This is above my pay grade ;) but some of you may likely find this Gil Kalai piece stimulating:
Thursday, April 22, 2021
Thursday, April 15, 2021
Tuesday, April 13, 2021
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?”
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
Sunday, April 4, 2021
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."
Friday, April 2, 2021
Tuesday, March 30, 2021
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
“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:
Friday, March 26, 2021
Timely post from Kaiser Fung on vaccinations and Simpson's Paradox:
Wednesday, March 24, 2021
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
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.
Wednesday, March 17, 2021
A little geometry, a little algebra, some permutations, and a little problem from Datagenetics:
Sunday, March 14, 2021
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.
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.
Friday, March 12, 2021
Futility Closet recently offered this probability conundrum that may give your neurons some exercise ;)
Tuesday, March 9, 2021
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.”
Sunday, March 7, 2021
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:
... a review of it here, from The Aperiodical:
...and Milo has his own YouTube channel here:
Thursday, March 4, 2021
IF Goldbach's Conjecture is UNprovable, well then, it must be true! (via Peter Lynch):
"... 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!"
Saturday, February 27, 2021
Tuesday, February 23, 2021
A new math podcast ("On the Mathematical Frontline") from "plus Magazine":
Monday, February 22, 2021
“…it’s kind of embarrassing that statisticians are always getting on everybody else’s case for not using random sampling, controlled experimentation, and reliable and valid measurements—but then we don’t use these tools in our own decision making.” -- Andrew Gelman
...from this post on the use of statistics in physics, medicine, social science… and, statistics:
Friday, February 19, 2021
Tuesday, February 16, 2021
Friday, February 12, 2021
I've said before that it wouldn't surprise me if covid case rates spiked upward after a couple of months of vaccinations because of the increased reckless behavior exhibited by large numbers of people, among other reasons. And in this piece Kaiser Fung covers several of the reasons why people can (and will) still get infected by covid-19 following vaccination:
It may take many months for the full benefit of vaccination programs to begin to appear (and that assumes the efficacy rate is anywhere near what's been touted). People need to remain vigilant and patient... and not be swayed by denialists' focus on every case of infection following vaccination.
Thursday, February 11, 2021
Just a li'l obvious numerology for today.... Have QAnon followers yet realized that "Nostradamus," "impeachment," "Donald Trump," "Dead in March," "Ides of March," and even "Nancy Pelosi" ALL contain 11 letters (...no mere coincidence). "Eleven" itself has 6 letters and is the atomic number of "sodium," also with 6 letters... and when 6 is multiplied by 11 (a prime number by the way, IF you know what I mean!) it yields 66, a precursor clearly to 666, sign of the beast! So beware March 15, the very day, incredibly, that H.P. Lovecraft (yet also 11 letters) passed from this planet, and when the Orange Julius may too thus face resurrection! Tremble if you must, and certainly stay tuned... the numbers can't lie (psssst... "Eric Swalwell" extends to 12 letters, OMG!), nor shall the lamb and the lion ever lie down together in this century (and despite misguided wishes, the answer my friend AIN'T blowin' in the friggin' wind). QAnon speaketh, for all who will but listen reverently and take appropriate action. Those who comprehend need no more explanation, and those who do not comprehend... well, misquoth the Raven, never shall. Let the liberal sheeple succumb to their hoax vaccines, while QAnoners resist all such stochastic mind-control attempts and take back control ("Don't tread on ye"). Covid, schmovid!!
In the meantime I leave you with this bit of carefully-coded message, easily translatable by all those in-the-know:
Where the Hell, indeed....
Tuesday, February 9, 2021
Friday, February 5, 2021
As if there aren't enough things to be bugged about in the world these days, here's another thing I've been grousing about for awhile (does it bug anyone else?):
I drink a fair amount of coffee, and enjoy trying out lots of cheap brands always in the (futile) hope of finding a cheapie I really, really like. Anyways, here’s the part that bugs me… almost always the container recommends using “1 to 2 tbsp. of coffee per 6 oz. of water.” First of all, “1 to 2” tbsp. is a big, 100% difference… even granting variability among consumers can’t they come up with a more precise statement (and then simply say add more or less according to personal taste). But the bigger problem is where the heck does 6 oz. come from??? A standard “cup” is 8 fluid oz. so why isn’t THAT the standard for directions? Anybody have a clue? Moreover, the question is (at least in America) does anyone even drink a “cup” of coffee anymore… most coffee mugs hold more than a standard “cup”…. checking out some of my mugs at home I found they generally held between 10 and 12 oz. of liquid, so hey, instruction-writers come on catch up to reality! (...or maybe I've just had a wee bit toooo much caffeine this morning).
Carry on… (i.e., go back to being concerned about covid, climate change, creeping fascism, and Redditors gaming Wall Street).
Tuesday, February 2, 2021
One statistician's "top 10 fallacies and paradoxes in statistics" (read the entire thread, and/or look up further info on Wikipedia):
....and for your bit of humor to start the day (or, whenever you read this):
Monday, February 1, 2021
From Gil Kalai, a nice quickie synopsis of the "Polymath Project" from beginnings with Tim Gowers to this year, here:
Sunday, January 31, 2021
Are you a math teacher? Nalini Joshi pointed out today on Twitter that there’s an active math educators stack exchange site on the Web:
Looks interesting, useful, collaborative.
...also from today, for math teachers, this interview/podcast with well-established British educator Jo Morgan on teaching math(s) online:
Thursday, January 28, 2021
Almost 20 years ago I knew a couple of math-wizard brothers who got into day-trading and were hugely successful at it — rare because 95+% of those who attempt it lose their shirts. But rarer still because this dynamic duo had no real prior experience in business, Wall Street, or the stock market whatsoever. What they DID have experience in (and lots of it) was gaming — and what they saw when they took a gander at the stock market one day was just one big mathematical game with little necessary connection to business fundamentals.
I’ve long since been out of contact with them (though I’m sure they’re still successful), but fast forward to today and if you follow Wall Street news at all you know the biggest story going now is GameStop -- the little guys/investors, gathering on Reddit (starting with some gamers) socking it to the big fellas (hedge funds) — and a fascinating David-and-Goliath story (or hive-mind vs. the elites) it is, sure to play out over several weeks if not months to come… I mean a billion dollars here, a billion dollars there, and pretty quickly you’re talking some real money changing hands… and real frazzled nerves (...seriously, won’t be surprised at all to see some suicides result from all of this).
If you already know the GameStop story you can skip this post, ‘cuz it’ll add nothing new to your knowledge, but if you don’t know what I’m talking about (or only vaguely so) well, go ahead and check out the links to bring yourself a little up-to-date (while the story is continuing):
…and here’s a video (one of MANY on the topic):
…or another, here:
Oh, but if you’re still confused and need a yet simpler version of what-the-heck is happening, well, check out this more basic explanation for clarification (…OK, NOT really):
Anyway, this whole storyline will no doubt be a great Michael Lewis volume one day in the future, or hey, maybe Cathy O’Neil will tackle it in one form or another.
...meanwhile, past performance is no guarantee of future results. ;)
...and if you still want some more, Slate’s Money Podcast with Felix Salmon did their whole show on the Gamestop story this weekend:
Tuesday, January 26, 2021
Wednesday, January 20, 2021
As of 11:49 am. EST we have a new President, and the prior disgraced, FAILED demagogue/traitor and faux “wife” are exiled to Mar-A-Schlago (where the call-girls shall no doubt have quite a $$$ week ahead)... and I feel compelled to yet again post this bit of music:
....may those of us who honestly care about this country, its history and its Constitution, be up to the monumental task ahead.
Tuesday, January 19, 2021
Maybe time for a head massage ASMR video as the week moves on:
...and a recent piece here on ASMR in the age of pandemic:
Sunday, January 17, 2021
Saturday, January 16, 2021
Knuckledraggers in search of love, bumble onward…
Wednesday, January 13, 2021
This is where we’re at as a country:
…and, in turn that piece links to this one:
If you’re on Twitter you can continue to follow the storyline here:
The next two weeks could well be unlike anything America has ever seen before.
Monday, January 11, 2021
It's Monday, and time to watch for needed impeachment proceedings in Wash. DC. -- assuming of course that VP Pence is unable to get half the Cabinet members (who are incompetent at their own jobs), to declare, the obvious, that the President is incapable at his. And so, as we await the next upcoming coup attempt (pssst... anybody keeping tabs on Michael Flynn lately?), perhaps also a moment to revisit this old post from over 3 years ago:
Friday, January 8, 2021
Ummm, quit with all the #%@^&!! optimism… covid is with us to stay for quite awhile… at least that is the precautionary presumption we ought be taking at this point in time.
In America, the surge we’ve experienced since Thanksgiving was totally predictable (indeed, even without a holiday there would have been a surge at about that time (what we have, as some have said, is more of a surge upon a surge), and now we will soon face the far greater surge from Christmas and New Years, when people came together in far larger, more boisterous, and extended gatherings. And then there was that wonderful super-spreader event in Wash. DC on Jan. 6th, involving unhealthy doofuses from all over the country, now returned home (if not in jail) and spreading their newly-acquired infectivity elsewhere, especially perhaps, to other like-minded victims-to-be.
Yet I keep hearing optimism from those reading about, or even getting, vaccinated, that we have turned the corner. Don't hold your breath. The first effect of the vaccinations will almost certainly be to contribute to a further spike in covid infections… at the very time when many (most?) hospitals will be out of beds for treating such… and good luck if you suffer a heart attack, stroke, seizure, gunshot, major injury, etc. during this time period. You can thank Donald Trump for the lack of care you’ll receive while millions of taxpayer $$ are spent on his medical care, safety, and golf outings, to keep this criminal functioning… but, I digress.
People receiving their first (of 2) vaccine inoculations will, after months of restraint and constrictions, feel suddenly safer and freed up to do as they wish… even though they will have been told otherwise… I’ve seen this ‘liberating’ attitude even in very bright people I myself know. Yet, these folks are hardly yet protected against the virus, and even once receiving the 2nd dose it is likely at least 2 more weeks before full protection sets in. In short, many people getting vaccinated WILL still get infected (and spread the infection) well before anything close to full immunity sets in. And a good chance that vaccines in the live population will not match the claimed 90+% effective results of the reported short-term experimental outcomes. Figure, at a minimum,10% of the recipients receiving little if any protection from the vaccines, but nonetheless acting as if they are protected. Also, figure in some folks, getting the vaccine midway or later in the year (in the disreputably slow roll-out of this fiasco) facing a virus that has circled the globe several times with a multitude of mutations, some of which make it more resistant to current vaccines in use.
Then of course you have the 20+% of the American population who will probably resist ever getting the vaccine, and another 15% who will want to wait some months to watch the results in initial users. And by the time you’re done adding such figures up the likelihood of reaching herd immunity (if you can ever even find agreement on a %) in America in the next 18 months seems unrealistic.
There has been huge over-emphasis on, and false confidence in, epidemiology studies from which little can be firmly concluded. Comparison of various country results for firm conclusions is especially illogical given the 1000s of variables uncontrolled for. Uncertainty is the rule of the day. But crunching numbers is what we love to do, and so it shall continue… with the corrections to the crunched numbers coming months later… followed months on by the corrections to the corrections… and then, well, on and on. I've never seen an epidemiology study that tells me anything much say about coffee consumption and never expect to (pretty impossible), nor have I seen one on covid that is terribly enlightening or precise... but admittedly, such studies are better than nothing at all, at least as a starting point.
And then we have all the problems in reporting. Recently the very credible BBC News tweeted:
“Covid: Nurse 'angry' over positive test despite vaccination
To which Jim Chalmers responded:
“Journalists are going to have to learn that if (a) a vaccine is ~95% effective; (b) millions of people are getting the vaccine and (c) covid is widespread, someone getting vaccinated and later getting covid is not even *close* to being a story.”
Yes, so many medical stories or headlines as written are not news at all, and yet will be taken as ‘proof’ of whatever point-of-view one wishes reinforced. And so it goes.
Another big unknown is the long-term variable effects of the virus on different organs both in those infected with quick recoveries or even asymptomatic, and those hospitalized for longer terms. Could take years to understand these health effects.
Maybe my cynicism is ill-founded (though for this year it's generally been on target), and all will go well… I’ll be getting my shots in a couple of months when available for my risk group, and will do so based on the science. Maybe, out of fear or peer-pressure, enough others will eventually also relent to receiving the vaccines to actually attain ‘herd immunity’ before the end of this year… but at this point it’s hard to see how that is likely to happen (70+ million voted for the anti-science dipwad in the White House; far easier to foresee many of them dying of covid, than proceeding to get a vaccine or follow PPE advice). Or, maybe the virus will peter out of its own accord before herd immunity is even attained. But if you’re planning for the future, i.e. the year ahead, it seems best to assume masking, social distancing, hand-washing, high unemployment, huge government deficits, increased mental illness, crime, divorces, and economic/political/social stresses and upheaval of all sorts are bound to stick around for quite awhile.
January 6, 2021, was of course a horrid day in the history of America, though I’m not sure it was really any worse than November 8, 2016, the day deranged Donald was absurdly elected, or January 20, 2017, when, conspiring with neo-fascist-sympathizing mentalities Bannon, Miller, and Gorka, he delivered the wretched Third Reichian inaugural speech, that made the next 4 years clear to anyone with their eyes and ears open, and some knowledge of history.
Luckily this unfit, half-wit regime will soon be out of power, but likely still best for us to remain strapped in for a wild ride through 2021… all the worse of course if civil war, in some form, comes to America, and makes covid among the least of our concerns. House-to-house fighting can ruin your day.
Ohhhh, Happy New Year folks.....
....Lastly (to end on a lighter note), this is how someone on the Web re-did an old Far Side cartoon:
Wednesday, January 6, 2021
Recently saw a web-post of someone listing their 5 favorite just-for-fun math books to read and got me to wondering what I might choose for such a list from my own bookshelf. There have been so many entertaining, fun reads in popular math over the last few decades (including MANY I don’t have on my bookshelf) it’s a near-impossible choice, but in a quick-scan here’s what I came up with in no particular order (in large part these are volumes that can be picked up, turned to any page or section, and land upon some fun or interesting content for the lay-reader; and oddly, with the exception of Ben’s book, these are mostly older offerings):
1. Curious and Interesting Mathematics by David Wells
2. Mathematical Fallacies and Paradoxes by Bryan Bunch
3. Math Charmers by Alfred Posamentier
4. The Colossal Book of Mathematics by Martin Gardner
…and, of course:
5. Math With Bad Drawings by Ben Orlin
Friday, January 1, 2021
To begin the new year an appreciation, from Dan Rockmore, of 3 creative mathematicians no longer with us, Freeman Dyson, John Conway, and Ronald Graham: