Thursday, July 19, 2018


To shorten tomorrow’s “potpourri” (over at MathTango) am posting a few of the week's interesting bits here today:

1)  James Dilts (who I interviewed HERE) does great job explaining “the most controversial axiom of all time,” the Axiom of Choice:

2)  Peter Woit updates us on Mochizuki/abc-proof news and controversy:

3)  And some welcome bibliophile news!: on the way from Thomas Lin and MIT Press this fall, a collection of Quanta Magazine math pieces:

...side-note: if you haven't voted yet in the semi-finals of The Aperiodical's "Big Internet Math Off," time to do so:

Monday, July 16, 2018

In the News…

In case you missed any of them, just a few bits of news from today following the meeting in Helsinki between our lying asshole and their lying asshole (a meeting which Putin reveled about as “a success,” meaning that Donald got played big-time):

1.  Former CIA Director John Brennan calls upon Mike Pompeo, John Bolton, and John Kelly to resign their positions, saying that Trump’s Helsinki behavior crosses the threshold of high crimes and misdemeanors” and “was nothing short of treasonous”:

2.  Russia's infiltration of the debased NRA and arrest of Maria Butina:

3.  Republicans criticizing Trump’s news conference with Putin (...perhaps even the odious GOP is reaching the end of its rope with this disgrace):

4.  Garry Kasparov called today, “the darkest hour in the history of the American presidency.”

5.  John McCain’s full statement on the meeting that he describes as a "pathetic rout... an illustration of the perils of under-preparation and inexperience":
It starts off thusly (and only gets worse):
“Today’s press conference in Helsinki was one of the most disgraceful performances by an American president in memory. The damage inflicted by President Trump’s naiveté, egotism, false equivalence, and sympathy for autocrats is difficult to calculate. But it is clear that the summit in Helsinki was a tragic mistake."
6.  Similarly, Anderson Cooper’s first comment following the press conference: “You have been watching perhaps one of the most disgraceful performances by an American president in front of a Russian leader I've ever seen.” (...echoing plenty of other watchers)

7.  The Atlantic on "the crisis facing America":

...And on Twitter, following the news conference, the hashtag #treason was trending nicely.

Every member of Trump's Cabinet and staff with any self-respect and dignity (let alone allegiance to the Constitution, or concern for their own reputation and credence) ought now resign... we'll see who does.

Sunday, July 15, 2018

n-body problems

Sunday reflection:
"...a lot of effort was devoted to the three-body problem: the motion of a system consisting of three point masses (such as Sun, Earth, Moon) moving under Newtonian gravitation. It's easy enough to write down the appropriate equations of motion; but immensely harder to solve them... As an aside: it has been said that one can gauge the progress of science by the value of n for which the n-body problem cannot be solved. In Newtonian mechanics the 3-body problem appears to be insoluble. In Relativity, it is the 2-body problem that causes trouble. Quantum Theory gets hung up on the 1-body problem (a particle); and Relativistic Quantum Field Theory runs into trouble with the 0-body problem (the vacuum)!"
                                                                                -- Ian Stewart

Tuesday, July 10, 2018

Alexander Bogomolny …cutting the knot

No doubt many are familiar with Terry Gross’s “Fresh Air” long-running show on NPR… so long running in fact that whenever someone famous dies, it turns out they are likely to have been interviewed on Fresh Air at some point, and NPR, in tribute, re-runs the episode.

This week my interview with Alexander Bogomolny, done 4+ years ago, abruptly spiked up significantly in weekly traffic, associated with his recent passing.

I’ve always wanted my simple interviews to be ongoing sources of additional information about the math communicators highlighted, but it only just suddenly hit me (not to be too morbid about it) that all these folks will pass on at some point, and the interviews also stand a bit as tributes that readers may draw some reminiscences from. Just a little odd/ironic to realize that these posts may accrue as many or more visits upon the death of an individual as when they were living.
Most of these interviewees will outlive me (at least I’m older than the majority of them), but in some cases at least, I s’pose that like Terry Gross, I may still be around to recall the blog time spent with one or more of these math communicators when they pass. Anyway, be sure to fully appreciate them while they're among us!

I'll end by passing along just one of the countless puzzles that Alexander posted (with 4 solutions as he would often do). It is the same 'lost plane-boarding pass' puzzle that Zoe Griffiths recently employed in the Big Internet Math-Off to win her first round:

[and a few more puzzles ;) can be found HERE]

Monday, July 9, 2018

21st Century Mathematics ...+ Psychics!

Keith Devlin’s latest blog post is a sort of wrap-up of several he’s had on the (needed) evolution of math education/application:

In it he links to this 28-min. talk he recently gave at a Swiss conference on the subject:

...and, for a bonus video today, here is Matt Parker with his Psychic Pets project, including Barry the psychic Labrador:

I've already requested that they ask Barry IF Trump will be impeached, but thus far I've heard nothing back. :(

[...and currently over at MathTango, my commentary on the ongoing "Big Internet Math Off"]

Sunday, July 8, 2018

Of Math and Cults

Sunday reflection:
“One of the most painful aspects of teaching mathematics is seeing my students damaged by the cult of the genius. That cult tells students that it’s not worth doing math unless you’re the best at math — because those special few are the only ones whose contributions really count.”
                                                                                             -- Jordan Ellenberg 

Friday, July 6, 2018

Carl to Carroll

This interesting math tidbit (showing Euler wrong about a power conjecture) was passed along by physicist Sean Carroll earlier in week (via Twitter):

…I don't usually make such comparisons, but it strikes me that Sean is perhaps becoming a new generation's version of Carl Sagan (yeah, there are differences, but some keen similarities, and hey, same initials in reverse order ;)). His new, wide-ranging podcast, “Mindscape” (for all who have the time for yet one more podcast!) is about to launch:
Should be good...

[...Be sure and visit MathTango later this morning, after 8am., for a potpourri of things I didn't cover here at Math-Frolic during the week.]

Thursday, July 5, 2018

Dueling Mathematicians...

First, in the Road-from-Ridicule-to-Nobel-Prize Dept.:
1)  In yesterday’s #BigMathOff competition Edmund Harriss linked to an older story I didn’t recall hearing, but found fascinating… that of Israeli scientist Daniel Shechtman ridiculed/mocked (even losing his job!) for discovering quasicrystals with never-repeating patterns, only to later receive the Nobel Prize for the same finding (after no less than Linus Pauling had said, There is no such thing as quasicrystals, only quasi-scientists”):

The story is a great lesson in the uncertainty of science, and even a cautionary tale of the occasional difficulty in distinguishing science from crackpottery.

As many or most of you know, in recent years, there has been much attention given to possible links between quasicrystals and prime numbers or the Riemann Hypothesis:


And from the Surprises-In-Probability Dept.:
2)  Harriss’s competition in this round of the ‘Math-off’ is Colin Wright whose exposition of some full-deck card-play is wonderfully entertaining, especially for those who like playing with probabilities. It is the sort of example that can be enjoyed by both young people and adults, with a result that will likely seem counterintuitive at first, making it all the more enjoyable. Warning: it can be a bit addictive!

Kudos to Aperiodical's Christian Lawson-Perfect for organizing this 1st Annual ;) Big Internet Math-Off. The above Harriss-Wright square-off, by the way, is match 4 of round 1 (and you still have time to vote for your fave). Much fun yet to come.

Wednesday, July 4, 2018

Coming To America...

Not very July 4th-ish but here's an image I have saved to my computer screen these days, because, well, I just do... as a reminder of the fight ahead….
               "Give me your tired, your poor, your huddled masses, yearning to breathe free...." Indeed.

...But it’s good to also be reminded of the America I grew up with... good to be "flushed with nostalgia and gratitude" on this day, and think back to a time of station wagons with wooden panels. If you’re a teacher (…or an American, or a human, or a dreamer, or a vertebrate ;)) and haven’t already done so, you must read this post from Phương now. That’s an order (...or no fireworks for you)!:
…perhaps with a little music playing in the background:

Tuesday, July 3, 2018

A Favorite Space?

Barnes & Noble always has a number of quirky (relatively-inexpensive) 'popular’-style math books scattered around the store giving introductory samplings of a variety of math topics — usually the books are from Britain, often from publishers I’m not familiar with, and I often don’t find them very appealing, but occasionally do.

One I picked up recently is called “Math Hacks” by Rich Cochrane, which, once you get past the first couple dozen topics (out of 100 total), touches on some slightly more advanced topics than is often the case.  I’m enjoying the range/variety of topics mentioned. On the downside, only 1-2 very pithy pages is devoted to each subject, so if you already know the topic, you won’t gain much (if anything at all), and if you don’t already know the topic, you’re not really given enough to grasp it well, despite the over-hyped pitches made for the volume. So I don’t really recommend it other than as a source to dabble with, that might prick one's further interest in some given area.

At any rate, today I ran across “the illumination problem” in it (#73 of the 100), something I’ve mentioned here in the distant past and had forgotten about as an interesting and non-abstract geometric conundrum — it deals with configuring a room of mirrored (light-reflecting) walls in such a manner that a point light source within the room does NOT fill the entire room with light, but leaves some area(s) in the dark.

When I previously posted about it, it was to mention George Tokarsky’s 26-sided polygonal room solution to the problem in 1995, which led in turn to D. Castro's similar 24-sided solution below... a  space that I could imagine Evelyn Lamb enjoying ;)
via HERE

(If light source is at point "A" then point "B," amazingly, is in the dark.)

There are other solutions (not all polygonal) to the problem, and the Wikipedia take on it is here:

…meanwhile the Numberphile treatment here:

Monday, July 2, 2018

Colliding Vortex Rings

This is cool and captivating on several different levels:

If someone can just compute the mathematics involved and post it in the comments section by noon today, would be very much appreciated!... ;)

Sunday, July 1, 2018

Teach Programming

Sunday reflection:

“My basic idea is that programming is the most powerful medium of developing the sophisticated and rigorous thinking needed for mathematics, for grammar, for physics, for statistics, for all the 'hard' subjects.... In short, I believe more than ever that programming should be a key part of the intellectual development of people growing up.”
Seymour Papert

Wednesday, June 27, 2018

Oh yeah, 8 years ago....

Funny, I don't feel 8 years older....
But I just realized that a few weeks back marked the 8th anniversary of this blog (...geeez, I've never done anything for 8 years!), started at a time when most didn't even foresee America's spiral to authoritarianism coming. In any event, I'll commemorate the anniversary by simply re-running verbatim two of the posts from that very first month (the 2nd one is an old favorite to pose to young people... or, anybody):


1)  Try this exercise, I've copied directly from another book:

"Answer the following questions as fast as you can:

  -2 + 2 = ?

  -4 + 4 = ?

  -8 + 8 = ?

  -16 + 16 = ?

Now quick! Pick a number between 12 and 5. Got it?
The number you picked is 7, isn't it?"

....I succumbed to this piece of 'mindreading' when I read it in Stanislas Dehaene's 1997 "The Number Sense: How the Mind Creates Mathematics." Did you?
He calls this a "demonstration of the automaticity of arithmetic memory" and explains it thusly:
"How did I read your mind? The mere presentation of the numbers 12 and 5 seems enough to trigger an unconscious subtraction 12 - 5 = 7. This effect is probably amplified by the initial addition drill, the reversed order of the numbers 12 and 5, and the ambiguous phrase 'between 12 and 5' that may incite you to compute the distance between the two numbers. All these factors conspire to enhance the automatic activation of 12 - 5 up to a point where the result enters consciousness. And you believed that you were exercising your 'free will' when selecting a digit!"
I'm not sure I find Dehaene's explanation completely satisfactory... but, I can't argue with the effect, which I did fall for.

...and then this, from polymath Cliff Pickover:

2)  The 3 jungle spiders.... a riddle lifted directly from chapter 9 of Clifford Pickover's "Wonders of Numbers":

"Dr. Googol was in a Peruvian rain forest, 15 miles south of the beautiful Lake Titicaca, when he dreamed up this tortuous brain boggler. A month later, while in Virginia, Dr. Googol gave this puzzle to all CIA employees to help them improve their analytical skills.

" Three spiders named Mr. Eight, Mr. Nine, and Mr. Ten are crawling on a Peruvian jungle floor. One spider has 8 legs; one spider has 9 legs; one spider has 10 legs. All of them are usually quite happy and enjoy the diversity of animals with whom they share the jungle. Today, however, the hot weather is giving them bad tempers.
"  'I think it is interesting,' says Mr. Ten, 'that none of us have the same number of legs that our names would suggest.'
"  'Who the heck cares?' replies the spider with 9 legs.

"How many legs does Mr. Nine have? Amazingly, it is possible to determine the answer, despite the little information given."

answer below:
Mr Nine has 10 legs... (Mr. Ten CAN'T have 10 legs, same as his name, and can't have 9, since the spider with 9 replies to him; therefore he must have 8 legs... from there you can likely solve the rest.)

Monday, June 25, 2018

Let the Betting Begin...

While patiently waiting for Donald Trump impeachment hearings (and maybe trial for treason) to begin, those wonderful folks at The Aperiodical have offered up some summer fun in the form of a 16-person, one-on-one, single-elimination, no-holds-barred, fight-to-the-proverbial-finish contest starting July 1st! — “The Big Internet Math-Off":
The brackets:

With no help whatsoever from Tim Chartier I’ve already filled in my bracket and have Evelyn Lamb trouncing Matt Parker in the final because, HEY, we can’t let some British dude who says “maths” and doesn’t even know how to spell “honor” win this thing! That would be unmitigated Bollocks!! [...Oooops, my bad! I've been corrected -- turns out Matt is an Aussie living in UK... same poor spelling, but if he's friendly with cockatoos then he's OK by me.]
[Unfortunately for Evelyn, my 39-year history with NCAA March Madness bracketology may indicate she’s now doomed, but ohh well. ...and it ought not go unnoticed that, by my quick reckoning, the creators have loaded/skewed this competition with ~10 British entrants out of the 16 total! -- so just like we did 230+ years ago, underdog America, we must whip their paltry English cardioid butts yet again!]

...if you're on Twitter you can follow all the festivities with the hashtag #bigmathoff.

Sunday, June 24, 2018

new appreciation....

Mathematician Richard Schwartz on his changed view of things:
" thing I appreciate more now is that the state of human knowledge is full of holes. When you’re young you have the impression that almost everything is known, but now I have this feeling that almost everything is unknown about mathematics. There are these very thin channels that people have gone along, like ants following each other along a trail. You find these long thin trails of things, and most things are undeveloped. I have more of a sense of the openness of it."

Friday, June 22, 2018

45%... recent Gallup Poll approval rating for Donald Trump!

"Think about how stupid the average person is, and then realize that half of 'em are stupider than that."  ~ George Carlin

10 years ago today George Carlin died, thankfully never having to witness America elect the Donald.... 

Sunday, June 17, 2018

Model-T Algorithms...

Sunday reflection:

“Algorithms don’t make things fair, if you just blithely, blindly apply them. They don’t make things fair. They automate the status quo…
“Science is our only hope and I feel like we’ve created a field we call ‘data science,’ but there’s no science in it. We have not demanded evidence. The sort of hallmark of science is that it needs to be tested and testable, and we need to see the evidence, and we need to test every assumption. And we just haven’t done any of that. We’ve just been driving blind in our Model-T algorithms.”

— Cathy O’Neil on TED Radio Hour

Tuesday, June 12, 2018

On a Jim Holt Kick... and RFI

I’m on a bit of a Jim Holt kick these days, so first a RFI:
I’d enjoy interviewing Jim for my interview series but haven’t found any email contact for him… if anyone has such that they can pass along, email me privately:, (or if I follow you on Twitter you could probably DM me there, @sheckyr ).
[p.s... hope folks have read my latest interview with economist Gary Smith a couple days ago.]
In another bit of serendipity, having recently written a post about humor and jokes, I just discovered that Holt previously wrote a small volume ( "Stop Me If You've Heard This”) on that very subject as well.

Meanwhile, I've now finished his volume, "When Einstein Walked with Gödel," and it is easily one of my favorite reads of the last several years; 350 richly, diverse, engaging pages on a fabulous variety of science/philosophy/history/math-related topics.
I’ll pass along one interesting tidbit he only mentions briefly that I was unfamiliar with. It’s called the “Bogdanov affair,” circa 2002, drawing my interest because it’s oft-referred to as a “reverse Sokal hoax” (a hoax against physics, opposite physicist Alan Sokal’s famous hoax against post-modernist analysis). It involves two French twin brothers and their buzzword-laden “work” in theoretical physics.
Here’s the Wikipedia page on it:

It’s a bit involved and so far as I can tell the degree of the brothers’ sincerity/legitimacy has never been completely settled, even lo these many years later (a real hoax or not?), but I trust highly-reputable John Baez’s take on it here:
Especially interesting to read about in light of all the criticism/skepticism of theoretical physics prevalent these days.

And here’s an old BloggingheadsTV end-segment from January 2008 with Holt and John Horgan taking a "quick foray into mathematics." It starts off with Jim espousing the non-Platonist view that mathematics is invented:
[ small error, when Jim references "Thomas Langlands" of Princeton, I believe he means Robert Langlands of Yale.]

More and more people seem to be espousing the math-is-invented-not-discovered, viewpoint in recent years (though my own guess is that the Platonist view still prevails overall), and I was a little surprised at the confidence with which Holt asserts the non-Platonist stand. Martin Gardner's simple rebuke to the non-Platonists was along the lines of saying that, well before Man existed (let alone any formal study of mathematics), if two dinosaurs were in a field and two more joined them, then there were now four dinosaurs in the field -- i.e., quantity or number, as well as addition, exist whether there is a human mind around to employ such labels or not (mathematics exists apart from human appreciation/use of it). I think he also cited the example of predicting Halley's comet's appearance decades in advance (or for that matter planetary movements) as a case of math being inherent (and discoverable) in physical laws, whether or not the "laws" are discovered or known.

I'm skeptical of binary, either-or questions to begin with, so the easy solution seems to me to just say some parts of math are discovered and other parts are created; these days mathematics is a very large, wide-ranging field so I'm surprised more people don't simply opt for such a middle-ground. And I wonder if Holt (or non-Platonists in general) believe that if an alien civilization, a million years more advanced than us, visits us one day, they might find our mathematics completely foreign and unintelligible to them (or would there not be many shared elements?). Further, if math is created, then does that not mean that all of physics (so firmly based upon math) must likewise be created, not discovered, and is that plausible as well? And chemistry is based on physics, and biology based on chemistry etc... i.e. is all of "science" just a human mental construction with no firm coupling to "reality"? If so, then WHAT? Is all of knowledge or existence just some sort of grand tautology? (Holt, at one point, cites Bertrand Russell's query of whether all of math is just tautology.) Or maybe this is all nothing more than semantic quibbling over the fuzzy meanings of "discovered" and "created."