"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
"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)
Sunday, December 28, 2014
I was expecting a slow week in the math blogosphere... but, I was WRONG! ...PLENTY to read; here's some of it:
1) The latest "Math Teachers At Play" Carnival here:
2) Five "math gems" passed along from a UK secondary math teacher:
3) Early in the week The Aperiodical pointed out a new math app game called "Just Get10". Check it out here (hard to tell how popular it might become; I never expected 2048 to be the 'hit' that it was):
4) A conversation with award-winning mathematician Ken Ono:
5) We hear a lot about chess, but here's a little bit of interesting checkers history from Futility Closet:
6) The world of big data/statistics is attracting more and more STEM women:
7) Statistics making the world a better place? (via Andrew Gelman):
8) Fun geometry from Mike Lawler (via James Tanton and James Key and a 3-D printer):
9) Another interesting piece from Evelyn Lamb, this time on the homotopy of "holes" (which end up being like Santa Claus!):
10) A quick list from AMS of some celebrities who enjoy mathematics:
11) In the unlikely event that some of my readers can even comprehend it, here is a recent update related to Mochizuki's proof of the ABC conjecture:
12) Will end with another fine geometry puzzle from Stephen Cavadino:
Friday, December 19, 2014
This week's grab-bag (and I will either have NO weekly potpourri next week, or else it will appear on Sunday, rather than on Friday, the day after Christmas):
1) Recent New Zealand interview with Marcus du Sautoy here:
...related Sautoy article here:
2) The best puzzle and game theory posts from Presh Talwalkar ("Mind Your Decisions") for 2014 -- catch up if you missed any of these:
3) Fascinating report on the "Umbral Moonshine Conjecture" (...no, I'd never heard of it either!, but related to the Monster Group):
4) Technical post from Terry Tao on latest work regarding "long gaps between primes":
5) "Boolean" vs. "additive" thinking from Andrew Gelman:
6) "Why Should You Learn Math?"... one student's answer:
7) I'm always eager to shine light on Dr. Keith Devlin and his endeavors in math communication. This week someone else did it for me:
8) And for your smile-of-the-week:
Friday, December 12, 2014
The good and diverse mathy stuff just keeps on comin'... ICYM any of these:
1) First, this wonderful, ranging interview with fascinating polymath Eric Weinstein ought not be missed:
2) Interesting interview with Caltech's Xinwen Zhu (former student of Edward Frenkel), who works on the Langlands program:
3) The Bayesian/frequentist debate goes on:
4) A bunch of "puzzles and starters" from Stephen Cavadino here:
OR, if you need a stronger challenge here are some 2014 Putnam problems:
5) A topic that will be increasingly crucial to newer generations... Teaching kids coding/programming as part of literacy:
6) More math and music/noise from Evelyn Lamb:
7) Some mathematical commentary on increasingly-pervasive personal genetic testing:
8) Princeton University Press has sent along this short list of some upcoming spring/summer offerings in popular math:
9) I'm not sure it's even possible for Fawn Nguyen to write anything that doesn't leave you with a tear in your eye before the end:
10) Keith Devlin's latest on math learning and math learning apps:
11) Andrew Gelman isn't the first, and won't be the last, to write about "the fallacy of placing confidence in confidence intervals":
12) The always-hard-to-predict Vi Hart was back this week (as probably everyone knows) with a lesson on our social/collective behavior via a mathematical game, "Parable of the Polygons":
13) The 117th Carnival of Mathematics is out now:
14) And per usual, check out MikesMathPage to see what Mike Lawler and the boys have been up to this week: http://mikesmathpage.wordpress.com/
....there, that should hold you through the weekend.
Tuesday, December 9, 2014
More from the book scene....
I briefly mentioned Matt Parker's new book (sight unseen), "Things to Make and Do in the Fourth Dimension," in my recommendations for the Holidays, based on reviews I'd seen, but am now reading it myself and can give an even more enthusiastic thumbs-up! It's a joyful read (unless you despise puns, in which case stay far, far away!! ;-)). It's really the only "recreational math" book on my list -- I did recommend Ian Stewart's latest puzzle compendium volume, but puzzle books are a bit different from recreational math which is a broader and rarer category these days. In fact, this is one of the very few books that I think could be mentioned in the same breath with Martin Gardner's recreational writings. While reading it I even found myself contemplating the slight similarities between the names, "Martin Gardner" and "Matt Parker"!
Anyway, most of you are likely familiar with stand-up comic/mathematician Parker from various YouTube appearances or elsewhere, and he brings the same lucid, lighthearted, but still instructive style to this book that he exhibits on the internet. His own infectious delight with math comes through both in the wide-ranging text and even his(?) simple hand-drawn illustrations. The book's subtitle offers some hint as to just how wide-ranging it is: "A Mathematician's Journey Through Narcissistic Numbers, Optimal Dating Algorithms, at Least Two kinds of Infinity, and More." As the book flap says, it's "a grand tour... both playful and sophisticated." I won't attempt a full review here (not even sure when I'll complete reading it), but simply highly commend it to your attention.
BUT... I do have a minor beef with it... or, perhaps more specifically with the publisher. This book is over 400 pages long and an inch-and-a-half thick, with an American retail price of $28.00 (and I wouldn't recommend reading it on an eBook reader, but that's me). A lot of folks who are already a tad phobic, or just naive, about math will be intimidated by the look/feel of this volume, as well as discouraged by the price. That means a lot of people who could benefit from reading it, and who it is partly intended for, won't purchase it... which is a shame... also means lost sales/profits for the publisher. With slightly smaller print, less white space, maybe thinner paper, and perhaps even a softcover, this volume could've been brought in well under 400 pgs. and at a lower price... and, been less imposing to readers. (I don't know if the British edition is any different from the American edition.) Even the title (probably meant to be intriguing) I suspect is a bit imposing, abstract, and maybe overly long to many, and could've been better chosen.
Anyway, I mention all this because I've seen several examples in the last couple years where a book's sales might've improved simply with a little more attention paid to certain physical elements of the volume, and greater consideration of the target audience -- and the goal should be to get these books into as many hands as possible... or at least not to scare off any more readers than needed. Matt has his own wide following, so those folks are an automatic audience, but I'm interested to see a book like this swept up by readers who have never heard of Matt Parker, or who usually avoid math books. (If I'm wrong here and the book's final features/format were actually the result of massive test-marketing and research than I'll be happy to hear about it.)
Might add, as a side-note, that I've long thought Princeton University Press (not Matt's publisher) is a publisher that generally does a great job with the physical presentation of their popular math books... maybe they've been at it longer, or specialize in it to some degree, but kudos to them for whatever the reason.
Well, I need to get back to reading Matt's volume; some reviews say the second half is even better than the first!
[And now that I've finished reading it, I've added another short blurb about it HERE.]
Friday, December 5, 2014
1) For the puzzle-minded, John Allen Paulos wrote up this clever one last weekend:
2) Evelyn Lamb experiences "existential angst" over music and integers... and that's a fascinating thing for the rest of us (but what would Sartre think? ;-):
3) In praise of Inquiry-based Learning (IBL) (h/t to Patrick Honner for pointing out this AMS piece):
4) Laura at "Math For Grownups" wants to interview people about how they use math in their jobs/careers:
5) Matt Parker is excited about the Stern-Brocot sequence. See why, via Numberphile:
6) Someone (I lost track of who) tweeted a link this week to this relatively new site that looks interesting (for sparking mathematical thought/ideas):
7) Alexander Bogomolny reviewed "The Best Writing On Mathematics 2014" here:
8) The fascinating case of a misprint in a 1970 math paper that gets Brian Hayes investigating:
9) Not even exactly sure why, but a basic piece on prime numbers made it into the "Business Insider" yesterday:
10) Per usual, you can check out MikesMathPage to see what Mike Lawler & the boys have been up to this week: http://mikesmathpage.wordpress.com/
Since we're approaching gift-giving time, you might want to start with Mike's positive review of a recent new math board game from our fellow bloggers over at Math For Love:
11) And lastly, I'm still curious (over at Math-Frolic) if anyone knows who "Andy Naughton" is and how did he end up reading minds? ;-) :
Have a good weekend all!....
Monday, December 1, 2014
I didn't believe 2014 could be as banner-a-year for popular math books as 2013 was, and, I don't believe it has been... but, still a dang good year!
Back in June, I predicted Jordan Ellenberg's "How Not To Be Wrong" would end up as my favorite book of the year, and that's proven true, though with a bit of semi-stretching (I'll get to later) it has a strong competitor. I've never seen a bad review of Ellenberg's book. If you haven't read it, get it! If you have read it, read it again!
Meanwhile, Alex Bellos gave us another fine effort this year with his "The Grapes of Math" (American title)... another fun, enjoyable, instructive read from Alex.
The above are the two main new volumes I recommend Xmas wrapping for a general readership of mathy stuff.
For the puzzle-lover on your list I don't think you can do much better than Ian Stewart's recent "Professor Stewart's Casebook of Mathematical Mysteries." Stewart's previous puzzle compendiums are just as good though, if you don't need to have his latest volume.
Also, worth noting that one of my favorite Stewart books, "Visions of Infinity," is newly-out in paperback (not a 2014 volume, but still worth suggesting).
Three more 2014 volumes I don't mind recommending to narrower audiences are: 1) "Mathematics and the Real World" by Zvi Artstein -- a volume I have some qualms about, but ultimately liked the overview it gave of math history 2) "Four Lives: A Celebration of Raymond Smullyan" from Jason Rosenhouse -- a volume suited primarily for Raymond Smullyan fans. I often don't see Rosenhouse's volumes distributed very well -- honestly, I believe he needs a new agent or publisher(!), because he's one of the best, most consistent math writers out there (and I say that as someone who doesn't always agree with him, but always finds his arguments thoughtful and well-stated -- for this particular volume though, I'll note, he is just editor). Finally, 3) a volume I'll recommend without having finished it yet, is the latest "The Best Writing On Mathematics 2014" ed. by Mircea Pitici -- each edition of this series has been better than the one before, and I think that trend continues in this rendition, which seems full of interesting stuff. I'm always impressed with Pitici's diversity of choices, even though there are always ones whose inclusion I don't quite understand. Anthologies are typically a mixed bag, but hopefully the selections you don't care for will be outweighed by the number and quality of those you do enjoy.
A couple of quick mentions to two volumes I haven't read, but have seen consistently good reports on: 1) Tim Chartier's "Math Bytes," and 2) Matt Parker's (British book) "Things To Make and Do In the Fourth Dimension." [I've now written a bit more about Parker's volume HERE and HERE.]
One volume to throw in simply because it may be a hit for the holidays is "The Mathematics Devotional" from Clifford Pickover. Personally, I'll wait 'til there's a soft-cover version, if I purchase it at all (may eventually buy it simply as a source for more "Sunday Reflections" over at Math-Frolic). As much as I love Dr. Pickover's earlier popular math output, I've not been a fan of the recent, more 'formulaic' and visually-gaudy series from him -- just my personal preference. Having said that, anything that gets math/science into the hands of more people I'm all for, and his books have succeeded at that (or at least they're dwelling on a lot of home shelves and coffee tables). So give it a look if it suits your taste, but I can't honestly recommend this pithy, glossy volume for those on limited budgets, who need more bang for the buck. Also, know that a "Physics Devotional" is in the works.
Reaching back to 2013. A couple of wonderful books from that year, are now out in paperback: "Love and Math" by ever-inspiring Ed Frenkel, and "The Simpsons and Their Mathematical Secrets" from Simon Singh (one of the most fun math reads ever). Both must-reads for the math-enthused, if there's anyone left who has missed them.
Finally, here is my 2014-stretch (alluded to above): Richard Elwes put out two 2013 books that are fantastic (but poorly distributed in the U.S.): "Math In 100 Key Breakthroughs" (a GREAT reference source) and "Chaotic Fishponds and Mirror Universes" an informative, wide-ranging (ill-titled) book that I didn't acquire until 2014, and enjoyed almost as much as the Ellenberg volume -- it's hard for me to even recommend one over the other, but in-the-end, Ellenberg is set apart from all competitors by his witty, fanciful style, so rare (indeed difficult) in a popular math book, so I give him the nod, but do VERY highly recommend Elwes' book.
Anyway, these are some of the book stand-outs for a general audience from my view, but there were LOTS of other popular math offerings in 2014. If you had a favorite you wish to make sure readers consider, feel free to mention it in the comments. And let's see what 2015 brings our way (among other things a new biography of Martin Gardner is on the horizon).
Friday, November 28, 2014
A somewhat-shortened week and another list of links:
1) Couple of Presh Talwalkar video problems from the week:
and here, Presh's explanation of "ultimate tic-tac-toe":
2) The interesting story of a mathematician who found a "massive net security hole" in email from a Google domain:
3) Cathy O'Neil explains Andrew Gelman (p-values):
4) Interesting piece re: RSA encryption:
5) Physicist Sean Carroll was thankful for Fourier transforms this Thanksgiving:
6) Meanwhile, algorithms going awry:
7) And once again, visit MikesMathPage for any number of weekly offerings:
Monday, November 24, 2014
Such serendipitous timing (and inspiration) once again from Dr. Keith Devlin. I was in the process of writing a post about "knowing" or "proof" in mathematics... and along comes Dr. D. to finish my post off for me!
First, the preliminary bit I'd been working on:
We'll start with an old joke that most readers are familiar with....
An engineer, a physicist, and a mathematician are riding a train through Scotland, when they look out the window and see a lone black sheep in a field. The engineer remarks, "Hmmm, I guess in Scotland all the sheep are black!" The physicist replies, "No, no, no! Only some Scottish sheep are black." To which the mathematician, rolling his eyes at his fellow travelers' sloppy logic, chimes in, "All one can say is that in Scotland, there is at least one sheep who has at least one side that appears to be black at least some of the time."
As often happens in comedy, the humor stems from an intrinsic kernel of truth... that mathematicians, unlike philosophers, physicists, and others, really are constrained by a stricter regimen of logic and deduction than prevails elsewhere. Of all the sciences, "induction" is probably least acceptable in mathematics, even though reams have been written about the philosophical shortcomings of induction more generally.
One can't conclude just because the first billion values plugged into the Riemann Hypothesis hold true, that therefore the hypothesis IS true, or if the first trillion digits of pi reveal no pattern, that by itself, wouldn't mean there was no pattern to pi. In fact, and sometimes hard for the layperson to comprehend, in mathematics, "billions" and "trillions" and the like, are really very very very very tiny numbers anyway.
A classic example of what mathematicians are up against was the 1885 Mertens Conjecture, which proposed that the sum of the first n values of the Möbius function had an absolute value of, at most, √n. ALL human/computer calculations support the conjecture, but 100 years later, in 1985, Andrew Odlyzko and Herman te Riele theoretically disproved it. So despite the fact that ALL calculations affirm the conjecture, somewhere out there is a "bad" n with a currently known upper bound of e^ (1.59×1040).
[A 2012 "Gödel's Lost Letter" post on "Apocalypses In Math," including Mertens, is worth reading http://rjlipton.wordpress.com/2012/12/21/what-would-be-left-if/ ]
You don't have to understand the technical details of the conjecture to sense the giiiiinormousness(!), of that upper bound value. Again, it means that even though the conjecture is TRUE for ALL values ever (so far) plugged into it, it's now known that somewhere out there lies some value for which it is UNtrue.
(And perhaps I should say, lest any reader s'pose that the Mertens Conjecture is some minor, off-the-wall bit of eclectic, unrepresentative math, that IF it had been proven true it would've implied the truth of the Riemann Hypothesis, and all the consequences that flow therefrom.)
Anyway, the word "proof" or "proves" has been an annoying pet peeve of mine across the years. There are NO proofs in science. There is simply the aggregation of evidence... "induction" is certainly rampant, but proof, not so much. E=mc^2 is NOT proven. Evolution is NOT proven. The existence of the moon, or for that matter my own existence is NOT proven... they just all seem to be the case given our perceptions/interpretations. The philosophical endpoint-conundrum here is that we can't demonstrate conclusively whether-or-not we are anything other than a "brain-in-a-vat," or automaton, completely under the control of a much higher Martian being. What we call "proof" is, at best, a notion residing in the self-enclosed, essentially tautological realm of concocted logic and math.
I once left a comment on a well-known scientist's blog when he wrote about something that was true and proven in physics. I took issue saying that technically it wasn't proven, but simply had a vast preponderance of evidence supporting it (as we perceive the evidence). His response (paraphrasing from memory) was that "Well, of course if you mean 100% absolute metaphysical proof you're right, but nobody seriously uses the term in that sense in everyday parlance, so for all-intents-and-purposes it is proven." And that of course is my beef, that "proof" has been so watered-down, polluted by language and argument, that its precise meaning is lost, and we ought, whenever possible in science, deal in precise, not compromised, meanings.
Recently someone in a Twitter stream stated something to the effect, 'Philosophy deals with ideas, physics with evidence, and only math with proof.' I came close to re-tweeting it, but in the end didn't feel comfortable enough with it. And one reason it didn't 'feel quite right' has to do with Keith Devlin's latest posting where he takes discomfort with the word "proof" to the next level, essentially saying (and I hope I'm not mis-stating him here) that induction and imprecision inescapably raises its ugly head even when and where we are unaware of it, including mathematics.
Read and savor his entry here:
...it has a number of links, and also leads in turn to a secondary, related post about his ongoing MOOC here:
Early on he says, "These days I have a very pragmatic perspective on what a proof is, based on the way people use them in the day-to-day world of mathematics: Proofs are stories that convince suitably qualified others that a certain statement is true."
"Proofs" as "stories" -- I love it, and surely a new way for most folks to wrap their brains around the term. Dr. Devlin spends the rest of the post fleshing out the idea.
I suspect the average bloke won't get much from Dr. Devlin's message, but for scientists and mathematicians I think it must-reading.
It's been awhile since Dr. Devlin had posted new blog entries. And reading these two pieces from him I almost feel like an addict who was long overdue getting a 'hit' from his drug-of-choice (and I mean that positively! ;-) I feel refreshed and reinvigorated just reading these two posts!
As Keith writes in the beginning: "What is a mathematical proof? Way back when I was a college freshman, I could give you a precise answer... But I was so much older then, I'm younger than that now." ;-) And then he links to the original Dylan version, but I think I'll opt for the smoother voices of the Byrds:
P.S.: so far as I'm aware the word "proofiness" was originally coined by Charles Seife in the title to one of his popular books.
ADDENDUM: in the course of an email someone mentions that they're not clear what my point is above since it seems like Dr. Devlin's view (of 'proofs as stories') contradicts my initial stance that "proof" is a more stringent term in math than other fields. That's my fault for not making the transition more smoothly: yes, I started this post thinking I would write about why the term "proof" ought be strictly relegated to mathematics and logic, and NOT used in other sciences nor in everyday parlance... but before I could wrap it up, along came Keith to say that e-e-e-even within mathematics "proof" is an inexact term, not being applied quite as people envision. I thought that was an awesome (and subtle) point and a better wrap-up than what I'd had in mind -- and I don't think it's so much a contradiction to my point, as it is yet a further extension of how loosely "proof" gets bandied about. Hope that helps.
Friday, November 21, 2014
Newest mathy grab-bag:
1) George Hart presents 4 mins. of an elliptic hyperboloid:
2) A MathMunch weekly wrap-up:
3) A couple more tributes to Grothendieck:
4) William Cook's "In Pursuit of the Traveling Salesman" is newly-out in paperback:
5) There's a new StackExchange now, specifically for the history of science and math:
6) Evelyn Lamb dabbles delightfully in monosyllablism and Rolle's Theorem here (...Theodor Seuss Geisel would approve):
7) A mathematical reporter tries to answer the question 'How much Hollywood glamor will rub off on mathematics?' from the 5 Breakthrough Prize mathematics winners:
8) Dr. Keith Devlin, Dr. Mark Saul, and recent Putnam Prize winner/Yale student Xiao Wu talk mathematics in a 50-minute radio interview (from WNPR), accessible here:
9) It's an exciting time for primes... so says a new 10-minute introductory video on the topic:
10) Lastly folks, I surrender -- I CAN'T keep up with all the nifty posts/videos Mike Lawler puts up and also read my email each week (you know, like walking and chewing gum at the same time ;-); so rather than pick out specific offerings from Mike, I'll just direct you to his page (which hopefully you already follow anyway!) and let you pick the ones most pertinent to your math interests; there's always somethin' good!:
Friday, November 14, 2014
...First off, biggest news of the week was the death of Alexander Grothendieck on Thursday, which I referenced (with links) in my Math-Frolic post earlier this morning:
Otherwise, bunch-of-links from the week:
1) A post from RJ Lipton on Stanislaw Ulam and an unproved conjecture:
2) Chris Harrow explored some geometry of squares and octagons in this post:
3) Several miscellaneous resources for teachers linked to from another blogger:
4) Via the Sante Fe Institute, the mathematics of scaling from physics to biology to beyond:
5) Another piece on Common Core, but what's really telling are the 100+ vociferous (mostly-anti) views in the comments section:
(...hard to see how this ends well :-((
6) With Mersenne Primes in the news this week, Mike Lawler took the opportunity to explore them with his boys:
(I don't remember how old I was when I first heard of Mersenne Primes, but I know I was a LOT older than Mike's kids! -- wonderful that they can be introduced to the subject at such an early age!)
7) Another new video from Ed Frenkel on the secret world of math:
8) Vanity Fair and Arne Duncan cover Sal Khan (Khan Academy) here:
9) A new Carnival of Mathematics here:
10) Princeton Alumni mag. profiles recent Fields Medalist Manjul Bhargava:
11) Nautilus covers the amazing, award-winning work of Japanese mathematician Kokichi Sugihara on optical illusions:
12) Wow! Terry Tao appearing on "Colbert Nation" this week:
13) Interesting Andrew Gelman take on the massive-online Facebook experiment from awhile back:
14) I'll end with this somewhat tangential (but I think highly important) piece to mathematics... NEJM addresses the crucial topic of communicating scientific "uncertainty" to a public that largely misunderstands science:
Friday, November 7, 2014
Some links from the week (potpourri links and blog posts may decrease somewhat as I'm busy with other Web stuff through end-of-year):
1) Mike Lawler offered up a bunch of fun math examples from the week in this post:
2) The mathematics of falling objects results in tragedy:
3) Of "points and lines" via Richard Elwes:
4) Princeton University Press announced the selections for its "Best Writing on Mathematics 2014" edition:
5) Keith Devlin's latest:
6) A fork in the road... classic-type logic puzzle from Futility Closet:
7) "a nice short documentary by student filmmaker Damiano Petrucci about mathematics and mathematicians" from The Aperiodical blog:
Friday, October 31, 2014
Links from the week:
1) Some puzzles from Presh Talwalkar started the week:
And some more puzzles here:
2) If you can't get enough of James Grime, Reddit did an AMA ('ask-me-anything') thread with him this week:
3) Evelyn Lamb told us about Euclid, geometry, and a possibly grumpy Omar Khayyam here:
and for Halloween, Evelyn takes on a hot (but scary?) topic in math -- homotopy groups:
4) Some instances of "bad math" from the popular press:
5) Rubik's Cube fans, have at it (...if you dare):
6) Back to Presh Talwalkar, who offers up an auditory example of the Bell curve:
7) Do you like your set theory made simple... see n-Category Cafe:
8) Lastly, in time for the Holidays... "The Mathematics Devotional" from Clifford Pickover is available:
Friday, October 24, 2014
Another jumble of links from the week gone by:
1) Okay, he may not be Martin Gardner, but Mike Lawler has been compiling quite a body of digital work week after week after week (both written and video). I'm astounded by his output, and don't even have time to catch it all, but here's one contribution from last week (...and seriously, if you're a math teacher or a parent you ought be FOLLOWING Mike's stuff regularly) :
His general blog here: http://mikesmathpage.wordpress.com/
and his video channel here: http://tinyurl.com/kftdekb
[and if you missed it, I interviewed him earlier this year here:
2) Several folks have pointed out this Terry Tao story problem from the beginning of week:
3) Agree or disagree with him, Gregory Chaitin has been putting out provocative, intriguing ideas for a long time now. "Mathematics Rising" briefly discusses some of them in this post touching on information theory, biology, consciousness, and the brain (includes some great quotes from Chaitin):
4) h/t to Cathy O'Neil for calling attention to this interesting (and longish) interview with computer scientist Michael Jordan about big data, computing, and artificial intelligence (he sees a "big data winter" ahead):
Jordan wasn't entirely happy though with the interview presentation, and wrote a followup here, for clarification:
5) Paul Lockhart's "mathematical lament" continues (deservedly) to make the rounds:
6) Plenty of variety at the 79th "Math Teachers At Play" Carnival here:
7) A few recent problems from Futility Closet if you missed them:
8) Jo Boaler on 'number sense' here:
9) A general article on mathematical modelling and epidemiology (in the day of Ebola):
10) Another interesting piece in the popular press (Forbes) on Common Core, focusing on the cognitive or developmental arguments:
11) Will just note, in closing, that one of my favorite fun mathematical reads, Simon Singh's "The Simpsons and Their Mathematical Secrets" is newly-out in paperback. Another great possible stocking stuffer for any math fans on your Xmas list (...if there's even anyone left who hasn't already read it).
Friday, October 17, 2014
Mathy stuff from the past week:
1) Andrew Gelman on liberal and conservative statistics:
and here, Gelman discusses the "statistical crisis in science" in latest edition of American Scientist:
2) A short piece on randomness (h/t Jennifer Ouellette), with some links and a video:
3) A series from io9 on logic puzzles:
4) A new Carnival of Math up here:
5) An epidemiological math model attempts to predict the curve of the Ebola outbreak here:
6) Ben Orlin recounts the symbiotic relationship between math and science:
7) Newly-posted 1994 interview with Martin Gardner from MAA this week on YouTube (wonderful!):
I don't usually hint ahead of time what the Sunday Reflection at Math-Frolic will be, but I will say that this coming Sunday's will be in tribute to Gardner, including the above video, in honor of the Centennial of his birth which arrives on Tues.
8) For those interested in some more technical reads, Nuit Blanche blog offered up this list of links yesterday, worth checking out:
9) Another biographical piece on Alexander Grothendieck:
10) Finally, this week, will leave you with this British piece for those math students who ask, "when will I ever use this stuff?," because you just never know when math might come in handy:
Tuesday, October 14, 2014
Recently treated myself to a few older books from Amazon, three of which I just want to pass along:
1) Have mentioned Steven Strogatz's 2009 "The Calculus of Friendship" multiple times in the past (at Math-Frolic). I read a library copy quite some time ago, and always wanted my own hard copy... delighted to now have it. Recommended to teachers, students of all stripes. And if any of you think it's just a simple, sentimental story, NO, it actually includes real math along the way, as only Dr. Strogatz can tell it (but, yes, buy it for the beautiful story, the math is a bonus!). Really, no math-lover should miss it.
2) Richard Elwes consistently amazes me with his knack for math explication. The book I ordered is his 2013 "Chaotic Fishponds and Mirror Universes" (subtitled, "The math that governs our world"), and so far, it is way surpassing my expectations (the title doesn't do it justice!). A splendid diversity of engaging topics made timely. Richard is British, and for reasons I don't fathom, his books often don't get very wide US distribution -- absolutely ashame! One of the best popularizers out there! Come on American distributors.
As we get close to the end of the year, Jordan Ellenberg's "How Not To Be Wrong," thus far remains my top popular math pick for 2014... BUT IF Elwes' book were from this year instead of 2013, it would be in the race for that designation! Another great choice for any young math-lovers on your Christmas list.
3) Finally, one of my old stand-byes: Renaissance-man and logician-supreme, Raymond Smullyan -- I have enough of his puzzle books, but ever since reading his Taoist-inclined, "The Tao Is Silent" (1977) I've wanted to read more of his output on spirituality. The book I got, "A Spiritual Journey" (2009), is essentially three small books in one: the first part focuses in a general way, on the philosophy of religion, the second part is on Ralph Waldo Emerson and Transcendentalism, and the last part is on Richard Bucke's notion of "Cosmic Consciousness" -- it won't suit everyone's taste, spirituality being such a personal matter, but if you liked Martin Gardner's "The Whys of a Philosophical Scrivener," you will likely enjoy this offering from Raymond, which so closely mirrors my own views and Gardner's (though the writing is a bit stodgier, less smooth and concise than Gardner). No math here either, but Smullyan on ANYthing is worth savoring.
There are of course plenty more recent top-notch 2014 popular math books on the shelves to choose from... but always fun to catch up on things one has missed from the past. Smullyan is now in his mid-90's with the quick, lucid mind of someone half-his-age, Strogatz is 55, and Elwes is the kid on-the-block at 36 -- each very different in style and interests, but each leaving us an outstanding body of work for our enjoyment and elucidation. Thanks guys, you've given me Christmas in October!
Friday, October 10, 2014
ICYM any of these:
1) Wonderful Atlantic piece on Steven Strogatz's introductory course for those who think they hate math:
2) For your statistics entree this week I need only offer up this smorgasbord from William Briggs that gives links to pieces he does, or does NOT, find enlightening:
3) Also, statistically-speaking, this rant about Washington Post coverage of a certain journal study, once again indicating why correlation is so much more fun than causation ;-):
4) Finally, before leaving statistics aside, this blog post, "Randomness: the Ghost in the Machine?" makes for some good reading:
5) Part of Mike Lawler's week revolved around the Koch snowflake, area, and infinity, ohh my!:
and in another (l-l-longish) posting, with LOTS of links, Mike spells out some of the real-world topics that ought make math interesting for the average person (plenty to chew on here):
6) This week's entry (…well, one of them) in the Common Core debate:
7) I've never had the least bit of interest in the Zombie craze, but if you do, Alexander Bogomolny reviews a volume that might suit your taste -- "Zombies and Calculus":
8) Keith Devlin's latest post defending Common Core:
From my perhaps-objective(?) perch outside the whole education system it seems that the opponents of Common Core are more organized, more unified, and more vocal than the supporters, and that will be a difficult combination to overcome in the current political climate (education being highly politicized) -- so, while I think supporters of Common Core will win this war (such as it is) in the long-run, in the shorter run, I suspect they'll be losing many battles.
9) And moving from primary/secondary education on to adult learning, NPR reports on the Pathways Project from the Carnegie Foundation and its new approach for adult math learners:
10) Jordan Ellenberg reviews Christian Rudder's new book, "Dataclysm" here:
11) New version of Euclid's Elements in scrumptious color:
And one last piece of book news... Ian Stewart has yet another compendium of math puzzles out: "Professor Stewart's Casebook of Mathematical Mysteries"... looks like a good collection, some classic and some fresher, or at least newly-rendered. If you've enjoyed his other volumes, or like math puzzlers more generally, give a look; or, if you're thinking ahead to Christmas, might be a good choice for some math lovers on your list!
...these should keep you busy for awhile.
Friday, October 3, 2014
This week's grabs:
1) Someone knows the whereabouts of reclusive mathematician Alexander Grothendieck, and obtained a photo of him for use in a Heidelberg Laureate collection:
2) Interesting interview with Terry Tao from early September:
Also, Terry Tao noted this week that the "final paper" summarizing the results of the Polymath8 project on the "bounded gaps between primes" problem has been uploaded to arXiv here:
3) The nature of evidence and proof via the Simons Foundation:
4) Science graduates have difficulty with math:
5) MatthewMaddux linked to a World Science Festival clip discussing what CAN'T be predicted with mathematics:
6) Interesting Nautilus piece on math, learning, memorization, and practice:
7) Another education piece from Keith Devlin in Huffington Post:
8) Finally, I got to interview one of my favorite writers last week: Paula Poundstone's cousin (William Poundstone):
Sunday, September 28, 2014
Math-Frolic Interview #26
"Our inability to recognize or produce randomness is the most invisible of problems. Randomness is like air, all around us and never noticed until the gale hits. We are not prepared to connect our difficulty with randomness to the real world of missed tennis serves, bad passwords, and Ponzi schemes."
-- William Poundstone, from the Epilogue to "Rock Breaks Scissors"
William Poundstone is one of my favorite writers (twice nominated for a Pulitzer), and one of the more eclectic folks I've had the pleasure to interview here. He has explored an odd and wide range of topics in his writing, but is not a mathematician nor mathematical writer per se, so many readers here may be unfamiliar with him. Still, his topics often impinge on underlying mathematics, while having an uncanny way of also sliding between the boundaries of science, logic, psychology, philosophy, and finance/economics. I reviewed (and enjoyed) his latest work, "Rock Breaks Scissors," HERE. Another of his books, "Are You Smart Enough to Work at Google?" was dedicated to the memory of Martin Gardner.
His homepage is here:
and I found an interesting podcast interview from 2011 with him here:
If you're not already familiar with him I hope his responses below may entice you to check him out further (but if they don't, then maybe knowing that he is Paula Poundstone's cousin WILL! -- though I can't imagine what genes they could possibly share ;-)):
1) Information on your background has been surprisingly hard to come by! (though I did learn that you studied physics at M.I.T. before becoming a writer). Your book bios and Wikipedia page don't have much info on your past, and even the quirky "about me" page at your personal website doesn't divulge much. Is that because you're secretly a CIA-operative? ;-) Seriously, can you fill readers in a little on your background and how you arrived at the interests/writing-life you have today?
Well, without saying too much about my age, I have been a full-time author for longer than the World Wide Web existed(!) I suppose that's why there's not much web presence for my pre-author life. I did spend a year as an editor (with Brentwood Publishing, now defunct, which produced trade journals). I found that very useful as it taught me fine points of grammar and usage that I never learned in my formal education ("that" v. "which," "vale of tears" not "veil of tears," etc.) As to my interests, I was a big reader from the time I could read, in science especially.
2) My favorite work of yours is an older one, "Labyrinths of Reason." And like it, many of your volumes touch upon human reasoning or logic to some extent. How did you go from M.I.T. physics to such a psychological/philosophical focus?
I'm glad to hear you mention Labyrinths. It remains one of my favorites too. The book is about how we know what we know, and that's always an issue in physics. Things like quarks started out being a mental shorthand, a way of getting the right answer. By pretending that quarks, which you can never see or isolate, exist, you can make accurate predictions about the entities that you can see and measure. So it started out as fiction and became "nonfiction"—at least, we agree to call it that.
One of my favorite Stephen Hawking quotes: "Reality is not a quality you can test with litmus paper."
3) As a full-time writer what is your typical (if there is such a thing) workday like? Do you have a set routine?
I get up about 6 AM, read the news, work out on a treadmill, and am generally at work by 8. I work until about 5, but it's not all writing/editing. I do a lot of reading, I do interviews (of people I'm writing about, or giving interviews to promote my books).
4) Your agent is John Brockman. I've long-enjoyed his books and Edge website. What can you tell us about the experience of working with John and the Edge group? Is it forever-stimulating, fun, argumentative, thought-provoking….?
John is a great guy, and all those adjectives apply. BUT let me clarify that I'm on the opposite coast and see or speak with him only infrequently. (In movies, the writer-character sees his agent every day, and they live down the street from each other. That's generally not the reality!)
5) Many of your books hover around mathematics, but without being too mathematical or technical. Can you say how math fits into your daily or intellectual life… is it front-and-center to a lot of your thought, or more lurking in the shadows of the things that most interest you?
Also, do you still follow physics these days, and have any thoughts on the controversies/debates surrounding modern cosmology -- especially in terms of certain recent writers who argue that some high-level physics is bordering on metaphysics or pseudoscience?
I do take a quantitative approach to a lot of things — not to everything, which would be nuts, but to things where many others might not. Counting grams of saturated fat and carbohydrates comes to mind. And definitely, as I say above, I think the (meta)physics debate over what is real is interesting. How can one show that string theory, or the many-worlds interpretation are worth pursuing? Everybody says they're for Occam's razor, but that 14th-century implement doesn't cut it in today's physics! For one thing, it's not always clear what it means to minimize assumptions in physics far removed from direct human experience. Also, as a practical and even careerist thing, you often have to put an awful lot of work into a theory before you find out how simple it is—or isn't.
6) One curiosity note: Your latest work is entitled, "Rock Breaks Scissors," but the chapter in the book on the betting game 'rock, paper, scissors' is actually only a small portion of the book -- just wondering if there's some story behind how that ended up as the title for the volume?
"Rock, paper, scissors" is a game that almost everyone has played in which you're trying to predict someone else's "random" choice (which in fact isn't all that random…) Though this element exists in many other games and situations and conflicts, you encounter it in its purest form in RPS.
I had thought of using the title "The Outguessing Machine," but that implies it's about machines predicting, when you can actually do a lot of the predicting in your head.
7) You've written over a dozen books, but only one biography… that of Carl Sagan. Are there any other figures you've considered doing a biography of?
I had thought of doing a standard Claude Shannon biography… but this evolved into Fortune's Formula, exploring just a tangent of his best-known achievements.
[hmmm... interesting, "Claude Shannon" another person with the initials "C.S." ...perhaps Cat Stevens next ;-)]
8) Are you currently working on a new book, and if so, what can you tell us about it?
I'm doing a book addressing the question: How important is it to know facts in the digital age, when it's easy to look up any fact? Part of the research involves demographically balanced polling. I look at what people know—about school subjects, current events, and pop culture—and how that knowledge correlates (or doesn't) with things like income, relationship status, self-reported happiness, and sources of news and information (TV, newspapers, Internet, etc.)
...sounds interesting, as this is a debate currently going on within mathematics education: how much rote memorization is still necessary given the ease with which such information is digitally accessible; should children spend more time on working mathematically/algorithmically, and less time committing facts to memory?
9) Who are some of your own favorite current authors (nonfiction) to read, and what are some of your favorite books for learning or inspiration?
I read more fiction than nonfiction, and at least half of what I read isn't necessarily "current." I recently read Mark Twain's Life on the Mississippi and (from this century) Persi Diaconis and Ron Graham's Magical Mathematics and Edward Tufte's Visual Explanations. In fiction I'm reading Don Delillo's Underworld.
I suppose I should take the opportunity to plug Harry Stephen Keeler. He was an eccentric American novelist that a group of friends and I "rediscovered." Keeler would break all the rules of detective fiction, in one case introducing the guilty party, for the first time, in the last sentence of the book. One novel concerns the "Flying Strangler-Baby," a little person who disguises himself as a baby and stalks victims by helicopter. There is a Harry Stephen Keeler Society with a newsletter at http://site.xavier.edu/polt/keeler/.
Like I said, Bill is a bit of an eclectic fellow. Wikipedia describes him as "an American author, columnist, and skeptic," which hardly does him justice. You can check out all his books at Amazon here: http://tinyurl.com/lq87gko
Anyway, THANKS for taking some time with us here Bill, but I'm still gonna try to figure out either your age or a CIA connection...
Friday, September 26, 2014
Have some other projects eating up my time these days so another short-list of mathy links for this week (...hope to have another interview up on site, though, sometime Sunday):
1) Correlation is not… 50%…. Jordan Ellenberg takes issue with some New Yorker statistics:
2) Another voice FOR Common Core:
3) Keith Devlin talks about the 5th incarnation of his MOOC "Introduction to Mathematical Thinking":
4) Who doesn't like math podcasts!? (…uhh, don't answer that, it's a rhetorical question)… anyway, Sam Hansen has a new kickstarter project to fund a second series (anywhere from 8 to 16 episodes) of his math podcast "Relatively Prime":
5) Colm Mulcahy, in the Huffington Post, looks at the math connections to 5 of this year's MacArthur Fellows:
6) In the news: some (potential) math behind the Ebola outbreak:
7) Will end with a fun piece today from Evelyn Lamb on a friggin' failure from Fermat:
Friday, September 19, 2014
A short compilation of math bits this week (been busy on other things):
1) RJ Lipton's blog posted a little tribute to the interesting work of Stanislaw Ulam:
(and on a side note, worth mentioning that RJ Lipton was recently awarded the 2014 Knuth Prize for contributions to computer science)
2) Stephen Wolfram announced an online (cloud) version of Mathematica this week:
3) Mathbabe takes Christian Rudder's new "Dataclysm" book to task:
and on another day she offered this thought experiment (which, like any good conundrum, drew LLLOTS of comments):
BUT (again a side-note), her most powerful post of the week, was NON-math (and very personal) here: http://tinyurl.com/k6pql3l
4) Interesting 'language of math' article:
5) Jacob Lurie, the Harvard math prof., who won a MacArthur Fellowship this week:
6) My own review of William Poundstone's latest book, "Rock Breaks Scissors" precedes this post.
Wednesday, September 17, 2014
I keep seeing William Poundstone's latest book, "Rock Breaks Scissors" in the 'business' sections of bookstores… which I think is ashamed, because a lot of readers who would enjoy it may miss it there. More appropriately, and like most Poundstone books, it should be in a science/math area, or perhaps under psychology. Poundstone is one of my favorite authors; a good writer, dealing with subjects I find interesting, and at a level accommodating a lay readership.
Some of his volumes are deeper and richer, and others less so, but interesting and timely. This new book is in the latter category. It is yet another of the surprising array of recent volumes dealing with probability and numbers to hit the popular book market. Poundstone isn't dealing with math or probability in an academic context, as some popular volumes have attempted, but in a very reader-friendly, real-life practical sort of way.
The book is divided into two broad parts: Part 1 relates to "randomness" and part 2 relates to 'hot hand theory' -- the author tries to get across two opposing ideas that govern our actions: i.e., we often perceive things as random when in fact there is actually a pattern involved, and conversely, in other contexts of life we perceive patterns, where none exists and greater randomness is at work.
I'll briefly mention several chapters of the book:
The Prologue begins with some discussion of the work of information theorist Claude Shannon, but also includes mention of Bernie Madoff, as well as an entertaining, famous example from the retailer Target, a couple years back, when one of their purchasing algorithms deduced that a certain young lady was pregnant long before even her parents knew -- I mention all this simply to indicate the sort of diversity of subject that typifies this volume all the way through.
Chapter 1 is a little introduction to randomness, with some focus on examples from parapsychology, and also a well-known example from psychology of how poor, people are at creating "random" sequences when asked to do so (a knowledgeable individual or professor can pick out a human-created sequence from a truly random sequence).
Oddly, the title of the book stems from the quite short chapter 2 which is a treatment of the betting game, "Rock, paper, scissors," and various strategies to employ for greater success.
Chapter 3 covers some of the oft-used strategies (and patterns to look for) when taking multiple-choice exams, such as the SAT.
Chapter 4 offers strategies for playing lotteries -- I didn't find these very convincing (but then I don't play lotteries, so what do I know).
Some chapters follow delving into certain sports actions (tennis and soccer), and then card games, again always about how to better recognize, as a player, human predictability.
Chapter 9 is a practical one on creating passwords for the internet (especially after the author informs us that one "free hacking program, can test millions of passwords a second," and another "forensic" program "claims it can check 2.8 billion passwords a second." :-(
Chapters 11-13 are some of the most interesting ones, centered initially around Benford's Law (of integer distribution), and the ways it can be used to detect fraud, financial malfeasance, or just manipulated numbers.
Chapter 14 begins the second part of the book focused on "hot-hand theory." Hot-hand notions have been written about a lot in recent years (popularly in relation to basketball scoring runs), and it remains a controversial subject. Poundstone also notes that "hot-hand" notions are exactly opposite of another oft-cited prediction failure: "the gambler's fallacy" -- in the former, people overly believe a trend (sinking basketball shots) will continue to occur because it has in the recent past, but in the latter people erroneously believe a change will happen because of a non-probable trend that has just transpired (i.e., a roulette wheel will come up "red" because it just had 6 "blacks" in a row and is 'overdue.')
Anyway, chapter 15 moves on from specific hot-hand ideas to basketball betting pools (as in the NCAA March Madness tournament) -- oddly there is no mention of Tim Chartier's methods here, though they've received a lot of publicity the last couple of years.
Chapter 16 moves along to football pools, and I'll relate one quote I enjoyed from it:
"One problem with sports betting systems is that anyone who looks hard enough for a pattern tends to find one. It might be that the Denver Broncos always won on odd-numbered days in February when playing teams named after animals. Analytics is good at finding such patterns. It's not good at saying whether you should believe in them."
I think that more-or-less captures the message or sentiment of the whole second half of Poundstone's book.
Chapter 18, on 'Big Data' (everyone's favorite topic these days) is a fun, interesting intro to all the ways we can barely fathom that info is collected on us. Also, he gives a practical hint on how to get discount offers flowing your way, calling it the "abandoned shopping cart play." Again, I'll quote what to do when you're on a retail website:
"Put whatever you want to buy in a retail site's shopping cart. Click 'check out.' Begin filling out the form. Make sure you enter your e-mail address but don't enter any payment information. Leave the purchase in limbo and wait for the discounts to roll in."
(the point being that once you've expressed interest, but departed, the retailer is going to do whatever it takes to entice you back to complete an order)
The next couple chapters deal with pricing, followed by a chapter on predicting the future, where he notes that even professional experts are generally much better at forecasting far-off broad trends than predicting near-term happenings (which one might think would be easier to predict being so much closer in time) -- you might think in terms of predicting the percentage of heads in a thousand coin tosses versus predicting the percentage in say 10 tosses.
At close to 35 pages, Poundstone's final chapter, on the stock market, is by far the longest one of the book. If you're active in the market (especially if you trade for yourself) there will be MUCH of interest here, but if you have no connection to the stock market, and talk of things like PE ratios (which the chapter is VERY focused on) cause your eyes to glaze over, then this chapter will be a yawner.
Anyway, the volume is chockfull of examples and is a fairly fun romp (even if sometimes shallow and choppy) through many different, often timely, ideas. I do recommend it to folks, as I think most people will find various chapters of interest, and learn some practical or quirky tips along the way, though I can't predict ahead-of-time which chapters will be most rewarding to you, the individual reader... but then Poundstone probably could've predicted my limitation.
Friday, September 12, 2014
Some math links from the week:
1) Evelyn Lamb interviews one of the first-ever African-American math PhDs in the country:
2) Folding pizza… and Gauss:
3) Interesting thoughts from a one-time math-phobe:
4) Some Common Core Common Sense:
5) Word choice in STEM fields (at least somewhat more interesting than I was expecting):
6) Fawn Nguyen is resurrecting her mathtalks site:
7) Is homotopy theory a new foundation for mathematics:
8) I love quirky stories about the genius of great mathematicians. Here's a quickie that John Golden passed along this week that I'd not heard before (about John von Neumann):
9) A snarky problem from Futility Closet this week:
10) Here's a bit of a mind-stretcher from R.J. Lipton taking on a challenge from Freeman Dyson:
11) Terry Tao offers some simple statistical/paradox discussion here (h/t to Nalini Joshi for this):
12) If you want a little philosophy with your weekend coffee, try this from Nautilus ("Angst and the Empty Set"):
13) Lastly, just two days ago I took a look at a couple of math history books here: