Monday, December 11, 2017

There once was a...

A dozen, a gross, and a score
Plus three times the square root of four
Divided by seven
Plus five times eleven
Is nine squared and not a bit more. **

For this supposedly celebratory time of year it’s been a pretty depressing month of news and politics (…on top of the entire last year of infamy), so just turning today to some light-hearted links with math limericks (I’ve referenced these before, but there are some good ones worth re-visiting, and the one above is classic):

…and these from Ben Orlin, who would probably be the head-writer for Saturday Night Live of Math... if there was such a thing:

** This limerick comes in some variations and is attributed to various authors, so I'm not sure of it's specific origin or composer.

Sunday, December 10, 2017

Math and Contemplation

Sunday reflection:

"[Bertrand] Russell's analytic approach had its origins in numbers; mathematics was his first love. In his autobiography he recalled his miserable adolescence and a footpath down which he would wander on England's south coast. 'I used to go there alone to watch the sunset and contemplate suicide. I did not, however, commit suicide, because I wished to know more about mathematics.'"

-- From "Wittgenstein's Poker" by David Edmonds and John Eidenow

Friday, December 8, 2017

“…it took AlphaZero only four hours to ‘learn’ chess. Sorry humans, you had a good run”

Again this week there will be no “Potpourri” over at MathTango (hope to return to it NEXT Friday), but if you want a nice varied collection of readings, the newest "Math Teachers At Play" carnival is out HERE. And I will pass along just a couple of things from last two days...

This story certainly would have been included in my potpourri had there been one:
Following in the footsteps of AlphaGo, that mastered the complex board game “Go,” the folks at Google have now come up with AlphaZero which took 4 hours to teach itself the game of chess from scratch, and then “obliterated the highest-rated chess engine” in existence (Stockfish). In a 100-game match, it won 28 games (25 times when it was playing white), had 72 draws, and ZERO losses. Remarkable! Fascinating story:

A bit scary to contemplate our possible Google overlords… though far less scary than the current deranged overlord in the White House.

Meanwhile Andrew Gelman reports that people have lost confidence in so many of our institutions (I can't help but think this loss of confidence coincides with the ever-rising income gap that leaves large numbers feeling bitter and resentful):

Wednesday, December 6, 2017

General Semantics...

Bit of an offshoot today...
I recently mentioned “General Semantics” in a post over at MathTango, forgetting that a lot of folks have no familiarity with the movement that faded from its limited popularity decades ago. A few readers emailed me with either questions or comments about it, so I thought I’d try to find an introductory video that wasn’t too long or too old-and-grainy expounding on General Semantics. I haven’t found one that in a brief, entertaining way covers the contents of GS, but this 6-minute one does offer a non-detailed overview:

...and this 10-minute effort gets into a few more specifics, while relating some ideas of Alfred Korzybski (the founder of General Semantics) to mathematical thinking and language:

[...I will add though that, unlike the presenter above (Corey Anton), I DON'T recommend that people try to read Korzybski's difficult-to-digest old anti-Aristotelian tome "Science and Sanity," but instead go with a more popularized, but still old, version of GS (if you can even find one) from S.I. Hayakawa, Stuart Chase, Wendell Johnson, or Irving Lee.]

[...on a different side-note, for any readers who may contemplate emailing me Martin Gardner's old critical commentary on General Semantics, yes, I'm well familiar with it, and consider it one of the worst errors/judgments he made in his long writing/skeptical career (with that said, he was primarily critical of Korzybski, less so of the popularizers who followed). I once mentioned to a Gardner specialist my upset with Martin's criticism of GS, and he in turn noted that almost every fan (like myself) of Gardner, has some one thing on which they deeply disagree with Gardner... problem is, it's a different 'thing' for each one of those fans. ;) ]

Monday, December 4, 2017

Some Twitter Trivia... plus Futility Closet

I only follow 250 accounts on my Twitter feed… a relatively small, but manageable number: Dunbar’s number +100  ;) 
Recently, having too much free time on-hand, I noticed that of those 250 I follow, 122 of them follow Evelyn Lamb — Twitter gives statistics on how many of the people that you follow, also follow any other given account you follow. I was actually surprised that more of the 250 didn’t follow Dr. Lamb (might’ve guessed it would be closer to 200), so then decided to check out how other Twitterers stacked up — who among people I follow are most followed by others that I follow (...follow me? ;) — a tree or group diagram of all the myriad connections might actually be interesting, but then I don’t have THAT much free time on-hand!

Anyway, the top 10 individuals (I’ve removed groups, magazines, news outlets, etc.), with the numbers of accounts (out of the 250 I follow), that follow them are below; in parentheses I’ve added the TOTAL number of followers (for some highly-variable further context) each of these accounts had at the time I looked:

@StevenStrogatz       155          (36,100 total followers)
@EvelynJLamb          122            (7,433)
@DivByZero               121          (10,500)
(Dave Richeson)
@JohnAllenPaulos     118          (26,900)
@MrHonner                116          (11,100)
@AlexBellos               114          (24,100)
@RepublicOfMath      113          (69,400)
(Gary Davis)
@CutTheKnotMath     109          (15,900)
(Alexander Bogomolny)
@JamesTanton           109          (11,600)
@ProfKeithDevlin        106          (12,400)

All of which doesn't mean much; just idly interesting to me to see the interaction between people I follow — i.e., who do people I follow, follow. Among individuals, only Dr. Strogatz is followed by over half (62%) of those I follow. (On-the-other-hand, he’s followed, overall, by 5 times more accounts than Dr. Lamb who edges into second place in my group, despite having the lowest total number of followers.)

Anyway, other folks might find it interesting to keep an eye on their “followers you know” numbers.


...And for something more fascinating and different, this morning’s new Futility Closet podcast tells the incredible story (I’d never heard before) of Marvin Hewitt, a 20th century American imposter who taught physics, math, and engineering in various academic venues:

Sunday, December 3, 2017

Mathematical Technique

Sunday reflection from G.H. Hardy:
“Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.” 

Friday, December 1, 2017

A Staggering Concept...

Again, won't be doing a Friday potpourri (over at MathTango this week; not sure if I'll get back to them before Xmas), but will pass along this tweet from the week that I enjoyed, along with it's lengthy comment thread:

Wednesday, November 29, 2017

Andrew Wiles in Conversation

I haven't had a chance to view this myself, but figure a conversation with Andrew Wiles must be good enough to pass along immediately:

Meanwhile, over at MathTango I'm in a bit of a Bah Humbuggery mood today:

Sunday, November 26, 2017

To Toss or Not to Toss

The paradox known as Buridan’s Bridge:
Bridge Gatekeeper to the approaching passerby: “If the next sentence you utter is true I will permit you to cross. But if you speak falsely, I will throw you into the water."
Passerby: “You shall throw me into the water.”

Saturday, November 25, 2017

Sean Carroll Expounds...

Very nice, recent 1-hour summary of modern physics thought (at least one physicist's interpretation) from Sean Carroll (if you've not heard Sean cover this material before this is a great presentation):

Sunday, November 19, 2017

A Little Self-referential Humor

for Sunday reflection... just an old, classic joke:
“There are three kinds of people in the world: those who are good at mathematics and those who aren’t.”

[...also, a new post over at MathTango today in honor of Thanksgiving approaching.]

Thursday, November 16, 2017

Sunday, November 12, 2017

Playing Games

From the inimitable John Conway:
“You get surreal numbers by playing games. I used to feel guilty in Cambridge that I spent all day playing games, while I was supposed to be doing mathematics. Then, when I discovered surreal numbers, I realized that playing games IS mathematics.”

Thursday, November 9, 2017

Happy Birthday Carl

It’s Carl Sagan’s birthday today; an apt time to re-read some of his words and view classic video:
    “If you wish to make an apple pie from scratch, you must first invent the universe.”
“Extinction is the rule. Survival is the exception.”
    “The nitrogen in our DNA, the calcium in our teeth, the iron in our blood, the carbon in     
    our apple pies were made in the interiors of collapsing stars. We are made of starstuff.” 
“We live in a society exquisitely dependent on science and technology, in which hardly
anyone knows anything about science and technology.”
    “The dangers of not thinking clearly are much greater now than ever before. It's not  
    that there's something new in our way of thinking -- it's that credulous and confused  
    thinking can be much more lethal in ways it was never before.”
Science is more than a body of knowledge; it is a way of thinking. I have a foreboding of an America in my children's or grandchildren's time -- when the United States is a service and information economy; when nearly all the manufacturing industries have slipped away to other countries; when awesome technological powers are in the hands of a very few, and no one representing the public interest can even grasp the issues; when the people have lost the ability to set their own agendas or knowledgeably question those in authority; when, clutching our crystals and nervously consulting our horoscopes, our critical faculties in decline, unable to distinguish between what feels good and what's true, we slide, almost without noticing, back into superstition and darkness. The dumbing down of America is most evident in the slow decay of substantive content in the enormously influential media, the 30-second sound bites (now down to 10 seconds or less), the lowest common denominator programming, credulous presentations on pseudoscience and superstition, but especially a kind of celebration of ignorance.
In memory...

Wednesday, November 8, 2017

Perception of Streaks

H/T to Dan Goldstein (on Twitter) for pointing out an Interesting plotting of (likely and VERY likely) “streak” probabilities:

The author looks mostly at "coin-tossing"-like scenarios, but notes such analysis potentially relates back to other theoretical discussions (such as "hot hand" observations). One can imagine a lot of other ways to play with similar data (and the author presents R code for doing such).

Tuesday, November 7, 2017

Twitter Quirkiness

Just a quirky episode from the other day... below is a verbatim copy of a tweet that someone posted (I've taken their name off) which I read quickly, thought was kind of fun, and re-tweeted to my followers, giving no more consideration.  If you've not already seen it, take a quick look, and then scroll further below for the little follow-up:


the non-commutativity of custard, according to . i'm going to have to try this. so weirddd  

A smidgen interesting I thought, but did you catch the error? (and no, I don't mean the spelling of the word "weird" which was clearly deliberate)... because it slid right by me, despite being rather obvious! And it interests me because of the way language and words function cognitively (psycholinguistics, including speech processing, was my primary focus decades ago).
So, in case, like me, you didn't notice it, the graphic example shown above is one of associativity, and is clearly labelled as such. Yet the poster's description calls it an example of "non-commutativity" (which of course it is NOT).
I simply found interesting the tendency (on my part anyway) to be so drawn to the graphic as to read right through the clear, posted words and not have them accurately register -- you think you know what they say, but the precise meaning may be translated in one's mind quite otherwise, overridden by expectation or the simple speed of processing (part of it too I think is just the mental 'appeal to authority,' resulting from invoking Eugenia Cheng's name, even though she is NOT the one who makes the error). It's almost like an optical illusion that you "see" one way, but is really another -- here, a word takes on an illusory effect.
Anyway, this may be of interest to no one else; I'm just eternally intrigued/concerned by how language plays with our minds (and often in far more deleterious ways!).
p.s.: Brian Hayes was the one who first pointed out the error above to me, and the author of the post apparently heard from several other folks as well; so to many, the mistake no doubt jumped right out.

In any event, I'm in the mood for some custard. :)

Monday, November 6, 2017