Math, Math... and More Math

Bursting at the seams this week:

1)  John Pavlus tries to explain, very briefly, why P vs. NP is such a big deal:
https://johnpavlus.wordpress.com/2012/10/04/p-versus-np-in-a-nutshell-and-why-its-fascinating/

2)  Another recreational math book to look forward to (but unfortunately not due out 'til January 2016, not in time for the holiday season):
http://scienceblogs.com/evolutionblog/2015/09/19/coming-soon-2/

3)  Keith Devlin has recommended the following site for some online math:
https://www.citizenmaths.com/#how-does-it-work
(I don't have any experience with it except that Dr. Devlin recommends it)

4)  Speaking of Keith, another Devlin podcast interview (38-min.), this time with Hemant Mehta:
http://www.patheos.com/blogs/friendlyatheist/2015/09/20/friendly-atheist-podcast-episode-73-dr-keith-devlin-mathematics-communicator-and-author/ 

5)  An interesting little problem, you may have missed, from DataGenetics this week:
http://datagenetics.com/blog/september42015/index.html

6)  "Mathematics Rising" blog considers the thoughts of Vladimir Voevodsky, homotypy theory, and the future of mathematics:
http://mathrising.com/?p=1328

7)  Tim Gowers wrote about Terry Tao's recent solution to the Erdős discrepancy problem:
https://gowers.wordpress.com/2015/09/20/edp28-problem-solved-by-terence-tao/

....and "Gödel's Last Letter..." covers it well here:
https://rjlipton.wordpress.com/2015/09/24/frogs-and-lily-pads-and-discrepancy/

8)  Venturing over to physics briefly, Peter Woit posts about Nima Arkani-Hamed and the future of physics:
http://www.math.columbia.edu/~woit/wordpress/?p=8002

9)  Guardian review of latest Alex Bellos effort, a coloring book not just for kids:
http://tinyurl.com/puupuk9

....and Aperiodical reviews it here:
http://aperiodical.com/2015/09/review-snowflake-seashell-star-by-alex-bellos-edmund-harriss/

10)  Using "Which one doesn't belong" in the classroom:
https://fivetwelvethirteen.wordpress.com/2015/09/23/which-one-doesnt-belong-three-weeks-in/
 
11)  Do you enjoy Ben Orlin's writing, drawing, perspectives?... then you'll enjoy hearing him in this 15-min. podcast:
http://challengingopinions.com/2015/09/challenging-opinions-episode-four-ben-orlin/

12)  More math education discussion/debate in NY Times:
http://tinyurl.com/pvz4d2c

13)  The world of Web algorithms:
http://tinyurl.com/ohesvl2 

...and Marcus du Sautoy on the same subject:
http://www.bbc.co.uk/guides/z3sg9qt?ns_mchannel=social&ns_campaign=BBC_iWonder 
 
14)  A link from Math-Frolic earlier in week that I think worth reiterating -- Lior Pachter's post on possible problems for Common Core:
https://liorpachter.wordpress.com/2015/09/20/unsolved-problems-with-the-common-core/


Potpourri BONUS! (extra NON-mathematical links of interest):

1)  Don't know how many of you have already seen this video that went semi-viral a couple weeks back, of an (extinct) pterosaur flying over Idaho! -- I just saw it this week and thought it was fun (despite its flaws)... most are presuming it's CGI (or some think it's a kite), but I'd find it more interesting if it's a drone dressed up in pterosaur garb:
https://www.youtube.com/watch?v=YreRe_vkTp4
(if anyone has learned an official, definite explanation let us know; I've seen plenty of speculation)

2)  More monkeying with the copyright law:
http://www.theguardian.com/world/2015/sep/22/monkey-selfies-copyright-lawsuit-peta

==> per usual, please let me know of any broken/incorrect links ASAP

Two More Books

Just mentioning a couple of volumes today for your consideration (both currently available in paperback, BTW)....

Won't have time to write a full review, but will recommend Alfred Posamentier's (with Bernd Thaller) latest book, Numbers: Their Tales, Types, and Treasures."  It's a typical Posamentier offering... clearly written and organized, without oversimplifying or dumbing-down the wide-ranging material; some interesting and fun things mixed in with historical and classic material.
I enjoyed the second half of the book, and especially the last few chapters, more than the first half with its focus on history (for whatever reason, math history, pre-1800 has never much held my interest). Again it is a great refresher for some adult math enthusiasts and an especially good read for the young person already inclined toward mathematics.
The final chapter of the book focuses on foundations and philosophy of mathematics, although near the end the authors seem to favorably quote Steven Weinberg's portrayal of philosophy as something that does not "provide... any useful guidance" to scientists. They even cite another philosopher as saying that philosophy is a "waste of time... from the point of view of the working mathematician." (Most of the book is definitely more mathematical than philosophical.)

Anyway, if you want to get a greater sense of the volume's overall content, here's a longer review from the Web:
http://tinyurl.com/o97tzvr

    A book I'm currently perusing (haven't finished, but willing to recommend) is "Professor Povey's

Perplexing Problems" by Thomas Povey, who will be familiar to many from his "Perplexing Problems" website:
http://perplexingproblems.com/

The book is a nice compendium of amusing problems with varying difficulty;  a little more challenging mix than often found in standard puzzlebooks. However, only about a quarter of the problems are strictly mathematical. The remainder are more physics-related (though often, of course, still requiring math), so for someone with little interest in physics this may not be a good book choice. Luckily, most math fans probably enjoy physics as well, and young, budding physicists should definitely enjoy.

In the last chapter Povey tells the story of Larry Walters who took flight from his backyard in 1995, in a lawnchair powered by helium balloons, just one of the typically entertaining segments of the book. You can read more about Larry here if you like:
http://www.markbarry.com/lawnchairman.html

You can even view news of Larry's oddball flight on YouTube here:
https://youtu.be/CFFVVo9usFY?t=33s 

And here's a couple of lines that cracked me up for some reason, from chapter 2 of the volume:

"Over dinner once I was told what I believe is a true story about the principal of a Cambridge college taking out a calculator to multiply a number by 100.  In a rare moment of lucidity I quipped, 'was it a difficult number that was being multiplied?' Only the scientists got the joke."

Anyway, you get the idea, in-between the puzzles are some entertaining bits.
To finish out, I'll adapt one of the simpler math problems from the volume for inclusion here (I'm telling it less entertainingly than Povey's rendition):

Captain Fishmonger goes on a treasure-hunting voyage.  He arrives at the deserted island for which he has a treasure map showing just two trees and the instructions, "Walk 50 paces from one tree AND also 50 from the other. There lies the treasure."
But as Fishmonger peruses the island he finds that in the time since the treasure was buried and the map drawn, now 14 more trees have grown up. There are now 16 trees all less than 100 paces from one another.
In the WORST CASE scenario, what is the MAXIMUM number of spots the Captain will need to dig to find his treasure?
.
.
.answer below
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
....................................................
.
. answer:  240  ...drawing 50-pace circles around any two tree-pairs gives you TWO possible digging (intersecting) points, and combinatorics can be used to calculate the total number of possible tree pairings (120).  2 x 120 = 240 as maximum number of digs required.

Math Incoming...

Another week, another math potpourri:

1)  Keith Devlin overviews "A Brilliant Young Mind" for NPR:
http://www.npr.org/2015/09/12/439727420/love-multiplies-at-a-math-olympiad-in-brilliant

2)  Last weekend Mike Lawler favorably pointed out something called "Idea Math" that I had not heard of:
http://www.ideamath.org/

Mike references it in this post: 
https://mikesmathpage.wordpress.com/2015/09/16/revisiting-lines/

...I also enjoyed hearing about a meeting Mike reported on where Cathy O'Neil spoke (among his many posts this week):
https://mikesmathpage.wordpress.com/2015/09/15/harvards-gender-inclusivity-in-mathematics-talk/

3)  Tim Gowers interviewed in MAA's "Math Horizons":
http://t.co/eCY5JsHRX3

4)  From last weekend, Crystal Kirch's list of helpful links for teachers from the prior week (and she should have a new list up this weekend):
http://flippingwithkirch.blogspot.com/2015/09/the-best-articles-resources-ive-found_13.html

5)  Robert Krulwich covers Tyler Vigen's wonderful "Spurious Correlations":
http://tinyurl.com/p5fp632

6)  An oddball cryptographic find at Futility Closet this week (is there a logical, deductive answer?):
http://www.futilitycloset.com/2015/09/14/heart-and-head/

7)  Meanwhile, Ben Orlin continues honing his skill at making me laugh (and not easy getting me to chuckle over trig):
http://mathwithbaddrawings.com/2015/09/16/13-trig-functions-you-need-to-memorize-right-now/

8)  Speaking of chuckling, I only discovered this "Wayward Algebra" blog this week, and it's worth some chortles:
http://waywardalgebra.tumblr.com/

9)  Another (as usual) fascinating post from Fawn Nguyen on her teaching, well, grading techniques (including a great little 'problem of the week'):
http://fawnnguyen.com/giving-feedback-with-a-highlighter/

10) The "Breakthrough Junior Challenge" prize got quite a bit of coverage this week, but in case you missed it, The Aperiodical gets you up-to-date:
http://tinyurl.com/pd7wshf
...and site for the prize here:  https://www.breakthroughjuniorchallenge.org/ 

11)  Here is the paper that just won the 2015 Ig Nobel prize for mathematics:
http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0085292

12)  Numberphile does it's aways fine job of introducing folks to math philosophy:
https://www.youtube.com/watch?v=vA2cdHLKYB8&feature=youtu.be

13)  I linked to a couple more reads in my prior MathTango post dealing with science and research:
http://mathtango.blogspot.com/2015/09/research-good-sometimes-often-bad-andor.html
...and Sunday here I'll be recommending a couple more recent books, so do come back then.

Potpourri BONUS! (extra NON-mathematical links of interest):

1)  Great article from "The Verge" on the war for dominance (to the death?) between Google, Facebook, and Apple:
http://tinyurl.com/nzt3xs4

2)  An interesting piece on bucket-drumming! (...yup, I said bucket-drumming):
http://www.vox.com/2015/9/14/9323365/bucket-drumming

Research: Good (sometimes), Often Bad and/or Ugly

A few days back Andrew Gelman favorably mentioned a Bloomberg column ("Why We Fall For Bogus Research") that touched on recent problems of unreplicability in psychology research:
http://andrewgelman.com/2015/09/12/yes/

The specific column referenced is here:
http://www.bloombergview.com/articles/2015-08-31/why-we-fall-for-bogus-research

Then, elsewhere, Tom Siegfried put up a great dove-tailing piece on the problems of so-called "evidence-based" science, centered around medicine here:
http://tinyurl.com/oj6otbx

 These pieces focus primarily, not-so-much on the quality, integrity, or analysis issues (which are significant themselves) of research studies, but on the issue of generalizability: how far out (or how big a population) can the results of a given study really be applied to? This is especially an issue for "social" or "soft" sciences. And the generalizability problem in turn touches on the even broader issue of "induction" in science. Previous work has focused on the "WEIRD" study samples employed in much western research (subjects drawn solely from a "Western, Educated, Industrial, Rich and Democratic" population pool; hardly a random sample). This deserves a longer post, but I don't have time.

I'll just say that people like to discuss "science" as if it were some monolithic practice, when in fact inherent differences reside between various fields of science: psychology, biology, medicine, anthropology, physics, engineering.... (there are even huge differences between practitioners WITHIN any given field!). Science is a continuum (ranging from excellent to good to average to mediocre to poor to piss-poor!), there is NOT some clean binary science/pseudoscience division; plenty of published science barely ranks above pseudoscience, if critically adjudged.
Even though I was a psychology major, I rarely saw psychology research that I'd hold up as good science. As recently as this year I took part in a psychology study under a well-funded, fairly well-known researcher (and author)... that I believe was essentially junk science (as commonly funded by the likes of NIH -- and to those who shudder every time NIH's funding is threatened, I have to wonder how you regard your own research... because chaff (of which there is plenty) is what is intended to be cut from the NIH budget; if you're doing excellent research you have little to fear from such cuts, but if you're just publishing-or-perishing for the sake of publishing-or-perishing pressures, well.... Anyway, enough soapbox, take a gander at the Bloomberg and Siegfried pieces (especially the latter).

One reason, by the way, that I think these issues are SO important is because the growing (even scary) anti-science sentiment in this country is, I believe, the result of a citizenry growing up with a false, idealized version of science in their heads.  If they understood the 'messiness' of science from the get-go they could better accept it, but learning of it only later in life (as if they'd been fed an elitist lie, before) they turn against it. :-(

...ADDENDUM:  Gelman has now done a further followup on this general subject:
http://andrewgelman.com/2015/09/16/harsh/

Math From the Week...

A little of this, a little of that:

1)  A review of Ed Frenkel's "Love and Math" that touches upon a surprising number of thoughts/ideas:
http://www.science20.com/physics_foundations/love_math_a_review_of_edward_frenkels_bestseller_a_math_planetarium-157069

2)  At the 4-year anniversary point, Deborah Mayo posts a summary of her "Error Statistics" blog:
http://errorstatistics.com/2015/09/05/all-she-wrote-so-far-error-statistics-philosophy-4-years-on/

3)  Scott, Scott, Scott!!

Scott Aaronson did an "Ask Me Anything" posting at his blog "Shtetl-Optimized" and at least some of the 150+ questions/answers are math-related:
http://www.scottaaronson.com/blog/?p=2458

 Nautilus ran a little intro to P vs. NP also featuring Scott:
http://nautil.us/blog/what-if-solving-math-problems-were-as-easy-as-checking-solutions

And finally, speaking of Scott, I recently re-visited a post of his I loved and linked to several weeks ago, and discovered there were now well over 100 comments to it (many interesting ones, though may be too-meta for many readers):
http://www.scottaaronson.com/blog/?p=2410

4)  Don't know if this will catch on or not, but one blogger suggests that MTBoS folks generate their own collection of math stock photos:
http://mathybeagle.com/2015/09/05/hey-mtbos-its-stockphoto-time/

5)  Natalie Wolchover updates us on quantum computing and encryption:
https://www.quantamagazine.org/20150908-quantum-safe-encryption/

6)  "The Princeton Companion to Applied Mathematics" is now out:
http://experimentalmath.info/blog/2015/09/the-princeton-companion-to-applied-mathematics-is-out-at-last/

7)  Ben Orlin explains exponentiation (in his own inimitable way)... and also explains why he does what he does:
http://mathwithbaddrawings.com/2015/09/09/the-exponential-bait-and-switch/

8)  Numberphile tackles infinitesimals:
https://www.youtube.com/watch?v=WYijIV5JrKg&feature=youtu.be

9)  Another review (in Harvard Magazine) of one of my favorite books from the year, Michael Harris's "Mathematics Without Apologies" (h/t Jordan Ellenberg):
http://harvardmagazine.com/2015/08/mathematics-from-the-inside-out

10)  Yesterday, Cathy O'Neil linked to a couple of interesting reads on gender stereotypes and inclusivity in STEM:
http://mathbabe.org/2015/09/10/bloggy-young-nerd-women/

11)  Tim Gowers, who spearheaded an earlier boycott of publisher Elsevier, announces a new "arXiv overlay journal," "Discrete Analysis":
https://gowers.wordpress.com/2015/09/10/discrete-analysis-an-arxiv-overlay-journal/

12)  Ken Ono, his students, and the Ramanujan story:
http://www.emory.edu/EMORY_MAGAZINE/issues/2015/summer/features/Ono.html#Ono


Potpourri BONUS! (extra NON-mathematical links of interest):

1)  If you missed it, an interesting FB entry from a Duke University neuroscience post-doc this week, announcing his resignation and academic exasperation (...among other things, he'll be pursuing a proof of the Goldbach conjecture!):
https://www.facebook.com/jfgariepyneuro/posts/466442776860755

2)  In a sort of twist on some other 'bias' studies, a fellow named Michael was unable to get his poetry published 'til he changed his name to "Yi-Fen Chou":
http://tinyurl.com/q4kn9p6

(...as always, let me know ASAP of any broken/incorrect links.)

Do You Believe In Magic?

Overview of "The Magic of Math" by Arthur Benjamin

I've never read an Amir Aczel book that I didn't more-or-less enjoy, BUT I've also never read an Aczel book that left me wanting to rush out and recommend it to others. I enjoy Aczel's books in a kind of ho-hum sort of way, but not an enthralling sort of way.

I say all that because I had the same reaction reading Arthur Benjamin's new popular math volume, "The Magic of Math." It's certainly an okay book, and indeed arrived with a long set of glittering endorsements from very reputable folks... but I almost felt like they'd read a different book than I had when they use words like dazzling, playful, joyful, fun, delightful, magical, etc. to describe it over and over. Many, perhaps most, readers know Benjamin from his online presences, where I think those words might more aptly apply, but this volume didn't seem that much above-average in such qualities.

There is SO MUCH popular math available these days in book form that it is difficult to write ANYthing very original or exciting anymore (and yet people do -- for example, Jordan Ellenberg's injection of wit, creativity, and humor into his 2014 "How Not To Be Wrong" volume elevated that book well above the crowd, and Alex Bellos regularly manages to approach well-worn topics in clever, engaging ways).

The first five chapters of Benjamin's offering, with discussion of some basic math, patterns, algebra, some combinatorics, and a whole chapter on the Fibonacci sequence, slightly bored me, though if you're unfamiliar with that content or Benjamin's video work, it may well be more interesting for you. It isn't that the material is covered badly, but simply that the material has been covered so many times before by others, and I didn't find Benjamin's treatment that superior to prior efforts. In parts of the book, Benjamin drops his hints/tricks for mentally computing faster or more easily. This is perhaps what some will view as "fun," though I find it a bit formulaic or dryly recipe-like.

The volume picked up (for me) with chapter 6 on "the magic of proofs" followed by chapters on geometry, pi, trig, i and e (perhaps my favorite chapter), calculus, and infinity; a progression of deeper, weightier topics, although again there wasn't that much in Benjamin's presentation setting it above others.  The chapter on calculus is a nice, straightforward textbook-like introduction to basics of differential calculus. It all makes for fine (if slightly pedantic) adjunct reading for a middle or high school student already inclined toward math; I'm just leery of how enlightening or fun this volume will be for the greater mass audience it claims to be targeting.

The book also contains numerous "Asides" in gray boxes where the author sidetracks to briefly highlight some matter tangentially-related to the main discussion -- in the Intro to the book Benjamin writes that the reader may skip these 'Asides' (if s/he so chooses), as being unnecessary to the main text. That may be true, but I actually found the 'Asides' to be the most interesting parts of the volume, so I recommend the reader NOT skip them!

Also on a positive note, the visual presentation, layout, illustrations, and organization of the book are excellent, and if the text had had a bit more pizzazz I'd rate it higher. As it is, I enjoyed the book, and for the right reader it will serve well, but for the broader reading public there are more scintillating math picks.  It will easily merit an honorable mention in my year-end favorites-list, but probably won't crack the 'top 10' for the year.

Worth noting, for those seeking more of a challenge, that Benjamin (as co-author) has another volume already out this year, "The Fascinating World of Graph Theory" that is likely quite good on that particular topic, though I haven't read it.


Anyway, do I believe in magic?... you betcha, and will shamelessly use any excuse I can to play some '60s pop music ;-) (combining it with Harry Potter making it all the sweeter):

Another Week, More Math...

ICYM any of these:

1)  More John Conway via Siobhan Roberts and Quanta Magazine:
https://www.quantamagazine.org/20150828-john-conway-a-life-in-games/

2)  Samantha Oestreicher writes of her journey to becoming a mathematician:
http://socialmathematics.net/2015/08/31/social-norms-and-other-challenges/

...in related matters, NPR reported this week on the math gender disparity issue in youngsters:
http://tinyurl.com/ocu8xqd

3)  Distinguishing between "a pattern" and a "repeating block" (when it comes to pi):
http://tinyurl.com/nelzwra

4)  A new Numberphile video this week with Ed Frenkel:
https://www.youtube.com/watch?v=PFkZGpN4wmM&feature=youtu.be

5)  Joselle Kehoe takes a look at cognition by way of computers, mathematical proof, and foundational theory:
http://mathrising.com/?p=1322 

6)  For the sake of "critical thinking," "everyone needs to take a class in statistics" (from Slate):
http://tinyurl.com/nbxsjr5

7)  NPR's "Science Friday" covered the replication-in-psychology controversy last Friday:
http://sciencefriday.com/segment/08/28/2015/putting-scientific-research-to-the-test.html

...and a few days ago I linked to Deborah Mayo's take on the brouhaha:
http://math-frolic.blogspot.com/2015/09/parsing-failure-to-replicate.html

8)  h/t to Patrick Honner for passing along this interactive geometry game I'd not heard of (haven't explored it much, but if Patrick recommends it that's good enough for me):
http://isohedral.net/goodfences/

9)  Once again, Ben Orlin grows a smile on my face... this time with Haikus! (which is your favorite?):
http://mathwithbaddrawings.com/2015/09/02/the-mathematicians-haiku-book/
 (...dare he try limericks next? ;-)

10)  This "curious equality" from Futility Closet (via John Conway) got passed around a bit during the week: 
http://www.futilitycloset.com/2015/09/02/a-curious-equality/

11)  Robert Talbert discusses the classic 'Wason selection test' and the importance of context:
http://rtalbert.org/blog/2015/quick-puzzle/ 

12)  Interesting ecology/nature read... the mathematics of predator-prey relations (h/t Egan Chernoff):
http://tinyurl.com/opjr5lo

13)  Mike Lawler and his two able assistants did loads of math this week:
https://mikesmathpage.wordpress.com

14)  I'll end this week with Jason Rosenhouse's entry on political correctness while being a math professor:
http://scienceblogs.com/evolutionblog/2015/09/03/back-to-school/


Potpourri BONUS! (extra NON-mathematical links of interest):

a couple of 'cerebral' choices this week:

1)  h/t to Lior Pachter for pointing out this long, interesting piece on genetics and human variation:
http://cshperspectives.cshlp.org/content/7/9/a023358.full

2)  and h/t to David Montgomery for this David-Auerbach introduction to Wittgenstein:
http://tinyurl.com/qzeacu3