(AMS Bumper Sticker)

Web math-frolic.blogspot.com

Tuesday, October 18, 2016

Blog Changes...

A number of recent changes in the math blogosphere, perhaps worth mentioning:

1)  Math Drudge blog is shutting down following the death of one of its founders, Jonathan Borwein:

…but (at a very similar URL) the new Math Scholar blog will carry on from David Bailey (the other co-founder of Math Drudge):

2)  Antonio Cangiano announced that Math Blog would be going on hiatus following a devastating fire interrupting his life:

…although that was quickly followed by John McGowan saying he would take over administration of the blog for the interim (honestly, I had always thought McGowan was the principal administrator of this blog, which is among my favorites, so I’m not clear how big a change this is, or how mistaken I was?):

3)  Jason Rosenhouse covered a lot more than just math at his long-running Evolution Blog, and I always found him to be one of the clearest (and perhaps under-appreciated) explicators of math and science out there. So, quite sad to see him calling it quits after more than 10 years of elucidation:

(hoping he’ll change his mind after some rest-and-relaxation)

Jason's “The Monty Hall Problem” volume is MUST-reading, by the way, for anyone interested in that classic puzzle.
And his “Four Lives” is MUST-reading for any Raymond Smullyan fans out there.
(just to mention two of his books)
Luckily Jason has more books on the way, but will still miss his succinct, well-reasoned blog-post musings.
There may well be some other blog changes worth mentioning that I’ve missed. Feel free to mention in the comments any you think worth passing along.

Sunday, October 16, 2016


For this Sunday, just a little arithmetic humor:

Husband:  Dear, I’m calling you from the freeway on my new cell phone.

Wife:  Well Honey, please be careful out there; the radio says some nut is driving the wrong way on the freeway.

Husband: Hell, one nut? There are 100s of them!

Friday, October 14, 2016

"On With the Song, I Don't Give a Damn"

No math, just music (re: "jingoistic" politics) to finish the week with:


This isn't for the ones who blindly follow
Jingoistic bumper stickers telling you
To love it or leave it and you'd better love Jesus
And get out of the way of the Red, White and Blue

This isn't for the ones who buy their six-packs
At the 7-Eleven where the clerk makes change
Whose accent makes clear he sure ain't from here
They call him a camel jockey instead of his name

No, this is for the ones who stand their ground
When the lines in the sand get deeper
When the whole world seems to be upside down
And the shots being taken get cheaper, cheaper

This isn't for the ones who would gladly swallow
Everything their leader would have them know
Bowing and kissing while the truth goes missing
"Bring it on," he crows, puttin' on his big show

This isn't for the man who can't count the bodies
Can't comfort the families, can't say when he's wrong
Playing 'I'm the decider' like some sort of Messiah
While another day passes and a hundred souls gone

No, this is for the ones who stand their ground
When the lines in the sand get deeper
When the whole world seems to be upside down
And the shots being taken get cheaper, cheaper

This is for the ones that I see above me
Three little stars in a great big sky
Light for the world and hope for the weary, they try
This isn't for the ones with their radio signal
Calling for bonfires and boycotts, they rave
Exhorting their listeners to spit on the sinners
While counting the bucks of advertising, they'll say

This isn't for you and you know who you are
So just do what you want 'cause I know that you can
But I gotta be true to myself and to you
So on with the song, I don't give a damn

-- Mary Chapin Carpenter (2007)

Tuesday, October 11, 2016

Put On Your Thinking Cap

ICYMI, I enjoyed this little logic brain-twister from Alex Bellos in The Guardian yesterday. So as not to copy it verbatim, I’ll entirely re-word it below if you want to try it out, but then you can go here to see his original statement of it, with the neat solution:

Alan, Bob, and Carl play checkers among themselves, with the rule that the winner of each game keeps playing, while the loser awaits for another turn to play after each game. When they are done for the day they have each played the following numbers of games: 
Alan played 10
Bob played 15
Carl played 17
Question: Who lost the 2nd game?

Sunday, October 9, 2016

'struck with the power...'

Sunday reflection:
"So I would say that like Turing, I am absolutely struck with the power of mathematics, and that's why I'm a theoretical physicist. If I want to answer questions, I love that we can all share the mathematical answers.  It's not about me trying to convince you of what I believe or of my perspective or of my assumptions. We can all agree that one plus one is two, and we can all make calculations that come out to be the same, whether you're from India or Pakistan or Oklahoma, we all have that in common.  There's something about that that's deeply moving to me and that makes mathematics pure and special."
          -- Janna Levin (interviewed in Krista Tippett's "Einstein's God")

Friday, October 7, 2016

Truth and Stereotype...

Just a fun read leading into the weekend, from the widow of a mathematician who misses “the crazy good times” with her absent-minded husband:

Fondly she writes:
I miss mathematicians! They have such a good time with each other. They are like eager children swarming into the same old playground and creating ever-new uses for the same old equipment.“

Wednesday, October 5, 2016

"the manipulation of noise" (quantitatively speaking)

Andrew Gelman, interesting as always, on psychology's replication crisis:

Specifically mentioning work by Bargh, Cuddy, Bem, Lacour, and others, but applicable to a wider throng.

Sunday, October 2, 2016

Mathematics... Powerful Medicine

This morning's 'Sunday reflection' comes from Morris Kline (in "Mathematics and the Search For Knowledge"):
"Mathematicians had given up God; so it behooved them to accept man, and this is what they have done. They have continued the development of mathematics and the search for laws of nature, knowing that what they produced was not the design of God but the work of man. Their past successes helped them to retain confidence in what they were doing, and fortunately, hosts of new successes greeted their efforts. What has preserved the life of mathematics was the powerful medicine humans had themselves concocted -- the enormous achievements in celestial mechanics, acoustics, hydrodynamics, optics, electromagnetic theory, and engineering, and the incredible accuracy of its predictions. Thus, mathematical creation and application to science have continued at an even faster pace."

Tuesday, September 27, 2016

Prepare For Our Poker-playing Overlords

via WikimediaCommons

In a new Wired article, Adam Kucharski explains why poker may be more difficult/interesting to AI researchers than either chess or Go, where all strategic information is right in front of the players:

He quotes chess master Garry Kasparov (who lost to IBM's Deep Blue computer in 1997), saying that computers play games like chess and Go "like a machine." And then writes further,

"Kasparov hoped that games such as poker would be different. You cannot win by following a fixed set of rules because some cards are hidden, and your information is imperfect. The same is true of many other situations in life, from negotiations to auctions and trading."

Kucharski reports that the latest poker-playing robots "are revealing new and innovative ways of juggling risks and making decisions with imperfect information" and "The world's top poker bots have taught themselves to bluff, feign aggression and even manipulate their opponents."

One successful poker bot from Canada that Kucharski cites (and that progressively learns "by playing billions of simulated games") is "Cepheus" (specifically for a limit version of Texas hold 'em):

And, no doubt, more are on the way.

Sunday, September 25, 2016

Authentic Math...

Short and simple; for Sunday reflection, this recent tweet from Eric R. Weinstein:
"Unless you majored in math you have no idea whether you are good at math. That thing you weren't good at? Yeah, so, that wasn't really math."

Wednesday, September 21, 2016


Yeah, sure, James Grime, Vi Hart, Matt Parker, are good, buuuuuuut...
is there any more mesmerizing voice for presenting math videos than Tadashi Tokieda!? The Perry Como of math perhaps... ;-) 
His latest for Numberphile here, on non-transitive dice:

And his other great vids here:

(Non-transitive dice, by the way, come in different forms, some of which are available here:
https://mathsgear.co.uk/collections/dice )

Monday, September 19, 2016

Sir Roger Penrose Expounds

A blurb today about a new book I’m less than 100 pages into…

“Fashion, Faith, and Fantasy in the new physics of the Universe” is the latest from renowned Sir Roger Penrose. This is another beautifully produced, beautifully laid-out and diagrammed book from Princeton University Press. Given the breadth of these 400+ pages and Roger’s age I can’t help but wonder if this may be the last major work from him for a general audience. For all those reasons (and hey, simply because it IS from Roger Penrose) I’m sure it is worth recommending it to all readers interested in modern physics/cosmology. Peter Woit wrote a favorable review here (which I’ll point you to, since I won’t write a review):

I imagine the catchy main title (“Fashion, Faith, and Fantasy”) is especially intended to attract a wide general audience. Make no mistake about it though, it is heavy reading for anyone lacking acquaintance with theoretical physics, focused on the standard theory, inflation, quantum mechanics, string theory, and Penrose’s own twistor theory. There is a fair amount of math in the volume as well, and in fact, for math fans, the 70-page “Mathematical Appendix” may even be the best part of the book.

I won’t attempt a full review though because so much of the physics is simply beyond my grasp. Despite having read many popular cosmology books in the last two decades, the whole field is less, not more, comprehensible to me over time. I well understand the frustration (and rise) of the many skeptics of modern physics in recent years (Penrose himself is skeptical of many aspects). I don’t know of any other field where the more I’ve read, the fuzzier and less-comprehensible it all seems (not to mention being vociferously-debated-over by those who DO understand it!).
But with that said, I am looking forward to slowly slogging my way through this volume and gleaning from it what I can; there is possibly no better or more original expositor than Penrose to draw from. If modern physics theory is of interest to you you certainly won’t want to ignore this book either, and the more you already understand, the brighter read it will be.

I do have one curiosity about the book that maybe some knowledgeable reader can comment on in a few sentences:
I no more comprehend the specifics of the Langland’s Program in mathematics than the advanced cosmological theories in physics, but am still interested to hear about progress in cutting-edge Langlands work that hopes to unify mathematics (and in so doing may offer some unification to physics as well). Given that Penrose is a mathematical physicist I hoped there might be an update on Langlands somewhere in these 400+ pages, but it appears absent (not included in the Index to the volume). Am I wrong to think Langlands should tie in to some of this very theoretical discussion, or is there some reason one would NOT expect to see it in such a volume — is it too early on in Langlands work to be tying it back to "fashionable" ;-) physics, or perhaps the opposite problem, and it is simply too advanced for inclusion in a general audience volume? Just curious, if someone can enlighten me; I was looking forward to seeing Penrose's take on it all (or maybe it's just an area he has not much dabbled in?).

Anyway, here's how Woit ends his review of Sir Roger's volume:
"The range of non-crackpot speculative ideas about fundamental physics that normally get much attention is unfortunately quite narrow. In this environment Penrose is a breath of fresh air, providing here a different point of view on several topics, backed by serious and detailed argument. In some ways this is a popular book, but in others it is something else, deserving the attention of experts in the subject. I can’t recommend it too highly to anyone with a serious interest in fundamental questions about physics."

p.s.... Penrose will be at the Museum of Math in NY this coming Wed. evening promoting his book.

Sunday, September 18, 2016

"...a fundamentally creative act"

Sunday reflection:

"Early encounters with math can be misleading. The subject seems to be about learning rules -- how and when to apply ancient tricks to arrive at an answer. Four cookies remain in the cookie jar; the ball moves at 12.5 feet per second. Really, though, to be a mathematician is to experiment. Mathematical research is a fundamentally creative act. Lore has it that when David Hilbert, arguably the most influential mathematician of fin de siecle Europe, heard that a colleague had left to pursue fiction, he quipped: 'He did not have enough imagination for mathematics."

-- Gareth Cook in NY Times (2015)

Wednesday, September 14, 2016

20 Years Ago...

Last weekend I noted that this year marked the 20th anniversary of one of the greatest events in academic publishing.
...and now serendipitously, yesterday, Keith Devlin notes this is also the 20th anniversary of his column "Devlin's Angle":
A lot to celebrate! ;-)

I briefly searched to see what other notable math-related events took place in 1996. Here are a few:

a.  Paul Erdös died.
b.  IBM's "Deep Blue" became the 1st computer to win a chess game against a World Champion (Garry Kasparov).
c.  Harvard-educated mathematician Ted Kaczynski was finally arrested as the "Unabomber," one of the most sought-after criminals of all time!

Tuesday, September 13, 2016

Count 'em

Today, just passing along, verbatim, one of Alex Bellos’ Guardian brainteasers from this week, if you haven’t seen it:
“F is the first and the seventh letter of this sentence."
Using the sentence above as a model, fill in the gap in the following sentence to make it correct:
C is the first and the [….] letter of this sentence.
What I like about this problem is not only that it’s easy-to-state and is recursive, but even though it sounds harder, it solves fairly quickly just working through it logically. However, in the end I’m not sure there’s any algorithmic or logical system for reaching the final answer other than brute-force trial-and-error with the ultimate solution candidates. Bellos simply states the answer with no further explication, and I give it below:
C is the first and the forty-sixth letter of this sentence.

Sunday, September 11, 2016

Now In the Bookstores


The math-powered applications powering the data economy were based on choices made by fallible human beings. Some of these choices were no doubt made with the best of intentions. Nevertheless, many of these models encoded human prejudice, misunderstanding, and bias into the software systems that increasingly managed our lives. Like gods, these mathematical models were opaque, their workings invisible to all but the highest priests in their domain: mathematicians and computer scientists. Their verdicts, even when wrong or harmful, were beyond dispute or appeal. And they tended to punish the poor and the oppressed in our society, while making the rich richer…

“Big Data has plenty of evangelists, but I’m not one of them. This book will focus sharply in the other direction, on the damage inflicted by WMD [weapons of math destruction] and the injustice they perpetuate. We will explore harmful examples that affect people at critical life moments: going to college, borrowing money, getting sentenced to prison, or finding and holding a job. All of these life domains are increasingly controlled by secret models wielding arbitrary punishments.
“Welcome to the dark side of Big Data.

— Cathy O’Neil, from the Introduction to “Weapons of Math Destruction

Friday, September 9, 2016

"Given These Premises"....Inference

Am copying this verbatim from a recent Futility Closet posting about a hand of cards:

Given these premises, what can you infer?
  1. If there is a king in the hand then there is an ace, or if there isn’t a king in the hand then there is an ace, but not both.
  2. There is a king in the hand.
What is your answer???
Now, go read the Futility Closet post:
As you will see, the post claims that “almost no one sees” the correct answer, and "practically everyone" infers (wrongly) instead that “there is an ace in the hand.”  The correct answer seems fairly obvious to me, but the post implies that most all fall for this “cognitive illusion.” Unfortunately there’s no way for me to know how many readers here immediately see the proper answer, but I’m wondering if math fans, perhaps more grounded in logic than the general populace, don’t answer this correctly at a much higher rate than other groups of people... IF that were indeed the case, it would be another indication of why training in mathematical thinking ought be encouraged.
The article says it is "unclear" why people mess up on this particular problem, though I think it's just one more example of how verbal cues are often very ambiguous or misleading for people... language is rarely as precise as individuals tend to assume. It all even reminds me a bit of a very old classic math conundrum that throws most people off (most of you will be familiar with it), which in one version (from Wikipedia) runs like this:
"Three people check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realizes the bill should only be $25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn't know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 as a tip for himself. Each guest got $1 back, so now each guest only paid $9, bringing the total paid to $27. The bellhop has $2. And $27 + $2 = $29 so, if the guests originally handed over $30, what happened to the remaining $1?"
OR, alternatively, here's a more recent example from the Web that many of you will recall, where the answer is actually fairly simple, yet many people, once again, are misdirected by the wording**:
Jack is looking at Anne, but Anne is looking at George.
Jack is married, but George is not.
Is a married person looking at an unmarried person?

A) Yes       B)  No       C)  Cannot be determined
...I s'pose the ability of language to hinder or interfere with rational thought has never been better demonstrated than by the current American presidential election :-( 

**  the correct answer is "A"

Thursday, September 8, 2016

"Authentic Maths" (...and proofs)

A sort of fun read from the week, "The Time I 'Nearly' Solved the Twin Prime Conjecture":


With some important points toward the end, including:

a)  recognizing "failure" as "an inevitable part of the problem-solving process," and experiencing math "in a manner that engenders the learner’s sense of identity as a problem-solver."


b) "Authentic maths relies on having students develop and confront their intuitions as they straddle the lines between truth and uncertainty."