Sunday, December 31, 2017

Physics and the Unconscious

For Sunday reflection, this passage from Stephon Alexander's "The Jazz of Physics":

 "I walked into his spacious office and saw Dr. [Chris] Isham relaxing on a reclining armchair with his feet up... Notes on topos theory -- incredibly complicated algebraic-type manipulations of rules on topological spaces -- decorated the board behind him, so grand, they couldn't possibly fit on A4 paper. He was smiling warmly. He wasted no time and got straight to the point. 'Why are you here?' he asked. I responded, with some nervousness in my voice, 'I want to be a good physicist.' Chris then surprised me. 'Then stop reading those physics books. You need to develop your unconscious mind; that's the wellspring of a great theoretical physicist.' As if his scientific repertoire weren't impressive enough, what I didn't know at the time was that he was both seriously spiritual and philosophical. He calmly and earnestly told me that he had trained his mind to do tedious calculations while he was dreaming. He followed that remarkable revelation with another question: 'What are your hobbies?' Dumbstruck by his feats during slumber (I just slept at night), I distractedly replied, 'I play jazz at night.' There was a pause. 'You should play more music. I sing. I find that music is an ideal activity to engage the unconscious.' Another pause. 'You see these books here?' He pointed to the complete volumes of Carl Jung's writings, the founder of analytical psychology. 'I have fifteen years of training in Jungian psychoanalysis. Read volume nine, part two, Aion: Researches into the Phenomenology of Self. There is a mystical side to doing physics.'"

Tuesday, December 26, 2017

Looking Back...

Today just a space-filling retrospective of a few of my favorite simple posts (from the two blogs) in the year gone by (though only a few actually contain math!). In no special order:

didn't do a lot of puzzles this year, but here were a couple of quick ones:

a little math regarding primes:

a couple of lists (of websites & books):

and some commentaries, by me (rant) and by Eric Weinstein (video):

For whatever reason, the most popular (most hits) "Sunday reflection" was this one from Stanislas Dehaene:

My personal favorite reflection of the year may go all the way back to January 1 with Keith Devlin:
I couldn’t really pick out a favorite 'Friday potpourri' post, so will instead just cite two of the longer lists from the last 12 months:

That's a wrap!....

Sunday, December 24, 2017

The Trouble With Math

Sunday reflection...:

"The trouble with college math classes -- which classes consist almost entirely in the rhythmic ingestion and regurgitation of abstract information, and are paced in such a way as to maximize this reciprocal data-flow -- is that their sheer surface-level difficulty can fool us into thinking we really know something when all we really 'know' is abstract formulas and rules for their deployment. Rarely do math classes ever tell us whether a certain formula is truly significant, or why, or where it came from, or what was at stake. There's clearly a difference between being able to use a formula correctly and really knowing how to solve a problem, knowing why a problem is an actual mathematical problem and not just an exercise."

-- David Foster Wallace

Thursday, December 21, 2017

Elusive Conversation (brainteaser)

A mind-bender showed up on Twitter yesterday from a logic blogger. It's very similar to a puzzle that went viral a couple years back, which you may well remember (...but will likely still require some thoughtful-time to solve again). I’ve slightly adapted yesterday's Twitter version as follows:
Alice and Bob are each given a different fraction of the form 1/n where n is a positive integer. Each of them knows their number (fraction) but does not know the other’s number (but does know they are different). Assume each participant thinks in a perfectly logical/rational manner (and understands the other individual is doing so as well), the following conversation takes place:

Me:  I gave each of you separately a different fraction of the form 1/n that you have had a chance to look at. Which of you has the larger number (fraction)?

Alice:  I don’t know.

Bob:  I don’t know either.

Alice:  I still don’t know.

Bob:  Yes, now I know who has the larger number.

Alice:  In that case, so do I, AND I know both numbers!

What numbers (fractions) were they each handed?

[yes, there is one exact, correct solution... have fun]

.answer below
I find this puzzle especially appealing because of a sort of 3-tiered evolving process it likely follows for most solvers:

1)  Upon first reading, it doesn’t seem like it will be solvable.

2)  Upon further contemplation it appears partially solvable, but seems like multiple solutions are possible.

3)  The final step needed to reach the one correct solution requires a bit of recursive thought that, once made, is both illuminating and very satisfying.

....with that said.....
Bob has 1/3
Alice has 1/4

see HERE

Tuesday, December 19, 2017

"Think Twice"

If you make math videos you can’t do much better than get a thumb’s-up recommendation from Grant Sanderson (of 3Blue1Brown). Recently, Grant recommended a youngish YouTube site called “Think Twice” that's putting up some nice, short little animated math videos. Here's one example (feel free to explore more!):

Sunday, December 17, 2017

Mathematicians As Adults and Infants

From Sylvain Cappell, this Sunday reflection:
“All mathematicians live in two different worlds. They live in a crystalline world of perfect platonic forms. An ice palace. But they also live in the common world where things are transient, ambiguous, subject to vicissitudes. Mathematicians go backward and forward from one world to another. They’re adults in the crystalline world, infants in the real one.” 

Thursday, December 14, 2017

Need Some Things To Read...?

I'll have a Friday potpourri tomorrow morning at MathTango, but just to make sure you have enough to read/hear ;) below are some lists I've come across recently that may be of interest:

a)  Fine list of online math resources (including free online math-related magazines) that was tweeted out this week:

b)  Sean Carroll tweeted out this long list of 300+ philosophy interviews, at least a few of which may pertain to math or mathematical thinking:

c)  And a compendium here of Marcus du Sautoy’s many entertaining and varied podcasts (I don't think these were always readily available in U.S.):

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: