End-of-week Potpourri

Links from the week:
1)  Some puzzles from Presh Talwalkar started the week:
http://tinyurl.com/ntgfqpk
And some more puzzles here:
http://cavmaths.wordpress.com/puzzles-and-starters/

2)  If you can't get enough of James Grime, Reddit did an AMA ('ask-me-anything') thread with him this week:
http://tinyurl.com/o75p57h

3)  Evelyn Lamb told us about Euclid, geometry, and a possibly grumpy Omar Khayyam here:
http://blogs.scientificamerican.com/roots-of-unity/2014/10/28/omar-khayyam-grumpy-with-euclid/

and for Halloween, Evelyn takes on a hot (but scary?) topic in math -- homotopy groups:
http://blogs.scientificamerican.com/roots-of-unity/2014/10/31/higher-homotopy-groups-are-spooky/

4)  Some instances of "bad math" from the popular press:
http://www.bloombergview.com/articles/2014-10-28/bad-math-that-passes-for-insight

5)  Rubik's Cube fans, have at it (...if you dare):
https://www.youtube.com/watch?v=SnsEobXdvzQ#t=137

6)  Back to Presh Talwalkar, who offers up an auditory example of the Bell curve:
https://www.youtube.com/watch?v=YmOsDTczOFs

7)  Do you like your set theory made simple... see n-Category Cafe:
https://golem.ph.utexas.edu/category/2014/10/maths_just_in_short_words.html

8)  Lastly, in time for the Holidays... "The Mathematics Devotional" from Clifford Pickover is available:
http://www.amazon.com/exec/obidos/ASIN/1454913223/cliffordpickover

Some Weekly Picks

Another jumble of links from the week gone by:

1)  Okay, he may not be Martin Gardner, but Mike Lawler has been compiling quite a body of digital work week after week after week (both written and video). I'm astounded by his output, and don't even have time to catch it all, but here's one contribution from last week (...and seriously, if you're a math teacher or a parent you ought be FOLLOWING Mike's stuff regularly) :
http://tinyurl.com/k54fdkd

His general blog here: http://mikesmathpage.wordpress.com/
and his video channel here:  http://tinyurl.com/kftdekb
[and if you missed it, I interviewed him earlier this year here:
http://mathtango.blogspot.com/2014/04/mike-lawler-of-mikesmathpage.html ]

2)  Several folks have pointed out this Terry Tao story problem from the beginning of week:
https://plus.google.com/u/0/114134834346472219368/posts/CR1ZoNe9ojQ

3)  Agree or disagree with him, Gregory Chaitin has been putting out provocative, intriguing ideas for a long time now. "Mathematics Rising" briefly discusses some of them in this post touching on information theory, biology, consciousness, and the brain (includes some great quotes from Chaitin):
http://mathrising.com/?p=1206

4)  h/t to Cathy O'Neil for calling attention to this interesting (and longish) interview with computer scientist Michael Jordan about big data, computing, and artificial intelligence (he sees a "big data winter" ahead):
http://t.co/KSezoA11ub
Jordan wasn't entirely happy though with the interview presentation, and wrote a followup here, for clarification:
http://tinyurl.com/mvluf3x

5)  Paul Lockhart's "mathematical lament" continues (deservedly) to make the rounds:
http://www.businessinsider.com/lockharts-lament-math-education-is-wrong-2014-10

6)  Plenty of variety at the 79th "Math Teachers At Play" Carnival here:
http://letsplaymath.net/2014/10/22/math-teachers-at-play-79/

7)  A few recent problems from Futility Closet if you missed them:

a) http://www.futilitycloset.com/2014/10/23/a-dice-puzzle/
b) http://www.futilitycloset.com/2014/10/22/presto-5/
c) http://www.futilitycloset.com/2014/10/13/stretch-goals/ 

8)  Jo Boaler on 'number sense' here:
http://youcubed.org/teachers/2014/fluency-without-fear/ 

9)  A general article on mathematical modelling and epidemiology (in the day of Ebola):
http://tinyurl.com/pfphke6 

10)  Another interesting piece in the popular press (Forbes) on Common Core, focusing on the cognitive or developmental arguments:
http://tinyurl.com/lybgco5 

11) Will just note, in closing, that one of my favorite fun mathematical reads, Simon Singh's "The Simpsons and Their Mathematical Secrets" is newly-out in paperback. Another great possible stocking stuffer for any math fans on your Xmas list (...if there's even anyone left who hasn't already read it).

Potpourri

Mathy stuff from the past week:

1)  Andrew Gelman on liberal and conservative statistics:
http://andrewgelman.com/2014/10/10/conservative-liberal-comes-statistics/

and here, Gelman discusses the "statistical crisis in science" in latest edition of American Scientist:
http://www.americanscientist.org/issues/id.16259,y.2014,no.6,content.true,page.5,css.print/issue.aspx

2)  A short piece on randomness (h/t Jennifer Ouellette), with some links and a video:
http://motherboard.vice.com/read/is-it-always-possible-to-find-order-in-chaos

3)  A series from io9 on logic puzzles:
http://io9.com/can-you-solve-the-worlds-other-hardest-logic-puzzle-1645422530

4)  A new Carnival of Math up here:
http://mathtuition88.com/2014/09/13/carnival-of-mathematics/

5)  An epidemiological math model attempts to predict the curve of the Ebola outbreak here:
 http://t.co/v7p94XYGy5

6)  Ben Orlin recounts the symbiotic relationship between math and science:
http://tinyurl.com/kg2zw5t

7)  Newly-posted 1994 interview with Martin Gardner from MAA this week on YouTube (wonderful!):
https://www.youtube.com/watch?v=nY41_O2SAlY&feature=youtu.be

I don't usually hint ahead of time what the Sunday Reflection at Math-Frolic will be, but I will say that this coming Sunday's will be in tribute to Gardner, including the above video, in honor of the Centennial of his birth which arrives on Tues.

8)  For those interested in some more technical reads, Nuit Blanche blog offered up this list of links yesterday, worth checking out:
http://tinyurl.com/khg92vr

9)  Another biographical piece on Alexander Grothendieck:
http://inference-review.com/article/a-country-known-only-by-name

10)  Finally, this week, will leave you with this British piece for those math students who ask, "when will I ever use this stuff?," because you just never know when math might come in handy:
http://tinyurl.com/lzvo7yk

Three For Your Consideration

Recently treated myself to a few older books from Amazon, three of which I just want to pass along:

1)  Have mentioned Steven Strogatz's 2009 "The Calculus of Friendship" multiple times in the past (at Math-Frolic). I read a library copy quite some time ago, and always wanted my own hard copy... delighted to now have it. Recommended to teachers, students of all stripes. And if any of you think it's just a simple, sentimental story, NO, it actually includes real math along the way, as only Dr. Strogatz can tell it (but, yes, buy it for the beautiful story, the math is a bonus!). Really, no math-lover should miss it.

2)  Richard Elwes consistently amazes me with his knack for math explication. The book I ordered is his 2013 "Chaotic Fishponds and Mirror Universes" (subtitled, "The math that governs our world"), and so far, it is way surpassing my expectations (the title doesn't do it justice!). A splendid diversity of engaging topics made timely. Richard is British, and for reasons I don't fathom, his books often don't get very wide US distribution -- absolutely ashame! One of the best popularizers out there! Come on American distributors.
As we get close to the end of the year, Jordan Ellenberg's "How Not To Be Wrong," thus far remains my top popular math pick for 2014... BUT IF Elwes' book were from this year instead of 2013, it would be in the race for that designation! Another great choice for any young math-lovers on your Christmas list.

3)  Finally, one of my old stand-byes: Renaissance-man and logician-supreme, Raymond Smullyan -- I have enough of his puzzle books, but ever since reading his Taoist-inclined, "The Tao Is Silent" (1977) I've wanted to read more of his output on spirituality. The book I got, "A Spiritual Journey" (2009), is essentially three small books in one: the first part focuses in a general way, on the philosophy of religion, the second part is on Ralph Waldo Emerson and Transcendentalism, and the last part is on Richard Bucke's notion of "Cosmic Consciousness" -- it won't suit everyone's taste, spirituality being such a personal matter, but if you liked Martin Gardner's "The Whys of a Philosophical Scrivener," you will likely enjoy this offering from Raymond, which so closely mirrors my own views and Gardner's (though the writing is a bit stodgier, less smooth and concise than Gardner). No math here either, but Smullyan on ANYthing is worth savoring.

There are of course plenty more recent top-notch 2014 popular math books on the shelves to choose from... but always fun to catch up on things one has missed from the past. Smullyan is now in his mid-90's with the quick, lucid mind of someone half-his-age, Strogatz is 55, and Elwes is the kid on-the-block at 36 -- each very different in style and interests, but each leaving us an outstanding body of work for our enjoyment and elucidation. Thanks guys, you've given me Christmas in October!

Friday Wrap-Up

ICYM any of these:

1)  Wonderful Atlantic piece on Steven Strogatz's introductory course for those who think they hate math:
http://www.theatlantic.com/education/archive/2014/10/teaching-math-to-people-who-think-they-hate-it/381125/

2)  For your statistics entree this week I need only offer up this smorgasbord from William Briggs that gives links to pieces he does, or does NOT, find enlightening:
http://wmbriggs.com/blog/?p=14126

3) Also, statistically-speaking, this rant about Washington Post coverage of a certain journal study, once again indicating why correlation is so much more fun than causation ;-):
http://hotair.com/archives/2014/10/08/study-shows-people-dont-know-difference-between-correlation-and-causation/

4)  Finally, before leaving statistics aside, this blog post, "Randomness: the Ghost in the Machine?" makes for some good reading:
http://www.3quarksdaily.com/3quarksdaily/2014/09/randomness-the-ghost-in-the-machine.html

5)  Part of Mike Lawler's week revolved around the Koch snowflake, area, and infinity, ohh my!:
http://tinyurl.com/qasmz3f

and in another (l-l-longish) posting, with LOTS of links, Mike spells out some of the real-world topics that ought make math interesting for the average person (plenty to chew on here):
http://mikesmathpage.wordpress.com/2014/10/10/responding-to-david-coffeys-challenge/

6)  This week's entry (…well, one of them) in the Common Core debate:
http://www.vox.com/2014/4/20/5625086/the-common-core-makes-simple-math-more-complicated-heres-why

7)  I've never had the least bit of interest in the Zombie craze, but if you do, Alexander Bogomolny reviews a volume that might suit your taste -- "Zombies and Calculus":
http://www.mathteacherctk.com/blog/2014/10/review-of-zombies-and-calculus-by-colin-adams/

8)  Keith Devlin's latest post defending Common Core:
http://devlinsangle.blogspot.com/2014/10/the-straw-teacher.html

From my perhaps-objective(?) perch outside the whole education system it seems that the opponents of Common Core are more organized, more unified, and more vocal than the supporters, and that will be a difficult combination to overcome in the current political climate (education being highly politicized) -- so, while I think supporters of Common Core will win this war (such as it is) in the long-run, in the shorter run, I suspect they'll be losing many battles.

9)  And moving from primary/secondary education on to adult learning, NPR reports on the Pathways Project from the Carnegie Foundation and its new approach for adult math learners:
http://tinyurl.com/kwav98c

10)  Jordan Ellenberg reviews Christian Rudder's new book, "Dataclysm" here:
http://tinyurl.com/pzycv2y

11)  New version of Euclid's Elements in scrumptious color:
http://www.studio360.org/story/sideshow-seeing-math-new-language-geometry-euclid-oliver-byrne/

And one last piece of book news... Ian Stewart has yet another compendium of math puzzles out: "Professor Stewart's Casebook of Mathematical Mysteries"... looks like a good collection, some classic and some fresher, or at least newly-rendered. If you've enjoyed his other volumes, or like math puzzlers more generally, give a look; or, if you're thinking ahead to Christmas, might be a good choice for some math lovers on your list!

...these should keep you busy for awhile. 

Weekly Potpourri

This week's grabs:

1)  Someone knows the whereabouts of reclusive mathematician Alexander Grothendieck, and obtained a photo of him for use in a Heidelberg Laureate collection:
http://tinyurl.com/pbojgj8
https://twitter.com/logicians/status/516375161428123648/photo/1

2)  Interesting interview with Terry Tao from early September:
https://docs.google.com/document/d/1rinL25rC8LnMTzZcGjg1axT-0r-oiCnoKKH1DLQlmVA/preview?sle=true

Also, Terry Tao noted this week that the "final paper" summarizing the results of the Polymath8 project on the "bounded gaps between primes" problem has been uploaded to arXiv here:
http://terrytao.wordpress.com/2014/09/30/the-bounded-gaps-between-primes-polymath-project-a-retrospective/

3)  The nature of evidence and proof via the Simons Foundation:
http://www.simonsfoundation.org/features/foundation-news/symposium-evidence-in-the-natural-sciences/

4)  Science graduates have difficulty with math:
http://phys.org/news/2014-09-science-hot-maths.html

5)  MatthewMaddux linked to a World Science Festival clip discussing what CAN'T be predicted with mathematics:
http://matthewmadduxeducation.com/post/98814950454/what-cant-we-predict-with-math-enjoy

6) Interesting Nautilus piece on math, learning, memorization, and practice:
http://nautil.us/issue/17/big-bangs/how-i-rewired-my-brain-to-become-fluent-in-math-rd

7)  Another education piece from Keith Devlin in Huffington Post:
http://tinyurl.com/q2n5fwj

8) Finally, I got to interview one of my favorite writers last week: Paula Poundstone's cousin (William Poundstone):
http://mathtango.blogspot.com/2014/09/william-poundstone-eclectic-writer-and.html

William Poundstone... Eclectic Writer and Paula's Cousin!

Math-Frolic Interview #26

  "Our inability to recognize or produce randomness is the most invisible of problems. Randomness is like air, all around us and never noticed until the gale hits. We are not prepared to connect our difficulty with randomness to the real world of missed tennis serves, bad passwords, and Ponzi schemes."

    -- William Poundstone, from the Epilogue to "Rock Breaks Scissors"

William Poundstone is one of my favorite writers (twice nominated for a Pulitzer), and one of the more eclectic folks I've had the pleasure to interview here.  He has explored an odd and wide range of topics in his writing, but is not a mathematician nor mathematical writer per se, so many readers here may be unfamiliar with him. Still, his topics often impinge on underlying mathematics, while having an uncanny way of also sliding between the boundaries of science, logic, psychology, philosophy, and finance/economics.  I reviewed (and enjoyed) his latest work, "Rock Breaks Scissors," HERE. Another of his books, "Are You Smart Enough to Work at Google?" was dedicated to the memory of Martin Gardner.

His homepage is here:
http://home.williampoundstone.net/

and I found an interesting podcast interview from 2011 with him here:
http://www.smartpeoplepodcast.com/2011/07/11/episode-28-bill-poundstone/

If you're not already familiar with him I hope his responses below may entice you to check him out further (but if they don't, then maybe knowing that he is Paula Poundstone's cousin WILL! -- though I can't imagine what genes they could possibly share ;-)):

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

1)   Information on your background has been surprisingly hard to come by! (though I did learn that you studied physics at M.I.T. before becoming a writer). Your book bios and Wikipedia page don't have much info on your past, and even the quirky "about me" page at your personal website doesn't divulge much. Is that because you're secretly a CIA-operative? ;-) Seriously, can you fill readers in a little on your background and how you arrived at the interests/writing-life you have today?

Well, without saying too much about my age, I have been a full-time author for longer than the World Wide Web existed(!) I suppose that's why there's not much web presence for my pre-author life. I did spend a year as an editor (with Brentwood Publishing, now defunct, which produced trade journals). I found that very useful as it taught me fine points of grammar and usage that I never learned in my formal education ("that" v. "which," "vale of tears" not "veil of tears," etc.) As to my interests, I was a big reader from the time I could read, in science especially. 

2)  My favorite work of yours is an older one, "Labyrinths of Reason."  And like it, many of your volumes touch upon human reasoning or logic to some extent. How did you go from M.I.T. physics to such a psychological/philosophical focus?  

I'm glad to hear you mention Labyrinths. It remains one of my favorites too. The book is about how we know what we know, and that's always an issue in physics. Things like quarks started out being a mental shorthand, a way of getting the right answer. By pretending that quarks, which you can never see or isolate, exist, you can make accurate predictions about the entities that you can see and measure. So it started out as fiction and became "nonfiction"—at least, we agree to call it that. 

One of my favorite Stephen Hawking quotes: "Reality is not a quality you can test with litmus paper."

3) As a full-time writer what is your typical (if there is such a thing) workday like? Do you have a set routine?

I get up about 6 AM, read the news, work out on a treadmill, and am generally at work by 8. I work until about 5, but it's not all writing/editing. I do a lot of reading, I do interviews (of people I'm writing about, or giving interviews to promote my books).

4) Your agent is John Brockman. I've long-enjoyed his books and Edge website. What can you tell us about the experience of working with John and the Edge group?  Is it forever-stimulating, fun, argumentative, thought-provoking….? 

John is a great guy, and all those adjectives apply. BUT let me clarify that I'm on the opposite coast and see or speak with him only infrequently. (In movies, the writer-character sees his agent every day, and they live down the street from each other. That's generally not the reality!)

5) Many of your books hover around mathematics, but without being too mathematical or technical. Can you say how math fits into your daily or intellectual life… is it front-and-center to a lot of your thought, or more lurking in the shadows of the things that most interest you?

Also, do you still follow physics these days, and have any thoughts on the controversies/debates surrounding modern cosmology -- especially in terms of certain recent writers who argue that some high-level physics is bordering on metaphysics or pseudoscience?

I do take a quantitative approach to a lot of things — not to everything, which would be nuts, but to things where many others might not. Counting grams of saturated fat and carbohydrates comes to mind. And definitely, as I say above, I think the (meta)physics debate over what is real is interesting. How can one show that string theory, or the many-worlds interpretation are worth pursuing? Everybody says they're for Occam's razor, but that 14th-century implement doesn't cut it in today's physics! For one thing, it's not always clear what it means to minimize assumptions in physics far removed from direct human experience. Also, as a practical and even careerist thing, you often have to put an awful lot of work into a theory before you find out how simple it is—or isn't.

6) One curiosity note: Your latest work is entitled, "Rock Breaks Scissors," but the chapter in the book on the betting game 'rock, paper, scissors' is actually only a small portion of the book -- just wondering if there's some story behind how that ended up as the title for the volume?

"Rock, paper, scissors" is a game that almost everyone has played in which you're trying to predict someone else's "random" choice (which in fact isn't all that random…) Though this element exists in many other games and situations and conflicts, you encounter it in its purest form in RPS. 

I had thought of using the title "The Outguessing Machine," but that implies it's about machines predicting, when you can actually do a lot of the predicting in your head. 

7)  You've written over a dozen books, but only one biography… that of Carl Sagan. Are there any other figures you've considered doing a biography of?

I had thought of doing a standard Claude Shannon biography… but this evolved into Fortune's Formula, exploring just a tangent of his best-known achievements.

[hmmm... interesting, "Claude Shannon" another person with the initials "C.S." ...perhaps Cat Stevens next ;-)]

8) Are you currently working on a new book, and if so, what can you tell us about it?

I'm doing a book addressing the question: How important is it to know facts in the digital age, when it's easy to look up any fact? Part of the research involves demographically balanced polling. I look at what people know—about school subjects, current events, and pop culture—and how that knowledge correlates (or doesn't) with things like income, relationship status, self-reported happiness, and sources of news and information (TV, newspapers, Internet, etc.)

...sounds interesting, as this is a debate currently going on within mathematics education:  how much rote memorization is still necessary given the ease with which such information is digitally accessible; should children spend more time on working mathematically/algorithmically, and less time committing facts to memory?

9) Who are some of your own favorite current authors (nonfiction) to read, and what are some of your favorite books for learning or inspiration?

I read more fiction than nonfiction, and at least half of what I read isn't necessarily "current." I recently read Mark Twain's Life on the Mississippi and (from this century) Persi Diaconis and Ron Graham's Magical Mathematics and Edward Tufte's Visual Explanations. In fiction I'm reading Don Delillo's Underworld.

I suppose I should take the opportunity to plug Harry Stephen Keeler. He was an eccentric American novelist that a group of friends and I "rediscovered." Keeler would break all the rules of detective fiction, in one case introducing the guilty party, for the first time, in the last sentence of the book. One novel concerns the "Flying Strangler-Baby," a little person who disguises himself as a baby and stalks victims by helicopter. There is a Harry Stephen Keeler Society with a newsletter at http://site.xavier.edu/polt/keeler/.

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

Like I said, Bill is a bit of an eclectic fellow. Wikipedia describes him as "an American author, columnist, and skeptic," which hardly does him justice. You can check out all his books at Amazon here:  http://tinyurl.com/lq87gko

Anyway, THANKS for taking some time with us here Bill, but I'm still gonna try to figure out either your age or a CIA connection...

Weekly Grab Bag

Have some other projects eating up my time these days so another short-list of mathy links for this week (...hope to have another interview up on site, though, sometime Sunday):

1)  Correlation is not… 50%…. Jordan Ellenberg takes issue with some New Yorker statistics:
http://quomodocumque.wordpress.com/2014/09/20/what-correlation-means/

2)  Another voice FOR Common Core:
http://www.usatoday.com/story/opinion/2014/09/15/common-core-math-education-standards-fluency-column/15693531/

3)  Keith Devlin talks about the 5th incarnation of his MOOC "Introduction to Mathematical Thinking":
http://mooctalk.org/2014/09/21/here-we-go-again-2/

4)  Who doesn't like math podcasts!? (…uhh, don't answer that, it's a rhetorical question)… anyway, Sam Hansen has a new kickstarter project to fund a second series (anywhere from 8 to 16 episodes) of his math podcast "Relatively Prime":
http://aperiodical.com/2014/09/relatively-prime-podcast-series-2-kickstarter/

5)   Colm Mulcahy, in the Huffington Post, looks at the math connections to 5 of this year's MacArthur Fellows:
http://www.huffingtonpost.com/colm-mulcahy/you-dont-have-to-be-a-gen_b_5834768.html

6)  In the news: some (potential) math behind the Ebola outbreak:
http://www.businessweek.com/articles/2014-09-26/ebolas-deadly-math

7)  Will end with a fun piece today from Evelyn Lamb on a friggin' failure from Fermat:
http://tinyurl.com/k8hxg6n


  

Weekly Potpourri

A short compilation of math bits this week (been busy on other things):

1)  RJ Lipton's blog posted a little tribute to the interesting work of Stanislaw Ulam:
https://rjlipton.wordpress.com/2014/09/14/some-strange-math-facts/
(and on a side note, worth mentioning that RJ Lipton was recently awarded the 2014 Knuth Prize for contributions to computer science)

2)  Stephen Wolfram announced an online (cloud) version of Mathematica this week:
http://blog.wolfram.com/2014/09/15/launching-today-mathematica-online/

3)  Mathbabe takes Christian Rudder's new "Dataclysm" book to task:
http://mathbabe.org/2014/09/16/christian-rudders-dataclysm/

and on another day she offered this thought experiment (which, like any good conundrum, drew LLLOTS of comments):
http://mathbabe.org/2014/09/17/the-green-eyed-blue-eyed-puzzle-conundrum/

BUT (again a side-note), her most powerful post of the week, was NON-math (and very personal) here: http://tinyurl.com/k6pql3l

4)   Interesting 'language of math' article:
http://online.wsj.com/articles/the-best-language-for-math-1410304008

5)  Jacob Lurie, the Harvard math prof., who won a MacArthur Fellowship this week:
http://news.harvard.edu/gazette/story/2014/09/a-macarthur-for-math-prof/

6)  My own review of William Poundstone's latest book, "Rock Breaks Scissors" precedes this post.

Poundstone on People and Predictions

"Rock Breaks Scissors"  by William Poundstone



I keep seeing William Poundstone's latest book, "Rock Breaks Scissors" in the 'business' sections of bookstores… which I think is ashamed, because a lot of readers who would enjoy it may miss it there. More appropriately, and like most Poundstone books, it should be in a science/math area, or perhaps under psychology. Poundstone is one of my favorite authors; a good writer, dealing with subjects I find interesting, and at a level accommodating a lay readership.

Some of his volumes are deeper and richer, and others less so, but interesting and timely. This new book is in the latter category. It is yet another of the surprising array of recent volumes dealing with probability and numbers to hit the popular book market. Poundstone isn't dealing with math or probability in an academic context, as some popular volumes have attempted, but in a very reader-friendly, real-life practical sort of way.

The book is divided into two broad parts: Part 1 relates to "randomness" and part 2 relates to 'hot hand theory' -- the author tries to get across two opposing ideas that govern our actions: i.e., we often perceive things as random when in fact there is actually a pattern involved, and conversely, in other contexts of life we perceive patterns, where none exists and greater randomness is at work.

I'll briefly mention several chapters of the book:
The Prologue begins with some discussion of the work of information theorist Claude Shannon, but also includes mention of Bernie Madoff, as well as an entertaining, famous example from the retailer Target, a couple years back, when one of their purchasing algorithms deduced that a certain young lady was pregnant long before even her parents knew -- I mention all this simply to indicate the sort of diversity of subject that typifies this volume all the way through.

Chapter 1 is a little introduction to randomness, with some focus on examples from parapsychology, and also a well-known example from psychology of how poor, people are at creating "random" sequences when asked to do so (a knowledgeable individual or professor can pick out a human-created sequence from a truly random sequence).

Oddly, the title of the book stems from the quite short chapter 2 which is a treatment of the betting game, "Rock, paper, scissors," and various strategies to employ for greater success.

Chapter 3 covers some of the oft-used strategies (and patterns to look for) when taking multiple-choice exams, such as the SAT.

Chapter 4 offers strategies for playing lotteries -- I didn't find these very convincing (but then I don't play lotteries, so what do I know).

Some chapters follow delving into certain sports actions (tennis and soccer), and then card games, again always about how to better recognize, as a player, human predictability.

Chapter 9 is a practical one on creating passwords for the internet (especially after the author informs us that one "free hacking program, can test millions of passwords a second," and another "forensic" program "claims it can check 2.8 billion passwords a second." :-(

Chapters 11-13 are some of the most interesting ones, centered initially around Benford's Law (of integer distribution), and the ways it can be used to detect fraud, financial malfeasance, or just manipulated numbers.

Chapter 14 begins the second part of the book focused on "hot-hand theory." Hot-hand notions have been written about a lot in recent years (popularly in relation to basketball scoring runs), and it remains a controversial subject. Poundstone also notes that "hot-hand" notions are exactly opposite of another oft-cited prediction failure: "the gambler's fallacy" -- in the former, people overly believe a trend (sinking basketball shots) will continue to occur because it has in the recent past, but in the latter people erroneously believe a change will happen because of a non-probable trend that has just transpired (i.e., a roulette wheel will come up "red" because it just had 6 "blacks" in a row and is 'overdue.')
Anyway, chapter 15 moves on from specific hot-hand ideas to basketball betting pools (as in the NCAA March Madness tournament) -- oddly there is no mention of Tim Chartier's methods here, though they've received a lot of publicity the last couple of years.

Chapter 16 moves along to football pools, and I'll relate one quote I enjoyed from it:

"One problem with sports betting systems is that anyone who looks hard enough for a pattern tends to find one. It might be that the Denver Broncos always won on odd-numbered days in February when playing teams named after animals. Analytics is good at finding such patterns. It's not good at saying whether you should believe in them."

I think that more-or-less captures the message or sentiment of the whole second half of Poundstone's book.

Chapter 18, on 'Big Data' (everyone's favorite topic these days) is a fun, interesting intro to all the ways we can barely fathom that info is collected on us. Also, he gives a practical hint on how to get discount offers flowing your way, calling it the "abandoned shopping cart play." Again, I'll quote what to do when you're on a retail website:

"Put whatever you want to buy in a retail site's shopping cart. Click 'check out.' Begin filling out the form. Make sure you enter your e-mail address but don't enter any payment information. Leave the purchase in limbo and wait for the discounts to roll in."
(the point being that once you've expressed interest, but departed, the retailer is going to do whatever it takes to entice you back to complete an order)

The next couple chapters deal with pricing, followed by a chapter on predicting the future, where he notes that even professional experts are generally much better at forecasting far-off broad trends than predicting near-term happenings (which one might think would be easier to predict being so much closer in time) -- you might think in terms of predicting the percentage of heads in a thousand coin tosses versus predicting the percentage in say 10 tosses.

At close to 35 pages, Poundstone's final chapter, on the stock market, is by far the longest one of the book. If you're active in the market (especially if you trade for yourself) there will be MUCH of interest here, but if you have no connection to the stock market, and talk of things like PE ratios (which the chapter is VERY focused on) cause your eyes to glaze over, then this chapter will be a yawner.

Anyway, the volume is chockfull of examples and is a fairly fun romp (even if sometimes shallow and choppy) through many different, often timely, ideas. I do recommend it to folks, as I think most people will find various chapters of interest, and learn some practical or quirky tips along the way, though I can't predict ahead-of-time which chapters will be most rewarding to you, the individual reader... but then Poundstone probably could've predicted my limitation.

Weekend Potpourri

Some math links from the week:

1)  Evelyn Lamb interviews one of the first-ever African-American math PhDs in the country:
http://blogs.scientificamerican.com/roots-of-unity/2014/09/05/mathematics-live-evelyn-boyd-granville/

2)  Folding pizza… and Gauss:
http://www.wired.com/2014/09/curvature-and-strength-empzeal/

3)  Interesting thoughts from a one-time math-phobe:
http://www.usnews.com/opinion/articles/2014/09/05/how-to-excel-in-stem-math-and-science

4)  Some Common Core Common Sense:
http://www.mathforgrownups.com/common-core-common-sense-the-series/

5)  Word choice in STEM fields (at least somewhat more interesting than I was expecting):
http://tinyurl.com/pq2pteh

6)  Fawn Nguyen is resurrecting her mathtalks site:
http://fawnnguyen.com/mathtalks-net/

7)  Is homotopy theory a new foundation for mathematics:
https://www.rdmag.com/news/2014/09/new-foundation-mathematics

8)  I love quirky stories about the genius of great mathematicians. Here's a quickie that John Golden passed along this week that I'd not heard before (about John von Neumann):
http://curiosamathematica.tumblr.com/post/96957528974/there-was-a-seminar-for-advanced-students-in

9)   A snarky problem from Futility Closet this week:
http://www.futilitycloset.com/2014/09/08/wheres-the-father/

10)  Here's a bit of a mind-stretcher from R.J. Lipton taking on a challenge from Freeman Dyson:
http://rjlipton.wordpress.com/2014/09/09/a-challenge-from-dyson/

11)  Terry Tao offers some simple statistical/paradox discussion here (h/t to Nalini Joshi for this):
https://plus.google.com/app/basic/stream/z12ewdbivreculcqh04cdvvwas3egfs4dhs

12)  If you want a little philosophy with your weekend coffee, try this from Nautilus ("Angst and the Empty Set"):
http://m.nautil.us/issue/16/nothingness/angst-and-the-empty-set

13)  Lastly, just two days ago I took a look at a couple of math history books here:
http://mathtango.blogspot.com/2014/09/so-you-want-some-math-history.html

So You Want Some Math History...

Recently finished a quickread of history professor Amir Alexander's "Infinitesimal," which has received plenty of rave reviews, a few of which I'll reference below, (as I won't fully review it here):

http://tinyurl.com/pe2dd7w
http://tinyurl.com/nopb85a
http://tinyurl.com/mxchx6h

For whatever reason, I've never been much fascinated with math history (at least not pre-19th century history). This book recounts the sometimes surprisingly controversial disputes over the early history of infinitesimals in mathematics. It ends right before the part that I would've found interesting… the Newton - Leibniz rivalry and history of infinitesimals and limits since then (David Berlinski previously wrote a popular book, "A Tour of the Calculus," covering that history which I find more intriguing). Thus, though Alexander's writing is good, and the narrative sometimes dramatic, it wasn't subject matter that particularly grabbed me. But if history is among your foci this volume comes very highly recommended and you should definitely give it a look. It certainly captures events and conflicts that most people will be unacquainted with.

A few days back I briefly mentioned "Mathematics and the Real World" by Zvi Artstein… a read, which once again, because of its older historical context started off slowly for me. However, the last half of the book, moving into more modern math history, improved considerably. The writing is still somewhat stilted, but I did enjoy more of the material being covered from chapter 5 (an introduction to randomness) on, and especially the last few chapters. If you're looking for a more lively narrative and interesting story-line than "Infinitesimal" will better suit your taste, but if you want a broader sweep of math history I do recommend the Artstein book, even though parts of it are a bit of a slog. I'm not sure it's all that helpful, but the most extensive review of the book I've seen is here:
http://www.euro-math-soc.eu/review/mathematics-and-real-world

Recently on social media, Steven Strogatz and currently Evelyn Lamb have talked about teaching math history courses… don't know if this is a new trend, or such courses have long been around. In any event, both these works could be useful to an instructor of such a course -- the Alexander book, while perhaps more engaging, only deals with a sliver of history, while Artstein chronologically covers a wider swath and range of history, and is, I think, more useful. An older, more concise, historical overview of mathematics I've previously enjoyed, again comes from Berlinski, "Infinite Ascent."

By the way, I was not previously familiar with the name "Zvi Artstein," but he certainly appears to be a well-established, well-credentialed professional Israeli mathematician -- I mention this only to indicate he is not some crackpot opinionated writer, because of what follows:

Artstein finishes his volume with a 30-page, almost polemical, chapter on math education that is quite an assault on Dr. Keith Devlin's well-distributed viewpoint regarding "mathematical thinking." (He never mentions Devlin by name, but seems to clearly be directing much of his commentary toward Devlin's writings.) I've seen others sometimes voice arguments similar to Artstein's, but not with the same tenacity and self-assuredness of Artstein. I think Artstein makes some valid points along the way… but then too, I don't believe in any 'one-size-fits-all' solution to teaching youngsters math. He seems to favor a form of teaching first proposed by Louis Bénézet in the earlier 1900's that never caught on widely.
Anyway, Artstein asserts, "The truth is, there is no such thing as mathematical thinking." He argues there are only two types of thinking ('comparative' and 'creative,') which apply to most all disciplines, not just math, and that they can't be taught, but can only be learned through experience and practice!
He goes so far as to say that, "Presenting 'mathematical thinking' as a necessity, or as beneficial to life beyond mathematics and its applications, is likely to cause harm." I won't try to fully explain Artstein's viewpoint (because I'm afraid I would misstate it in some manner), but he does offer many examples, and it makes for an interesting, if oddly contentious, final chapter (in fact, I suspect he could write a whole 'nuther controversial book based on the ideas expressed in this chapter -- the chapter sticks out oddly from the rest of the book, though I think in his mind it was more of a natural conclusion that the book was always building towards).
So, I do recommend the Artstein offering (despite sometimes pedantic writing style, and the harsh ending), based on the second half historical discussion he delivers, and issues he will force you to think about.

On short notice, I asked Keith Devlin (via email) if he'd care to respond with any comment about Artstein's views -- I haven't heard anything back, but will add it here later if I do.


[ ==> housekeeping note: the usual Friday potpourri links here will, this week, begin appearing either late Friday or early Saturday (instead of early Friday) -- this is simply a practical change to better accommodate capture of Friday math posts that were showing up hours after my linkfest was being posted.]