Saturday, October 9, 2021

A Grim Paradox

 You've likely heard of Thomson's Lamp paradox (or you can look it up), but have you heard of the Grim Reaper paradox:

Friday, October 8, 2021

Drugs and People, Duhhh

 People's genetics and metabolism differ... this is such an obvious truism that it's kind of a shame articles like this even need to be written... but folks prefer thinking along binary, all-or-nothing, black-and-white lines, instead of in terms of continuities and nuances, so yes it needs be said aloud:

Saturday, October 2, 2021

Tuesday, September 28, 2021

Monday, September 27, 2021


 Almost every year I find some excuse to run one of my favorite quotes ever from a math volume, a bit of linguistics and recursive philosophy from provocateur David Berlinski in "The King of Infinite Space" (about Euclid). Berlinski is nothing if not an artiste of wordplay, and recently finishing "Shape" by Jordan Ellenberg's (no slouch at wordsmithing himself; though a bit more fun), simply reminded me of it once again:

"Like any other mathematician, Euclid took a good deal for granted that he never noticed.  In order to say anything at all, we must suppose the world stable enough so that some things stay the same, even as other things change. This idea of general stability is self-referential. In order to express what it says, one must assume what it means.

"Euclid expressed himself in Greek; I am writing in English. Neither Euclid's Greek nor my English says of itself that it is Greek or English. It is hardly helpful to be told that a book is written in English if one must also be told that written in English is written in English. Whatever the language, its identification is a part of the background. This particular background must necessarily remain in the back, any effort to move it forward leading to an infinite regress, assurances requiring assurances in turn.
"These examples suggest what is at work in any attempt to describe once and for all the beliefs 'on which all men base their proofs.' It suggests something about the ever-receding landscape of demonstration and so ratifies the fact that even the most impeccable of proofs is an artifact."

Saturday, September 25, 2021

Scientific American, Scott Aaronson, and Warning Against Indifference

 Scott Aaronson wonders aloud if Scientific American was Sokal’d in this posting:

…but perhaps my favorite part is this bit he adds in the comment section:

“Yeah, I’ve been bummed about it all day, and there’s a part of me that’s genuinely surprised how all my friends are just ignoring it and going about their day. It’s like, do they not understand what Scientific American used to be, in its 50s/60s/70s heyday? Can they not see that for Scientific American to print such self-parodying dreck is as shocking, in its way, as for the January 6 insurrectionists to gallavant all over the US Capitol waving Confederate flags? Or was no one else shocked by that either? I mean, if you support either ravaging of our culture’s main symbols of democracy and reason, then by all means say so, celebrate, cheer in the streets about this, but for God or Bertrand Russell’s sake don’t be indifferent about it! 🙂

Friday, September 24, 2021

Cantor's Attic

 Just can't get enough of Georg Cantor?...want to explore his work/ideas further?... Is that what's buggin' you! In a tweet yesterday, Richard Elwes pointed out this site doing just that:

Thursday, September 23, 2021

Getting Into "Shape"....

 Recently finished Jordan Ellenberg’s latest, “Shape” (plenty of reviews online), a great followup to his fantastic “How Not To Be Wrong” volume. It’s 400+ pages of “the hidden geometry” of life, but this is not your daddy’s (or necessarily even your own) geometry, rather a bit more modern and diverse take than Euclid ever provided. Anyway, great read, though possibly a tad more pedagogical than his earlier best-selling work, if only because much of the subject matter is drier or just more pedagogical in nature (Ellenberg’s writing style always enlivens it though).

With all that said, at the end of the volume Jordan lists many of the topics he wanted or considered including in the book, but in the end left out… another great, varied list of subjects (that sound to me even more interesting than the topics he did include!), so hopefully, maybe, perhaps, Jordan is now hard-at-work on a third volume!?

Sunday, September 19, 2021

A Few Health Numbers (by the book... or, buy the book)

 Recently finished, and much enjoyed, Dr. Robert Lustig’s latest volume on nutrition/health/food, “Metabolical,” a fairly searing take on the American diet and how it got to be this way. Toward the end of the volume comes this passage hinting at the insidious countervailing pressures at work:

Which addictive substance is the cheapest to produce and procure, yet the most expensive burden to society? Nicotine used to be the cheapest. At its worst, lung cancer claimed 443,000 people a year and cost healthcare $14 billion annually. But it also made the U.S. government lots of money, because the median smoker died at age sixty-four, before they started collecting Social Security and Medicare….

[he goes on to dispatch with alcohol in a similar vein, before coming to his conclusion that “By far and away, the most expensive burden to society is sugar,” which he has spent much of the book detailing].

Not terribly mathematical (though plenty of facts and figures), but a good, if scathing, read on processed food in America.

Thursday, September 2, 2021

Wednesday, September 1, 2021

Just For Fun & Amazement (illusions)

This is old (…well around 5 years old), but Cliff Pickover retweeted one of my favorite static illusions yesterday, the Scintillating Grid Illusion” by gamer Will Kerslake. The grid contains 12 black dots at intersections but you can’t see them all at the same time! Be befuddled:

Here’s one piece on it:

...shortly after preparing the above post yesterday, I then came across this Tweet introducing me to the Ames Window motion illusion, which was possibly new to me (and definitely worth checking out if you're unfamiliar with it):

And here is Veritasium's great take on it:

Sunday, August 29, 2021

Analysis With Norman J. Wildberger

 Yesterday’s post with Joel David Hamkins led me in turn to Daniel Rubin’s hour-long similar interview a month ago with math iconoclast Norman J. Wildberger:

Saturday, August 28, 2021

Wednesday, August 25, 2021

Sunday, August 22, 2021

Wednesday, August 18, 2021

Friday, August 13, 2021

Saturday, August 7, 2021

"Total Gibberish"

 H/T to Cliff Pickover for recently linking to this 7-yr.-old piece on gibberish in science (makes you wonder a tad about what's sitting out there right now in the journal stacks?):

Wednesday, August 4, 2021

Math Illiteracy Is Long-running

 How long (if ever) before education tackles the math innumeracy of the populace... and what will be the eventual consequences of not doing so (latest from Keith Devlin)?

Monday, August 2, 2021

Whoa, 4 Colors Not So Sufficient...

 Things never seem to be as simple as they appear... "Computational Complexity" notes that, subtly, 4 colors are not so sufficient in the Four Color Map Theorem as most assume...:

Sunday, August 1, 2021

Veritasium Does the Collatz Conjecture

 After the usual routine introduction to the Collatz Conjecture, Veritasium plunges on with this wonderful recent exploration of it, enjoyable by young and old:

Wednesday, July 28, 2021

Midweek ASMR

 Time to slip in another ASMR video. "Angelo" has probably become my favorite within the shoeshine genre, so yet another from him:

Monday, July 26, 2021

Chess Thoughts....

 A lot of folks interested in mathematics are also interested in chess, so without further adieu, a post with some interesting chess thoughts:

Sunday, July 25, 2021

Waxing Eloquent on Weinberg...

 There have been, and will be, many tributes to Steven Weinberg this week; I highly recommend this very personal one from Scott Aaronson:

Wednesday, July 21, 2021

Saturday, July 17, 2021

Models and Monte Carlo

 This weekend you can either breeze your way through Tolstoy's "War and Peace" or slowly work your way through the latest from Brian Hayes ;))

Thursday, July 15, 2021

Interesting Math....

 Starting with this equality (from a Cliff Pickover tweet):

           \displaystyle  \sqrt{2\frac{2}{3}} = 2\sqrt{\frac{2}{3}}

Futility Closet points out this further elaboration:

Tuesday, July 13, 2021

Stephen Wolfram with Sean Carroll

 Haven't had a chance to view it myself yet, but Sean Carroll's latest guest on his Mindscape podcast is Stephen Wolfram, so ought be interesting (over to 2.5 hrs.):

Friday, July 9, 2021


 ICYMI, here was July's very varied Carnival of Math (the 195th such compendium), full of interesting reads for your weekend:

Sunday, July 4, 2021

Science Musings Fit For a Sunday Sermon

 Joselle (...and David Deutsch), at "Mathematics Rising," waxes eloquently about knowledge, mathematics, and the universe... nice read/contemplation for a Sunday morning:

Saturday, July 3, 2021

Vitally Linked, Music and Math

 Have always found the linkage between math and music interesting, especially since encountering so many individuals over time who were music majors with math minors, or, vice-versa. Anyway, noticed newish book during trip to bookstore this morning that looked interesting (but haven't read, so just supposing), "Music, Math, and Mind: the physics and neuroscience of music" by David Sulzer:

Friday, July 2, 2021


 A little end-of-week humor... I don't see a lot of new math humor these days that really makes me chuckle any more, but this bumper sticker recently seen on Twitter (H/T Simon Pampena) did (...though perhaps it's quite old and I've just missed it or forgotten it):

Thursday, July 1, 2021


 I've talked of self-describing sentences or "autograms" here before (I love 'em, and their Gödelian flavor!), and recently Futility Closet posted this fine example (with Lee Sallows involved as he often is):

Monday, June 21, 2021

Solving Serial Murders....

 Perhaps for the true-crime podcast addicts out there a new podcast, with at least some math involvement, about a law enforcement algorithm for tracking down serial murderers; not necessarily for the sensitive or faint-hearted, but if crime investigation is one of your things, this is (I think) the first of a 2-part episode:

Sunday, June 20, 2021

Can Research Integrity Ever Prevail in a Marketplace...?

 "Research integrity"... perhaps once assumed, is now threatened and very much in question given multiple pressures that abound:

(H/T to Ivan Oransky)

Sunday, June 13, 2021

More Jordan....

 In case you were wanting almost 3 more delicious hours of Jordan Ellenberg hitting on a range of topics (in conversation with Lex Fridman), you got it:

Thursday, June 10, 2021

Quasicrystals In Atomic Debris

 "Mathematically perfect quasicrystals—a 'forbidden' kind of matter whose existence had long been contested" were born with the 1945 nuclear bomb test in New Mexico:

Friday, June 4, 2021

Friday ASMR

OK, for anyone wanting a li'l ASMR to begin the weekend, here's 3+ hours of finger-tapping for your delectation:

Tuesday, June 1, 2021

Collatz Conjecture... perhaps a new approach

 For any in the mood for some heavier reading here's "An Automated Approach To the Collatz Conjecture" newly out from Scott Aaronson

Thursday, May 27, 2021

Must Human Civilization Have Numbers...

 Lengthy, interesting, thought-provoking new piece from Stephen Wolfram asking 'if numbers are inevitable?' (and concluding that at least for now, for humans, they are):

Monday, May 10, 2021

Emily Riehl With Sean Carroll

 Sean Carroll with Emily Riehl in his latest Mindscape podcast, on topology and category theory (~75 mins.):

Saturday, May 8, 2021

ASMR Saturday

 Will head into weekend with another Angelo shoeshine ASMR video:


Friday, May 7, 2021

Gelman Bemoaning Postmodernism

 For today's entertainment, Andrew Gelman rants about postmodernism, Elon Musk, and spending gov't. money:

Postmodernism” in academia is the approach of saying nonsense using a bunch of technical-sounding jargon. At least, I think that’s what postmodernism is . . ."  -- A. Gelman


Thursday, May 6, 2021

"Progress" In Mathematics...

 The always interesting, if not indeed provocative, Michael Harris muses critically (in the first of what he says will be “a series of texts”) on “progress” and “the mechanization of mathematics” (he even manages to get Godwin’s Law in):

"...the notion of 'progress' in its current usage is so thoroughly entwined with technological determinism, European colonialism, genocide, and environmental devastation, that it is a struggle to find an interpretation of the word, applicable to mathematics, whose connotations are unequivocally positive."

                                                                        -- Michael Harris

Wednesday, May 5, 2021

Of Math and Twitter

 I almost find it hard to imagine that there's anyone engaged in math who isn't by now on Twitter, but if in fact you are one such person and debating over taking the plunge, then Ben Orlin has written a post just for you:

(...seriously, the incredible array of math resources, people, and inspiration accessible through Twitter ought not be missed... though, granted, venture into other corners of Twitter at your own peril ;))

Friday, April 30, 2021

Recommending a Podcast Sight Unseen... or Heard

 I haven't even had time to listen to this yet (sometime this weekend though), but Ben Orlin recommends it (ohh, and he happens to be on it), and that's good enough for me:

Tuesday, April 27, 2021

Monday, April 26, 2021

Math, Chalk, and Art

 Quirky little piece from Scientific American on mathematics and chalkboards (as art):

"Even when it is inscrutable, math is beautiful....

As Wynne began to travel to different universities to meet more mathematicians, she discovered how diverse their chalkboard styles are. 'Some were very clean and neat and very carefully considered,' she recalls. 'And some were just this explosion and chaos. The chalkboards almost felt like portraits of the person and depended on the personality of the mathematician'.


Thursday, April 15, 2021

Tuesday, April 13, 2021

Tuesday ASMR

 Haven't posted an ASMR video for awhile, so without further adieu...:

Thursday, April 8, 2021


 You are hopefully familiar with knight/knave logic problems (made famous by Raymond Smullyan) — knights are truthtellers who always tell the truth, while knaves always lie. The following is a nice, interesting one (in which Leon & Larry are liars, and Tim a truthteller), originally from Smullyan, but quoted in Jason Rosenhouse’s current volume “Games For Your Mind”:

You meet triplets named Leon, Larry, and Tim. They are visibly indistinguishable, but Leon and Larry are knaves, while Tim is a knight… What one question  could you direct to one of the brothers to determine whether or not he is Larry?

answer below:


















Suppose you simply randomly ask one of the brothers, “Are you Larry?” This does no good. Both Tim and Larry will say “no,” and Leon will say “yes.” A yes answer would identify Leon, but a no answer could come from either Tim or Larry, and fails to ID which is which.

If instead we ask, “Are you Tim?” then everyone will simply respond “yes” and we gain nothing. 

The intriguing part is that if we ask, “Are you Leon?” the responder will give away whether he is or is not Larry. Larry will lie and answer “yes.” Tim will tell the truth and say “no,” and Leon will lie, also saying “no.” We know anyone answering “no” is not Larry, and anyone replying “yes” must be Larry.

Tuesday, April 6, 2021

Puzzle This!


Interesting Twitter thread (h/t to Keith Devlin for pointing to it) on "decreasing" and "increasing" numbers:

Sunday, April 4, 2021

For the More Advanced and Insightful Readers of This Blog....

 Apologies for being a few days late in posting this (H/T to Colm Mulcahy for pointing to it):

If you find this video too difficult to wrap your brain around you may want to wait and bone up a bit by first reading a basic topology text, or perhaps alternatively, Jordan Ellenberg's latest upcoming volume "Shape."

Tuesday, March 30, 2021

Put On Your Thinking Caps

Just fun stuff this morning, starting with two puzzles adapted from a recent edition of AARP Magazine (which somehow found its way into my hands ;)

1)  Every six-digit integer which is made up of repeated pairs of three-digit numbers, like 573,573, 831,831, or 107,107, is evenly divisible by the same four-digit integer. What is that integer?

2)  and a less mathy, word puzzle:

Look over the following 7 verbs. Taken together they share a specific, unusual trait. What is it?








(…I’m usually fairly good with word puzzles, but this one stumped me)

ANSWERS at bottom of post.

…and lastly, from Twitter this recent post:


























ANSWERS:  1)  1001

            2)  the past tense of all these verbs rhyme, even though none of the present tenses do

                       (brought, bought, caught, fought, sought, taught, thought)

Monday, March 29, 2021

"Lethal Force"... The Escalation of Antiscience

 Antiscience has emerged as a dominant and highly lethal force, and one that threatens global security, as much as do terrorism and nuclear proliferation….

The full antiscience agenda of the Republican Party has now gone beyond our national borders. In the summer of 2020, the language of the antiscience political right in America was front and center at antimask and antivaccine rallies in Berlin, London and Paris.”

Not strictly math at all, but Scientific American piece on the “anti-science” movement (largely of the Republican Party) as the politically, societally, security threat that it is:

Wednesday, March 24, 2021

Statistical Practices — the Bad Driving Out the Good

 H/T to Mike Lawler for pointing out this essay (and “belly-aching”) from Darren Dahly on common statistical (mal)practice, particularly in medicine:

Too many great sentences in this (about the author's slog against research "bullshit") I’d love to quote, but will simply give you the opening lines:

I am interested in research integrity and reproducibility. I believe that a lack of statistical expertise throughout the sciences is a substantial driver of problems in these areas (poor data practices being another). I feel especially strongly about this thesis as it applies to medical research.”    — Darren Dahly

Friday, March 19, 2021

The Partisanship of Vaccine Reluctance


Andrew Gelman explores a bit of the possible sharp dichotomy (as well as confounding variables) in Republican versus Democrat reluctance to receive the Covid vaccine:

  The prospect of Republicans dying off at a far greater rate than Democrats (if such a dichotomy exists) due to their own skepticism/negligence, may cause some to recollect Melania's sentiments... but the prospect of Republican intransigence possibly gumming up the medical system for everyone else (and prolonging the pandemic), by their lack of involvement is concerning.