...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, November 27, 2016

Eclectic Book Wrap-up [...+ADDENDUM]

via WikimediaCommons

With holiday shopping underway I should probably go ahead and post an end-of-year book wrap-up.  Once again there were a great many popular math volumes put out in 2016, but I read fewer, and was enamored of fewer, than in prior years, so this is a bit more of a mish-mash than previous year-end posts.

Last year I greatly enjoyed several volumes, especially my top 3 picks for 2015: ”Genius At Play," "Mathematics Without Apologies," and "Single Digits”:  

This year pickings were slimmer.
Here are several books I probably would’ve enjoyed, but simply never got around to reading...:

My Search For Ramanujan   by Ken Ono and Amir Aczel

The Mathematics of Various Entertaining Subjects   eds. Jennifer Beineke and Jason Rosenhouse

The Perfect Bet   by Adam Kucharski  

What the Luck   by Gary Smith

What We Cannot Know   by Marcus du Sautoy (more philosophy/science than mathematics)

...and for the musically-inclined, From Music to Mathematics by Gareth Roberts looks interesting


Among books I did read or leaf through I enjoyed these to varying degrees:

Fluke   by Joseph Mazur

The Best Mathematics Writing of 2015  ed. Mircea Pitici (the 2016 edition will probably be out soon?)

Burn Math Class   by Jason Wilkes

The Elements of Math  by John Stillwell

The Circle    by Alfred Posamentier

Summing It Up  by  Avner Ash and Robert Gross

The Seven Pillars of Statistical Wisdom    by Stephen Stigler

The Call of the Primes   by Owen O'Shea


For the first time though I’m choosing as book-of-the-year (in popular mathematics) a volume I never even reviewed here (simply because it got soooo much buzz and so many reviews I could add nothing to its coverage)…. drumr-r-r-r-rroll ;-) .… and that is Cathy O’Neil’s, “Weapons of Math Destruction,” just a fun and informative read from start to finish on the algorithms that increasingly govern our lives — if you’re a regular reader of Cathy's blog (“Mathbabe”) then you’ll be very familiar with both her engaging writing style and much of the content of this volume.  It has some technical information in it, but is mostly an easy read for a general audience, transferring a lot of important timely information and ideas about 'Big Data' along the way. So if somehow you haven’t encountered it yet, by all means add it to your holiday shopping. It raises very important issues about the ways mathematics currently encroaches on our daily lives (and offers some solutions/reforms as well).

I’ll cite one other volume from the year for special mention, completely different from Dr. O'Neil's book. It is Barry Mazur’s and William Stein’s, “Prime Numbers and the Riemann Hypothesis.” This is not really for a mass audience, but for those with some serious math grounding and an interest in (what probably most mathematicians see as) the most important unsolved problem/proof in all of mathematics.  It’s a wonderfully slim, succinct introduction (and beyond) to the Riemann Hypothesis. The sort of book one might expect may inspire upcoming generations to assiduously tackle this long-held problem. Some young person reading this volume today or in the near future might well be the one in decades hence who finally nails down the Riemann Hypothesis (…and collects $1 million in the process).

Anyway, the two books above are great, utterly different reads for very different tastes.

So much for math. In another change from the past, I'll mention three non-math, nonfiction books that I think are so outstanding they need be recommended for any book-lover's Holiday season:

The Big Picture (physics, science, philosophy)  by Sean Carroll 
(I don’t always find Sean convincing, but do love his passion for science outreach, and his entertaining/interesting style. And this book touches on so many fascinating topic areas for discussion, it ought not be missed.) 

I Contain Multitudes (biology)   by Ed Yong
(first book from perhaps the best young science writer, mostly biology, to come along in decades)

Naked Money (economics)   by Charles Wheelan
(a fabulous overview, for a lay audience, of our complex, interconnected national and world economy)

I also scanned a number of popular physics takes this year though none grabbed me particularly. The one I'm most interested in, but haven't read yet, is Richard Muller’s “Now.”

Finally, FWIW, I’ll end this year-end mixed-bag with two of my favorite reads from the last 11 months even though they are, oddly, quite old volumes that I simply chanced upon this year:

Keith Devlin’s “The Language of Mathematics” and Alan Sokal’s “Fashionable Nonsense” (I wish Dr. Sokal would write much more than he does!)

That’s it for this year-end wrap-up [...unless something shows up in December that I want to add to it!]. Now get shoppin'!

[There were lots of math books I missed this year, so feel free to mention your own favorites and recommendations in the comments.]

ADDENDUM:  I'll add to this post as needed through December... 

1)  a new volume from British writer Brian Clegg looks good: "Are Numbers Real," another introduction to the Platonic vs. non-Platonic nature of mathematics
2)  I'm currently reading Stephen Wolfram's delightful recent compendium of anecdotes/mini-biographical notes about several important scientists/mathematicians, entitled "Idea Makers." Nice bite-sized essays.
3)  And just discovered that one of my all-time favorite reads, Noson Yanovsky's "The Outer Limits of Reason" (2013) is finally out in paperback -- a fabulous stocking-stuffer for any scientist/mathematician on your list.
4)  Daniel Levitin's latest book, "A Field Guide to Lies" looks great to me... and extremely important/timely in the new TrumpWorld we inhabit!
ADDED: I'VE JUST FINISHED THIS VOLUME on 12/30/16, and had I read it earlier it would have listed alongside Cathy's book as favorite of the year. Most of the material is not new, and has been covered elsewhere, but Levitin does a great job of bringing it together in one book in a nicely organized way. I suspect while writing it, he may not even have fully recognized how timely it would be in the current political climate.

Friday, November 25, 2016

Thanksgiving Leftovers For the Math Crowd

Another foreshortened weekly potpourri:

1)  Sierpinski numbers:

2)  More post-election stuff from Andrew Gelman:

...and from Allen Downey here:

3)  Physicist Adam Frank now finds statistics interesting:
4)  The "mathematics of overhang'" from Quanta:
5)  Favorite sets from Chalkdust Magazine (tennis fans won't be disappointed!):
6)  Another edition of "Faculty Lounge Math":
7 And ICYMI, earlier in week, as a public service, I interviewed the U.S.'s President-elect (such-as-it-were) ;-) :

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

1)  Most of Sean Carroll's October Gifford Lectures on "Natural Theology" have now been posted at his blog:

2)  Been a hectic, disquieting couple of weeks, so will just close out with a little calming music:

Monday, November 21, 2016

Donald J. Trumpster… if a meteor doesn’t propitiously hit us first, the 45th President of the U.S.

Math-Frolic Interview (of sorts) #39

Haven’t done an interview here for awhile so I thought, what could be more relevant and timely than an interview with our new incoming U.S. President, who we should all get to know better! So, as a public service, without further adieu:

1)  Mr. President-elect (…and forgive me if I almost choke every time I say that), this is a math blog, so let me begin by asking what your background in mathematics was like?

Well, I can’t say I really ever attended much to math; I mean the whole numbers thing just never made much sense to me. Now if you put dollar signs in front of those numbers then I did like to play with them and move them around a bit, but in general I always wondered, “When, pray tell, will I, Donald J. Trump, ever use this?

2)  I see, well that’s actually something we still hear a lot from math students these days and there are ongoing efforts to improve math education throughout this country. Do you have any thoughts on current reforms?

Ahhh yes, I know it well, Common Crap as I call it; my own 10-yr.-old son brings home the goofiest problems you ever saw from this new flooozy math. Yes, I’ll be scrapping it immediately my first day in office. It’ll be a two-fer… ObamaCare & Common Crap into the trashbin together with a bigly bonfire. (And on Day 2, by the way, we'll crush ISIS.)

3) Uhh-huhh, well what do you propose to offer in its place, sir, because math education is increasingly important in today's world?

I’m a back-to-basics sorta guy… drills, LOTS of drills, speed drills, memory drills, test drills, drill drills, 6-7 hrs-a-day, exercise those little brains; maybe bring back Roman numerals too! And the slide rule, hey, whatever happened to the slide rule!?

4)  Maybe we should move on to another topic. You’re a lifelong businessman, which is not the usual path to the American Presidency; in fact you’re the first person ever to win the presidency with no political or military experience. Care to comment?

Is America a GREAT country or what! …wait, no, er, uhh, I take that back, right now America is a rotten, stinkin' country because of that Kenyan dude, but I will make it GREAT again! Presidents are deal makers — that’s all! I’m a dealmaker extraordinaire, the best the world has ever seen… perfect match for the job. Soon the Chinese will be eating out of my big hands.

5)  Some people say you don't have the temperament or thoughtfulness to be President. What do you say to them?

Eat my shorts, peasants!

6)  What books have you found inspiring in your life?

well, truthfully I don’t read a lot… words are, you know, kinda boring and time-consuming, but I did always have a certain fondness for Grimm’s Fairy Tales.

