Sunday, January 29, 2017
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
[eiπ + 1 = 0] reaches down into the very depths of existence."
Thursday, January 26, 2017
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.
==> ADDENDUM (1/31): well, well, guess who won that tournament:
Monday, January 23, 2017
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.)
Sunday, January 22, 2017
"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
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
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
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
"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
"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:
Wednesday, January 11, 2017
A couple days back I asked aloud who might I interview this year for the blog, and the first 2 emailers to suggest a name had the same one in mind: Francis Su. If you’ve followed news in math circles lately you understand why that name arose. Last Friday Su gave his ‘retirement’ address as outgoing MAA President to the Joint Math meetings in Atlanta, and it became one of the most linked-to pieces I’ve ever seen in the math blogosphere.
Deservedly so. The title was “Mathematics For Human Flourishing.” There are plenty of words many of us easily associate with mathematics, but “ human flourishing” may not be among the ones that come rapidly to mind.
“…if you asked me: why do mathematics? I would say: mathematics helps people flourish. Mathematics is for human flourishing…“What I hope to convince you of today is that the practice of mathematics cultivates virtues that help people flourish. These virtues serve you well no matter what profession you choose.”
And then he proceeded to flesh out five virtues: play, beauty, truth, justice, love. The first three of these are easy to imagine in connection to math, but “justice” may not quickly come to mind. Yet “justice” is actually the one he spent the most time on, and it is a very important read.
…Su, being Asian, falls into one of the stereotypes sometimes held for mathematicians, but his articulate, moving prose easily breaks him out of the oft-held, narrowly ‘nerdy’ stereotype.
The entire piece is wonderful, one tweeter calling it a 'pep talk, wake-up call, and call-to-action' all wrapped in one. MANY called it “inspiring,” and Fawn Nguyen, no stranger to powerful writing herself, deemed it “heartbreakingly beautiful.”
The very phrase, "Mathematics for human flourishing" is a beautiful conjunction of ideas in an often unflourishing world, so if you missed it, do read on:
Su is based at Harvey Mudd College, one of the Claremont Colleges, which are my old haunting grounds, and at some point I’ll try to rope him into an interview here.
[* above photo taken from Tim Chartier's Twitter feed... if someone else deserves credit(?) for it, let me know]
Tuesday, January 10, 2017
For quite awhile now this country's student loan debt crisis has concerned me more than the housing crisis of 9 years ago ever did — the housing crisis had potential, if painful, solutions (some of which I suspect have been avoided)... I’m not sure the student loan debt dilemma has realistic solutions going forward. Most concern addresses the younger generations strapped with these loans, and the ramifications both for them directly and longer-term implications for the overall economy, but something I didn’t even realize was how many “baby boomers,” specifically over 60, are hampered by the problem as well!
This Marketwatch piece focuses on the issue:
“The number of older Americans with student debt is growing faster than any other age group, according to the CFPB, and it appears they’re struggling. Nearly 40% of federal student loan borrowers over age 65 are in default…”
For many it means, having Social Security garnished, in turn leaving them with poverty-level income in their retirement years.
Check out more about general student loan debt at Phil Ebersole's blog:
We’re in deep doo-doo, that, just like the housing bubble, no one seems to much talk about (perhaps because they have little positive or intelligent to say). Worse yet, we’ll soon have an Administration bent on concentrating yet more wealth in the few, while sending the rest into deeper, more drawn-out recession/depression. Long-term, there may be a solution as brick-and-mortar colleges go the way of brick-and-mortar bookstores, and the cost of education significantly comes down -- but that's VERY long-term; in the meantime several generations have a tough future ahead... tougher lives than their parents had.
Four years from now, it will once again be the Democrats screaming, “It’s the economy stupid!” …but will it already be too late? It remains a bitterly horrible irony that so many of those who voted for Trump and retrograde Republicans, will be those most adversely affected by what passes for their “policies.”
Monday, January 9, 2017
Came across yesterday's Parade Magazine at a coffeehouse this morning so looked at Marilyn vos Savant's column and found a clever little riddle... has the ring to it of a classic old 'lateral-thinking' type puzzle, so if you missed it here goes:
A fellow is in town to buy a 5-ft. fishing pole. Following the purchase he begins to board a bus home, but the driver informs him that objects longer than 4 ft. are NOT permitted on the bus. Disappointed, the fellow walks back to the store, only to emerge briefly later, still with the same fishing pole, and boards a bus with no problem.
What has he done (...and no, the pole has not been collapsed, telescoped, or in any other way adjusted)?
he placed the pole diagonally in a 3 x 4 cardboard box and walked on-board with the box.
Have done ~40 transcribed interviews here (well, mostly at MathTango) over the years, so maybe can push it to 50 this year. Always have a few possible names in the back of my mind, but if you are a math-enthusiast willing to be interviewed please let me know...
You may be someone with a popular math-related book out or on its way, or someone with a blog or website you want to publicize a bit (though I may have reservations about some strictly commercial sites); or maybe you're involved in education or 'big data,' or some other applied area of professional math. Or finally maybe you simply enjoy talking math for some other reason. Don’t be shy… drop me a note at: SheckyR [at a gmail.com acct.]
OR, if you're not interested in being interviewed, but know someone you’d enjoy seeing interviewed feel free to send their name along (and if possible their email address).
Thanks in advance....
Sunday, January 8, 2017
For today, just this old classic reflection from Donald Rumsfeld:
"Reports that say that something hasn't happened are always interesting to me, because as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – the ones we don't know we don't know. And if one looks throughout the history of our country and other free countries, it is the latter category that tend to be the difficult ones."
Thursday, January 5, 2017
Eric Weinstein is a bit of an odd duck… child prodigy, adult polymath, and I would almost say provocateur; sometimes fascinating, sometimes perhaps infuriating. In addition to math he more than dabbles in economics, physics, and public policy. Below is the first of a 3-part interview with Dave Rubin from The Rubin Report. I’ve posted it primarily for the first 10 minutes-or-so that include some interesting thoughts on math and science. After that they wander to other, but still interesting topics:
Here is a link to Part 2 of the interview:
Part 2 is mostly social/political in nature, but Part 3 turns out to include a lot more math/science so am adding it below:
Part 2 is mostly social/political in nature, but Part 3 turns out to include a lot more math/science so am adding it below:
Wednesday, January 4, 2017
I studied cognitive psychology back in the day when George Miller’s piece "The Magical Number Seven, Plus or Minus Two” was still a key, seminal paper in memory and cognition. And so I was slightly amused to see the number 7 arise once again today in the completely unrelated context of "starling murmuration," where individual birds must optimize their behavior within "a dynamic system in which the parts combine to make a whole with emergent properties":
"Just incredibly cool," as Barbara King writes.
I think George Miller would smile...
…and, sidenote, lest anyone dare forget, 7 was also Mickey Mantle’s jersey number:
I'm assuming most readers are somewhat familiar with bird murmurations since there have been so many videos posted in the last few years, but if somehow you've missed them you can find plenty at YouTube HERE, including this one set to music:
By the way, there really is math here, under the biological heading of "swarm behavior." A small bit from Wikipedia:
"Swarm algorithms follow a Lagrangian approach or an Eulerian approach. The Eulerian approach views the swarm as a field, working with the density of the swarm and deriving mean field properties. It is a hydrodynamic approach, and can be useful for modelling the overall dynamics of large swarms. However, most models work with the Lagrangian approach, which is an agent-based model following the individual agents (points or particles) that make up the swarm. Individual particle models can follow information on heading and spacing that is lost in the Eulerian approach."
Sunday, January 1, 2017
Keith Devlin in "The Language of Mathematics":
“The use of a symbol such as a letter, a word, or a picture to denote an abstract entity goes hand in hand with the recognition of that entity as an entity. The use of the numeral ‘7’ to denote the number 7 requires that the number 7 be recognized as an entity; the use of the letter m to denote an arbitrary whole number requires that the concept of a whole number be recognized. Having the symbol makes it possible to think about and manipulate the concept.
“This linguistic aspect of mathematics is often overlooked, especially in our modern culture, with its emphasis on the procedural, computational aspects of mathematics. Indeed, one often hears the complaint that mathematics would be much easier if it weren’t for all that abstract notation, which is rather like saying that Shakespeare would be much easier to understand if it were written in simpler language.
"Sadly, the level of abstraction in mathematics, and the consequent need for notation that can cope with that abstraction, means that many, perhaps most, parts of mathematics will remain forever hidden from the nonmathematician; and even the more accessible parts — the parts described in books such as this one — may be at best dimly perceived, with much of their inner beauty locked away from view.”