Sunday, January 21, 2018

Of Heavens and Math

From G.K. Chesterton:
“The difference between the poet and the mathematician is that the poet tries to get his head into the heavens while the mathematician tries to get the heavens into his head.” 

Friday, January 19, 2018

Fly Away

Is snow keepin’ ya inside, or are you otherwise bored, or down with a cold/flu, than a post just for you today, full of practical application ;)

… a few videos (making similar claims), for constructing long-flying paper airplanes.
 Do it!:

[...for a little more mathy content a short, new Friday potpourri is now up at MathTango ]

Tuesday, January 16, 2018

Stayin' Alive...

May be busy with a project for awhile, possibly slowing down blogging... but will try to keep y'all entertained, somehow... oh yeah!:

Sunday, January 14, 2018

'I was in prison and might be shot'

An entranced Arthur Koestler, in "The Invisible Writing":
“I went on to recall Euclid’s proof that the number of primes is infinite… the scribbled symbols on the wall represented one of the rare cases where a meaningful and comprehensive statement about the infinite is arrived at by precise and finite means. I must have stood there for some minutes, entranced, with a wordless awareness that ‘this is perfect, perfect’, until I noticed some slight mental discomfort nagging at the back of my mind, some trivial circumstance that marred the perfection of the moment. Then I remembered the nature of that irrelevant annoyance: I was, of course, in prison and might be shot. But this was immediately answered by a feeling whose verbal translation would be: 'So what? Is that all? Have you got nothing more serious to worry about?' -- an answer so spontaneous, fresh and amused as if the intruding annoyance had been the loss of a collar-stud.”

Friday, January 12, 2018

A Suggestion for Nigerian Email Scammers

By coincidence, shortly before our Il Duce was referencing “shithole” countries I was re-reading an old Presh Talwalkar post from a few years back that I always enjoyed on ‘Nigerian’ email scammers. It explains, as many know by now, why ’Nigerian’ email scams got stupider and stupider over the years, full of misspellings, bad grammar, poor English, outrageous narratives, etc. — the scammers wanted to make their messages SO obviously fraudulent that only the most gullible, naive, unthinking people would even respond (why waste time on thinking-folks wary enough to not follow through with the scam):

Anyway, I have a suggestion for how the scammers can be even more efficient: Just buy a copy of the mailing lists used by the Republican National Committee -- boy, talk about a sucker-list…

Thursday, January 11, 2018

Richard Schwartz Does Not "Have a Mature Attitude Towards Math"

Hopefully by now you're all tuned into Quanta Magazine, but if somehow you missed it, wonderful interview this week with mathematician/author Richard Schwartz, connoisseur of 'simple problems':

I've said it before, mathematicans are eternal children with the Universe as their playground, and Richard evokes that sense.

Monday, January 8, 2018

He Said She Said

Yo, logic enthusiasts, when I saw a post entitled, “Smullyan and the President’s Sanity” listed on the feed this morning it caught my attention. Have fun:

Sunday, January 7, 2018


Sunday reflection: 

Bedraggled old man:  "....5, 1, 4, 1, 3 -- DONE! at last."

Passerby:  "You look exhausted; what did you just do?"

B.O.M.:  "Recited the complete decimal expression of pi backwards."

-- old Wittgenstein joke

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