem is to make the mistakes as fast as possible.”
-- physicist John A. Wheeler

"Fallibilism [a philosophical notion that any given human belief or understanding of the world could be wrong, and yet still be justified in holding given current knowledge], correctly understood, implies the possibility, not the impossibility, of knowledge, because the very concept of error, if taken seriously, implies that truth exists and can be found. The inherent limitation on human reason, that it can never find solid foundations for ideas, does not constitute any sort of limit on the creation of objective knowledge nor, therefore, on progress."
-- David Deutsch

"What made my reputation as a mathematician is the hidden links I've uncovered between different areas of mathematics. These links are so precious! They allow you to cast light on two different areas at once, in a game of ping-pong where every discovery made on one side flips back and gives rise to a corresponding discovery on the other side."
--C'edric Villani (Fields Medalist)

"Good mathematicians see analogies between theorems or theories, but the very best ones see analogies between analogies."
-- Stefan Banach

"Rigor Deeply Improves Our Intuitions!"

A week-ago post on the role of rigor versus intuition in mathematics, initially focusing on Hilbert versus Poincare:

http://lenhoang.wordpress.com/2013/08/01/rigor-and-intuition-in-mathematics/

brief excerpt:

"In some sense, both Hilbert and Poincaré were right. Mathematics is a matter of intuitions, but rigor is essential to get the intuitions right. Only then, when the intuitions are right, can we do complex reasonings on difficult problems….
"I believe the role of mathematics in schools to be precisely to use rigor to get intuitions right. Or, at least, less wrong."

The author also links to this related Terry Tao post that I've linked to before (where he discusses "pre-rigorous," "rigorous," and "post-rigorous" math education, interweaving with intuition):

http://terrytao.wordpress.com/career-advice/there%E2%80%99s-more-to-mathematics-than-rigour-and-proofs/

Monday Morning Workout...

Again, regulars here know I'm fond of self-reference puzzles, and "MathMama" recently cited a 'self-referential number square' from Jack Webster:

http://mathmamawrites.blogspot.com/2013/08/self-referential-puzzle-by-jack-webster.html

(...it ain't easy!)
Here's an updated, 'cleaner' version of the same puzzle from Jack (…with the solution available):

http://jaxwebster.wordpress.com/2012/06/20/self-referential-number-square-1-updated/

and MathMama also links to this Webster page with a few more in the same genre, if your brain is ready for additional punishment:

https://sites.google.com/site/jlnwebster/mathematics/puzzles-1

"Setting Us Back 100 Years"

A dash of the offbeat today….

Some weeks back, NPR's "This American Life" ran its 500th show, playing bits from dozens of favorite episodes over the years. Early on, was a 2002 episode piece with an individual who was born female, but always felt more male, and took testosterone shots later in life to finally make the transition in gender. The end of this little segment still rattles around in my mind… After relating a lot of already interesting stories to host Ira Glass about how the change in gender affected him, the interviewee is asked by Ira if there are any other alterations due to testosterone he thinks worth mentioning. The individual responds that after taking testosterone he "became interested in science; I was never interested in science before." To this Ira can't help but chuckle and respond, "NO WAY!" adding that such a response is "setting us back 100 years." The individual goes on to insist that testosterone resulted in "understanding physics in a way I never did before."
You can hear the whole episode here (but the specific exchange occurs around the 22:30 point):

http://www.thisamericanlife.org/radio-archives/episode/220/testosterone?act=2

Anyway, what an amazing thought that a few shots of testosterone could, waaah-laaah!, boost science aptitude! I assume math aptitude would be susceptible as well, so I googled testosterone +math which led to this 2007 piece showing some connection:

http://www.halfsigma.com/2007/05/biological_basi.html

Toward the end it concludes:

"The important thing to get out of this is that there is an intra-sex correlation between sex hormones and math scores, and this is in the direction one would expect. More prenatal exposure to the male sex hormone testosterone correlates with higher math scores."

before adding this cautionary, anecdotal note:

"However, I also believe that this finding, by itself, does not fully explain the connection between math ability and sex hormones. The  stereotype is that the kids who are good at math are the nerdy non-athletic kids, the opposite of the high-testosterone football playing kids. So although there is a scientifically validated correlation between prenatal testosterone and math, there is an anecdotal opposite correlation for teenage boys. Less testosterone in the teenage years seems to predict higher math performance." 

This is just one study of course and there are other studies of the relationship between hormones and science/math ability... and plenty of complicating, intervening variables, as well. Still, it is fascinating that at least one individual, albeit on a pop radio show, feels that the administration of testosterone, like a magic potion, brought on an interest in science that previously didn't exist.

The Uses of Mathematics (via Keith Devlin)

I had a different post all prepared for today, but Keith Devlin put up a new post at his "Devlin's Angle" blog yesterday, and I think it more important to call attention to:

http://devlinsangle.blogspot.com/2013/08/will-this-mathematics-be-of-any-use.html

Keith has been concerned and outspoken on Twitter about the whole NSA/Edward Snowden affair since its inception… so much so that I interviewed him on that very topic for my MathTango blog awhile back (I thank Keith for linking to that interview at the end of the above piece, but I really think his own blog post transmits even more of the passion I was trying to draw out in my interview with him). Can't help but wonder what, if any, feedback Dr. Devlin has gotten back from his mathematician peers on his strongly-stated views… at any rate, at the beginning of the above piece, in direct reference to what he sees as "illegal NSA surveillance," he urges that "none of us in mathematics and mathematics education can ignore that debate."

A couple of excerpts that capture some of the essence he is communicating:

"The rise of math-based corporations such as Google that form a large and influential part of today’s global world, and the closely related growth of the modern, math-driven security state, as iconicized by the NSA, make it impossible to maintain any longer the fiction (for such it always was) that we can pursue mathematics as a pure activity, separate from applications, be they good or ill."

"As the Google founders Larry Page and Sergei Brin eventually discovered, 'Do no evil' is a wonderful grounding principle, but the power of mathematics renders it an impossible goal to achieve. The best we can do is try to make our voice heard, as many mathematicians and nuclear physicists did during the Cold War, who spoke publicly about the massive scale of the danger raised by nuclear weapons.
"Finding out (as I have over the past few weeks) that the work I’d done over the past twelve years – for various branches of the U.S. government (intelligence and military) and for commercial enterprises (in my case, the video game industry) – was part of a body of research that had been subverted (as I see it) to create a massive global surveillance framework, I felt I could not remain silent."

I know some folks are already tired of this ongoing story, or otherwise set in their opinion, but I'd still urge you to read Keith's whole piece which isn't overly long.

Mathematicians Having Fun

A couple of disparate items, each of which I thought were quite instructional in their own ways…:

1) One of the lovely things about mathematics is that simple-sounding problems/puzzles may nonetheless lead to sharp disagreements over the correct answer (the Monty Hall puzzle being a classic example of this), but with little more than pencil and pad, the disagree-ers can talk through the differences, reaching agreement and an AHA! moment… no ill feelings had, just the enjoyment of learning and thinking! (…now if only cosmology was that simple!).
Anyway, if you follow mathy things on Twitter you may have seen the recent back-and-forth-and-back-again dispute over a recent Paul Krugman blog post in the NY Times in which Krugman nonchalantly gave the answer to a conundrum dealing with traffic flow.

http://krugman.blogs.nytimes.com/2013/07/26/friday-night-music-sprawl-again/?_r=0

A certain mathematician of some repute, who we shan't name, but will simply call Stefanovich Stroganoff ;-) took issue with Krugman's answer on Twitter (and was quickly warned by some that questioning Krugman on math matters was playing with fire -- there were also many replies/comments directly to the post itself in the Times ). What followed were many more tweets debating the proper approach to the problem (fascinating that a mathematical debate can even be carried out in 140 characters or less!).
Anyway, in the end (given certain assumptions) Krugman's answer was vindicated after-all (the last tweet I recall from Stefanovich was hashtagged #EggOnFace), and Krugman himself responded with another short NY Times piece about 48 hrs. later:

http://krugman.blogs.nytimes.com/2013/07/28/life-in-the-slow-lane-trivial/

A good time was had by all, I do believe… and now further, a Cornell engineering student has put up a longer piece (pdf) recounting the whole affair with fuller explanation of the mathematics involved:

http://ruina.tam.cornell.edu/research/topics/miscellaneous/KrugmanTraffic.pdf

2) Meanwhile, and a bit heavier than the above, over at Huffington Post, of all places, there is a very good (...as far as I can tell) elucidation of the ABC conjecture for anyone wishing to read more on that subject that was brought into the limelight about a year ago by Shinichi Mochizuki:

http://www.huffingtonpost.com/shunsuke-katayama/abc-conjecture_b_3352657.html