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Sunday, February 19, 2017

Mathematical Thinking, Not Rule-Following

Sunday reflection:

"What books are to reading, play is to mathematics... I believe we have the power to make mathematical thinking flourish everywhere. We can't afford to misuse math to create passive rule followers."

-- Dan Finkel (TEDTalk)

Wednesday, February 15, 2017

What I'm Reading...

In the middle of reading several books simultaneously, three of which I'll mention as likely recommendations (possible reviews or longer blurbs later):

The Best Writing on Mathematics 2016” ed. by Mircea Pitici 
Newly out, Pitici’s latest (7th) volume of this anthology. I’ve barely started it and it already looks fantastic; quite possibly the best yet in the series. Will review at a later date.

Know This— another of John Brockman’s Edge/essay compendiums with a great set of science thinkers on a wide variety of topics bearing on our future. Very short nuggets of thought. Once-in-awhile his volumes disappoint me, but so far not this one.

Superforecasting” by Philip Tetlock & Dan Gardner 
A volume I’ve seen nothing but positive reviews for. Since Trump’s November election I’ve especially been touting books that pertain to critical thinking and this falls in that genre.

These are all available in paperback and I think worth your consideration.

Finally, in honor of Raymond Smullyan I'm very tempted to order one of his later books, "Reflections," which appears to be very autobiographical, and reminiscent of Martin Gardner's own rambling autobiography. I always think of Gardner and Smullyan together and they were close friends (also, just recently realized that Smullyan, like Gardner, had attended the University of Chicago and studied with Rudolf Carnap).

Monday, February 13, 2017

Canary In the Press?

(image via pixabay)

We seem to be living, as noted by many, in an anti-intellectual, anti-expert, anti-science time-frame. I’ve been tempted to write a commentary on the relatively tepid response from the STEM community to the Trump presidency, and earlier voiced dismay at how few scientists spoke out loudly and often during the election campaign (THANK YOU to those who did)… but for now, I'll refrain adding my puny voice here to the growing numbers finally speaking up, almost in a sudden panic (…now that he’s in office slowly dismantling democracy).

BUT… last week Raymond Smullyan died. I’ve been taken aback at the paucity of press for Smullyan’s passing. The NY Times finally ran an obituary 5 days after his death. Where are the articles though from the Washington Post, the LA Times, the Boston Globe, Chicago Trib, USA Today...? Obviously too, I might expect something more expansive soon from MAA, AMS, philosophy associations, and others. 
What does it say about our times (where a demagogue can not only run for president, but win) that a major proponent/author of rationality, logic, and clear thinking, passes away and is accorded so little attention. Losing Smullyan, at the age of 97, is not particularly unexpected, but the lack of coverage of this loss is discouraging. The silence is like a canary within the press dying, and indicating something awry with our values and focus. What two-bit celebrity will die next month and receive multi-columns of notice? Have we, after 200+ years, lost our way? In the word of our (so-called) President, it is “sad.”

Sunday, February 12, 2017

Assault on Truth

As most know, Hans Rosling passed away this week. As a Sunday reflection, a few timely sentences from Keith Devlin, in tribute to him, via a comment at his own blog:
For all his engaging presentation skills, the numbers were at the heart of Rosling's talks. It was not his oratory that convinced us, in an instant, that our preconceptions of our world were wrong -- often violently so. It was the data -- the numbers displayed on the screen in front of us…“As it happens, Rosling's death comes at a moment in time when people in highly powerful positions are waging an assault on scientific facts, on numerical data, and indeed on truth in general…“An attack on truth is an attack on Society in general. Those of us whose lives revolve around discovering and communicating numerical and mathematical truth have a duty to speak up forcefully, in opposition. If our Society loses the respect for, and dependency on, truth, the loss of mathematics will be the least of our worries.”

Thursday, February 9, 2017

Raymond Smullyan, A Knight Among Men... +ADDENDA

"Recently, someone asked me if I believed in astrology. He seemed somewhat puzzled when I explained that the reason I don't is that I'm a Gemini." -- R. Smullyan

At a time when we need his likes more than ever, brilliant polymath Raymond Smullyan has died at the age of 97. One of the undersung thinkers of our times — with a name far less well-known to the public than several other mathematicians.
As word gets out, I’m sure there will be many wonderful tributes to follow, but for now, I’ll just leave here a few of the Tweets I quickly found popping up:
from @shanewag1 :
Very sad to say goodbye to one of the world's great polymaths. Rest In Peace, Smullyan. There was something a little wrong with dualism. 

from @mathematicus :
I don't really do heroes but if I did Smullyan would be one of mine

from @J_Lanier :
The brilliant and playful Raymond Smullyan has passed away. I am grateful for the many happy hours I've spent reading and sharing his books.

from @bphopkins :
RIP the great Raymond Smullyan, many of whose books I shall someday gleefully subject my children to. So goes the Dao.

from @BradleyPallen :
The two sentences in this tweet are false.
Raymond Smullyan will never die.

I'll mention again that Jason Rosenhouse edited a nice tribute volume, "Four Lives," to Smullyan some years back:

Smullyan is best known for his logic works (both recreational and academic), but he also wrote several volumes on "spirituality." The best known was probably "The Tao Is Silent," but my own favorite is perhaps "A Spiritual Journey."

And lastly, I'll end with one more quote from Raymond:
"A joke is told that Epimenides got interested in eastern philosophy and made a pilgrimage to meet Buddha. He said to Buddha: 'I have come to ask you what is the best question that can be asked and what is the best answer that can be given.' Buddha replied: 'The best question that can be asked is the question you are asking and the best answer that can be given is the answer I am giving.'"

==> [It’s now 2:30pm EST and I had expected by now to see some more official notice or more-detailed obituary for Dr. Smullyan than the Facebook posting that started the news. I've seen at least a couple of people pass the news along who I don’t believe would have done so if they were not certain of its validity, but once some more official press links are available I will add them here.]

==> Apologies, that I may have multiple updates to this post as warranted…
For those who haven’t seen it, the initial news on Raymond was broken by a Facebook post from a personal friend HERE
I only just now noticed the post’s date is Feb. 7, saying Dr. Smullyan died “yesterday” (so, I assume Feb. 6), making it even more surprising that there are by now (3 days later) no formal press releases (though the poster does say she expects the NY Times to have a “big tribute” to him soon. Who knows what clever final instructions the iconoclastic Smullyan may have left for any announcements of his death… or alternatively, perhaps his lesser name recognition (compared to say his dear friend Martin Gardner) is causing a delay in more details getting out.

In any event, stay tuned… Raymond straddled a world between mathematicians, logicians, philosophers, recreationalists, cognitive scientists, academics, and layfolk… and musicians and magicians… and punsters ;) and he deserves the highest recognition.

==> 2/10/17  Perhaps Raymond has left us, as he lived, giving us one more puzzle to ponder. I awoke at 5 this morning and immediately searched Web for official news of his demise, and still it awaits. People have repeatedly tried to edit his Wikipedia page only to be rebuffed by editors who are also waiting for official confirmation. Maybe Feb. 11, being a prime number, will be the day of notification (…and I’m only half-joking). 
For those repeatedly asking, no, I think it clear this is not any sort of hoax or prank, but for whatever reason, and despite his worldwide fan base, official news just hasn’t come yet. I did glean from all my searching that Dr. Smullyan apparently died “peacefully in his sleep” from “complications of a stroke,” I believe the evening of Feb.6.
And I have to admit there is something almost delicious, that even in death, Dr. Smullyan continues to puzzle us from the great beyond.

For any readers who don’t know much about Smullyan or wonder why I'm spending this much time on him, until longer tributes appear, you can get a feel for him and his impact from the messages flowing in on this Facebook page:

==> Wikipedia page finally updated based in part on this account:

Probably much more to follow in next 24 hrs.

2/11/17 : The NY Times has weighed in with their obituary:

Tuesday, February 7, 2017

"Now" for a Book Blurb

In my 2016 end-of-year book wrap-up I briefly mentioned that Richard Muller’s book, “Now” (focusing on the nature of time and entropy) was one popular physics book I was looking forward to reading. I’ve now read it, and generally do recommend it (finding it less inscrutable and more satisfying than most popular physics books)… but with a caveat. While the volume has had mostly positive reviews there have been a few negative ones that are often put off by a couple of chapters near the end of Dr. Muller’s book. Muller is known as a rather independent thinker with a gadfly streak, and toward the end includes significant discussion that some will find too metaphysical (almost supernatural). I actually enjoyed seeing a physicist’s take on such matters, but some won’t. He is especially skeptical of “physicalism,” the approach most physicists take to scientific study; i.e. that everything is ultimately explainable in terms of “physical” elements that we do or can eventually understand. 
One of the examples he uses over and over of something we simply don’t understand is what it means to “see” the color “blue,” nor do we know if other people see (inside their brains/minds) blue the same way we see it. This is one of those profound questions that many children ask (and never receive an adequate answer), and you either get what he means by the query or you don’t. Philosophers have long discussed it at length, with no resolution. He also dives into a long discussion of free will, and why he views it as incompatible with "determinism" (some don't), again a topic too philosophical for many. 
One can get even more abstract by asking what does it mean to feel “wonder,” or “awe,” or “love,” and if these are nothing more than neurons firing in certain patterns (as many would say), then can we construct robots that experience these “feelings.” Also, long amazing to me, as someone with an interest in psycholinguistics, is our lack of real understanding of how everyday speech is either produced or processed, even though all normal humans do it effortlessly. Anyway, I’m going far astray from the discussion Muller has, just as a way of saying I’m not put off by seeing a physicist talk about things he finds inexplicable within a “scientific” framework. But yes, the chapters do stick out a bit awkwardly in an otherwise empirical look at some of the deepest questions faced by physics theorists today.
For an actual review of the volume see here:
…and here, an excerpt from the book:

Sunday, February 5, 2017

Number Sense

Sunday reflection:
 "[Alain] Connes thinks that expert mathematicians are endowed with a clairvoyance, a flair, a special instinct comparable to the musician's fine-tuned ear or to the wine taster's experienced palate that enables them to directly perceive mathematical objects: 'The evolution of our perception of mathematical reality causes a new sense to develop, which gives us access to a reality that is neither visual, nor auditory, but something else altogether'."  
-- from "The Number Sense" by Stanislas Dehaene

Wednesday, February 1, 2017

Who Doesn't Want More Evelyn Lamb!

For all of you who were just saying to yourselves, 'Ya know I need to subscribe to just one more email newsletter'... have I got good news. Evelyn Lamb announces she will begin putting out such a newsletter, which she describes in a tweet as “Math, math, math (And other stuff)," and the first issue will even be today!
Go here to subscribe (…that’s an order!):

Sunday, January 29, 2017

the depths of existence...

Sunday reflection from Keith Devlin, on Euler's formula:

"Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than skin deep, Euler's equation
[e + 1 = 0] reaches down into the very depths of existence."

Thursday, January 26, 2017

Update on Poker-playing Robot

A couple of weeks ago I mentioned that AI programs were now taking on poker, and a nice followups to that storyline appear this week:
In an ongoing Texas hold’em tournament a poker-playing robot named “Libratus” is so far up by almost $800,000 against its human competitors.
From the the first article: 
“Poker requires reasoning and intelligence that has proven difficult for machines to imitate. It is fundamentally different from checkers, chess, or Go, because an opponent’s hand remains hidden from view during play. In games of ‘imperfect information,’ it is enormously complicated to figure out the ideal strategy given every possible approach your opponent may be taking.”Further it is noted that “...an AI player has to randomize its actions so as to make opponents uncertain when it is bluffing.”
And from the 2nd article:
"One of the things Libratus does well is bluff..."Mastering the art of the bluff requires AI that can calculate risk and reward in real time without having perfect information about what its opponent can do in return. It implies the system does more than simply play a perfectly safe game where it only grinds out wins when it has the stronger hand."
Libratus is specifically programmed (as I understand it) to be skilled at just one specific poker game, so even if it wins this tournament (and it looks like it will, as it seems to be getting stronger over time), it doesn’t mean that bots are on the verge of taking over all professional poker… or, at least not yet. Of course the real congratulations go, not to the bot, but to the clever humans (in this case from Carnegie-Mellon) programming it.

Monday, January 23, 2017

Winning At Blackjack... and more

To start the week, this delightful (19-min.) Planet Money podcast on Ed Thorp, starting with his blackjack-beating escapades (h/t to Francis Su for this one):


Try to find time for it (all the more so if you don't already know Thorp's story.)

via WikimediaCommons

Sunday, January 22, 2017

Seen and Unseen...

"We have never seen any curve or solid corresponding to my square root of minus one.  The horrifying part of the situation is that there exist such curves or solids. Unseen by us they do exist, they must, inevitably; for in mathematics, as on a screen, strange, sharp shadows appear before us. One must remember that mathematics, like death, never makes mistakes. If we are unable to see those irrational curves or solids, it means only that they inevitably possess a whole immense world somewhere beneath the surface of our life."

-- Yevgenii Zamyatin, quoted in Michael Harris's "Mathematics Without Apologies"

Friday, January 20, 2017

A Pig Is A Pig...

Given the events in Wash. DC. today, seemed only fitting to end the week with a joke... so, a little recursive humor I came across in Thomas Cathcart’s and Daniel Klein’s volume “Plato and a Platypus Walk Into a Bar.” Quoting verbatim:
“A woman sues a man for defamation of character, charging that he called her a pig. The man is found guilty and made to pay damages.  After the trial, he asks the judge, ‘Does this mean that I can no longer call Ms. Harding a pig?’ The judge says, ‘That is correct.’ ‘And does it mean that I can’t call a pig Ms. Harding?’ ‘No,’ says the judge, ‘you are free to call a pig Ms. Harding. There is no crime in that.’ The man looks Ms. Harding in the eye and says, ‘Good afternoon, Ms. Harding.’”
(Yeah, I was tempted to re-write the joke somehow so as to change “Ms. Harding” to “Mr. Trump,” but I restrained myself.)

Have as happy a weekend as you are able, under the circumstances....

Wednesday, January 18, 2017

"Ideology In Math Education"

At 70 pages (pdf), the latest “Archimedes Mathematics Education Newsletter” from David Wells (h/t A. Bogomolny) is almost more a small booklet than a newsletter, and is chockfull of rich, interesting discussion on math education:
It includes reviews, philosophy, quotations, history, arguments, discussion of pure vs. applied mathematics, an interview with Douglas Hofstadter... in short, something for anyone involved with math education to enjoy or tussle with. Don't expect to read it all in one sitting.
...prior issues of Wells' newsletter are listed here, by the way: http://amendavidwells.blogspot.com 

Monday, January 16, 2017

Staying In The Middle...

Been some discussion around math-Web this week about the “Median Game.” It got started with this Gil Kalai posting:

A quick, simple game (requires exactly 3 people to play, and just a pad-and-pencil), intriguing because of its recursive nature, and the resultant strategizing required.
The game actually shares origins with games called “Hruska” or “Mediocrity,” created by ever-inventive Doug Hofstadter, and described in Chapter 28 of his fantastic volume, “Metamagical Themas.”
Mike Lawler took the plunge and played Median with his boys recently and they quickly picked up on some of the nuances of the game:

As has been done with other games, would be interesting to have AI people write programs to compete at Median and hold an all-computer tournament to see which program (strategy) works best (…or perhaps this has already been done?)
Anyway, check it out at Gil’s site, and if you can, get 3 folks together to wile away some time playing it.

But fair warning, it can quickly play havoc with your brain! ;)

Sunday, January 15, 2017

Numbers and Mind

Sunday reflection:
"As archetypes of our representation of the world, numbers form, in the strongest sense, part of ourselves, to such an extent that it can legitimately be asked whether the subject of study of arithmetic is not the human mind itself. From this a strange fascination arises: how can it be that these numbers, which lie so deeply within ourselves, also give rise to such formidable enigmas? Among all these mysteries, that of the prime numbers is undoubtedly the most ancient and most resistant."
         -- Gerald Tenenbaum and Michel Mendes France, in "The Prime Numbers and Their   

Friday, January 13, 2017

Is Bluffing Just Another Algorithm...

"You've got to know when to hold 'em
Know when to fold 'em
Know when to walk away
Know when to run
You never count your money
When you're sittin' at the table
There'll be time enough for countin'
When the dealin's done.

Every gambler knows
That the secret to survivin'
Is knowin' what to throw away
And knowin' what to keep
'Cause every hand's a winner
And every hand's a loser
And the best that you can hope for
Is to die in your sleep."

-- Kenny Rogers, The Gambler

First computers mastered chess, then Go, and now AI is facing the complexity of everyone's favorite, Poker.
 A program called DeepStack is taking on the  “10160 possible paths of play for each hand in heads-up no-limit Texas hold’em”:

Professional poker players have been defeated and researchers say they may indeed be on to "a significant advance in game-playing AI.” Another (20-day) tournament just got underway in Pittsburgh, testing Liberatus (another poker-playing bot) against an expert field. You can follow along more here: