Book News...

Will just end the week with a few book notes:

1.  John McGowan reviewed Barbara Oakley's "A Mind for Numbers" ('good not great') here:
http://math-blog.com/2015/01/26/book-review-a-mind-for-numbers/

2.  Peter Woit reviewed a new book, "Mathematics Without Apologies" that I hope to read and review in the future (looks quite interesting and different, leafing through it):
http://www.math.columbia.edu/~woit/wordpress/?p=7479

3.  Katie Steckles gives an overview of Hannah Fry's "The Mathematics of Love" here:
http://aperiodical.com/2015/01/review-the-mathematics-of-love/

4. ...and one more new book out, "The Fascinating World of Graph Theory" (from Princeton University Press):
http://press.princeton.edu/titles/10314.html

"Hackerdashery"

Hat tip to MatthewMaddux (Egan Chernoff) for passing along this entertaining video on 'what is math?' Some stuff gets oversimplified, but then it tries to pack a lot into just 7 minutes -- hope you're good at listening fast ;-)

Lip Service to Lipitor... and Social Psychology and more

(via WikimediaCommons)

It's a statistical Monday...:

First, a bit about truth-in-advertising (Big Pharma style):
http://wmbriggs.com/post/1/
[I believe the above is an earlier version of the referenced post, which I guess was a re-run(?) before Briggs' site was hacked, and had to be restored.]

....and as long as we're talking stats criticism (moving from pharma to psychology), here's another scathing overview via Deborah Mayo:
http://tinyurl.com/ptnps4w

From Nassim Taleb, this graphic has been getting passed around of late, a "genealogy" of the Black Swan/"fat-tails" problem (be sure to refer to the color coding key too):
http://fxdiebold.blogspot.com/2015/01/nassim-taleb-graphic.html 

And, finally, lo-and-behold, even xkcd is thinking about statistics this morning:
http://xkcd.com/1478/

ADDENDUM:  this afternoon, A. Gelman posted the following which looks toooo good/appropriate not to include along with the above entries:

http://andrewgelman.com/2015/01/26/statistical-crisis-science-talk-thurs-harvard-psychology-department/

James Gleick On Mathematics

This week's 'Sunday reflection,' a few succinct lines from an old NY Times James Gleick piece:

"…unspoken, but always present, is the faith that doing mathematics purely, following an internal compass, seeking elegance and beauty in a strange abstract world, is the best way in  the long run to serve practical science. As physics or biology progress, they will inevitably find that the way ahead has been cleared by some odd piece of pure mathematics that was thought dead and buried for many decades."

"A physicist is content to say that the earth orbits the sun; a mathematician will say only that there is convincing evidence."

"It has been said that the ideal mathematics talk has three parts. The first part should be understood by most of your audience. The second part should be understood by four or five specialists in your field. The third part should be understood by no one -- because how else will people know you are serious?"

-- all from "But Aren't Truth and Beauty Supposed To Be Enough?" NY Times, August 1986; anthologized in "The New York Times Book of Mathematics"

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

The Years of Eternity

(via WikimediaCommons)

Don't know how many readers are already well familiar with this?:

In 1999, the "Eternity" puzzle, a jigsaw puzzle on steroids, composed of 209 pieces shaped as equilateral triangles and half-triangles, was launched by Christopher Monckton, with a prize of one million pounds for the first person to solve it within 4 years. Naively, Monckton thought it would take at least that long to solve it (and even put up half the reward from his own funds). One of the early websites for the contest is here (where one of the pages gives the original rules; several other links are now dead):
 http://mathpuzzle.com/eternity.html

Less than a year later though it was solved, and the prize awarded to 2 Cambridge mathematicians. You can read more about it from this 2001 plus.maths article:
http://plus.maths.org/content/os/issue13/features/eternity/index   

With a little more study, Eternity 2 was launched in 2007, a 259-piece puzzle comprised this time of squares with colored edges that had to match up for the solution. It has better lived up to the hype, as the new $2 million award went unclaimed after Jan. 2011, the deadline for the prize -- and so far as I'm aware it remains unsolved!

AMS posted this blurb about the puzzles just last year:
http://blogs.ams.org/mathgradblog/2014/06/01/eternity-ii-puzzle-unsolved/#sthash.Ev6LZp2J.dpbs

I don't believe the puzzle is for sale any longer, other than second-hand copies.

More of Life's Paradoxes

Long-time readers here know that I'm especially fond of paradoxes, so was naturally drawn to a post from blogger Tony Mann where he employs some logic from Martin Gardner and Curry's paradox to demonstrate his knack for predicting sport outcomes, and beating "the pundits" :-):
http://tonysmaths.blogspot.com/2015/01/logical-paradoxes.html

Meanwhile, NPR has another new hour-long science-oriented show called "Invisibilia" -- the first two episodes that I've heard have been fantastic. Check your local station to see if it's available in your area, or you can pick it up off the Web here:
http://www.npr.org/programs/invisibilia/

Anyway, the latest episode on "fear" included a segment that ended with an odd little paradox of its own.  Turns out there is a very rare amygdala-destroying genetic disorder known as "Urbach-Wiethe disease" which eliminates the human experience of fear -- literally, individuals feel NO FEAR because they lack the biological requisites for its sensation. The end result of this bizarre condition is fascinating: it means that such a sufferer has many MORE "bad" experiences in their life, because they lack the necessary fear to avoid such experiences. On-the-other-hand, a normal person, with proper fear response, avoids a lot more of life's dangers, BUT experiences MUCH MORE fear/stress, and essentially unhappiness, via the fewer instances that they do experience... i.e., the individual who suffers more often (or has more bad things happen to them) is happier than the individual who suffers less often, because of how the suffering is experienced. Anyway, no math, just interesting, and counterintuitive. And paradoxes are part of life, not just logic textbooks.

The Ascent... and Descent... of Man

Not particularly mathy... but classic words that ought never be forgotten:

“It's said that science will dehumanize people and turn them into numbers. That's false, tragically false. Look for yourself. This is the concentration camp and crematorium at Auschwitz. This is where people were turned into numbers. Into this pond were flushed the ashes of some four million people. And that was not done by gas. It was done by arrogance, it was done by dogma, it was done by ignorance. When people believe that they have absolute knowledge, with no test in reality, this is how they behave. This is what men do when they aspire to the knowledge of gods."

-- Jacob Bronowski, The Ascent of Man

Forever timely, because of "the itch for absolute knowledge and power":



....To end on a less somber note, I'll close with a different classic: Leonard Cohen as rendered by K.D. Lang at the 2010 winter Olympics:

Tricky...?

 Greg Ross at Futility Closet writes in a very succinct explanatory style that usually makes his puzzles both clever and understandable. I think he came close to being too succinct on this one though that he just put up ("Ice Work"). It looks (and is really) a very simple problem, but the bare bones presentation required several minutes for me to grasp the simple solution. Do others find it initially confusing, or is it more obvious to most readers?:

http://www.futilitycloset.com/2015/01/15/ice-work/

The Research Game

Research improprieties have always been with us, but we live in a day where (luckily) they are exposed with greater regularity (rather than remain hidden).
A long, I think important, commentary (and not heavy on mathematics) from statistician Deborah Mayo, this morning, giving a whistleblower's perspective on a well-known scandal emanating from one Duke oncology lab. Ought be read by anyone interested in ethics, statistics, and reproducibility in research:

http://tinyurl.com/lf5jq6a

Toward the end she writes this before giving a counterview:

"I have recently received letters from people who tell me that any attempt to improve on statistical methodology or to critically evaluate -- in a serious manner -- people’s abuses of statistical concepts, is an utter waste of time and tantamount to philosophical navel gazing. Why? Because everyone knows, according to them, that statistics is just so much window dressing and that political/economic expediency is what drives kicking data into line to reach their pre-ordained conclusions."

And I dare say, as problems with research methodologies go, this represents but one of the iceberg tips toward which one must remain vigilant.

A Sunday Reflection in One Sentence

Friday, at MathTango I posted the longest math potpourri I've ever done... To compensate, today's Sunday reflection is the shortest passage I've ever used ;-):

"As mathematicians the world over say, everything is either impossible or trivial."

-- from Ian Stewart's charming, "Letters to a Young Mathematician"

James Tanton on Common Core

James Tanton has started a video series in support of Common Core. The first is below. Anyone involved in this debate should probably view it (important stuff!):

For Joiners...

I may be the last one to know about this(?), but only recently discovered the MathTwitterBlogoSphere group -- it's primarily for math teachers (which is probably why I missed it, as I'm not one), but I do enjoy following their Twitter hashtag #MTBoS to see what they're up to.  If you are a math teacher, and have possibly missed their presence, worth checking out.
Learn more about them at these sites (or follow their hashtag on Twitter):

http://mathtwitterblogosphere.weebly.com/

https://exploremtbos.wordpress.com/what-this-is-all-about/

...also learn more about them with a Google search:
https://www.google.com/?gws_rd=ssl#q=mathtwitterblogosphere

Another group that formed more recently is an email group, "Popular Math," for math enthusiasts of various stripes, again to share thoughts/ideas/solutions. Check them out here:
http://popularmath.strikingly.com./

...and older standby hashtags for those on Twitter are #mathchat and #mathed (or British versions, #Mathschat and #Mathsed).

Easy-to-See, Hard-to-Solve Problems

This has been around for awhile, but still contains some interesting problems to play with... Responses to the Quora question, "What are some unsolved problems in math which seem easy at first glance?":

http://www.quora.com/What-are-some-unsolved-problems-in-math-which-seem-easy-at-first-glance

Meanwhile, ICYMI, I've posted a bit of a year-end blog retrospective over at MathTango:
http://mathtango.blogspot.com/2015/01/proverbial-look-back.html

...and hope before month's end to have 1-2 new interviews over there as well.

Gardner Reflects...

What better way to begin a new year of Sunday reflections than with some words of reflection from Martin Gardner (from his autobiographical "Undiluted Hocus Pocus"):

"Writing the column for more than twenty-five years was one of the greatest joys of my life. If you look over all my columns you'll find that they steadily become more sophisticated mathematically. That was because I was learning math. I had not taken a single math course in college, although I loved the low-level math I learned in high school. And I had always been fond of recreational math ever since I was introduced to it as a boy by Sam Loyd's mammoth Cyclopedia of puzzles.
"One of the pleasures in writing the column was that it introduced me to so many top mathematicians, which of course I was not. Their contributions to my column were far superior to anything I could write, and were a major reason for the column's growing popularity. The secret of success was a direct result of my ignorance. Even today my knowledge of math extends only through calculus, and even calculus I only dimly comprehend. As a result, I had to struggle to understand what I wrote, and this helped me write in ways that others could understand."


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

Teach the Children Well...

Fitting I s'pose that I should start a new year with Keith Devlin, who has probably graced my posts more often than any other individual. His blog-year started off (yesterday) with another piece about the educational system in his ongoing attempt to persuade Americans of the need for Common Core. I'm afraid by now he's preaching to the choir -- views on this topic are so hardened. Either you believe in Common Core (perhaps with some reservations, but nonetheless support it), or you think it the product of overly-liberal educators and incompetent, intrusive government... and not a lot of wiggle-room in-between.
Keith writes succinctly at one point:

"The fact is, any parent who opposes adoption of the CCSS is, in effect, saying, 'I do not want my child prepared for life in the Twenty-First Century.' They really are. Not out of lack of concern for their children, to be sure. Quite the contrary. Rather, what leads them astray is that they are not truly aware of how the huge shifts that have taken place in society over the last thirty years have impacted educational needs."

Common Core opponents focus on the past, which somehow they think was just fine, while Keith is focused on the future, especially in terms of needed job skills for rising generations.
He also links to some great TEDTalks (Sugata Mitra and Ken Robinson) that I suspect most readers here have seen... but if you haven't, by all means, watch.

Read Keith's entire piece here:
http://devlinsangle.blogspot.com/2015/01/your-fathers-mathematics-teaching-no.html

A central part of his post is a chart showing the "skills" most sought-after in new workers by Fortune 500 companies back in 1970 versus 1999 (is there not an even more up-to-date list?)
"Problem-solving," which didn't appear in the top 10 in 1970, is #2 in 1999 (and certainly one of the impetuses for education change). In fact, the top 3 sought-after skills had completely changed by 1999, and I have to give some cynical, non-mathematical commentary about the other two:

1)  #3 on the list is "interpersonal skills," non-existent in the top 10 from 1970! I can't help but think that this is partly the result of today's world becoming a courser, less-civil place than the world of 1970. Perhaps in 1970 it was presumed that if you made it to adulthood and were seeking employment, then you had sufficient interpersonal skills for a workplace -- today employers must seek out people with such interpersonal skills! Also, on an even more cynical note, I suspect there are more jobs today (sales, marketing, public relations, management etc.) that require a person to be persuasive and controlling of others, than in 1970, when "honesty" or "sincerity" may have been greater virtues than the ability to manipulate and sway people.

2)  Meanwhile, #1 on the 1999 list is "Teamwork" (it was #10 in 1970) -- this troubles me a bit! One of the most common questions prospective employees hear these days is along the lines of "Are you a team player?" I've felt for some time now that this is often code for, "will you do whatever the company asks you to, regardless of laws and ethics?" Employers don't want workers with consciences or personal ethics (who might object to something or be whistleblowers), so much as company drones who will 'look the other way' when needed and march to the company anthem. That's a broad generalization, but from observation of big business behavior over the last 3 decades (yes, there are some ethical businesses out there; their numbers just seem in steady decline).

I usually agree with Dr. Devlin's views, but was once troubled by a response he gave me to a question I posed to him last year. He wrote:
"...the only possible answer to the provision of good education in this country is by private enterprise. The state system is a century out of date and broken beyond repair."

Wow!, "broken beyond repair"... As a proponent of public education and critic of private industry, that gloomy reply stung! The thought of private companies in charge of our education system (and it's already happening in some places) disturbs me (I continue to believe it possible for public education, and for that matter, big government, to work successfully). Keith is part of a small entrepreneurial company (BrainQuake, Inc.) and I suppose his optimism stems in part from that experience. I'm not concerned with enterprises of that size... but am worried by the companies that will, if Keith's company is successful, gobble up his enterprise and strictly subordinate whatever its good works and intentions are, to a bottom-line (...and then burp, ignominiously).

No doubt in my mind that Dr. Devlin is right and the educational system badly needs reforming... but it's so much broader than that... the Fortune 500 itself is also in desperate need of reform! And, unfortunately, I'm not convinced either will happen anytime soon.

Keith and I are close to the same age, and he once again closed out his post with some classic 60's music... so once again he inspires me to do the same ;-):

HAPPY 11111011111

(via WikimediaCommons)

YES, in binary,  2015  is a palindromic year!  Lookin' forward (...and backward?) to it ;-)

...And wishing everyone a multitude of merry math moments in the many months ahead!!