Monday, October 20, 2014

Some Monday Stuff

So many interesting, varied things passing by my computer screen the last 48 hrs.; have to pass a few along rather than hold onto until the Friday "potpourri" collection:

First, this wonderful video on P vs. NP... about as good as any quick (11-min.) intro I've ever seen on this important subject:

On the education front, fans of Robert Talbert should read his "Medium" piece outlining the future of his "Casting Out Nines" blog.

And Grant Wiggins has an update on the education post that made the rounds at his blog last week, and turns out to have been written by his daughter! More soon to come from her:

And finally HERE, Tracy Zager re-visits the below Robert Kaplinsky video, covering an interesting problem/issue that actually goes back to at least 1986:

Sunday, October 19, 2014

A Martin Gardner Sunday

This coming Tuesday marks the 100th anniversary of Martin Gardner's birth, so for a Sunday reflection, some quotes about the man:
[several of these are taken from the Martin Gardner "testimonial" page: ]

Douglas Hofstadter, in tribute to Martin, upon his death in 2010:
"This is really a sad day…  sad because his  [Gardner's] spirit was so important to so many of us, and because he had such a profound influence on so many of us. 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, the idea of intellectual hoaxes done in order to make serious points... and on and on and on and on. 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."
"Several decades passed by before I rediscovered the elegance, simplicity, and depth of his writing, and most importantly, the validity of his approach to mathematics. Then, in due course, I had the great pleasure of meeting him in his old age. He was nothing like the stern-looking man on all those book covers: in reality he was a sweet-natured, kind, wise and modest to a fault, with a twinkle in his eye, and a total joy to be with. While I can't say that Martin's columns or books steered the early course of my life, his extraordinarily diverse written legacy, his devotion to learning, his generous sharing of his toys, and his sheer decency, all conspired to reset my course in midlife.
He was also extremely egalitarian and generous with his time: he didn’t care if you were a prince or a pauper, if you had an interesting idea then he wanted to know about it, and he’d encourage you to get it in front of others. In a sense he was the original (mathematical) community organizer, at a time when it was neither profitable nor popular."
-- Colm Mulcahy  
"Martin Gardner was an artist of mathematical writing. His work stands and will continue to stand the test of time. It is a springboard for others. I can gaze and contemplate his work over and over and see new things and create new ideas."
-- Tim Chartier
 "All of us who dare to aim our writing at 'the general reader' follow as best we can in Martin's footsteps. He is the Archimedes of mathematical writing."
        — Keith Devlin
and this:
"We glibly talk of nature's laws
but do things have a natural cause?
Black earth turned into yellow crocus
is undiluted hocus-pocus."

-- Piet Hein
used as the frontispiece to Martin's autobiography, "Undiluted Hocus Pocus"

To conclude, this wonderful, older and rare (14-min.-edited) interview with Martin was uploaded this week to YouTube... delightful:

Finally, has this tribute page running this month in honor of the Gardner Centennial:

Friday, October 17, 2014

"A New Universal Law"

Natalie Wolchover never fails to enthrall. Her latest piece at Quanta is on a "curiously pervasive statistical law" that connects math, physics and biology.  It's known as the Tracy-Widom distribution, after the founders who discovered that "Systems of many interacting components — be they species, integers or subatomic particles — kept producing the same statistical curve." In other words, similar to the bell curve, the Tracy-Widom distribution seems to operate universally, describing many complexly-interacting systems. Unlike the bell curve though, the tails are asymmetric in some manner relating to the universal nature of phase transitions, and phase transitions, the article notes, "are for statistical physicists 'almost like a religion.'" The article also notes that where physicists are often satisfied with "a preponderance of evidence," mathematicians want more rigorous "proof" of a relationship. Read more here:

Thursday, October 16, 2014

A Mathematical Parable... and Ebola

I've shortened and simplified this post considerably. It wasn't even intended for the regular math-literate readership here who almost certainly know the classic story of grains of wheat accumulating on a 64-square chessboard; but rather for their possible math-phobic friends who need a more vivid understanding of the potential exponential nature of numbers-growth, in lieu of the Ebola story unfolding.

Ever since the virus spread (completely unlike prior decades) beyond the villages it was usually confined to, and especially since its spread beyond the shores of West Africa, some of us have had a more cautionary, skeptical view than the CDC's confident stance, because of the simple mathematics of the situation (combined with the fact that NO amount of medical protocols/regulations realistically offers 100% prevention of spread, given that humans who must carry out such protocols are imperfect, suffer lapses, make mistakes, are forgetful or tired or ill-trained, or in a hurry, etc.etc. (And that's no fault of theirs, that's just being normal humans, instead of machines). While the 70+ contacts of the Dallas Liberian victim might seem a manageable number, 300, 500, or 1000 potential contacts/exposures will not be easily manageable. (The fact that the virus doesn't spread through the air is lucky for us, but by no means precludes widespread infection.). Enough said:

[p.s., in a recent release the World Health Organization warned that before the end of this year there could be as many as 10,000 new cases of Ebola in Western Africa alone every week -- I'd be a bit surprised if that happened... but that IS the point of the above video, it could happen that fast.] Somewhere between calm and panic there is an appropriate state of alarm and alertness that the American public needs to find, to be prepared for the major disruption this epidemic, and consequent public health measures, could cause society. "Be prepared" is often a more trenchant maxim than "stay calm." Or, to put it a different way, the "precautionary principle" again takes hold (better to be overly precautious, than not precautious enough).

As an aside, in the short term, I'll say that my own confidence lies, not in our ability to necessarily control the spread of this disease, but rather in our ability to attain early diagnosis and more effective treatment for it, cutting the current 70% fatality rate significantly (but that too certainly isn't assured).

Wednesday, October 15, 2014

Grant Wiggins Presents "A Veteran Teacher Turned Coach"

 Chances are, if you read this blog, you've already seen this... because at last check well over ~300,000 500,000 had... a super piece from Grant Wiggins -- actually a posting he's taken from another educator/writer ("a veteran teacher turned coach") -- about a teacher becoming a student for a day (because we all forget too quickly what it's like!).
If somehow you've missed it, take a gander; it makes so much common sense, of the sort we often look right passed, with lots of suggestions (and lots of interesting comments as well):

This morning, I noticed someone on Twitter responding to the post by mentioning that they knew a couple of classrooms where regular school seats were replaced with ball chairs -- I thought that was a fascinating idea, even if not always practical -- just an example of the simple (and perhaps healthier?) outside-the-box thinking the article encourages.
By the way, Grant promises that the writer will be doing a follow-up to the piece.

ADDENDUM: Michel Reed, the teacher who mentioned the above ball chairs example, later tweeted this photo of such a classroom :-):

Monday, October 13, 2014

A Puzzle to Kickstart the Week

A sweet, simple puzzle to kickstart your week, taken directly from a recent Brian Brushwood "Scam School" episode; and it's one of those grand facepalm-type puzzles, you'll kick yourself for, IF you don't solve it:

Multiply together a long sequence as follows:

(a-x) X (b-x) X (c-x) X (d-x)...... (y-x) X (z-x)  i.e., utilizing ALL the letters of the alphabet once

What will be the end product of this sequence multiplied out???

["Scam School" has been around a long time, but if you've missed it by any chance, you can check out it's many entertaining videos HERE.]
.Answer below
Answer = 0 ...just before the final two sequence entries listed (but not shown), would be (x-x)

Sunday, October 12, 2014

The Tao of Tao ;-)

Terry Tao from his blog, "What's New":

"The point of rigour is not to destroy all intuition; instead, it should be used to destroy bad intuition while clarifying and elevating good intuition. It is only with a combination of both rigorous formalism and good intuition that one can tackle complex mathematical problems; one needs the former to correctly deal with the fine details, and the latter to correctly deal with the big picture. Without one or the other, you will spend a lot of time blundering around in the dark (which can be instructive, but is highly inefficient). So once you are fully comfortable with rigorous mathematical thinking, you should revisit your intuitions on the subject and use your new thinking skills to test and refine these intuitions rather than discard them. One way to do this is to ask yourself dumb questions; another is to relearn your field."

[…If you have a favorite math-related passage that might make a nice Sunday morning reflection here let me know ( If I use one submitted by a reader, I'll cite the contributor.]

Friday, October 10, 2014

"Right Now the Math Still Favors the Virus"

This started out as a link, but turned into a bit of commentary...

Society often walks a fine line between panic and laxity over any potential crisis. Ebola is no different, and I understand why the medical community took a somewhat pollyannish view toward it in pronouncements to the public. But the numbers involved, our highly mobile society, and the fact that complex containment protocols on paper will not be completely carried out (because they never are) calls for a more sober assessment. This Washington Post article, "The Ominous Math of the Ebola Epidemic," offers a somewhat more realistic view of the numbers and potential exponential growth involved:

I'm not terribly confident of success in "containing" Ebola in the short-term, but I do suspect we will find effective treatments for managing it in those diagnosed early, and thus significantly cutting the fatality rate (the successes we've already had are quite encouraging). In trying to avoid panic the CDC and others bent over too far in the direction of preaching calm and confidence. And the problem with that scenario is the backlash it may lead to.
This country already has a perturbingy large, vocal anti-science component in it. If the medical community misplays the Ebola epidemic it will add ammunition to their arsenal: 'see, we can't trust scientists; they don't really know what they're doin'. The anti-vaccers, anti-evolutionists, climate-denialists etc. will have a field day, long-term, if, after all the calls for calm/trust, the epidemic spreads widely. I'm almost as concerned over that as I am over the medical crisis itself.
In so many ways of course we have a wonderful medical community in this country, especially when it comes to medical emergencies. One just hopes they're not already in over their head in this case. We are probably already in the stage of swinging from calm to panic (there is so little middle-ground):

I don't know if the medical community could've done any better in their public communications -- they were caught between a rock and hard place... walking a tightrope... over a mass public that little understands how real science operates.
Anyway, to those on the front lines, where so much courage, care, commitment, and selflessness are now required, I sit in awe of you.

ADDENDUM:  highly-respected Laurie Garrett has now posted a piece that I think pretty well nails the proper cautionary stance/tone needed in this circumstance, while addressing "five myths about Ebola" (glad to see her do it!):

Thursday, October 9, 2014

"The Upside-Down World Paradox"

Given my fondness for paradox, just linking today to this quirky, fun little (non-mathematical, but logical) post about the 'upside-down world game' (an offshoot of 'the liar paradox'):

The blogger's seven-year-old daughter enjoys the game in the post, so if you have young kids maybe they will as well.

Wednesday, October 8, 2014

Of Friends, Face-to-Face and Virtual

Always love to see math making it into the popular or mainstream press, so nice to see this Maria Konnikova article on Dunbar's Number and social networks (and the new ramifications of digital social media) in the New Yorker:

As the article states, " one really knows how relevant the Dunbar number will remain in a world increasingly dominated by virtual interactions," or as Dunbar himself is quoted, “We haven’t yet seen an entire generation that’s grown up with things like Facebook go through adulthood yet.

There are potential neuroscience, and in turn social, implications to all this reliance on virtual interaction. It is, for now, a sort of grand, ongoing experiment, outcome unknown.

Tuesday, October 7, 2014

Happy Birthday Neil Sloane and OEIS!

Wonderful Alex Bellos piece in The Guardian today, on Neil Sloane and the OEIS (Online Encyclopedia of Integer Sequences) he founded. Fascinating reading:

I was happy to learn of the Kolakoski sequence which combines a number sequence with self-reference (one of my favorite topics), and of which Bellos writes, "Mathematicians drool over this sequence."
 The OEIS has been around as a go-to resource for mathematicians of all stripes for 50 years now, and today includes some 250,000 number sequences, while still growing, according to the article, at a rate of about 40 new sequences each day! Some sequences can be quite creative of course, and open up interesting, difficult-to-solve questions.
Rutgers' Doron Zeilberger goes so far as to say that the OEIS has made Sloane the world's most influential mathematician!
Lots more in the article, including a video.

Sunday, October 5, 2014

Couple of Physicists' Views

Sunday thoughts on science...:

"Science in its everyday practice is much closer to art than to philosophy. When I look at Gödel's proof of his undecidability theorem, I do not see a philosophical argument. The proof is a soaring piece of architecture, as unique and as lovely as a Chartres cathedral. The proof destroyed Hilbert's dream of reducing all mathematics to a few equations, and replaced it with a greater dream of mathematics as an endlessly growing realm of ideas."
-- Freeman Dyson in "Nature's Imagination"

...and from another physicist, a related view:

"…to sum up, science is not about data; it's not about the empirical content, about our vision of the world. It's about overcoming our own ideas and continually going beyond common sense. Science is a continual challenging of common sense, and the core of science is not certainty, it's continual uncertainty -- I would even say, the joy of being aware that in everything we think, there are probably still an enormous amount of prejudices and mistakes, and trying to learn to look a little bit beyond, knowing that there's always a larger point of view to be expected in the future."
-- physicist Carlo Rovelli in "The Universe" edited by John Brockman

or, just perhaps, Richard Feynman summed it up succinctly ;-):

"Physics is like sex: Sure, it may give some practical results but that’s not why we do it.”

[…If you have a favorite math-related passage that might make a nice Sunday morning reflection here let me know ( If I use one submitted by a reader, I'll cite the contributor.]

Thursday, October 2, 2014

How Would American Kids Do?

An interesting pair of successive tweets from Alexander Bogomolny this morning, showing a Hong Kong 1st-grade "admissions" test question :

Wednesday, October 1, 2014


Seeing an awful lot written on Bayesian ideas in the last year (and week!).
Jason Rosenhouse uses the Monty Hall problem and a NY Times article as a launching point for a discussion of the subtlety of Bayes here:

Rosenhouse takes the Times' article to task, and ends simply with:
"Applying statistics correctly is hard, even for people with professional training in the subject. But the problems are found in the complexity of real-life situations, and not in the underlying philosophical approaches to probability and statistics."
(Rosenhouse's 2009 book on the The Monty Hall problem is great, by the way, if you've never read it -- yes, an entire volume on that one problem)

Meanwhile, The Guardian also presented Bayesian statistics this week:

And in other statistics briefs, Jeff Leek tries to come to the defense of much-maligned p-values here: 

Tuesday, September 30, 2014

True Grit

Another TEDTalk today. This is actually from 2013, but I just saw it getting passed along #MathChat/#EdChat circles today. It's about success in math and beyond. If you missed it, set aside 6 mins. for it:

Monday, September 29, 2014

Mathematics a-a-and Sex

Don't know how I missed this very fun TEDTalk from a few months back, but h/t to Cliff Pickover for tweeting it this weekend:

The speaker, mathematician Clio Cresswell, actually has a book out with the same title ("Mathematics and Sex"):