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?

bring

buy

catch

fight

seek

teach

think

(…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:

https://twitter.com/PhDemetri/status/1376692648753397766

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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)

"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:

https://www.scientificamerican.com/article/the-antiscience-movement-is-escalating-going-global-and-killing-thousands/

Still More Statistical Pitfalls

 Timely post from Kaiser Fung on vaccinations and Simpson's Paradox:

https://junkcharts.typepad.com/numbersruleyourworld/2021/03/note-on-a-simpsons-paradox-in-real-world-vaccine-effectiveness-studies.html

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:

https://statsepi.substack.com/p/how-bad-statistical-practices-drive

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

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:

https://statmodeling.stat.columbia.edu/2021/03/18/huge-partisan-differences-in-who-wants-to-get-vaccinated/

  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.

Of Beads, Rectangles, and Bracelets

 A little geometry, a little algebra, some permutations, and a little problem from Datagenetics:

https://datagenetics.com/blog/march82021/index.html

Jason Rosenhouse

Recently bought Jason Rosenhouse’s “Games For Your Mind The History and Future of Logic Puzzles,” his 2020 volume on, well, the history and future of logic puzzles. Just scanning through it’s pages I can tell it is a delightful compendium of puzzle and logic topics, certainly including many familiar classics, but also with material I think most readers will find new to them. On top of that I have always enjoyed Rosenhouse’s writing (indeed I’m surprised he isn’t a bit better known in the popular and recreational math writing arena). His “The Monty Hall Problem” is a fabulous treatment of that popular puzzle, and he did a similarly wonderful full volume on Sudoku, as well as co-editing other volumes on recreational math, and editing a great tribute to Raymond Smullyan.

https://tinyurl.com/yz9cs9go

Many who are familiar with Rosenhouse first became aware of him though through his former “Evolution Blog” at the old Science Blogs site. That blog title became a bit of a misnomer after he ventured into all manner of topics, having started off focusing on the evolutionist/creationist wars. His writing was always crisp and incisive whether covering math, puzzles, chess, education, politics, or culture, in addition to the original evolution theme (which he also authored a book about). Even when I disagreed with his viewpoint I always admired his logical step-by-step commentary and argumentation, and highly recommend, if you're not already familiar with him, get so, with this current Princeton University Press volume likely a great place to start.

Put On Your Thinking Caps...

 Futility Closet recently offered this probability conundrum that may give your neurons some exercise ;)

https://www.futilitycloset.com/2021/03/11/being-there-3/

Math vs. Psychology....

 OK, today just a little humor... a joke I recently ran across in an old Reader's Digest:

“See that kid?” a barber says to his customer during a haircut, pointing to a 12-year-old standing outside the barbershop. “He is the dumbest kid in the world. Watch. I’ll prove it to you.” The barber takes out a one-dollar bill and a five-dollar bill, then calls the boy inside. He holds out both bills and asks, “Which one do you want?”

The kid takes the one-dollar bill and leaves the shop.

“See?” the barber says, laughing. “The dumbest kid in the world.”

The customer leaves the barbershop and spots the boy coming out of an ice cream store. He says, “If you don’t mind my asking, son, why didn’t you take the five-dollar bill?”

The boy takes a lick of his ice cream cone and says, “Because the day I choose the five, the game is over.”

Math Without What!

Haven't been doing much reading in last year, but am currently enjoying Milo Beckman's fun, jaunty volume "Math Without Numbers" which, if you can believe it, covers several topics in the foundations of higher and abstract mathematics... without any mention of numbers, equations, formulas, and the like!  Difficult to think of another volume quite like it. Highly recommended for those wanting a simple introduction to some advanced math topics:

https://www.amazon.com/Math-Without-Numbers-Milo-Beckman/dp/1524745545

... a review of it here, from The Aperiodical:

https://aperiodical.com/2021/01/review-math-without-numbers-by-milo-beckman/

...and Milo has his own YouTube channel here:

https://www.youtube.com/channel/UCURP6q1VjGEFfy7GPP3Tm0w

Goldbach... if unprovable, then true!

 IF Goldbach's Conjecture is UNprovable, well then, it must be true! (via Peter Lynch):

https://thatsmaths.com/2021/03/04/goldbachs-conjecture-if-its-unprovable-it-must-be-true/

"... if it were false, there would be some finite even number that is not the sum of two primes. A finite search could confirm this, making the conjecture 'provably false'! In other words, falsehood of the conjecture is incompatible with unprovability. This contradiction forces us to an ineluctable conclusion: if Goldbach’s Conjecture is unprovable, it must be true!"