Make It An Ed Frenkel Weekend

Ed Frenkel

NOT Ed Frenkel

'Some truths are out there...'  -- Edward Frenkel

The hottest ticket in mathematics these days surely must be Ed Frenkel!

Yesterday I offered plenty of mathy links for the weekend over at MathTango (including a podcast with Ed)… but when you're done with those, carve aside another hour+ for the below video of Dr. Frenkel giving a public presentation (for about 20 minutes) at the LA Public Library before Chris Carter of X-Files fame joins him on stage (and later they take questions from the audience) -- I absolutely LOVE this whole talk which covers a lot of ground, but nothing too technical! (my favorite video yet involving Dr. Frenkel). If you don't find it inspiring, well, you may need to go have your pulse checked ;-)

Edward Frenkel and Chris Carter: Love, Mathematics and The X-Files from ALOUDla on Vimeo.


[p.s. -- as I watched this I suddenly couldn't help but think how much Dr. Frenkel resembles David Duchovny! ;-) -- above pics, Frenkel from his Google+ page and Duchovny from Wikipedia]

Secondly, in a 15 minute NPR "Snap Judgment" segment Frenkel describes his incredible, inspiring math upbringing in the then Soviet Union (even if you've read or heard of his Russian background before, again, I recommend listening to this wonderful narrative):

http://tinyurl.com/oxdpym7

Freethinker Dyson...

via Wikipedia

Fascinating article and interview with mathematician/thinker/puzzlemeister/physicist (and "rebel") Freeman Dyson over at Quanta Magazine:

https://www.simonsfoundation.org/quanta/20140326-a-rebel-without-a-ph-d/

Somehow I never realized that he DOESN'T have a PhD. and at 90-years-old sounds as feisty, insightful, brilliant as ever! I'd quote some lines from the article but it's SO good (especially the interview portion) it's impossible to pick, so go enjoy the whole thing (also includes a 5-minute video).

A couple years back I did a short post on "Dyson numbers" which included a famous anecdote about Freeman here:

http://math-frolic.blogspot.com/2012/10/next-up-dyson-numbers.html

I think some evening I'd like to have Dyson and Raymond Smullyan (94 years-old) over for pizza (maybe throw in 76-yr.-old whippersnapper John Horton Conway, as well) and see if, bouncing ideas off one another, they couldn't prove the Riemann Hypothesis before David Letterman comes on ;-)

[side-note: tomorrow I should have some weekly potpourri picks posted at MathTango.]

In Honor of a Non-mathematician...

Dave Richeson, just back from Atlanta and the 11th Gathering For Gardner (which got rave reviews!) reports on the interesting "gift exchange" therefrom:

http://divisbyzero.com/2014/03/25/gabriels-paper-horn/

The theme for the conference was "John Horton Conway," though I dare guess presentations and activities strayed pretty far afield, covering Martin Gardner's wide-ranging interests in math, magic, science, and philosophy.

I suspect there will be more blog reports (from some of the 350 attendees) in the next week on the always-unique conference … anyone who attended and writes a blog-post, please feel free to add a link to your post in the comments.

Also, note the new wonderful Martin Gardner website in honor of this, his Centennial year:

http://www.martin-gardner.org

One can imagine Martin, wherever he is, almost embarrassed by all the attention (while he plays nimbly with a hexaflexagon) :-)

I'll end with some of the words from Doug Hofstadter's eulogy to him that I've quoted previously:

"He is totally unreproducible -- he was sui generis -- and what's so strange is that so few people today are really aware of what a giant he was in so many fields -- to name some of them, the propagation of truly deep and beautiful mathematical ideas (not just 'mathematical games,' far from it!), the intense battling of pseudoscience and related ideas, the invention of superb magic tricks, the love for beautiful poetry, the fascination with profound philosophical ideas (Newcomb's paradox, free will, etc. etc.), the elusive border between nonsense and sense... Martin Gardner was so profoundly influential on so many top-notch thinkers in so many disciplines -- just a remarkable human being -- and at the same time he was so unbelievably modest and unassuming. Totally. So it is a very sad day to think that such a person is gone, and that so many of us owe him so much, and that so few people -- even extremely intelligent, well-informed people -- realize who he was or have even ever heard of him. Very strange. But I guess that when you are a total non-self-trumpeter like Martin, that's what you want and that's what you get." 

 Thanks to all who keep spreading his name and legacy to a wider audience and future generations.

"Streetfighting Math"

I've not seen this book myself, but if Steven Strogatz endorses it I figure it must be worth passing along:

http://streetfightingmath.com/

Here's a promotional trailer for it:



It's also a course over at EdX:

https://www.edx.org/course/mitx/mitx-6-sfmx-street-fighting-math-1501

Finally, there is an interesting review of the book in AMS Notices here:

http://www.ams.org/notices/201107/rtx110700960p.pdf

It starts off somewhat negatively, and than wavers back-and-forth between positive and negative points, before concluding as follows:

"…'Street-Fighting Mathematics' is an engaging, well-written, insightful book. I do know that the book will provide any reader with new tools for making quick estimates and will introduce new ways of viewing problem solving. And I do know that I will read this book again. And again. And again. And maybe one day I will take the leap and actually use these methods to solve a problem."

T.S. Eliot Teaches Evelyn Lamb Some Math

Well not exactly, but I do love the way Evelyn brings Eliot's words into a mathematical context for this wonderful meditation at her "Roots of Unity" blog:

http://tinyurl.com/lwo6cbz

Patrick Honner similarly notes in a tweet that "reinventing the wheel" is in a sense what a teacher needs to do in order "to learn to teach something well."

It is a common complaint that too often students learn mathematics procedures or methods, without really comprehending the deeper process behind those methods.
Evelyn's mention of calculus, in this regard, caused me to recall my own dismal experience with college calculus:

[Evelyn's words]: "Calculus is far from a basic topic in math, but it is one that is learned very early, before we understand much about just how intricate it is. We do a lot of exploring before we come back and truly understand calculus for the first time." 

My experience: most days our prof would spend 45 mins. with his back to us as he wrote on the blackboard some long drawn-out proof of whatever we were covering that day, and then with 3 minutes of time left on the clock would turn around and ask, "any questions?" Those of us who hadn't fallen asleep didn't have the nerve to explain that we were lost from step 4 on… and then the bell rang anyway. On the one hand it was a horrible way to teach, but in retrospect I also understand now that he believed to really grasp the 'intricacy' of calculus you needed to be shown how each piece of it was derived from the ground up.

I mention all this because most of my younger life I had little interest in (or patience for) proofs or explanations, but just wanted to learn the 'facts' of math and how to apply them. Only later in life did I come to appreciate that it is by fully understanding such proofs or processes that one acquires a deep grasp of mathematics and mathematical thinking. My concentration on doing the methods and working the numbers got me through high school in fine form, but probably contributed to my math downfall in college.
Moreover, in the logic, reasoning, and proofs of mathematics, once comprehended, lie more of the beauty that is so easily missed if you treat math as just a bag of manipulative symbolic tricks, as many may perceive it.
As Evelyn implies, math is more a constant "exploration" than a rote process or recitation, and that remains so whether you are a student… or teacher.

The Bigness of Math and Other Things

Unification... it's not just for physics anymore. A "theory of everything" (or TOE), unifying our knowledge of the Universe's laws), has been a goal of physicists for quite awhile now. In a nice, short piece, Peter Lynch points out that unification is similarly an ongoing objective within mathematics:

http://thatsmaths.com/2014/03/20/the-unity-of-mathematics/

He writes that there is a "tendency for mathematics to fracture into many disparate areas," but "From time to time, sweeping simplifications arise [in mathematics] when seemingly unrelated areas are embraced in a single unifying framework."

He points out a few historical examples before noting that there is "a marked distinction between discrete and continuous mathematics," and then citing the Langlands Program, which is also "intimately related to modern physics," as the current attempt to unify all of mathematics (it was given widespread publicity with Ed Frenkel's 2013 book, "Love and Math.")

Anyway, a quick, non-technical read. 

In another straightforward, non-technical... and timely... read, Mark Chu-Carroll explains why it could take soooo long to find Malaysia flight 370 -- i.e., why our intuition for big numbers is not very good. A Boeing 777 is a big, BIG, BIG plane... but even a patch of ocean is so many times BIGGER!:

http://www.goodmath.org/blog/2014/03/19/big-numbers-and-the-lost-plane/

[...As I type these words the latest news rumor coming in is that debris spotted off of Australia MIGHT be from the lost plane...]

 

New Interview...

If you can pull yourself away from today's BICEP-2 cosmology news ;-), the latest interview over at MathTango is with author/math professor John Allen Paulos!:

http://mathtango.blogspot.com/2014/03/john-allen-paulos-spreading-math.html

Math is...

...beautiful, satisfying, useful, real, true, social, creative, fun! according to some bloke named Strogatz.

Steven Strogatz's recent interview with Patrick Honner for "Math Horizons" is now up, and, of course wonderful (particularly enjoy his description of his writing process):

http://www.maa.org/sites/default/files/pdf/horizons/strogatz_feb14.pdf

From the piece: "One of the great mistakes that a lot of teachers make is that they think, 'I need to cover this material' instead of 'I need to help this person who is my friend.'”

As much as anyone, Dr. Strogatz puts humanity back into mathematics! (thanks for bringing him to us Patrick).

Whole interview sorta makes me want to buy 100 copies of his Joy of x book and just stand on a street corner somewhere handing them out (...but, I'll refrain) ;-)

p.s. -- Dr. Strogatz will be on NPR's "Science Friday" tomorrow in honor of "Pi Day."


...Tomorrow, there will be another weekly potpourri up over at MathTango (miscellaneous links I found interesting during the week, but didn't post about). Also, just realized I never linked from here to my last interview over there, with Alexander Bogomolny (of "Cut the Knot") in case you missed that.

For All Knights and Knaves!

Fabulous book news!:

Jason Rosenhouse has edited a new anthology devoted to Raymond Smullyan, "Four Lives: a celebration of Raymond Smullyan":

http://scienceblogs.com/evolutionblog/2014/03/09/now-available-2/#comment-54672

This is the sort of book I will heartily recommend, sight unseen (although I'll now be looking for it!).

I think my first of several posts involving Smullyan was this one from the first few months of the blog:

http://math-frolic.blogspot.com/2010/08/plug-for-raymond-smullyan.html

Besides his math and logic books I also very much enjoyed his book on Taoism entitled "The Tao Is Silent." If you can find it, and are into Eastern religion/philosophy, I recommend it.

(....For any who don't know, the "knights and knaves" of the post-title is a reference to a common set of Smullyan logic puzzles involving an island of knights and knaves, or truthtellers and liars.)

Magic... Or... Math

just some fun today....

Last weekend I linked to this post from Keith Devlin talking about "breakthroughs" happening when disparate mental parts make certain connections (producing the so-called "Eureka" moment); in his case, he related it to mountain biking:

http://devlinsangle.blogspot.com/2014/03/how-mountain-biking-can-provide-key-to.html

I thought back to Dr. Devlin's piece the other day, when I experienced my own simple "Aha" moment in a different context:

Fawn Nguyen tweeted a link to a really fun puzzle on the Web:

http://www.cs.nyu.edu/~dodis/magic-ball.swf

It's called the "Flash Mind Reader" and if you're not familiar with it, go play with it RIGHT NOW, so I don't spoil it for you with what follows.
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I can usually figure out puzzles fairly quickly from having seen so many and being familiar with them… when I'm NOT familiar with a given puzzle, then I'm as big a sucker as anyone! And this puzzle initially stumped me (even though it was just a variation off some other tricks I've seen). In frustration I put it aside, did some other things, and then went to take a shower, the puzzle cast from my mind.
My shower-head spews forth a broad stream of droplets… somehow my mind suddenly flashed with the image of those droplets being the array of right-hand number choices given for the puzzle… in a moment (which I still can't well-explain) the thought occurred that if some subset of those droplets, which looked random, was actually always identical to one another, and, if my attention could somehow be consistently drawn to THAT subset, than this would solve the puzzle. Stepping out of the shower I needed only think about it for another 60 seconds to realize how the problem worked. (If you don't know how it works even after this hint I've given, you can always just google "flash mind reader" to find the solution somewhere; I won't spell it out here.)

Decades ago, Arthur Koestler promoted his notion of "bisociation" between two autonomous mental constructs as being the key to not only scientific and artistic creativity, but to humor as well. Some of the best jokes, in short, result from a comedian weaving together an analogy that the audience never saw coming! (as a complete sidelight, perhaps worth noting that Douglas Hofstadter's latest tome, Surfaces and Essences, also focuses on the central role of analogies in our thinking processes; not just for creativity but for all thought).
Interesting too, that the mathematician-writers of the animated Simpsons TV show, likewise discern a strong link between their senses of humor and their mathematical ability. As author Simon Singh noted of the jokes/math-puzzle linkage: "Both have carefully constructed setups, both rely on a surprise twist, and both effectively have punch lines. Indeed, the best puzzles and jokes make you think and smile at the moment of realization." So who says that underlying mathematics there isn't a lot of fun to be had... be it mountain biking, writing jokes for Homer Simpson, working out puzzles, or showering!

The New Culture of Collaboration

Nice piece in Nature about the rise of collaborative Web efforts in science, with special focus on Tim Gowers' ongoing Polymath Project (started as an experimental project in 2009):

http://www.nature.com/news/crowd-sourcing-strength-in-numbers-1.14757

"Gowers' online challenge was a radical suggestion for mathematics — a field that is often viewed as the domain of lonely, secretive figures who work for years in isolation. And it went against the grain of the wider academic culture, which tends to encourage researchers to share their ideas only by publishing them."

The article points out that there are now some commercial or incentivized collaborative projects as a way to increase participation, with even the Government getting involved: https://challenge.gov/

Business, mass education, and social media (and porn!) may be among the Web's most dominant uses, but I've long thought that truly the most ideal and promising use of the Internet would come in the form of scientific collaboration… the hive-mind solving problems, one-after-another, in a fraction of the time formerly required, leading to an exponential growth of knowledge/progress previously inconceivable. We've barely just begun... kudos to Gowers, Terence Tao, and others at the forefront.

Math Is UGLY

....sometimes!

Below is yet another recent article espousing the "math is beautiful" theme, but a bit more original in that it focuses on the link between math beauty and current fMRI research studying "the neural basis of beauty."
What I found even more interesting though comes at the end of the article when it cites the above formula (from Ramanujan) as the equation a consensus of mathematicians deemed the 'most ugly'! (can't say as I blame them... but it still remains beautiful that a human mind could even come up with it!):

http://www.scientificamerican.com/article/equations-are-art-inside-a-mathematicians-brain/

LA Times, The Atlantic… The Message of Math Going Mainstream

Ed Frenkel's latest piece for the LA Times, with his message of bringing math appreciation (and ability) to a wider circle of students, has already been cited quite a bit around the Web, but in case you missed it:

http://tinyurl.com/l5l3czc

In it he notes that, "...abstraction is all around us — and math is the language of abstraction...
"For the next generation to operate effectively, they must gain proficiency with abstraction, and that means mathematical knowledge plus conceptual thinking times logical reasoning — all things that a wider view of math would bring to the math classes at our schools."

Others frequently talk about this same focus on abstraction in terms of 'pattern recognition,' and in turn, many now use that focus on patterns to stress engaging children in math via their natural, playful interest in patterns.

The Atlantic had a great piece with Maria Droujkova that nicely dovetails, and fleshes out, Frenkel's article (somewhat interestingly, both Frenkel and Droujkova are immigrants from the old USSR):

http://tinyurl.com/mr9tlsk

Droujkova notes that the complexity of ideas and the difficulty of doing them "are separate, independent dimensions,” and children are capable of much more (math) learning than people think. She notes a progression from more informal ideas to more abstract ones and maintains that a "playful aspect" can be "retained along the entire journey": “This is what mathematicians do—they play with abstract ideas, but they still play.”  
Both Droujkova and Frenkel are combating the contagion of so many young people being turned off to math at an early age.


I would urge all parents and educators of youngsters, not already familiar with Droujkova's work, to read the article, and followup with visits to her "natural math" website and related online materials:

http://www.naturalmath.com/site-pages/about-us.html

I've said it before, and will say it again, we are so lucky to be living in a time when not only does the Web present a vast array of resources at one's fingertips for learning math, but a time when so many passionate people actively take the message of math farther and wider than ever before.


ADDENDUM: on a tangential subject, this morning's Diane Rehm Show (NPR) spent the last hour in a wide-ranging discussion of the controversial Common Core standards (as wide-ranging as could be squeezed into 1 hour):

http://tinyurl.com/kkuwlej

Clones Amongst Us? ;-)

Two people who have pretty obviously been cloned, since they keep showing up everywhere(!) evangelizing for mathematics literacy, are Ed Frenkel and Keith Devlin... (no doubt, in some sort of brilliant disinformation strategy, they've been cloned by the very governmental agencies they keep warning us about ;-)

As for Frenkel... science sites, sure; math sites, well of course; NY Times, why not; and needless-to-mention Twitter... now this week Ed  (or one of those clones) appears in Mother Jones online edition exhorting the importance of mathematics and his frequent message that it is not just for the gifted few, but IF taught right, for the masses.
Includes a podcast interview with Frenkel, whose Russian accent is almost as enticing as Keith Devlin's British one!

http://www.motherjones.com/environment/2014/02/inquiring-minds-edward-frenkel-math-doesnt-suck

Lots of good points made by the man who dared to title a book, "Love and Math."
excerpt (from Mother Jones):

"...Frenkel views math as an 'archipelago of knowledge' that's universally available to all of us, and he's been everywhere of late spreading the word. In particular, Frenkel is intent on warning us about how people are constantly using (or misusing) math to get our personal data, to hack our emails, to game our stock markets. 'The powers that be sort of exploit our ignorance, and manipulate us more when we are less aware of mathematics,' said Frenkel."...
"To him, math—not religion—is the one shared body of firm, unchanging knowledge that we all possess and that nobody can ever take away from us… 'It's a great equalizer,' Frenkel says"....

"Forget the idea that [math is] alienating and hard. According to Frenkel, life is hard without it."

And Keith Devlin continues his math promotion, equating solving math problems with mountain biking (another of his passions), while hailing the lowly amygdala!:

http://devlinsangle.blogspot.com/2014/03/how-mountain-biking-can-provide-key-to.html

His discussion of math's "Eureka" moments is especially interesting:

"How does the human mind make a breakthrough? How are we able to do something that we have not only never done before, but failed many times in attempts to do so? And why does the breakthrough always seem to occur when we are not consciously trying to solve the problem?
"The first thing to note is that we never experience the process of making that breakthrough. Rather, what we experience, i.e., what we are conscious of, is having just made the breakthrough!
"The sensation we have is a combined one of both elation and surprise. Followed almost immediately by a feeling that it wasn’t so difficult after all!
"What are we to make of this strange process?"

All of which leads to some interesting cognitive/neuroscience speculation and praise for the amygdala's role in problem-solving.
Enjoy the whole piece... and then, go take a bike ride!