...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, September 23, 2016


There was a lot more out there in the Math-o-sphere this week, but these were a few of the items that caught my eye:

1)  This month James Propp got down to the basics of why 'minus times minus equals plus':

2)  Barbara Oakley on rewiring the brain for 'math fluency':

3)  Ben Orlin is reporting from the Heidelberg Laureate Forum, as an "invited blogger" (how cool is that!):

...and check out all his dispatches since that initial one. Good stuff.

4)  Julie Rehmeyer has been covering the story of the bad science/statistics behind 'chronic fatigue syndrome' treatment for a long time. Her latest here:

5) The 138th Carnival of Mathematics served up piping hot:
6)  Andrew Gelman isn't very pleased with Susan Fiske's defensive response to psychology's credibility-and-replication 'crisis':

7)  Cathy O'Neil did a Quora Q & A this week with lots of good, succinct questions and answers that are definitely worth scanning through:

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

1)  I've long regarded speech/sentence processing as one of the most fascinating subjects out there, almost akin to the mystery of consciousness itself. And from this Scientific American piece, it looks to me that very little real progress (since my college days) has been made in understanding how we, and all children across the world, manage to do it!:

2)  ICYMI, "hacker-proof code" via Quanta Magazine:

Friday, September 16, 2016

Friday Potpourri

A mishmash from the week:

1)  Only a little mention of mathematics in it, but I enjoyed this interview with mathematician/physicist Freeman Dyson:
2)  Some math book recommendations for children:

3)  Brian Hayes on a conference for Mochizuki's ABC work, and connection to Fermat's Last Theorem:

4)  Deborah Mayo honors one of her heroes, Charles Peirce:
5)  Beautiful math theorems get ranked:
6)  Rather timely, with the recent release of Cathy O'Neil's book, "Weapons of Math Destruction," last week's TED Radio Hour on NPR was all about 'Big Data':

7)  An interesting take on Bayes Theorem and neuroscience:

8)  And further speaking of neuroscience, in the "Too-good-not-to-pass-along-Dept."... this optical illusion that went viral last week (known as "Ninio's Extinction Illusion") -- one of the best and newest I've seen (there are 12 dots in the picture, but few can be viewed at any moment):

9)  "The Most Obvious Secret In Mathematics" (category-theory-related):
10)  This article (and comments) that John Carlos Baez pointed out on Twitter is fascinating (and scary, about taking down the Internet):

11)  New book is on the way from Ian Stewart, "Calculating the Cosmos":

12) Last weekend I paid tribute to Alan Sokal:

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

1)  From a couple of weeks back, an interesting little tale of music's role in a life decision for physicist Sean Carroll: 

2)  Coffee perks up engineering education (from NPR):

Sunday, September 11, 2016

20th-Year Anniversary (Alan Sokal's Hoax)

[…another post only tangentially-related to math.]

In a recent post at Math-Frolic I alluded to how language interplays with math and science to misguide people’s thought processes.  It is a frequent interest of mine… and mulled it over again a bit this weekend.

Beyond the Hoax” (2008) by mathematician/physicist Dr. Alan Sokal, is one of my favorite volumes of all time; in fact I think it ought be required reading by all students before they leave college. The book crosses boundaries between science, philosophy, culture, linguistics, education, and cognitive psychology. Some may find the 400-page opus (chockfull of great notes) overly pedantic, though I think any pedantry is overwhelmed by the richness and depth of ideas under discussion, while skewering postmodernism. "A Sokal hoax," by the way, is now a pretty generic term to label academic publishing hoaxes that occur almost every year.

I suddenly realized that this year marks the 20-year anniversary since the publication of the original nonsense “hoax” article ("Transgressing Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity," 1996) which Sokal managed to hilariously/ridiculously/embarrassingly get published in the postmodern cultural journal, “Social Text,” and on which the above book is based. 
Early in the creation of Math-Frolic I placed a permanent link to the hoax piece in the right-hand column, because I consider it one of the most important, defining events of my lifetime interest in science. If by any chance you don’t know what it’s all about, by all means read the original (below), which Alan himself described as, "a pastiche of left-wing cant, fawning references, grandiose quotations, and outright nonsense... structured around the silliest [postmodern] quotations he could find about mathematics and physics”:

Anyway, this all comes up now because this weekend at a used book sale I stumbled across Sokal’s earlier book, “Fashionable Nonsense” (American title) — it too is good, and I never realized that it was actually published in 1998, a full 10 years before “Beyond the Hoax," and just a couple of years after the renowned hoax was sprung.

A great deal more can be found about Sokal’s writings at this page he has devoted to such (there was a lot of press and commentary followup to the so-called 'Sokal affair'):

One of the great services that Sokal performed was to make journal editors aware of how easily they could be duped. Of course a journal like "Social Text" was especially vulnerable, but these days even more 'empirical' journals fall prey to fraudsters (who can be difficult to detect) as reported on regularly by Ivan Oransky's "Retraction Watch."

In part, this post is also a continuation of a recent Math-Frolic post I did mentioning some folks I find particularly worth reading, for the richness and variety of their thoughts, each in their own way (James Propp, Brian Hayes, Scott Aaronson, Lior Pachter). Add Alan Sokal to that list, although unlike the others he has no blogging presence, and I know of no new writings from him on the way unfortunately.

For those who want to hear more about math, here are the words that conclude Alan’s original piece:
“…a liberatory science cannot be complete without a profound revision of the canon of mathematics. As yet no such emancipatory mathematics exists, and we can only speculate upon its eventual content. We can see hints of it in the multidimensional and nonlinear logic of fuzzy systems theory; but this approach is still heavily marked by its origins in the crisis of late-capitalist production relations. Catastrophe theory, with its dialectical emphases on smoothness/discontinuity and metamorphosis/unfolding, will indubitably play a major role in the future mathematics; but much theoretical work remains to be done before this approach can become a concrete tool of progressive political praxis. Finally, chaos theory -- which provides our deepest insights into the ubiquitous yet mysterious phenomenon of nonlinearity -- will be central to all future mathematics. And yet, these images of the future mathematics must remain but the haziest glimmer: for, alongside these three young branches in the tree of science, there will arise new trunks and branches -- entire new theoretical frameworks -- of which we, with our present ideological blinders, cannot yet even conceive.”
 Hope that satisfies you ;-)

Again (as I hinted at the end of my 9/9/16 Math-Frolic post), I find the general discussion of how language can misguide and misdirect people about science or just rational thinking, of especial note today because of what we are witnessing in American (if not worldwide) politics. Oy vey!....

Our beloved Martin Gardner, as many know, was quite the prankster himself, and pulled off some doozies in his time. But none as searing as Dr. Sokal's. So, Happy 20th Anniversary to Alan and his monumental fakery (and insight).  I'm surprised I haven't seen other celebratory acknowledgments of the anniversary. We shouldn't risk younger generations forgetting it.
The journal “Social Text,” by the way, remains in publication and states online that, since its founding in 1979, it has “forged creative connections between critical theory and political practice.” I find “forged” an interesting term. ;-)

Friday, September 9, 2016

Friday Mix

Weekend reads, ICYM them:

1)  Stephen Wolfram expounds on teaching "computational thinking":

2)  A quick, fun essay on teaching math:

3)  Monte Carlo methods and computer game-playing:

4)  New, free online issue of European Mathematical Society newsletter (including an interview with Andrew Wiles):

5)  For the philosophically-and-math-foundations-inclined, this discussion from Mark Chu-Carroll on some "Cantor crackpottery":
6)  John Baez on the "Struggles With the Continuum":

...and, ICYMI, Baez is now on Twitter here: @JohnCarlosBaez

7)  For a couple of fun-reads:

a.  There's always Ben Orlin:
b.  and this on "Janitor Math":
9)  p.s...: there's a rabid rumor going around that Mathbabe Cathy O'Neil has a new book out (something about mathematics intruding in our lives).... ;-)

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

1)  This "DNA Journey" video went semi-viral this week, but if you missed it, worth watching to the end:

2)  This week's "On Being" episode on NPR with Krista Tippett is a great interview with Wikipedia's Jimmy Wales:

Friday, September 2, 2016

Weekly Potpourri...

From the week gone by....

1)  Odd/interesting little genealogical study tracing back the origin of mathematicans to primarily "24 scientific families":
(...can't help but think how the '6-degrees of separation' notion plays into this)

2)  Math, patterns, tilings, crystals, oh my:

3)  Presh Talwalkar uses a Three Stooges pie fight to talk about modeling, game theory, and this year's presidential election:

4)  A short, but rich, new Carnival of Mathematics:

5)  And another rich offering from Ben Orlin this week:

6)  I've never been able to get my mind to wrap around "category theory," but maybe next time I try I'll use this post from John Cook:

7)  Addition to multiplication, via Evelyn Lamb:

...also, Evelyn reviewed Cathy O'Neil's new book, "Weapons of Math Destruction" this week:

...AND, an excerpt from Cathy's book was available in the Guardian this week:

8)  A fun take on Bayesian stats:

...and Deborah Mayo points to this Bayes paper that she deems "superb":

9)  Haven't explored it very much myself, but math fans who enjoy board games may want to check out this new one:

10) "A Mathematician Goes to Washington" (and works for Al Franken):

11)  John C. Baez is newly on Twitter. If you're on Twitter you should follow him: @baez72033757

12)  Math-Frolic posts this week touched on Ford Circles and Lior Pachter, and a techie browser question.

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

1)  I've long thought a lot of "social science" ought more accurately be called "social studies," and beginning to feel similarly a lot of "neuroscience" might better be deemed, "neuro studies":

2)  With a long-time interest in psycholinguistics I found this recent bit of Twitter banter interesting (...may have to think about it briefly to catch what's going on):

Friday, August 26, 2016

Some End-of-week Picks

A short potpourri this week:

1)  One blogger's list of "7 Must-See Mathematics Movies":

2)  ...and Fawn Nguyen's "7 Deadly Sins of Teaching":

3)  Also for teachers, Christopher Danielson announces that his "Which One Doesn't Belong?" book is now in print:

4)  Brainteasers from the NSA:

5)  Seeing is NOT believing... Evelyn Lamb on a few of the best illusions:

6)  Primes and Conway's 'Game of Life':

7)  My own Math-Frolic blogposts this week dealt with Martin GardnerPaul Erdös, and John Cook.

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

1)  Someone on Twitter recommended this 'mind-blowing' RadioLab episode (on forest fungi) that I had missed, and I'll just pass along the recommendation:

2)  My favorite piece of classical music, Pachelbel's Canon, played in a fingerstyle manner I've not seen before on guitar, by Trace Bundy (enjoy watching & listening):

Friday, August 19, 2016

Wrapping Up the Week


1)  "Phantom" traffic jams:

2)  There is no shortage of proposals of what problem the Polymath Project should tackle next:

3)  Mathematics joins in on the parodies of Alexander Hamilton:

4)  Deborah Mayo again on p-values:

5)  An old, delicious and deceptive math Olympiad problem that got some attention on Twitter this week, starts on Numberphile here:

6)  Searching for math geniuses:

7)  The latest "Carnival of Math":

8)  Ben Orlin's round-faced buddy explains logarithms:

9)  Appropriate to an election year, James Propp tackles "Bertrand's Ballot Problem":

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

1)  I got a kick out of Futility Closet's post on an analysis of "stupid people":

2)  Nice Guardian piece on Daniel Kahneman:

Friday, August 12, 2016

Math Potpourri Served Up

End-of-week mishmash of math miscellany:

1)  Medical tests... false positives and negatives:

2)  Exploring Mersenne numbers a bit:

3)  Donald Knuth wins the John von Neumann Lecture Prize:
4)  Evelyn Lamb lists a few keen educational math blogs (for different levels) here:

5)  Deborah Mayo on Popperian falsification etc.:

6)  A review (pdf) of the latest volume from Raymond Smullyan, "Reflections: the magic, music, and mathematics of Raymond Smullyan":

7)  Speaking of booksI wrote this week about an older volume from Keith Devlin that, if you can find it, is worth having:

8)  And of course if you need more math for your weekly fix, you can always visit "Mike's Math Page":

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

1)  One physicist's interesting take on the LHC results:

2)  ICYMI, "60 Minutes" Anderson Cooper met playful Bonobos in the Congo last weekend:

...and lastly, perhaps my favorite tweet from the week (from @AdamSacks):
"The party of Lincoln is now the party of John Wilkes Booth."

Monday, August 8, 2016

"Making the Invisible Visible"

Some years ago I mentioned stumbling across Keith Devlin’s older book (1997), “Goodbye Descartes” and really enjoying it. Dr. Devlin’s interests in cognitive topics, as represented in that volume, overlap my own, and often aren't broached by math writers. Cognitive psychology was a major focus in college, and to this day I find the linkages between mathematics, language, music, and semantics fascinating — despite all that has been written about such topics, I suspect they remain little deeply understood. (And some of it even links back in my own mind to the “General Semantics” of Alfred Korzybski, and the way words and meaning govern/manipulate human thought/behavior).

Anyway, last week I stumbled upon another similar, vintage Devlin volume, “The Language of Mathematics: Making the Invisible Visible” (1998)… and am yet again enthralled by Keith’s beautifully-straightforward exposition! The book obviously can’t qualify for my end-of-year list of best popular math books of 2016, but may nonetheless turn out to be my favorite read of this entire year! And while most of you won’t go searching for an almost 20-year-old volume, that’s what I’d urge you to do, if you've not already read it!.

Keith articulates his theme of math as the science of patterns, while offering excellent introductions to math foundations, history, logic, set theory, calculus, geometry, symmetry, knot theory, topology, probability, and some physics, while admitting there is much he is leaving out. As he writes in a postscript, rather than 'serving up a vast smorgasbord of topics, each one allotted a couple of pages' (as other books often do) he has tried to show that the "mathematical study of any one phenomena has many similarities to a mathematical study of any other." Where so many introductory books to mathematics focus on the logic and procedures of math, Keith emphasizes here the abstract and interwoven nature of real mathematics.
Even though the book's age means a few passages are out-of-date, for the up-and-coming young person interested in math, I don't know a better, clearer overview of what the field is all about.

This extended quote from the volume's Prologue I think captures an essence Dr. Devlin often addresses:
The use of a symbol such as a letter, a word, or a picture to denote an abstract entity goes hand in hand with the recognition of that entity as an entity. The use of the numeral ‘7’ to denote the number 7 requires that the number 7 be recognized as an entity; the use of the letter m to denote an arbitrary whole number requires that the concept of a whole number be recognized. Having the symbol makes it possible to think about and manipulate the concept.
 “This linguistic aspect of mathematics is often overlooked, especially in our modern culture, with its emphasis on the procedural, computational aspects of mathematics. Indeed, one often hears the complaint that mathematics would be much easier if it weren’t for all that abstract notation, which is rather like saying that Shakespeare would be much easier to understand if it were written in simpler language.
"Sadly, the level of abstraction in mathematics, and the consequent need for notation that can cope with that abstraction, means that many, perhaps most, parts of mathematics will remain forever hidden from the nonmathematician; and even the more accessible parts — the parts described in books such as this one — may be at best dimly perceived, with much of their inner beauty locked away from view. 
In turn, all of that reminds me, oddly enough, of a favorite passage (I’ve used here before) from controversial David Berlinski in his book about Euclid, “The King of Infinite Space.”  Sometimes I flip-flop between thinking that this odd passage is just wordplay sophistry, and feeling that it is actually a rather profound statement about the nature of proof or certainty (...and I hope Dr. Devlin won't mind that something he has written reminds me of words from Berlinski ;-):
"Like any other mathematician, Euclid took a good deal for granted that he never noticed.  In order to say anything at all, we must suppose the world stable enough so that some things stay the same, even as other things change. This idea of general stability is self-referential. In order to express what it says, one must assume what it means. 
"Euclid expressed himself in Greek; I am writing in English. Neither Euclid's Greek nor my English says of itself that it is Greek or English. It is hardly helpful to be told that a book is written in English if one must also be told that written in English is written in English. Whatever the language, its identification is a part of the background. This particular background must necessarily remain in the back, any effort to move it forward leading to an infinite regress, assurances requiring assurances in turn. 
"These examples suggest what is at work in any attempt to describe once and for all the beliefs 'on which all men base their proofs.' It suggests something about the ever-receding landscape of demonstration and so ratifies the fact that even the most impeccable of proofs is an artifact."
[I do loves me some recursion! ;-) ]

Anyways, there have been many wonderful popular math books in recent years, but sometimes you can't improve much on older volumes, when it comes to a timeless subject like mathematics. And Keith's writing is always as lucid as there is.
Finally, for an older review of Dr. Devlin's book, see here: