Rocky Mountain Mathematical High

"When his friend Ronald Graham bet Erdös $500 he couldn't quit amphetamines for a month, Erdös won the bet but complained, 'I didn't get any work done... I'd have no ideas, like an ordinary person. You've set mathematics back a month.' Erdös went back to taking pills and writing papers.
"Hamilton and Erdös indulged their drug habits, it's said, to maintain their stamina. California chaos theorist Ralph Abraham is the only mathematician I know who has claimed drugs actually affected the contents of mathematical research, and for the better. In a 1991 interview with the style magazine GQ, Abraham claimed, 'In the 1960s a lot of people on the frontiers of math experimented with psychedelic substances. There was a brief and extremely creative kiss between the community of hippies and top mathematicians. I know this because I was a purveyor of psychedelics to the mathematical community.' The interview is maddeningly short on specifics. Molecular biologist Kary Mullis 'seriously doubt[s]' that he would have invented the PCR technique for which he won the Nobel Prize if he hadn't taken LSD. Timothy Leary wrote in 1977 that he expected 'the new wave of turned on young mathematicians, physicists, and astronomers... to use their energized nervous systems... to provide new correlations between psychology and science.'...
"Pharmaceutical enhancement may be redundant if mathematics is itself the drug. Mathematicians stress the addiction even more than the buzz:

"Marcus du Sautoy: 'Doing mathematics is like taking a drug. Once you have experienced the buzz of cracking an unsolved problem or discovering a new mathematical concept, you spend your life trying to repeat that feeling.'"

-- From "Mathematics Without Apologies" by Michael Harris [my review of this new book now up at MathTango]

Plethora of Podcasts

If you're a member-in-good-standing of the Cathy O'Neil Fan Club ("mathbabe") you'll want to give this recent 46-minute Samuel Hansen interview with multi-talented Cathy a listen:
http://www.acmescience.com/2015/02/scc-52-cathy-oneil/

If you wish to catch up on older Hansen interviews go here:
https://itunes.apple.com/us/podcast/the-new-strongly-connected/id472720298

And finally, in a guest post at Cathy's blog, Sam has listed many other math podcasts that may interest you (this ought keep you occupied until Season 2 of "Serial" returns ;-):
http://mathbabe.org/2015/02/12/guest-post-a-survey-of-mathematical-podcasts/

One Word... and It Ain't "Plastics"

Yeah, I'm talkin' to YOU, "data scientists"... at least, according to the brief article below, 'data science' may well be "the sexiest job of the 21st century." So to all those who eternally ask, "When will I ever use this stuff?" read the below:

http://tinyurl.com/nryel8o

Actually, of course, a good bit has been written about the promising future ahead for those who major in mathematics (and other STEM fields), and data science is, in many ways, still in its infancy. So, circa 2015, the word for the future, may well be "data," NOT plastics:



Some other fun from the week:
A tool created by Ben Schmidt got a fair amount of play.  Using data from the "RateMyProfessor" website it displays differences, by gender, in words used to describe professors who were reviewed across an array of disciplines (plug in whatever words you want):

http://benschmidt.org/profGender/#

Without knowing a lot more about the reviewer-sample the data is based upon, it's difficult to draw much meaning from it... though that won't stop people from leaping to conclusions! Anyway the author has a helpful page with more details, questions, and critique here:

http://benschmidt.org/2015/02/06/rate-my-professor/

And criticisms aside, the graph/tool is still fun to play with.

Sunday Musing…

For rumination, two quotes that Brian Hayes employs at the start of Chapter 11 of his volume, "Group Theory In the Bedroom":

"Suppose I had once borrowed your boat and, secretly, replaced each board with a similar but different one. Then, later, when I brought it back, did I return your boat to you? What kind of a question is that? It's really not about boats at all, but about what people mean by 'same.'"  -- Marvin Minsky

"I have heard of a touchy owner of a yacht to whom a guest, on first seeing it, remarked, 'I thought your yacht was larger than it is'; and the owner replied, 'No, my yacht is not larger than it is.'"  -- Bertrand Russell

[…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.]

A Bygone Era Remembered...

Fantastic new (longish) Nautilus piece from Amanda Gefter on some persons and quirky history you may never have heard of (Walter Pitts and Warren McCulloch). A great read:

http://nautil.us/issue/21/information/the-man-who-tried-to-redeem-the-world-with-logic


[...and later this afternoon there will be many more reading links for the weekend over at MathTango]

'There once was a ....'

Just a little more frivolity today... ICYMI, this bit of fun has been bouncing around the Web for about a year (not sure where it originated?) -- a (true) mathematical formula that creates its own mathy limerick :-):

If you like that one, here's a more complex one taken off of "Futility Closet" many years ago:

Translated:
The integral z-squared dz
From one to the cube root of three
Times the cosine
Of three pi over nine
Equals log of the cube root of e.


...And if that all puts you into a limericky mood, the below page has a good many more of a scientific-bent to enjoy:

http://www.aps.org/publications/apsnews/features/limericks/finalists.cfm

"Gauss can recite all of pi -- backwards" ...(& a book)

Of course he can barely hold a candle to Riemann ;-) ...but I do still love me some Gauss!
I should return to this site more than a couple times a year... so many of these just crack me up:

http://www.gaussfacts.com/top?page=1

(thanks to whoever originally created it!)

 --------------------------------------------------------------

Meanwhile, I'm currently reading (halfway through) "Mathematics Without Apologies" by Michael Harris:

Wow!... This is only February, but already pretty sure this book will be in the running for my favorite math volume of 2015! It's one of the oddest, richest, most unpredictable math volumes I've ever seen for a general audience; with a somewhat mind-bending writing style and approach... difficult to briefly describe (Peter Woit calls it "a sometimes gonzo version of post-modern academic style.")
Should quickly add that my love for it WON'T be shared by all... this book will be too odd, toooo eclectic for some, I'm sure. I'll have a more detailed review some time in the future, but you may wish to check it out on your own before then. Or, in meantime, you can read Peter Woit's review here:
http://www.math.columbia.edu/~woit/wordpress/?p=7479

View From the Top of the Forest...

This Sunday re-running a quote from Keith Devlin that I first posted last year and that derives originally from his Sept. 2013 appearance on NPR's wonderful "On Being" podcast :

"...that's when I became a mathematician; that's what I stumbled on at age 15 or 16 when here I was learning all this mathematics because I needed it. I had a utilitarian view of mathematics. I was learning it because I needed to solve the equations because I was going to be solving them in physics. And then, at the age of about 16 or 17, it all fit because it all came together in my mind. It was no longer this disjointed collection of techniques you could use to solve problems. It all fell into place, into this wonderful landscape. It was as if I'd been stumbling around in a forest, and suddenly I've climbed to the top of a tree and looked out and thought, this is the most beautiful place in the world. You can't tell it when you're down in the trees, which I had been, but the moment you reach an elevation where it all falls into place and you can see the whole topographic display in front of you, then the beauty is incredible. And the moment I discovered it, I said, um, I want to study mathematics. And I've been studying it ever since."

[p.s. -- just yesterday, Keith was in a bad biking accident, when some of his equipment failed... I believe the bicycle suffered more damage than Keith (at least his tweeting hand seemed to be working :-), but in any event, I'm sure we all wish him well in any recovery needed.]

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).