7)  Well then, maybe certain TV shows or movies have touched you?

oh yes, too many to mention, but including “Married With Children,” “Talladega Nights,” “West Wing,” and of course ANYthing with Jennifer Aniston in it.

8)  Would you call yourself a deeply-religious man, and do you read the Bible much?

Let’s just say I’m truly a strong believer in begatting, as often and as long as possible.

9)  You said you were going to “drain the swamp” in Washington, but you seem to be filling all key positions with standard, white, insider Washington old-timers?


10)  People have been surprised though at some of the folks you’ve interviewed for positions; people who said verrrry harsh things about you (and you about them) on the campaign trail.

Well, frankly so many people are refusing to serve in my Administration that I have to reach to the bottom of the barrel to fill some slots.

11)  Will you ever release your tax returns to the American public?

I promise that if I’m lucky enough to serve out four terms as your beloved President I WILL make my tax returns public to all. Next question...

12)  When you’re not playing golf or counting gold coins what do you enjoy doing just for fun?

ohhh, gee so many things… but I can’t mention them on a family-oriented blog like this (the press would have a field day).

13)  Lastly, anything else you'd want to say to an audience of math readers?

Just a kindly reminder to Keith Devlin and Ed Frenkel that I haven't ruled out waterboarding.

Well, President-elect (cough, hack, choke, arghhh…) it’s been a joy to chat with you today and get to know you a little better.

My pleasure, but next time let’s do this in a locker room somewhere, so I can give you the real answers.


And if you’re on Twitter and want to continue to follow the future of our new esteemed leader, I recommend you follow the #TheResistance hashtag.

Friday, November 18, 2016

Potpourri, Such As It Is...

Well, I've been too distracted by the ongoing unraveling of democracy this week 8-((( to curate much, so this is all I got for ya (sorry, I'll try to do a little better next week, BELIEVE ME):

1)  Deborah Mayo reviews some of the factors affecting the recent Presidential pre-election polling:

2) And another statistician Allen Downey did some post-analysis here:

3)  Mike Lawler is starting a "Weapons of Math Destruction" (Cathy O'Neil's book) study group on Facebook:
4)  Michael Lewis on Daniel Kahneman and Amos Tversky (from his newest book):

5)  Interesting puzzle from Numberphile:

[also, hope everyone has seen my favorite piece of the week, from James Propp, cited yesterday over at Math-Frolic.]

Friday, November 11, 2016

Potpourri, For A Week That May Live In Infamy....

What a week!... Some folks warned months ago that Donald Trump would be elected President WHEN the Chicago Cubs won a World Series (meaning, at the time, when Hell froze over!). Anyway, a quick request if anyone cares to take me up on it:
There's been a lot of discussion/criticism of prior polling since the election outcome... often proclaiming the polls surprisingly inaccurate. In fact though, as best I can tell (and others have noted), IF you take into account margin-of-error, the polls were pretty darn on-the-mark!... it was THEIR INTERPRETATION by press pundits and others that was off-base and poorly-understood.
In any event, I'm curious to hear, from anyone involved who can speak to it, just how, representative, randomized national/state polls are even conducted these days when such a reduced percentage of the population have landlines (which I presume were the staple for most polling in the past). Just what are the basic procedures now for attaining a random, but representative sample?
If you can answer that in a few lines in the comments great, OR, if someone would like to write something up as a 'guest post' here about the mechanics and difficulties of current polling methods, let me know what you have in mind [sheckyr at a gmail account]; I'd be interested.

Meanwhile, this week's math-mix:

1)  Looks like the folks over at "DataGenetics" may have had a little too much time on their hands one day ;-):

2)  A post on pseudoscience and the 'garden of forking paths' from Scott Alexander for the tinfoil-hat crowd:

3)  Mathologer videos are always worthwhile, and the latest is no exception:

4)  The gender bias in math journals:

5)  Simon Singh reviews Alex Bellos' latest:

...and if you like 'hat' problems Alex had this good Monday workout for you:

...and still more examples from his book:

6)  Ben Orlin's latest:

7)  John McGowan considers Facebook, algorithms, echo chambers, fake news, and the election:

8)  And the latest from Evelyn Lamb, more on Ramsey Theory:

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

1)  Yanis Varoufakis on capitalism and democracy, from TED Radio Hour:

2)  "Squirrel Cop" was one of those classic (and hysterical) "This American Life" episodes (from 2013). They re-ran it last weekend:


ADDENDUM: No one has yet offered to do a guest post, but a reader did send me a few pertinent links about election polling, the two most helpful being these:

Seems clear that current methods/options for polling are especially vulnerable to a variety of problems. In fact I’m even more impressed now with someone like Nate Silver’s ability to ‘massage’ or tweak meta-poll data to attain the level of accuracy he does!

Sunday, November 6, 2016

What Is The Title Of This Post?

Jim Propp will probably do a post on self-referential sentences in the middle of this month. His take should be intriguing (and he's posted self-referential "aptitude" tests before)… Doug Hofstadter and Noam Chomsky are among those who think recursion/self-reference are defining attributes of human thinking and brain operation. Interesting that even discussing 'self-reference' is itself, self-referential. ;)

Anyway, I don't think I'll steal Jim's thunder (but maybe can prick readers’ interest in the topic), if I re-run some of the things I've posted before on the topic.
Starting with this post from a year ago:


"This sentence contains ten words, eighteen syllables, and sixty-four letters." (from J. vos Post)

While researching the above sentence I came across this entertaining list of 150+ recursive or self-referential sentences:

In a related note, earlier this week Futility Closet posted about a new pangram or autogram in Lee Sallows' tradition:

And lastly, this is the final sentence of this particular post, which would appear to end with the word, hippopotomonstrosesquipedaliophobia.**

  ** yes, that's a real word

Meanwhile, there are plenty more self-referential sentences at these pages:

And over five yrs ago I ran this just-for-fun post (entitled: "There is no title for this post."):


This is the first sentence of the post titled, 'There is no title for this post.' This appears to be the sentence that follows sentence #1 of that post. This is the sentence following the previous sentence, but preceding the next sentence. This is the next sentence... or is it? Apparently this is sentence #5. This is the sentence you just finished reading. The last sentence of this post will come at the end. Thus, this is NOT the last sentence of this post. It is untrue that the prior sentence was false. This sentence begins with the word "this," followed by the word "sentence," followed by the word "begins," followed by the word "with," followed by the word "the," followed by the word "word," ...AND also ends with the word "word." And this is the sentence that informs you that the very next sentence is the final sentence of this post. This is the last sentence of the post, but why oh why does it end with a question-mark?


We'll end with more humor, starting with a well-known, geeky aphorism:

    "In order to understand recursion, one must first understand recursion."

...which reminds me in turn of one of mathematicians' favorite jokes:
Q:  What does the "B" in "Benoit B. Mandelbrot" stand for?
A:  Benoit B. Mandelbrot

Then, there is this thoughtful quote that I've used before:

"If my mental processes are determined wholly by the motion of atoms in my brain, I have no reason to believe that my beliefs are true... and hence I have no reason for supposing my brain to be composed of atoms."
--- J.B.S. Haldane, "Possible Worlds" (1927)

In a slightly similar vein, this famous refrain out of AI:
"If the brain were so simple that we could understand it, then we would be so simple that we couldn't."

There is always xkcd's classic treatment of self-reference:

And finally, this bit of parody-absurdity:

I'm guessing Jim will be taking a more technical, deeper, perhaps, set-theory approach to self-reference (so apologize if I'm stepping on any humorous bits he's employing)... you can bet his take will be good!

Friday, November 4, 2016

Some Remnants From the Week

1)  A little history of 'Question Number 6' from a 1988 Math Olympiad (h/t Egan Chernoff):

2)  Colm Mulcahy reviews Ken Ono's 'Ramanujan' volume:

...also from Colm this nice tribute to George Boole (on the occasion of his 200th birthday this week):

3)  RJ Lipton and KW Regan's fun post for Halloween:

4)  Samantha Schumacher with a wonderful post about a recent White House panel on 'math and the movies':

5)  Rotten-to-the-core? Andrew Gelman again on social science research:
6)  New puzzle book on the way from Alex Bellos (available in UK now, not 'til next year in U.S.):

7)  Lot of fun geometry over several posts from Mike Lawler this week:

...speaking of geometry, an area problem from "Solve My Maths" this week:

...and from "Maths By a Girl" still more interesting geometry:

8)  Some interesting musing (about scientific progress) here from Lance Fortnow (and commenters) toward end of week:

9)  And I departed entirely from math earlier in the week to talk of STEM and politics (or should I say demagoguery):

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

1)  A slight cautionary tale about one sort of genetic testing:

2)  NPR's TED Radio Hour replayed one of the most remarkable stories I've ever heard on the radio (have cited it here before); that of Daniel Kish, who taught himself a sort of human sonar (that he teaches to others) to "adapt" to his blindness: