...a companion blog to "Math-Frolic," specifically for interviews, book reviews, weekly-linkfests, and longer posts or commentary than usually found at the Math-Frolic site.

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." ---Bertrand Russell (1907) Rob Gluck

"I have come to believe, though very reluctantly, that it [mathematics] consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-legged animal is an animal." ---Bertrand Russell (1957)

******************************************************************** Rob Gluck

Friday, July 27, 2018

Final Potpourri

NOTE: This will be the last ‘Friday potpourri’ or post at MathTango. With the country in seriously deep-doo-doo I'd rather free up some collusion time to work on expunging orange-puppets or others who find 1930s Germany peculiarly appealing (…also, got some reading to catch up on ;).  [Math-Frolic posts will also decrease substantially for remainder of year, until maybe, just perhaps, we get our country back.]:

1)  This is an old (2003) piece, but Jordan Ellenberg pointed to it last week as his favorite magazine piece he ever wrote, and it is indeed wonderful:

2)  Kevin Hartnett on ‘hard problems’:

3)  plus Magazine describes “uncertainty” this week in two posts:

4)  “Squaring the square” passed along, from Reddit, by C. Pickover (and the comments at Reddit sorta remind me why I almost never read Reddit...):

5)  Interview with popular mathematician/writer/lecturer Eugenia Cheng:

6)  One of my pet peeves is food labelling (…or, mislabelling as it were). Now Vi Hart takes it on:

…Potpourri BONUS! (extra NON-mathematical links of interest): 

1)  A viral (of sorts) detective story, from Ed Yong:

2)  And this:

p.s.... I see Omarosa's supposedly "explosive" tell-all memoir, "Unhinged" is due for release in a couple of weeks:

Friday, July 20, 2018

I Would or I Wouldn't...

Wasn’t sure if I would or wouldn’t compile a potpourri this week, but in the end (and with NO collusion, mind you, NONE, noooo collusion whatsoever) here it is:

1) “The biggest skill to learn moving forward…” (h/t Gary Davis):

2)  A maddening puzzle passed along by Lior Pachter this week:

3)  A checklist of statistical problems (to avoid) for researchers (h/t Frank Harrell):

4)  A “Commencement Address” from Joe Schwartz:

5)  Pillows, knitting, and mathematics:

6)  An intro to Brouwer constructivism in 2 pieces from plus Magazine:

7)  A little history of zero and the empty set:

8)  The semi-finals of the Big Internet Math Off have been appropriately close with Nira Chamberlain winning a nail-biter, and voting continuing in the final pairing:

9)  Also, be sure to check out a few additional links I posted at Math-Frolic yesterday:

…Potpourri BONUS! (extra NON-mathematical links of interest): 

1)  A rare, negative review of Douglas Hofstadter’s “Gödel, Escher, Bach”:

2)  Tom Toles' Twitter feed:

...and a cool new Munker visual illusion via Cliff Pickover:

Sunday, July 15, 2018

Further "Big Internet Math-Off" Analysis

Just continuing my earlier Round 1, off-the-cuff analysis of the Big Internet Math-Off competition, now that Round 2 is near closing...

Have been quite surprised by several of the outcomes thus far in the contest, either by who won, or by the margin of victory. A recent such surprising match was Edmund Harriss vs. Paul Taylor, with the former choosing to write about the Collatz conjecture and the latter about non-transitive dice. I thought this would be a very close match-up, but in fact Harriss ran away with it.  Both topics are inherently very interesting and come up regularly on popular math sites, though I think the Collatz conjecture arises more frequently, in part because it is so easy to state and understand, yet fascinatingly eludes proof. Both the idea of it and the resultant pictures/graphics are “beautiful.” It probably makes everyone’s list of favorite topics, and Harriss offered up a nice standard rendition of it.

Still I ended up voting for Taylor, because he took that extra step of showing me something I’d not seen before, in his discussion of non-transitive dice, by bringing up "NON-non-transitive dice," an added side-twist, I found creative and interesting. In retrospect though, Harriss’s post is more strongly VISUAL, while Taylor’s post may require a bit more thinking/imagining/effort on the reader's part and perhaps that’s a handicap in such a contest. 
So now I’m thinking that maybe in these matches an advantage comes to the competitor who presents the more visually-appealing (or at least less abstract) math bit.  This may also help explain Zoe Griffith’s win over Evelyn Lamb — Evelyn hitting readers with high-dimensional spaces (that can’t be easily pictured or imagined) while Zoe stuck with Benford’s Law and numbers we can all relate to in everyday lives.

Despite those who argue anyone can learn math, I’ve long believed there is a large swathe of people who have real difficulties with “abstraction” (which is fundamental to math) and hit mental blocks because of it. I’ve known folks for example who if asked what “3 apples plus 2 apples” is, will immediately respond 5 apples, but if asked “what is 3x + 2x?” are immediately confused and uncertain, so powerful is this blockage when symbols are introduced.

One thing we don’t know is who the bulk of voters are in this contest… professional and/or amateur mathematicians, or is there a major contingent of lay people who just enjoy reading mathy stuff? I don’t know? But to the extent there is a latter group, easy-to-follow and visually-attractive posts may likely win out — or, hey, maybe I'm looking for patterns that don’t exist (and the results are much more random)! At any rate, participants turned in all there entries before the contest began, so nothing I say here can influence what they will be presenting.

My own actual daily picks have been fairly abysmal, picking only 4 out of the 12 winners (well, one not fully settled yet). As usual, I'm out of step with the masses. :(((
Anyway, we're almost down to the Final Four, and in one more week we'll know the names of the two final jousters. Better stock up on some popcorn and beer (or Guinness) now.

Friday, July 13, 2018

Friday the 13th

hot air, anyone?

Been so busy this week watching Britain and U.S. race to see who can disintegrate first, that I didn’t have much time left over for compiling math bits, but here’s a few:

1)  New Alex Bellos puzzle book now available in U.S.:

2)  Null and alternative hypotheses:

3)  Numeracy/Innumeracy:

4)  Searching for primes and why it matters:

5)  Hope you all are still following and voting in The Aperiodical’s "Big Internet Math Off":
[my recent take on the first round was HERE.]

6)  The Aperiodical also noted the recent death of Alexander Bogomolny here:
...and I spoke of the same here:

…Potpourri BONUS! (extra NON-mathematical links of interest): 

1)  Articulate Alice Dreger was just one of the initial guests on Sean Carroll’s new podcast “Mindscape”:
[Am already amazed at the range of guests he is inviting.]

2)  A good one to end the week with:

Sunday, July 8, 2018

A Little Commentary... The Big Internet Math-Off

Well, it’s not the Thrilla-In-Manila, nor the Olympics, nor even the Soccer World Cup (to which, as an American, I can only say ho-hum), but a perfect, that is Lawson-Perfect, summer diversion for math geeks devised by The Aperiodical’s Christian Lawson-Perfect — intended to crown the "world’s most interesting mathematician" (well, at least of the 16 participating  — and as Jim Propp notes, that real honor goes to John Horton Conway… so perhaps it should be called the "John Conway prize” ;)

With tons of interesting math bits to choose from, most of which are well covered, part of the fun is discovering exactly which intriguing bits various participants find most interesting (or at least think their readers will find most interesting), and then seeing exactly how they manage to present those bits.

I tried to look for some pattern or commonality among the winners thus far, but don’t really see one (does anybody???), though I haven’t yet run a complete astrological analysis ;). 
But with Round 1 of the contest drawing near conclusion, a few general comments:

1)  Even though this could be expected, still heartening to see so many entrants cite Martin Gardner for inspiration. Martin was not even a trained mathematician, yet as the saying goes, he “...turned 1000s of children into mathematicians, and 1000s of mathematicians into children.”

2)  16 seems a perfect number of competitors — not too many, to drag the contest out too long, potentially losing public interest, but enough for variety, diversity, and sustained interest.

3)  It’s not just the topic an entrant chooses that is important, but the presentation is vital! Some folks chose ideas that were new to me and vote-worthy on that account, while others selected material that is more well-worn, but presented in such a clear, clever or creative manner that they got my vote.

4)  One thing I’m not clear about is why vote totals vary so much from one matchup to another, ranging from ~180 to 878! — unless it’s just a case of some competitors having more nieces, nephews, friends, relatives, dogs and goldfish to draw upon for an assist than others!?

5)  Some players gave relatively short presentations that just basically said ‘look at this, it’s interesting!’ while others gave more lengthy fleshed-out verbal descriptions and/or longer videos. I couldn’t tell that either approach was more consistently successful; seemed to me that clarity and creativity were more important than novelty, length, or technicality.  Some topics were more abstract and some more hands-on, but again, I’m not sure either approach dominates — both can produce the “Aha!” moment Lawson-Perfect is seeking.

6)  Finally, does anyone really WANT the burden of the title “World’s Most Interesting Mathematician” — think of the pressure, the stress, the nervous self-doubt and performance-anxiety!! Maybe just leave all that for John Conway, afterall (...he's already got gray hair).

In any event, so far it looks like 5 of my 8 initial bracketology picks will make it to the next round (from the “Sweet 16” to the “Elite 8,” as we would say in America), and what ought be a fun week ahead. Brits outnumber Americans and 2-syllable surnames outnumber all others! — so if you want to root for the underdog, then Lamb is your choice. ;)

Anyway, kudos to The Aperiodical folks for giving us at least a temporary distraction from the Brexit, Trump, and other insanities of daily news, with a contest that includes both wonderful writing and wonderful links. May it become an annual event!

…ALSO, I’d love to continue the fun by collecting a ‘Greatest Hits’ list of links from a wide variety of math communicators for a future post (NOT a competition, but just a sort of listing of single FAVORITE links contributed by great bloggers) — more on that in a future post over at Math-Frolic, but please be thinking what you might submit if asked to refer math fans to ONE single awesome old or new mathy link to read or view (NOT your own material) that they may have missed or forgotten about.

Friday, July 6, 2018

Potpourri Time

And now for some math:

1)  Sphericons!:

2)  Frank Harrell recommends this piece on Thomas Bayes’ work:

3)  The Slippery Math of Causation” (via Quanta):

4)  Just sort of a fun tweet & comments:

5)  More selections via the 118th “Math Teachers At Play” blog carnival:

6)  New interview with John Horgan and Jim Holt:

7)  Evelyn Lamb’s chockfull latest TinyLetter is out (reviewing what she wrote and read about in June):

8)  An intro to mathematical constructivism from plus Magazine:

9)  I was expecting a slow week over at Math-Frolic, BUT, lo-and-behold, ended up with varied posts on Mon., Tues., Wed., Thur., AND Fri.! (inspired by fluid dynamics, a quirky room, a Calif. teacher ;), a contest, and Sean Carroll). So please check out whatever you missed!

…Potpourri BONUS! (extra NON-mathematical links of interest): 

1)  h/t John Carlos-Baez for this fascinating ‘bit’ of info:

2)  Longish, interesting piece on Tim Berners-Lee and today’s World Wide Web:

Friday, June 29, 2018

Time for Another Math Grab-bag

While the Donald was spit-shining his jackboots this week, I hosed off my Crocs and compiled another potpourri:

1)  Interview with philosopher Clark Glymour on probability, causality, science, free will (h/t Sean Carroll):

2)  Some interesting history on Cantorian crankery:

3)  Andrew Gelman plans to soon discuss Deborah Mayo’s new book defending (statistical) frequentism at his blog:
…and Blll Briggs’ take on same here:

4)  Speaking of statistics, nice, simple explanation of flaw with null hypothesis testing via Jacob Cohen/Frank Harrell:

5)  I balanced a lot of centrifuges in my working life… and never, ever thought about the math involved… ’til now:

6)  Schwenk dice from Futility Closet:

7)  Cathy O’Neil on a Gates Foundation education study:

8)  Century+ old hypothesis proved, opening up fresh lines of study in number theory, quantum computing (h/t Graham Farmelo):

9)  A new review of Vicky Neale's "Closing the Gap":

10)  July 1st (this Sunday) is the stated onset of “The Big Internet Math Off,” so the weekend ought not be an entire waste:

 …Potpourri BONUS! (extra NON-mathematical links of interest): 

1)  Apparently people sometimes get angry over one thing or another on Twitter:

2)  IF you’re not tired of reading about the male/female divide, a long analysis from Emily Yoffe (h/t Steven Pinker):

Friday, June 22, 2018

A Few Bits From the Week

The "I really don't care, do u?" edition of the Friday math potpourri:

1)  Some discussion of statistics, and cause-and-effect (…and a recent book); h/t Frank Harrell:

2)  Prime numbers, kids, and math education:

3)  Some cool geometry from Patrick Honner, involving squares, points, and colors:

4)  Jim Propp on James Tanton’s “exploding dots”:

5)  Andrew Gelman on Sabine Hossenfelder’s new book, “Lost In Math”:

6)  And the latest effort from wacky cartoonist Len Robin:

 .…Potpourri BONUS! (extra NON-mathematical links of interest): 
1)  In case you didn’t hear already, Koko the Gorilla died this week:

2)  Finally, just because it's been one of those weeks:

The only thing necessary for the triumph of evil is for good men to do nothing.”  
      ~ E. Burke

via HERE

Friday, June 15, 2018

Friday Potpourri

While the Appeaser-and-Chief was working out a few details for a new Trump Tower Pyongyang, I compiled another weekly collection of math bits:

1)  A potpourri within a potpourri… the latest Carnival of Mathematics blog carnival is out:

2)  A recent video interview with Ed Frenkel:

3)  Math, science, engineering… and origami (via Erik Dermaine):

4)  Brief interview with Eli Maor, author of “Music By the Numbers”:

5)  “Statistics — the Rules of the Game”:

6)  Just a little quickie commentary about commentary (…and causation):

7)  The Mediterranean Diet, clinical studies, randomization, oh my…:

8)  Economist Gary Smith, who I interviewed last week, has a new column for Marketwatch on the probability of a good company becoming a great company… and, the Feynman trap:

10)  Meanwhile, early in week I was enamored of Jim Holt:

…Potpourri BONUS! (extra NON-mathematical links of interest): 

1)  Physicist Frank Wilczek with Krista Tippett on “On Being”:

2)  Just what we all need at the end of a long week, more street posters:

Sunday, June 10, 2018

Gary Smith.... Teaching In the Classroom and Beyond

Math-Frolic Interview #44

"Ronald Coase cynically observed that, 'If you torture the data long enough, it will confess.' Standard Deviations is an exploration of dozens of examples of tortuous assertions that, with even a moment's reflection, don't pass the smell test. Sometimes, the unscrupulous deliberately try to mislead us. Other times, the well-intentioned are blissfully unaware of the mischief they are committing. My intention in writing this book is to help protect us from errors -- both external and self-inflicted. You will learn simple guidelines for recognizing bull when you see it -- or say it. Not only do others use data to fool us, we often fool ourselves."
-- from the Introduction to Standard Deviations by Gary Smith

Gary N. Smith is an award-winning Professor of Economics at Pomona College in California (...which happens to be my wonderful alma mater — and though he’s been there 37 years, I graduated before he arrived, so we never crossed paths).
He’s also the author of several popular books. “Standard Deviations” is one of my favorite takes on statistics that everyone should know about.  He followed that up with “What The Luck,” a similarly entertaining, engaging volume on probabilities in major parts of our lives. And I also enjoyed his very readable and instructive “Money Machine,” a great introduction to the sort of “value investing” I believe in and wish I had started earlier in life!  Later this year he’ll be out with “The AI Delusion,” more on that below.
If you’ve missed any of his books you should check them out…

And now a little more:


1)  Tell us a little about your background and the path that led to your interests in economics and statistics?

Way back when (in junior high school?), I became fascinated with mathematical puzzles, including several of Martin Gardner’s books, such as The Scientific American Book of Mathematical Puzzles and Diversions and Fads and Fallacies in the Name of Science. I went to Harvey Mudd College, here in California, and I majored in math, but I was also on the debate team and the national topic my freshman year was, “Resolved that the federal government should establish a national program of public works for the unemployed.” I was drawn to economics for the same reasons that attracted many economists, including James Tobin, who would become one of my mentors when I went to graduate school at Yale:
"I [Tobin] studied economics and made it my career for two reasons. The subject was and is intellectually fascinating and challenging, particularly to someone with taste and talent for theoretical reasoning and quantitative analysis. At the same time it offered the hope, as it still does, that improved understanding could better the lot of mankind."

After earning my PhD in economics at Yale, I accepted a job there as an assistant professor, initially teaching statistics and macroeconomics. Then the Yale economics department asked students what courses they would like added to the curriculum and the runaway winners were Marx and the stock market. I wasn’t interested in Marx, but James Tobin was the chair of my thesis committee and would be awarded the Nobel Prize in Economics, in part for his analysis of financial markets. So, I volunteered to create a stock market course. I loved it because of the wonderful combination of mathematical theories, empirical data, and real world relevance. My main interests today are statistics and finance.

2)  When I thought about interviewing you and clicked on your webpage I discovered you have a brand new book on the way later this year, “The AI Delusion,” so go ahead and tell us about that. I assume from the title you feel a lot of what we hear/read about AI is overhyped? 
p.s., just curious too, have you ever ridden in a driverless car?

I have not yet ridden in a driverless car.
A few years ago, I wrote Standard Deviations: Flawed Assumptions, Tortured Data, and Other Ways to Lie With Statistics, which is a compilation of examples of statistical errors and mischief that I collected over the years. Recently, a lot of these errors and mischief come from data mining—ransacking data for statistical patterns, without being guided or constrained by any coherent theory. Big data and powerful computers have made the problem much worse because they make the data mining so easy.
For example, back in 2008, Chris Anderson, editor-in-chief of Wired, wrote an article with the provocative title, “The End of Theory: The Data Deluge Makes the Scientific Method Obsolete.” Anderson argued that,
"With enough data, the numbers speak for themselves…. The new availability of huge amounts of data, along with the statistical tools to crunch these numbers, offers a whole new way of understanding the world. Correlation supersedes causation, and science can advance even without coherent models, unified theories, or really any mechanistic explanation at all."

That is a dangerous argument. Too many people think that computers are smarter than humans and should therefore be trusted to make important decisions for us based on statistical patterns unearthed by ransacking data. For example, courts all over the country are using computer models to make bail, prison-sentence, and parole decisions based on statistical patterns that may be merely coincidental, but cannot be evaluated because they are hidden inside black boxes.
The truth is that, while computer algorithms are great and getting better, they are still designed to have the very narrow capabilities needed to perform well-defined chores, not the general intelligence needed to deal with unfamiliar situations by assessing what is happening, why it is happening, and what the consequences are of taking action.
Artificial intelligence is not at all like the real intelligence that comes from human brains. Computers do not know what words mean because computers do not experience the world the way we do. They do not even know what the real world is. Computers do not have the common sense or wisdom that humans accumulate by living life. Computers have no way of judging whether the patterns they discover are meaningful or meaningless, and when the algorithms are inside black boxes, no one knows.

3)  Since you're an economist and a statistician I’m curious if there are any specific economists and statisticians you would especially recommend for mathematically-inclined readers to follow on the internet (on blogs, websites, Twitter, Facebook, wherever)?

Nate Silver and Andrew Gelman are reliably interesting.

Also, besides your books do you have Web-accessible pieces you would recommend to readers wanting to get a taste of your own work?

I write regularly for MarketWatch and RealClearMarkets. Here is one column on black-box investment algorithms, and one on Bitcoin .

4)  In some places I see a push in secondary education for some sort of statistics and data science course to be a required part of the math curriculum (probably replacing one of the currently-mandated math offerings). Do you have any thoughts on that?

I was a math major, I love math, and I use math and write computer programs for almost all my academic research, but I think that a basic understanding of statistics and data science are more useful and relevant for most citizens. Understanding the difference between good data and bad data, the nature and limitations of statistical inference, and the dangers of data mining are essential.

5)  When you’re not trying to raise math and financial literacy in this country ;) what are some of your other main interests/hobbies/activities?

I used to play soccer, squash, and all sorts of sports but I had to have knee replacement surgery a year ago. Now I’m mainly trying to be a good husband and father.


Thanks Gary, I've never before interviewed either an economist or a Fighting Sagehen (Pomona mascot) here, so thanks for two firsts! ;)
[In retrospect, I'm only sorry that you weren't the 47th interview here (...inside joke)]
And again, Gary's books are fun... AND timely reads if you're not already familiar with them.

Friday, June 8, 2018

Mathy Things You May Have Missed

After pardoning myself for all the things I’ve said, or will in the future say (or think or whisper) about our dysfunctional (to put it kindly) President, I proceeded to compile another weekly math potpourri:

1)  Eli Maor on math & music:

2)  Fermat primes and almost Fermat primes:

3)  Michael Harris on Peter Scholze and more:

4)  John Golden recommends these calculus videos from Paula Krieg as “beyond fabulous… beautiful and ingenious”!:

5)  Biking, mathematics, and Keith Devlin collide:

6)  An interesting tweet and some followup comments (on coincidences & math):

7)  Peter Woit reviews Sabine Hossenfelder's new (physics) book, "Lost In Math" here:

...also reviewed in Science magazine this week:

8)  Meanwhile, this week I had fun rambling around from language & gender HERE, to a couple of books HERE, and about cartoons and humor HERE.

…Potpourri BONUS! (extra NON-mathematical links of interest): 

1)  A tweet (and comments) that may contain some interesting links:

2)   Reporting on a conference on consciousness: