Sunday, October 14, 2018

Good Math + Bad Drawings = Great Book!

   At some point awhile back I wrote that Ben Orlin’s mind was either a marvel or a mutation… and I wasn’t sure which. Having finished his marvelous new book I’ll now opt for the former (though a final check with his wife and 23-and-Me might still be in order).
Won’t do a full review of “Math With Bad Drawings” but just make some comments/blurbs about the volume. The first of which is simply, BUY this book, if you enjoy math… or, want to enjoy math. It is suitable for a wide swathe of readers, from young people to college professors — all will gain insights from it, just different ones depending on your age and knowledge. Younger folks can be introduced to a lot of real life math, while adults/teachers/profs can learn new ways/examples with which to approach or think about topics. Its broad possible appeal reminds me a bit of Steve Strogatz's "The Joy of X," another sort of everyman book.
Despite only 5 sections (comprising 24 chapters) the volume touches on an impressive array of topics… with consistent wit, insight, humor, clarity. If you’re not already a Ben Orlin fan you’ll be one by the time you finish these 350 grin-inducing pages. You can figure on 4 chuckles per page (OK, so maybe 7 chuckles on some pages and 1 on others). Ben is simply one of the cleverest writers of math content going… you know this already if you’ve followed his blog for some time.
Amazingly, the book is all NEW material. When he originally announced the volume I assumed it would be a compendium of the best stuff from his blog — something surely to look forward to. Then he said it was all fresh material not from the blog, and I was amazed, even skeptical… and sad to think that so much great prior content would not be included; BUUUUT, it does not disappoint!  I especially like the middle parts on probability and statistics, which represent a large percentage of the book, and which are frequent/vital topics these days, that Ben still manages new ways to present.
Indeed Dr. Orlin seems incapable of writing bad or boring content; you get a feeling of precision, quality, tight control throughout this volume, despite the ever-present quirkiness… and bad (or, deceptively good) drawings. And the publisher, Black Dog & Leventhal, has simply done a fabulous job of presentation here — seriously, one of the best publishing feats in popular math I’ve ever seen, with, shall I say, oddball material. When I interviewed Ben back HERE, he mentioned the publisher did a great job, noting:
…they make gorgeous, colorful books so luscious you want to eat them. Having seen the final product I am 300% sure it was the right call.”
I thought he might be exaggerating… but, no, he wasn’t. The book is luscious (initially I had an urge to slather it with whipped cream ;).
My only beef at all with the volume is that there is no index provided. Dr. Orlin covers a rollicking range of topics, but if you want to look one up to see if it’s included and go directly to it, you’re out of luck (though the table of contents at front gives at least some guidance).
I’d be hardpressed to think of any math volume as original and creative as this one. And the best news may be that Ben is working on a followup volume, introducing calculus… with, of course, deliciously bad drawings. Pass me the derivatives and gravy!

Friday, October 12, 2018

Chi-i-i-i-i-i-ll Friday *

[*  "Chill Friday" is Math-Frolic's meditative musical diversion, heading into each weekend]

[...on Sunday evening, or Monday morning at latest, I'll say a little more about Ben Orlin's new book, "Math With Bad Drawings"]

Wednesday, October 10, 2018

Can I Hear You Now?...

No math today, just a personal anecdote perhaps having relevance to hearing-impaired others. Over the years I’ve had casual conversations with a number of scientists, mathematicians, and personal acquaintances, about hearing loss (afflicting close to 50 million folks as they get older), and what follows is just a personal experience from this sample-size of one:
[hearing loss comes in a multitude of forms, so my experience may not apply to others]

Close to 20 years ago I awoke one morning and quickly realized much of my hearing in one ear was gone! Bingo. (other ear unaffected) After some retrospection I realized my hearing had probably been gradually declining over the prior year and simply passed some threshold that made it readily apparent to me that morning. At any rate, the doctor could figure out no cause for the loss and was quite baffled, even though I logically deduced what I believe with near certainty was the cause (but won't take time to explain here) — every hearing doctor/otolaryngologist I’ve talked to says my explanation isn't valid, which frankly, only makes me distrustful of their understanding of hearing complexities! 

The doctor further said that the kind of hearing loss I had would get gradually worse over time, and that hearing aids would do little good; eventually a cochlear implant would be needed. Also, I should be checked every year to track the progression of the loss. 

Stubborn oaf that I am (when it comes to many medical matters) I’ve never been re-checked in the almost 20 years since, but have watched my hearing very slowly decline further. Hearing aids generally aren’t covered by insurance and are expensive, on the order of $2000 - $3000 or more including all the office visits — there are additional maintenance costs along the way, and they may only be good for 5 years or less, before you need to upgrade. In short, there are a few dozen causes (even more in the Trump era) I’d prefer to see that money go to than to my right ear (and getting by with one good ear is do-able, if limiting).

Over the years I’ve tried a few cheap Personal Sound Amplifier Products (PSAPs) sold over-the-counter, which are quick to emphasize they are NOT “hearing aids” but simply sound amplifiers.  They do what they say they’ll do — amplify sound, all sound (although you can purchase more expensive models that have some filtering and directional capabilities). I’ve been surprised though by how helpful they are — for listening to a TV, lecture, movie, or other point-source of sound; they are less helpful in noisy rooms/gatherings, and the like. So even the cheapest ones, ~$20, when compared to thousands of dollars for hearing aids or tens of thousands of dollars for a cochlear implant, actually have some value. They can however be awkward, inconvenient, and eat through expensive batteries, and be less usable during athletics or other physical activities, so I was never terribly thrilled with them. The quality and variety of these products seems to be significantly improving however, with time and expanding customer-base. 

Recently I had occasion to get one (again for $20) that is small, discreet, usable during many sports, and best-of-all, re-chargeable (no need to buy batteries every month). I’ve been pleasantly surprised at just how well it works — each year I’ve gotten closer to looking into cochlear implants, but at least for the moment, feel I can once again put that off for quite awhile.
I won’t name the cheapie model I got that beat my expectations, but will say there are LOTS of these small behind-the-ear PSAPs available now, ranging up to several hundred dollars (and given how well this $20 model works for me, I’d definitely consider upgrading to a more expensive one later). If you Google “hearing amplifiers” you’ll learn of a slew of them with varying features/styles (and various pros and cons).

One reason I put off for many years buying this particular device is because it not only looked and was cheap (and made in China), but I saw several bad reviews of it on the Web (also saw good reviews, but thought the number of bad reviews was telling). In retrospect, my cynical-self now wonders if any (many?) of those bad reviews are ‘planted’ by the hearing-aid industry who probaby don’t want folks looking at $20-$100 devices that might do some good, when they’re trying to sell you $2000+ devices? (and many of my friends with real hearing aids have significant issues with them, even after spending that amount of money). Of course you have to be somewhat leery of all reviews on the internet anyway! As the population continues to age, hearing aids are definitely a boom product with huge profits to be made, and a lot of competitors vying for a slice of those profits.

If you’ve been putting off dealing with hearing loss (as most do) for the usual sorts of reasons, these more-reasonably priced devices may be worth exploring (while also acknowledging that a do-it-yourself approach is not advisable in many cases). I've had good luck my entire adult life treating myself for typical health ailments, while also sensing when professional medical intervention may be called for. Your mileage may vary. ;) And if one day self-care or treatment costs me dearly, well, que sera sera... (I'm stoic about such matters).
Anyway, as someone who more-often-than-not is disappointed in products I purchase, this has been an instance of low expectations being happily well-exceeded... just a personal anecdote, for any who may get some encouragement from it.

Sunday, October 7, 2018

Insure THIS!

I found Chapter 14 (on “Weird Insurance”) of Ben Orlin’s delightful volume “Math With Bad Drawings” to be one of the most fun (of so many). It falls within an overall section on probability, and describes several non-standard insurances I’d never given much thought to. One of them he calls, “Oh No, My Employees All Won the Lottery” Insurance. We’ve all read stories in recent years of employees at a workplace banding together to purchase many tickets in some multi-million dollar lottery and then if one person wins, splitting the proceeds… and, then turning in their job resignations en masse.  As Ben puts it, it’s “like some kind of natural disaster” for the manager/proprietor of such a business. Oy.

Ben goes on to report that “In the 1990s, over a thousand British businesses invested in the National Lottery Contingency Scheme. If your staff won the jackpot, insurance payouts would help to cover recruitment, retraining, revenue losses, and temporary labor.

Ben also points out that the employer could potentially self-insure by simply joining the employee pool and being one of the winner recipients (of course that assumes the employees even let the boss know what they're up to: "hey Boss, we're all joining together to win the lottery and quit this blankety-blank, friggin' workplace!").

…And if that’s not weird enough for you, shortly thereafter comes a section on “Alien-Abduction Insurance” :)  [...where Ben reports that a British company that sold 37,000 such plans hasn’t made a single payout yet (go figure!), and one of the managers involved says, “I’ve never been afraid of parting the feeble-minded from their cash”... so much for British understatement.]
Yeah, insurance is an interesting, creative business (selling you something you hope to never have to use).

Anyway, Ben’s book is a chuckle-a-minute, so if you want to insure against boredom, get it!
[The sections on probability and statistics constitute close to half the book and are especially fantastic, but the entire volume is a joy ride!]

Friday, October 5, 2018

Chi-i-i-i-i-i-ll Friday *

[*  "Chill Friday" is Math-Frolic's meditative musical diversion, heading into each weekend]

Sunday, September 30, 2018

Rambling About Sorites

[Any resemblance between this graphic & the author of this post is purely coincidental]

Suppose a man starts off with100,000 hairs on his head, but on Wednesday he loses 50 hairs. Is he now “bald.” Of course not. But say you don’t see him for a decade and when you next run into him he has only 50 hairs left on his head. Is he now effectively “bald.” Yes. But when, in time, did he “become” bald. This is just one of many ways of stating the ancient “Sorites” paradox, also known as the “heap paradox” or trying to describe how many grains of sand constitute a “heap” of sand.

This all came to my mind a bit ago when Mike Lawler tweeted out, “It is almost impossible to imagine -> 4:40 per mile pace for the entire marathon,” while referencing a newly-set record for a marathon race. Indeed, I do find it impossible to imagine… yet, it was accomplished:

I’m always amazed at how, over time, so many track-and-field records keep falling. There are of course improvements made in nutrition, training, equipment, etc. but still limits to human performance must, in the end, rule — there is never going to be a 5-second 100-yard dash, nor a 1-hour marathon (at least not as humans are currently constituted). Yet finding that ‘boundary’ which can be asymptotically-approached but not crossed seems a difficult task.
Famously, Roger Bannister barely broke the 4-minute barrier for the mile-run in 1954, following a century of efforts by others. In the 60+ years since, the record has gradually dropped to almost 3:43. How much lower can it go (can it break the 3:40 level)? Read the history/progression for this track event here:

Of course the longer the race, the more likely there is room for improvement: easier to imagine shaving a second off a marathon or 10K run (or even a mile) than the 100-yard dash. How about the pole vault, the long jump, the hammer throw, the shot put?... how easy to keep setting records there?
[One philosophical approach to Sorites is to argue that a definite boundary exists, but that it is unknowable. Perhaps a similar take exists for athletic activities: there are human (physical/physiological) limits, but it's unknowable exactly what they are...?]

...In logic, the law of the excluded middle, is both a staple, but also controversial. Claiming that a statement can’t be both true and false, the law seems simple and innocent… except that in normal discourse meaning and language are rarely so binary. Is it true that John is tall, or smart, or fast, or…. Obviously, it depends on how you define “tall…etc.”, but moreover no definition will likely neatly fit precisely all cases (especially since you also enter into issues over measurement, precision, and context). As applied in math and logic the law is somewhat more clean, but still controversial, and Sorites, with its boundary-ambiguity, gives some indication of its ongoing murkiness.
Loosely, this all also reminds me a bit of mathematical “surreal numbers” and “Dedekind cuts” where it is the ‘boundary' or middle ground that again becomes all-important. Like many ancient paradoxes, the Sorites paradox has a lot of depth.
"Fuzzy logic" and other multi-valued logics (which include 3 or more truth-values) are one alternative to the classical logic of two truth-values.
...In the meantime, there are enough variables at work in running a marathon that record-breaking can probably go on for quite awhile!

Friday, September 28, 2018

Chi-i-i-i-i-i-ll Friday.... *

WHAT a week! As Seinfeld's Frank Costanza would say (...or scream):  "Serenity Now... SERENITY NOW!" ;)

[*  "Chill Friday" is Math-Frolic's meditative musical diversion, heading into each weekend]

Sunday, September 23, 2018

Some Bits Crossing My Mind This Month

A miscellany today...:

1)  FIRST, in case you've been living under a rock... on the planet Zorka... in Galaxy 134-18B this last week and don't know, TOMORROW (Monday) Michael Atiyah is giving a 45-min. talk entitled simply, "The Riemann Hypothesis" at the Heidelberg Laureate Forum, claiming "a simple proof using a radically new approach." I have no idea how serious of a "proof" this is (other than Atiyah being a serious mathematician, but still hard to take this at face-value, given how many radically new, simple approaches have already been tried). Either way, math cyberspace should be abuzz tomorrow with commentary following the presentation:

I believe the talk will be live-streamed and recorded at the HLF YouTube channel here:
Also, a couple of the Aperiodical bloggers will be in attendance and reporting on the meeting (I assume they'll check in after the dust settles, but maybe they'll do some live-blogging or tweeting  as well? -- surely there will be some live-tweeting from #HLF18).

==> ADDENDUM 9pm. 9/23... the proof, by contradiction, has now been posted here (h/t to @sigfpe on Twitter):

ADDENDUM II 9/24:  one of the live-tweeted threads from Atiyah's talk (now over) is here:

...needless to say, a lot of skepticism being expressed across the Web by those who understand the math/logic; no doubt there will be a lot more commentary today, and even if negative, much food-for-thought may still emerge from this.

2)  Speaking (loosely) of proofs... logician George Boolos would’ve been 78 this month… had he not died at the relatively young age of 55 in 1996. For any relative newbies, one of my favorite mathy pages on the Web is his famous, delightful single page explaining Gödel’s second incompleteness theorem “in words of one syllable” (worth reading for fun at least once every year!):

It can probably even make a nice introduction to Gödel for younger folks.

3)  Curses, curses, curses to Jordan Ellenberg who has gotten me regularly reading Martin Shkreli’s prison-composed blog, ever since Jordan cited it in a tweet.  I first wrote about it back here:

And in his 9/6/18 entry, after seeking help with some math he was working on, Shkreli ended by writing:

Thank you to all the professors, postdocs and other math professionals who have reached out to help me. It has been great to communicate with you all. Bear with me as I order my thoughts and respond in the limited way I can.”

I don’t know if this is bluster, bluff, or actuality, but if it is for real, I’d sure be curious to hear about what substantive math any “math professionals” have taken up with Martin, if you’d care to share? Ought to be some sort of interesting backstory there.

[...Also, Martin regularly recommends Bio-Pharm stocks to buy or avoid (or short), and even though I don't dabble in bio-pharm stocks myself I'd be curious if anyone else has found his judgments useful/profitable.]

4)  For those interested in cognition, science writer John Horgan has a new Web-accessible volume out on mind-body problems. I’ve enjoyed John’s writing in the past, but also tire a bit of this topic that seems forever shrouded in sound and fury, without much ever resolved. As John says, the book offers my subjective takes on my subjects’ subjective takes on subjectivity.” So I wasn’t expecting too much from his latest, but in fact enjoyed it immensely, partly because of the portraits it paints of specific diverse, fascinating thinkers; their foibles and makeup, in addition to their academic or cerebral selves, while delving into their thoughts on mind/body issues. You can read the whole volume here: 

…or you can download it from the Web for a small price.
There are probably many Douglas Hofstadter fans out there, so as one sample chapter, I recommend Chapter Two which is with Dr. Hofstadter (p.s… one small side-note that I learned here, and didn’t even realize before, is that David Chalmers did his PhD. under Hofstadter):

Speaking of books, Scott Alexander (just a bit behind the times) offers a long review of Nassim Taleb’s “The Black Swan” here (followed by 250+ comments):

5)  For those with the chops to follow it, Steve Strogatz recently passed along this history of the Langlands Program:


6)  And I'll close out with this gem that surfaced on my Twitter feed yesterday:

Friday, September 21, 2018

Chi-i-i-i-i-i-ll Friday…

For some variety, awhile back Evelyn Lamb introduced a feature to her Twitter stream of sharing a musical entry once each week. I kinda like the idea (and hey, there's a lot of math within music!), so will experiment with posting a music video (usually instrumental), without commentary, here at the blog every Friday.
In my case it’s not for variety, nor for your edification, BUT, for my sanity! ;)))  
By Friday, the current White House usually has me a tad bonkers, and a little meditative sojourn seems to be in order heading into the weekend. So we'll call it “Chi-i-i-i-i-i-ll Friday…” -- feel free to skip over these Friday interludes if not to your taste, just me here chillin’ out.
Have a pleasant weekend everyone:

Monday, September 17, 2018

The All-star Linkfest is Here...

Despite a few glitchy matters and some selections sent in that weren’t usable for various reasons, the “All-star linkfest” I sought is finally ready for prime-time. In retrospect, it seems like a near-impossible task, to pick out just 1 or 2 favorite math postings from a Web inundated with great mathematics, as the variety here will indicate:

Originally I kicked the project off citing a 2015 Lior Pachter piece on K-12 math education, with many great suggestions for math problems young people can work on:

…another long education piece I always think of in conjunction with Pachter’s piece (even though they are quite different) is this 2012 one from Fields Medalist Timothy Gowers on teaching math to non-mathematicians (with a couple hundred comments as well):

So much for me though, here are YOUR picks (in no special order):

Steven Strogatz surprised me a bit when he wrote that his first thought was this link to a mathematical fiction site (which is definitely useful for folks who like to link their love of fiction with their love of math — 100s of selections):

…but then as a more mathy choice (that he noted “everyone interested in math should read) Dr. Strogatz went with this classic from his former fellow Cornellian(?) William Thurston, “On Proof and Progress In Mathematics”:

No surprise that someone would pick Steven Strogatz himself for great postings, and Patrick Honner cited Dr. Strogatz's fantastic NY Times' series that started here (and led to an eventual book based on the series):

I would’ve been shocked if no one had chosen something from Grant Sanderson’s incredible 3Blue1Brown YouTube site, and I wasn’t disappointed. Sol Lederman (who it was great to hear from), formerly proprietor of the immensely popular “Wild About Math” blog, picked out Grant’s video on Euler’s Formula & group theory:

And Benjamin Leis also opted for the fabulous 3Blue1Brown, singling out this one on Pythagorean triples:

Mathematician/computer-scientist/author Rudy Rucker sent in this highly graphic selection on the Mandelbulb, a 3-D version of the better known Mandelbrot Set:

Colin Beveridge went with a StackExchange discussion of a Gaussian proof:

[…this made me think that another possible interesting “linkfest” might be to have readers send in their all-time favorite math questions/discussions/debates from forums like StackExchange, MathOverflow, Quora, Reddit, etc. I don’t read any of these sites regularly myself, but know there have been some great postings on occasion there.]

p.s.... any mention of Gauss can't help but also make me think of this favorite old humor site on "Gauss Facts" (too funny):

Of course none of us will forget the wonderful life-work Alexander Bogomolny left us with his Cut-the-knot site and Jim Wilder pointed to two problem-selections from there:

Jim Propp couldn’t contain himself and sent in the most links, six (including one from Evelyn Lamb and one from Ben Orlin), and because I like Jim so much I almost let him get away with it… am passing along 5 of his diverse picks here (the first four have a lot to say about mathematics, while the last one involves doing mathematics):

From Tim Chartier came this numerical math trick (requiring flash):

Meanwhile, leave it to Ben Orlin to send in cartoon work (not his own), on math myths, for readers to appreciate:

Statistician Adam Kucharski passed along this interesting one on random numbers and casinos:

An entry I particularly liked came from great math popularizer Richard Elwes with this longish piece on math foundations:

One individual wished to remain anonymous (not sure why) and sent in this somewhat classic Terry Tao piece (that’s readable by a general audience) on rigor in mathematics:

Colm Mulcahy went with Tyler Vigen’s spoofy, always-good-for-a-chuckle ‘Spurious Correlations’ website, illustrating, believe-it-or-not, 'correlation is not causation' ;)

 Another graphic site (Tumbler) came from Jo Morgan:

Meanwhile, James Tanton and Edmund Harriss sent along education-related websites:


That's it! It's been fun for me to collect these and offer up some sense of the great variety of items that mathematicians enjoy/recommend within their own field.

[…let me know of any non-working links or other problems, and you can still add your own "faves" in the comments]

Sunday, September 9, 2018

A Few Things Readers Have NOT Submitted Among ‘Greatest Hits’ Posts

When I asked folks to submit some of their favorite math postings of all time I had a definite idea what sort of things might show up.  I’ve been a li’l surprised by the sheer range of pieces people have suggested, as well as by some of the things that have been left out so far (…but please, please keep sending in your picks for now). [email: sheckyr at gmail..... ]

Anyway, will take this opportunity to mention a few varied bits that popped into my mind thinking about this, but that haven’t thus far been contributed by others:

Certainly Quanta Magazine can’t be ignored when it comes to memorable math postings (though no one has mentioned it yet). Just as one example from their great stable of writers, there's this 2016 Erica Klarreich piece on prime number digits:

David Mumford has written a number of great posts over the years at his blog. Here’s one cross-field example:

RadioLab,” one of the best long-running podcasts around, has done several episodes related to math. “Stochasticity” was a good one:

So much joyous math work from Numberphile over the years. Here was the incomparable Tadashi Tokieda with an early piece on “freaky dot patterns”:

As a Keith Devlin groupie, I can’t let him go missing. From his long-running “Devlin’s Angle” blog this is among my many favorites:

…and I also relished his appearance on Krista Tippett’s “On Being” broadcast several years back:

I’ll stop here… and almost hate even mentioning these, because there’s automatically so many great pieces I’m leaving out. No doubt if I searched more, I could find pieces by Barry Mazur, Doug Hofstadter, Jim Propp, Brian Hayes, Natalie Wolchover, Raymond Smullyan, maybe even L.E.J. Brouwer, and others I'd want to pass along, but those just represent some of my tastes/biases; yours will differ.
Anyway, in another week or so will hopefully have organized/formatted the picks readers did send in — but keep on contributing in the meantime. I never tire of seeing the math that others find interesting, inspiring, or just entertaining.

Monday, September 3, 2018

Two To Take Note Of

FIRST, great initial entries coming in to prior post. Please continue to send along your favorite postings for inclusion....
On to today's post:

While scanning my bookshelf recently I noted that two authors I’ve especially enjoyed, are less referenced (in my experience) than several others, so thought I’d toss a little light in their direction:

1)  One is British mathematician (and retired teacher) David Wells, who I suspect is better known ‘across the pond’ than here in the U.S. I have three of his books and love them all!:

The Penguin Book of Curious and Interesting Mathematics
Prime Numbers: The Most Mysterious Figures in Math
Games and Mathematics: Subtle Connections

Highly recommend all of these, or, sight unseen, any of his other volumes:

He has a Martin Gardner-like knack for drawing attention to interesting mathematical content/ideas.
Unfortunately, I couldn’t find web links to many of his articles, but here is one that is often cited, having to do with beautiful equations (from “The Mathematical Intelligencer” — also, many of his books are accessible on Google Books):
[If anyone knows of free links to others of his popular math essays, please pass them along in the comments.]

Here also, a transcribed interview with him concerning undergraduate math education:

Anyway, if you enjoy popular math writing and aren’t familiar with Wells’ work I suggest looking him up!

2)  The second person I want to cite here is Bart Kosko, a bit of a polymath with bachelors degrees in Philosophy and in Economics from the University of Southern California, a masters degree in Applied Mathematics from the University of California at San Diego, and Ph.D. degree in Electrical Engineering from the University of California at Irvine. He also has a J.D. degree from Concord Law School, and is a licensed California attorney. 
And he’s been previously called “a celebrated maverick in the world of science.”
A partial list of his essays here (including many for John Brockman's "Edge" organization):

Kosko is especially well-known for his promotion of "fuzzy logic" as opposed to the conventional Aristotelian or binary logic we are accustomed to. His most well-known book is “Fuzzy Thinking: The New Science of Fuzzy Logic,” which you can read about here:
[You can also find the volume on Google Books.]
And he’s also author of “Nanotime,” “Heaven In a Chip: Fuzzy Visions of Society,” and “Noise.”

Short YouTube video of him here:

And finally here is audio of him on the late night talk radio show “Coast To Coast” talking about defense, AI, technology, and other matters:

Anyway, two very different folks and writers, both of whom I think deserving of attention.

Sunday, August 26, 2018

PLEASE Contribute… All-star Linkfest!

 ==> UPDATE (9/10):  Barring problems, the final linkfest should post on Monday morning 9/17 (if, if, IF I have electricity at that point), so please get your contributions to me by then.
==> UPDATE (9/1): really enjoy seeing the range/variety of selections coming in thus far, so do keep on submitting! Am low on selections from females (though I don’t expect their picks to differ significantly from those of males) and few statistics-leaning picks yet…

Part of the fun/satisfaction from The Aperiodical’s recent Big Internet Math Off contest was not only the great posts entered, but the fabulous pieces they in turn linked to.

I’d love to see such a linkfest continue, so am hereby soliciting math bloggers/communicators/enthusiasts to send me ONE specific awesome mathy link that they think readers would enjoy, and may not be familiar with, or, have forgotten and is worth re-visiting. It could be a blogpost, a Wikipedia page or other website, magazine/journal article, or something from Google+ or Facebook, a classroom exercise, puzzle, or… or… or whatever you think math fans will enjoy/learn from.

The pieces ought relate to mathematics in some way, and NOT be your own work, but otherwise I have few criteria; could be long or short, simple or somewhat technical, very old or brand-spanking new; low-level math or higher level; rich and thoughtful or fun and recreational; I only ask that they be interesting, enriching, or inspiring in some way for readers. And while I only want ONE selection apiece, I realize some may find it impossible to cite just one, so promise not to spank anyone for sending along more than one.

Soon I’ll be sending out emails to a few dozen specific math folks asking for selections, but ANYone please feel free to contribute a suggestion now (whether I contact you or not) -- the more the merrier; drop me a URL reference at (or if I follow you on Twitter you could DM me there, or even just drop it here in the comments).
[...would like to have enough within a month to work with]

Eventually I want to present them, perhaps in a Carnival-like format, in a post of  ‘All-star links’ that could make for great reading.

Just as an example, to get the ball rolling, here's a longish 2015 math education post from Lior Pachter that I've always loved (and am surprised it only drew 12 comments):

[ADDENDUM:  I ought make clear that it's also OK to cite a favorite math video or podcast episode -- there are just so many great ones to choose from!]

ADDENDUM2:  I tried making this simple by requesting just one link, but in retrospect (and seeing most initial responders send along multiple links) I realize narrowing down to a single pick can actually be very hard, so feel free to send more than one selection… but don’t go crazy with it ;)

Monday, August 20, 2018

Spooky FMR….

Sometimes I like harking back to an ‘oldie but goodie’ that, just perhaps, there are enough newbies around by now to have missed it.  Over 4 years ago I first learned (via Fawn Nguyen) of the “Flash Mind Reader” from Andy Wolf, formerly Andy Naughton (though it had been around since 2002) and ever since it’s remained a favorite puzzle-of-sorts to me (it makes a certain always-accurate prediction after you randomly select a 2-digit integer). What I love is its ultimate utter simplicity while, like a great sleight-of-hand magic trick, creating wonder from basic distraction.

You can visit it here (and will need ‘flash’ installed to play it):

…or someone has done a completely different version (but based on same methodology) here:

This is especially fun to show young people… or, any of us who are young-at-heart! ;)

I last wrote about it on the blog here:
[the link I give to the puzzle there no longer works though; and my first mention of the puzzle, by the way, was HERE.]]

The only little bit of backstory I've ever found on this wonderful piece of legerdemain is here:
And so far as I know, Andy Wolf still works for Wolfman Ltd. as a freelance digital designer.(I've tried to make contact with him without success.)

For any who need an explanation of how it works there are plenty available on the Web (including on YouTube), just google “Flash Mind Reader,” so I won't give a 'spoiler' here.

[...I will say some do a much better job of explaining it than others, and it is the sort of puzzle Presh Talwalkar does a great job of explaining, so I was sorry to see that, as best I can tell, he’s never tackled it on his “Mind Your Decisions” site. Hey Presh, this seems right up your alley!]

Tuesday, August 14, 2018

Calling All Number Theorists

Maybe time for a cold shower....
I almost feel dirty for doing this, but I’ve gone back now and read all the posts (5 of them) at Martin Shkreli’s blog (written I guess while he’s in prison at Ft. Dix). This started when Jordan Ellenberg of all people referenced the blog in a tweet because it contained a review of his book, “How Not to be Wrong”:

So please don’t think less of me, blame Ellenberg for my new interest. Reading the blog you would barely know it was written by the guy with the same arrogant/pompous/smugness-drenched face we got used to seeing on the nightly news. At least it’s more interestingly and intelligently written than I expected (…though yes, still with some of that arrogance/pompousness/smugness included for free).

Anyway, I mention it, not so much for the Ellenberg review, but because toward the end of his 8/12/18 post/blathering comes this bit:
I have been busy reading proprietary research and, of all things, working on math. I am particularly interested in algebraic number theory — if anyone out there is a or knows a professor in this field, I would love to compare notes. is the best place to contact me.”

So, there you are… will one of you algebraic number theorists (who’s always wanted a prison pen-pal perhaps) please help the poor fellow out (I mean who knows, maybe he’s solved the Collatz conjecture in all that spare time)… just be sure to charge him appropriately (say $5,000 per note) for the assistance.

[Shkreli is, as I understand it, serving a 7-year sentence for fraud, and permanently banned from Twitter (not sure which he considers the graver punishment). Seven years might be just enough time to prove the Riemann Hypothesis...]