"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)
Friday, February 27, 2015
Some things that caught my eye this week (when my power was on!):
1) Evelyn Lamb with some wonderful math history in a few telling letters betwixt Gauss and Sophie Germain:
2) Having some fun with Wolfram/Alpha:
3) Entertaining podcast interview (40 mins.) with Jordan Ellenberg:
4) A bit of number-fun from Gary Davis and Ben Vitale:
5) Andrew Gelman notes the problem of press releases and mathematical hype in this quick post:
6) Wow! I see from Princeton University Press's Spring catalogue that an 800+ page "comprehensive" biography of Euler (by Ronald Calinger) is on the way... for ~$50.
Now, how about a bio of Riemann next! ;-)
7) Math podcasts are "burgeoning," and the key is to "tell a story"... read all about it:
8) An interview with Ken Ono, mostly on his study of Ramanujan's work, with some update on the upcoming movie about Ramanujan's life:
9) A research journal (in social psychology!) has banned the reporting of p-values (h/t to Jordan Ellenberg for this one):
10) This site has made an interactive version of Newcomb's Paradox (and is researching responses to the classic conundrum):
(h/t to Colm Mulcahy for this one)
11) A bunch of mathy links associated with the Cambridge Science Festival, given here:
12) Hannah Fry reviews Cedric Villani's "Birth of a Theorem" for The Guardian:
13) Mike Lawlers' place on the Web: https://mikesmathpage.wordpress.com/
....and on Sunday I'll have another new interview up here, so y'all come back now!
Potpourri BONUS! (extra NON-mathematical links of interest):
1) Last week's NPR TEDRadioHour ("The Unknown Brain") started off with what may still be my all-time favorite TED Talk, neuroscientist Jill Bolte Taylor's remarkable viral 2008 story of experiencing her own stroke:
If somehow you've missed it, listen to at least her first segment on the show, but the whole hour is great.
2) And a couple of interesting reads from Aeon magazine (also, neuroscience-related):
a) the tendency of fiction to 'trump fact' on the Web:
b) human brain elasticity:
Sunday, February 22, 2015
Math-Frolic Interview #27
We are all simultaneously experts and beginners, flaunting our talents while trying to cover our shortcomings the way an animal hides a wound. You could call this a 'math blog,' or a 'teaching blog,' but I would call it a blog about owning up to weakness and drawing strength from successes, however transient or trivial they may seem."
-- Ben Orlin (from his blog)
I'm sure many readers here have been entertained by the fanciful cartoons that Ben Orlin uses to delve into mathematics and education at his blog, "Math With Bad Drawings" -- a blog that has established itself as one of the more distinctive, easily discernible sites in the burgeoning field of secondary math blogs. And because so many of us enjoy Ben's take on things, I wanted to learn more about him. Not unexpectedly, the humor evident on his blog comes through here as well:
1) First, some confusion: I see on the "about" page for your blog that you now teach in Birmingham, England. I always thought of you as a (Oakland) California teacher... When and why did the move happen, and is that temporary or likely permanent?
Temporary! Back to America in 2017, after my wife's postdoc here ends.
In late 2013, she was finishing her PhD and applying for 50-100 postdocs across the US. I'm a Boston kid, and I loved the Bay Area, but I agreed to move elsewhere (like Missouri or Wisconsin) if the job was good for her. The less exciting the location, the better the job had to be.
One day she says, "There's a great research fit for me at University of Birmingham."
My future flashed before my eyes: mosquitoes, high school football, Confederate flags. I said, "Well... is it a GREAT fit? Because, I mean, Alabama isn't what I was--"
"No, not Alabama!" she said. "England!"
We moved out here in August, and it's been great. (My apologies to Alabamans; I'm sure your state is lovely.)
2) Please tell readers a little about your math background... When did your math interest begin? When did you decide to pursue it professionally? And what are your main specific academic interests within mathematics?
My academic interests run a mile wide and three feet deep. There are parallel universes where I majored in Econ/Biology/Philosophy/English/Spanish. The way some people fear romantic commitment, that's how I fear intellectual commitment.
So why math? Because I got pulled in by great teachers and great classes. (And because I knew it was a marketable degree.)
As for interests within math... well, I'm a dilettante there, too. I love probability. I got a huge kick out of Galois theory and fractal geometry. Years of talking to my wife about her research have turned me into a bit of an analyst, too.
I know a little about a lot, and a lot about nothing. Very liberal arts, I guess.
3) These days there are a multitude of blogs from math educators. You almost have to have a gimmick to break out from the crowd. How did your blog start, and how did the amateurishly endearing cartoons you use come about (had you already done cartoons in the past)?
I wanted to write about math. But I knew math is really hard to read. The ideas are so dense, you need to surround them with fluff: pictures, jokes, stories, asides.
My original plan was to ask friends to draw illustrations for me. But who wants to sketch out somebody else's ideas, for a blog nobody will probably read, for no payment?
I've always been terrible at drawing. But I'd been writing about the value of learning new things, and seeing your gaps not as weaknesses but as chances to grow. So I figured I ought to practice what I preach.
Hence, the drawings. And the title.
Also, math intimidates people. I hoped the images, so manifestly incompetent, would put people at ease. They'd send a clear message: "Even if you feel like you're bad at something, you shouldn't be afraid to try it."
And it seems to have worked. While my drawings still safely qualify as "bad," they've gotten a lot better!
4) Your blogposts seem to range from silly to semi-serious, often ending, it seems to me, with some sort of moral to the (mathematical) story -- is that a fair characterization of your postings, or how would you describe them?
Sounds right! I don't think there's much of a unifying principle for the blog, other than bad drawings.
And how do the posts evolve before we see the final result on the blog -- do you start with a message you want to get across, and then work backwards to figure out how to tell a storyline producing that message, or does the story enter your mind first, and then you figure out what lesson it can be used to teach?
The posts tend to evolve over a long period. I've got a big folder of half-baked ideas, most of which will never see the light of day. Each follows its own trajectory, but here's a frequent evolutionary path:
(a) I come up with a message/moral I want to share. In its initial form, it's overstated and overconfident.
(b) Thirty minutes into writing, I recognize my own hubris, and start asking, "Where did I get this conviction? How am I so sure about this?"
(c) I think back to the experience(s) that led me to this conclusion: little moments, year-long adventures, single lessons, whatever.
(d) I write that story instead, trying to limit my conclusions to what that story can justify.
(e) It comes out overly general and hubristic anyway. And that's okay.
5) Do certain of your blogposts stand out as personal favorites or ones that were the most fun to work on? And from the other side, which posts seem to have been most popular or attention-getting from your readers?
Yeah! My favorites:
I "filmed" the gifs for The Math Aficionado's Guide to High Fives in my old school, along with a bunch of friends and my (amazing) high school math teacher.
I accosted conference-goers at the 2014 Joint Maths Meetings and had them draw pictures for 39 Ways to Love Math.
I woke up one morning and wrote A Fight with Euclid before lunch.
The Kaufman Decimals came out of a fun conversation with a friend.
A Ray of Light is one of the my more honest pieces of writing.
The Church of the Right Answer is a recent soap-box tirade that was good to get off of my chest.
And as for most popular, I've had four big hits. What It Feels Like to Be Bad at Math is still my proudest. Also, two of my humor pieces "went viral," Math Experts Split the Check and Headlines from a Mathematically Literate World.
But my most popular post, by leaps and bounds, is Ultimate Tic-Tac-Toe. It's been viewed something like 800,000 times, and has spawned a whole mini-industry of mobile apps. Nothing I write will ever again reach such a wide audience. It turns out that people LOVE tic-tac-toe.
6) How, if at all, do you utilize online math resources in your own classroom? And do you employ your blog or any social media, as teaching tools, in your classroom as well?
I'm awful about this. My 2015 new year's resolution is to steal more stuff. I have the bad habit of writing all my own materials, which is a lousy, time-destroying instinct. There's so much great stuff out there: nRich, Dan Meyer's three-act lessons...
I don't use my own blog, except occasionally to copy and paste an image.
7) You've written for some other outlets, notably Slate and The Atlantic magazine... how did those opportunities arise, and would you like to freelance more in the future?
I have a friend who works at Slate, who very kindly passed "What It Feels Like to Be Bad at Math" along to an editor there. Aside from that, I just pitched them stories via email.
I may pitch pieces again in the future, although being back in the classroom (after a year off) is keeping me plenty busy!
8) When you're not teaching math or cartooning around what are some of your other main interests/hobbies/activities?
I live in Europe now! So I have two main hobbies:
(1) Exploring new places (and being stupidly fascinated by trivial differences, like the signage fonts and the retail brands)
(2) Skyping home! Speaking of which, I'm going to check if my family is awake now.
Thanks Ben for rounding yourself out a bit here. I think the personality that concocts those whacky caricatures shines through. And regarding those cartoons, just one small piece of advice: ...hold onto your day job! ;-)
If by any remote chance you've missed Ben's blog introduce yourself to it with some of the links above (caution, you'll soon be hooked).
Ben tweets at: @benorlin
and has a Facebook page here: https://www.facebook.com/MathWithBadDrawings
[p.s. -- I believe??? all the broken interview links on the Math-Frolic interviews-listed page have now been fixed. And for next weekend I've got one of my very favorite math writers lined up!]
Friday, February 20, 2015
See which of these you've missed...:
1) A Marcus du Sautoy "In Our Time" podcast on the work of Kurt Gödel:
2) "Medical research is in bad shape" -- that's the first line in this interesting retrospective of John Ioannidis' crusading work since he first noted 10 years ago that "...most published research findings are false":
3) Alex Bellos profiles Fields Medalist Cedric Villani and his work here (H/T to Egan Chernoff for this one):
4) Patrick Honner carried on a Google+ conversation this week over the question of why there is so much more editorial criticism of K-12 math education in the U.S. than there is of college math education (several viewpoints expressed):
5) Interesting history and tribute to R.A. Fisher ("father of modern statistics") here:
6) Keith Devlin on R.L. Moore and the "Moore Method" of teaching (better known today as "inquiry-based learning" or IBL):
7) Cathy O'Neil summarizing some of the problems in the "practices of 'big data'":
8) A brief summary from MAA of the annual joint math meetings held in San Antonio last month:
9) New "Wild Cool Math" from James Tanton:
10) The latest "opinion" from Doron Zeilberger relates to the future of mathematical proofs:
11) "Ask A Mathematician..." site offers a nice tutorial on quaternions, octonions, and beyond:
12) Nautilus Magazine has been putting out consistently GREAT stuff of late, including now, this fabulous interview (both video and transcribed) with computer scientist Scott Aaronson (of the blog "Shtetl-Optimized"):
13) Over at AMS blogs Evelyn Lamb introduces us to a blog, "Social Mathematics," that looks good, that I'm ashamed to say I was unfamiliar with even though it's been around since 2007! Check out Evelyn's post and the blog itself:
14) Keep an eye on what Mike Lawler is up to: https://mikesmathpage.wordpress.com/
15) Not mathematics, but a fascinating geeky, historical piece from Amanda Gefter for Nautilus about William Pitts (previously unknown to me and apparently many other readers):
16) Finally, last Sunday, over at MathTango, I reviewed the new book from Michael Harris, "Mathematics Without Apologies" (...I kinda liked it):
Meanwhile, THIS Sunday MathTango will have a new interview with another delightful instructor from the math blogosphere. Stay tuned....
[p.s. -- I think I've now repaired links to ALL the other interviews as well, in case anyone had tried those recently only to find several broken.]
Potpourri BONUS (extra NON-mathematical links of interest):
1) Another incredible podcast from NPR's RadioLab last week... amazing segments on surviving rabies, and on what major medical procedures DOCTORS choose to have carried out on THEMSELVES (almost none) toward the end of life:
2) Speaking of end-of-life, ICYMI, in this NY Times piece Oliver Sacks, who has entertained and enlightened people for so long with his writings and talks, faces the same subject with his usual thoughtful perspective:
Sunday, February 15, 2015
"Mathematics Without Apologies" by Michael Harris....
"Insofar as the present book is about anything, it is about how it feels to live a mathematician's double life: one life within this framework of professional autonomy, answerable only to our colleagues, and the other life in the world at large."
-- Michael Harris
"...the only way somebody can be a scientist is that somehow their personality gets frozen at an early age... at the playful stage."
-- Andrei Kolmogorov (as quoted in Harris's book)
For starters, I'll say that this will be among my favorite math volumes for all of 2015... to which I'll add, your mileage may vary! (it won't suit everyone's taste). This is a volume that almost defies adequate review, so vast, variegated, and tangled is its content. It is as odd, eclectic, even intractable a piece of mathematical writing as I have ever come across. Peculiar, dense, trenchant, hopscotchy, sometimes turgid, verbose, hard-to-follow, even inscrutable... but also interesting, rich, quirky, creative, original, a tad enigmatic, unpredictable, curious, cerebral and thought-provoking, sprawling across the landscape of ideas and interests. Gregory Chaitin, in his blurb for the book, writes, "Mathematical high culture collides with pop culture and all hell breaks loose! Harris takes us on a wild ride -- never a dull moment!" I couldn't agree more (and how often can you say 'all hell breaks loose' in a math book!). A press release for it states that it is for "intellectually curious readers" -- that is a colossal understatement! The same press release calls the volume "post-post-modern" -- I understand where the description comes from, but as someone who isn't a fan of post-modernism I prefer to avoid that terminology (even though it clearly fits some passages in the book); but, if not post-modern, it's certainly post-1950s! ;-)
The author says at some point that this is a book he always felt needed to be written... and only when no one else did it, did he take the task upon himself. And he writes: "My original aim in writing this book was to suggest new and more plausible answers to the 'why' question; but since it's pointless to say why one does something without saying what that something is, much of the book is devoted to the 'what' question [what is mathematics]."
I'll say up front that much of the technical math in this book (which is not the bulk of the content, but it does exist) is beyond my ability to even judge, though given the author's credentials I certainly assume it credible and valid. I'll be dealing here more with the style/approach/presentation than with the technical aspects.
There is a lot of focus in these pages on Galois, Grothendieck, and Robert Langlands as initiators of grand, sweeping programs in mathematics. I mention that just to indicate the level of mathematics that is often addressed in these pages, even though the discussion is more general, and intended for a broader audience. This is not the typical popular math book written at the level of high school or early college math. Even without including a lot of technical, computational mathematics, Harris's subjects are deep and abstract and, depending on your background, may be difficult for a lay reader to follow. I like that sort of challenge, but some may find it off-putting, if they get lost in Harris's commentary or occasional technical jargon.
The book ranges all over the place: math, literature, science, psychology, history, music, culture, film... it's all here in bites. I'm sure the author had some idea how it was organized in his own mind, but I can't offer a clue! And that's not said as a criticism, just a warning to readers, and for me it gave the book a rollicking, unpredictable style that made it spirited. The writing is sometimes less-than-scintillating... because the subject matter is sometimes less-than-scintillating. It is a strange mix of dense, heavy, at times convoluted or rambly stuff, that is yet made scintillating and engaging by its very originality.
So even though I sometimes found myself lost reading these pages, it was lost in an exciting, challenging way... not in a dark, foreboding forest, so much as in a sunny, expansive, amusement-filled park!
Along the way, the author intersperses conversations between an imagined "performing artist" and a "number theorist" to make various points -- it is reminiscent of a technique used by Douglas Hofstadter in the past. I think Harris does an even better (less tedious) job of it than Hofstadter did, and doesn't overdue it as Hofstadter may have.
If you like puzzles, equations, computations, proofs, etc., this is NOT the math book for you. It's hard to describe WHO this book IS for!... certainly someone more interested in the contemplation of, and philosophy underlying, math, and its role in society, more than in doing or learning mathematics. On the other hand, only those with an already deep background in math will fully appreciate the ideas Harris eagerly romps about in.
I've tried to think of any other book I've read with a similar feel to this volume. Perhaps William Byers' "How Mathematicians Think," but only very slightly so. Harris references Jeremy Gray a number of times, so I wonder if Gray's volume, "Plato's Ghost," might bear some similarity, but I've not read it and can't say. The writing style reminds me a tad of David Foster Wallace (who also gets an occasional nod in the volume), but that too is a stretch. The author cites Thomas Pynchon from time to time, and mentions Pynchon's "non-linear" writing style -- again, I've not read Pynchon myself, but "non-linear" or "Pynchon-esque" just may be an apt descriptor for Harris's prose. Finally, there's a slight similarity here to Ed Frenkel's "Love and Math," but only in so much as both volumes turn some attention to the Langlands program, and both touch on subjects well outside the perimeter of mathematics, but Harris scampers MUCH farther afield than Frenkel. Essentially, I'm doubtful this work can be readily compared to any other math volume.
And I'd love to have been a fly-on-the-wall for the editorial sessions that produced this book! I could be completely wrong, but I imagine much give-and-take, with the editor requesting lots of changes, and the author unwilling to assent to them. To my ear, the writing just seems less edited, less clean, more disjointed, than what's customary in a popular math book -- it's more like the unvarnished author coming through. I also imagine the author making changes/additions right up to the very last moment, as this volume could never really be finished. ...But these are all just idle (and perhaps wrong) impressions on my part. Again, not intended as criticism, but rather a sign of the uniqueness of this multifaceted effort.
I'll only touch upon a few highlights from the volume:
Early on, somewhat oddly, the author discusses "charisma" (and competition) in mathematics -- both in the field of math study, as well as in the practitioners who do math. The discussion revolves around the "sociology" of mathematics, which, unlike either the logic, philosophy, or computations of math, doesn't usually get wide play. Harris also ends up touching on the Elsevier boycott that was spearheaded by Fields Medalist Timothy Gowers, and the "fascinating questions about the possibility of reconciling the goals of science with the material organization of society."
Chapter 4 presents an interesting treatment of the 2008 financial collapse, the Black-Scholes equation, and failures of mathematicians... there's a good reason that economics has been called "the dismal science" and this chapter exposes it.
Chapter 6 on the "mind-body problem" covers a lot of mostly non-mathematical ground. Harris spends some significant time discussing Ed Frenkel's independent film "Rites of Love and Math." Though both men work on the Langlands program, Harris actually spends more time considering, not Frenkel's mathematical work, but rather his popular short film that replaces the geeky mathematician stereotype with a loving (even nude!) mathematician in an uncompromising search for truth. The chapter feels like something written by a devotee of the humanities, moreso than the product of an academic mathematician.
There are a couple of chapters focused on number theory (Harris's main field), parts of which may be hard to follow without a firm grounding in that subject, but I think I found chapters 7 and 8 the most difficult to follow of the more general chapters. One interesting segment in chapter 7 though, recounts the use of drugs by many who were successful mathematicians (Erdös and his amphetamines being a classic case). And then, Harris writes, "Pharmaceutical enhancement may be redundant if mathematics is itself the drug." Next he quotes several mathematicians who make reference to how doing mathematics is like being on a drug. It's an interesting notion that helps explain the addictive quality that math has for so many practitioners, that non-mathematicians often find inexplicable.
In chapter 8 he looks at "tricks" in mathematics, but these aren't the simple or quick tricks you might learn in a YouTube mathy presentation, but much higher-level or abstract tricks that may not be easily grasped. Later in the chapter the always-interesting relationship between math and music is discussed.
Chapter 10 is on the "math-is-beauty" and "math's-unreasonable-effectiveness-in-science" themes. Even in dealing with such oft-treated matter, Harris's presentation is fresh and thoughtful. And it is also in this chapter that he comes full circle back to G.H. Hardy's "A Mathematician's Apology," in order to reiterate that he makes NO apologies for the beauty and usefulness of pure mathematics in our lives.
I've barely scratched the surface here of this volume's contents -- I won't apologize for that or for the large chunks that fell beyond my comprehension. Nor can I fully communicate the oddity and freshness of this uncommon effort. Along with a regular index, at the end there is a separate "Index of Mathematicians" of those mentioned by name in the text -- this index includes well over 250 individuals within a book body of 325 pages! And as for others (non-mathematicians) who get more than a passing mention in the book, here are some of those names: Aquinas, Goethe, Huizinga, Kant, Kuhn, Mehrtens, Pynchon, Wittgenstein... to give a sense of the breadth of material here (what the publisher, Princeton University Press, calls "a ridiculously diverse assortment of... sources"). Indeed! Additionally, there are ~70 pages of 'notes,' and a wide-ranging 20+ page bibliography -- much of it technical (indeed, I was surprised that several "popular" math works I looked for weren't even included).
I've read through this book once... which doesn't do it justice -- it's the sort of volume you can pick up, randomly turn to any page, begin reading, and gain more insight than was bestowed by the first read-through. The professional mathematician will no doubt get more from these pages than the lay reader can... and, probably find more to disagree with as well. Having said that, I also suspect people will, Rorschach-like, read into many of Harris's passages what they think or want him to mean, rather than what he intended. Doug Hofstadter has written in the past, that despite the praise (and awards) lavished upon his first book, "Gödel, Escher, Bach," most reviewers got the book wrong. The same may happen for much of Harris's content.
Still, I love that this volume reveals a mathematician who breaks out of the nerdy math stereotype to talk philosophy, humanities, arts, culture, literature, and other subjects too often missing from the public's image of the professional mathematician. I can appreciate Harris's discussion... even when I don't fully comprehend it, because I value seeing the inner mathematician turned loose for public consumption. I don't recommend you all read this book once... I recommend you read it, indeed savor it, 2-3 times. It will certainly be re-appearing on the Christmas list I compile at the end of the year for readers. It stands, perhaps, in a category of its own.
Peter Woit reviewed the volume here:
...and there is an interview with the author here:
Friday, February 13, 2015
A non-spooky Friday-the-13th! edition of potpourri:
1) A summary of some recent math events from "Math Drudge":
2) Peter Woit gives this interview with Ed Witten a big thumbs-up (covers some thoughts on number theory, Langlands program, dualities, and other recent advances at the interface of math and physics):
3) A bit about thinking 'fast and slow' in this post on the "cognitive reflection test" and creativity:
4) Analyzing the long-and-the-short of crossword puzzles... an interesting (as always) tidbit from "Futility Closet":
By the way, on a side-note, if you've never seen what some consider the cleverest NYT crossword puzzle of all time ('predicting' the 1996 U.S. Presidential election) you should check that out:
5) A longread: in this, a further year of Alan Turing remembrances, Neil Gershenfeld reminds us why Claude Shannon also deserves much recognition:
6) The latest incarnation of Keith Devlin's "Introduction to Mathematical Thinking" course starts up this weekend:
7) The newest "Carnival of Mathematics" up here:
8) Khan Academy is launching "LearnStorm" a new initiative in math skills learning/competition, initially for 3rd through 12th graders in some California counties (to be broadened out if successful):
9) Game theory via Freeman Dyson and William Press in Quanta Magazine:
10) H/T to John Golden for pointing out this Boston Globe opinion piece by a math teacher weighing in on the education debates:
11) Pick-and-choose from MikesMathPage here :
12) And with tomorrow being Valentine's Day, MathMunch offers an appropriate posting:
...and for Math-Frolic, I once had a semi-Valentine's tradition of referencing this old Jennifer Ouellette post... I'll do so again:
P.S. -- Sunday, here at MathTango, I'll be reviewing Michael Harris's remarkable new book "Mathematics Without Apologies."
Potpourri BONUS (just extra NON-math links for your enjoyment) :
1) If you love the poetry of Mary Oliver you'll want to hear last week's podcast episode of Krista Tippett's "On Being" in which she interviews Mary for an hour (...and if you don't love the poetry of Mary Oliver, well, what... is... friggin' WRONG... with you!? ;-):
2) And from NPR another fantastic "Invisibilia" episode this week on the encroachment of computers in our lives, cool or creepy?:
[...please let me know ASAP of any broken/bad links]
Friday, February 6, 2015
ICYM any of these:
1) Having fun teaching calculus to non-calculus people:
2) Evelyn Lamb covered the current measles outbreak this week with emphasis on a key number:
3) Cathy O'Neil on math and medals:
4) "Futility Closet" offers up a paradox very reminiscent of Aristotle's "wheel paradox":
5) If you're into some of the critical names and issues surrounding applied statistics (especially in the social sciences) then this longish Deborah Mayo post is sure to entertain:
...also at Deborah's blog this week a guest post from Stephen Senn on statistically pooled data:
6) And a piece from the Washington Post also outlining two big issues for science: 1) explaining its findings to the public and 2) reproducibility:
7) I suspect these logic tasks/puzzles (Wason Selection Task) are familiar to most readers here, but if they're not, you should work through them, or perhaps try them out on some friends:
...and many more conundrums from this site listed here:
8) Not math, but just some nutty, ongoing fun from Andrew Gelman this week:
9) H/T to John Allen Paulos for pointing me to this interview ("The Stuff of Proof") with philosopher/writer Penelope Maddy on foundational aspects of mathematics; it's pretty 'meta' and philosophical, but if you like that sort of thing, quite interesting:
10) An intro to some topology ideas from "ThatsMaths":
11) A quick note that Max Tegmark's "Our Mathematical Universe" and Nate Silver's "The Signal and the Noise" are both newly-out in paperback.
12) pick and choose from MikesMathPage weekly entries:
...By the way, at the end of a number theory post today, Mike especially recommends the following 3-min. video of award-winner Manjul Bhargava, for young people interested in math:
The Potpourri BONUS (just extra NON-math links for your enjoyment) :
FOUR-for-the-price-of-1... I love bird nestcam websites of which there are now a large selection on the internet... a few current favorites:
a. Two Great Horned Owl sites:
b. California hummingbird nestcam:
c. Albatross nestcam (Hawaii):
(CAUTION: these live webcams can prove hopelessly addictive, rendering the viewer incapable of proceeding with work or other activities!)