...a companion blog to "Math-Frolic," specifically for interviews, book reviews, weekly-linkfests, and longer posts or commentary than usually found at the Math-Frolic site.

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." ---Bertrand Russell (1907) Rob Gluck

"I have come to believe, though very reluctantly, that it [mathematics] consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-legged animal is an animal." ---Bertrand Russell (1957)

******************************************************************** Rob Gluck

Sunday, September 28, 2014

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:

and I found an interesting podcast interview from 2011 with him here:

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...

Friday, September 26, 2014

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:

2)  Another voice FOR Common Core:

3)  Keith Devlin talks about the 5th incarnation of his MOOC "Introduction to Mathematical Thinking":

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":

5)   Colm Mulcahy, in the Huffington Post, looks at the math connections to 5 of this year's MacArthur Fellows:

6)  In the news: some (potential) math behind the Ebola outbreak:

7)  Will end with a fun piece today from Evelyn Lamb on a friggin' failure from Fermat:


Friday, September 19, 2014

Weekly Potpourri

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

RJ Lipton's blog posted a little tribute to the interesting work of Stanislaw Ulam:
(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:

3)  Mathbabe takes Christian Rudder's new "Dataclysm" book to task:

and on another day she offered this thought experiment (which, like any good conundrum, drew LLLOTS of comments):

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:

5)  Jacob Lurie, the Harvard math prof., who won a MacArthur Fellowship this week:

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

Wednesday, September 17, 2014

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.

Friday, September 12, 2014

Weekend Potpourri

Some math links from the week:

1)  Evelyn Lamb interviews one of the first-ever African-American math PhDs in the country:

2)  Folding pizza… and Gauss:

3)  Interesting thoughts from a one-time math-phobe:

4)  Some Common Core Common Sense:

5)  Word choice in STEM fields (at least somewhat more interesting than I was expecting):

6)  Fawn Nguyen is resurrecting her mathtalks site:

7)  Is homotopy theory a new foundation for 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):

9)   A snarky problem from Futility Closet this week:

10)  Here's a bit of a mind-stretcher from R.J. Lipton taking on a challenge from Freeman Dyson:

11)  Terry Tao offers some simple statistical/paradox discussion here (h/t to Nalini Joshi for this):

12)  If you want a little philosophy with your weekend coffee, try this from Nautilus ("Angst and the Empty Set"):

13)  Lastly, just two days ago I took a look at a couple of math history books here:

Wednesday, September 10, 2014

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):


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:

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.]

Friday, September 5, 2014

Friday Grab-bag

This week's mathy selections:

1)  Been wantin' to catch up on your Babylonian math history? …well, Evelyn Lamb is right there for ya:

2)  One of my favorites, James Grime, opened a brand-spanking new website recently (good stuff):

3)  Math, logic, Buddhism, and more from interview with Chris Mortensen here:

4)  Interesting guest post on Mathbabe this week from someone who is, ahem, a generation older than Mathbabe:

5)  Mathematics and gerrymandering:
(h/t to Steven Sltrogatz for this one)

6)  Statistician Andrew Gelman takes both Alan Turing and Daniel Kahneman to task:

7)  Mark Chu-Carroll finishes up his series on Gödel Incompleteness here:

8) Back to "Mathbabe" who recounts the noisiness of student evaluations here:

9)  I'm not sure that "sampling error" gets discussed enough, but here's a start:

10)  Finally, probably worth noting (for any science-buff who's been living under a rock the past week) that xkcd's proprietor Randall Munroe's new book, "What If?" is now out and getting fab reviews:

(and be sure to check out the blog "meme" I've casually pitched out to all math bloggers over at Math-Frolic...)

Monday, September 1, 2014

Robin Williams Redux... (background of a tweet)

Now for something completely different (for MathTango)…

I've written before how much I admire Cathy O'Neil's keen ability to touch on varying topics over at her blog. Despite coming from a mathematics academic background and titling her blog "Mathbabe," Cathy writes on a wide range of topics that rattle around in her head. So I'll sorta take that cue today to veer off and relate an odd, completely NON-mathy episode from my weekend…

I tweet under some different accounts, but lay low on Twitter, and neither expect nor have many of my tweets re-tweeted.  Saturday I posted a simple tweet linking to someone else's tweet about Robin Williams, which I thought was interesting, then went on about my way....

(the original tweet I was re-tweeting here): https://twitter.com/JessieJessup/status/505463065089830912/photo/1 which included this commentary:

When I returned five hours later, the tweet, to my astonishment, had taken on an incredible life of its own. By the following day the response blew me away! (eventually almost 6000 retweets). Clearly, Robin Williams is beloved, and concern over mental health issues touch a nerve for lots of folks in this country!  Most people seemed positive about the passage above, and quite sure of what it said (often, the response was along the lines of, 'YES! this needs to be said more often').

SO, here's the weird thing! -- I wasn't at all sure in my own mind, what exactly the above anonymous poster was trying to say!? I just thought it was an interesting take, but with two completely opposite interpretations possible, so am asking now for any clarification anyone may choose to offer.
Here were my two interpretations:

1) on the first quick read I thought the individual was noting how weak and inadequate our mental health system is, because here was Robin Williams, who did everything right (accessing the system) and yet stiiiiill killed himself at age 63.

BUT, upon further readings (and some of the Twitter comments) I concluded, that actually the writer was saying, just the opposite:

2) that this is an instance where the system DID WORK, because Robin DID access the system, got help, and we had him around, as a highly successful, productive individual, for decades longer than we might have IF the system had failed.

In short, I think the writer is saying that despite how things look and feel, Robin's case is more a success story than a tragedy, and needs to be viewed that way… BUT, I'm still not completely certain!??? (or maybe there's a more-nuanced in-between interpretation?).
(I should quickly add that another clearer, less ambiguous message the writer conveys is that mental illness still unfortunately carries a stigma associated with it that other long-term illnesses do not have.) 

Thoughts from others?....