Wednesday, October 1, 2014

Bayes-mania


Seeing an awful lot written on Bayesian ideas in the last year (and week!).
Jason Rosenhouse uses the Monty Hall problem and a NY Times article as a launching point for a discussion of the subtlety of Bayes here:

http://scienceblogs.com/evolutionblog/2014/10/01/a-poor-description-of-the-monty-hall-problem/

Rosenhouse takes the Times' article to task, and ends simply with:
"Applying statistics correctly is hard, even for people with professional training in the subject. But the problems are found in the complexity of real-life situations, and not in the underlying philosophical approaches to probability and statistics."
(Rosenhouse's 2009 book on the The Monty Hall problem is great, by the way, if you've never read it -- yes, an entire volume on that one problem)

Meanwhile, The Guardian also presented Bayesian statistics this week: http://tinyurl.com/ojjazs4

And in other statistics briefs, Jeff Leek tries to come to the defense of much-maligned p-values here:
http://simplystatistics.org/2014/09/30/you-think-p-values-are-bad-i-say-show-me-the-data/ 

Tuesday, September 30, 2014

True Grit


Another TEDTalk today. This is actually from 2013, but I just saw it getting passed along #MathChat/#EdChat circles today. It's about success in math and beyond. If you missed it, set aside 6 mins. for it:




Monday, September 29, 2014

Mathematics a-a-and Sex


Don't know how I missed this very fun TEDTalk from a few months back, but h/t to Cliff Pickover for tweeting it this weekend:



The speaker, mathematician Clio Cresswell, actually has a book out with the same title ("Mathematics and Sex"):
http://www.amazon.com/Mathematics-Sex-Clio-Cresswell/dp/1741141591


Sunday, September 28, 2014

Sunday Reflection on Big Data


Living in a digital web....

"…faceless Big Data's predictions are hard to opt out of.
"One Minnesota man learned that a few years ago. He stormed into a suburban Minneapolis Target department store, demanding to speak to the manager. 'My daughter got this in the mail,' the man explained. The manager took a look at what the customer had brought. It was a Target mailer, like millions sent out every year, addressed to the man's daughter. This one looked harmless enough, with pictures of adorable infants, baby furniture, and maternity wear.
" 'Are you trying to encourage her to get pregnant?' the man sputtered. His high-school age daughter was unmarried.
"The manager apologized and said he'd look into it. When he did, he learned that Target was using predictive analytics. It aggregated the information it had on its customers -- from visits to the website, purchases in bricks-and-mortar stores, calls to customer support, and the use of coupons or rebates. Software parsed this haystack of data in order to make specific, actionable forecasts of individual customers' future behavior.
"One secret initiative was to predict which customers were pregnant. Expectant mothers have to buy a lot of products that they may never have purchased before. With novelty comes indecision. This makes mothers-to-be receptive to advertising discounts, and anything else that might nudge them in the direction of buying at Target. A customer who comes to depend on Target while expecting a baby may decide to do her grocery shopping there -- for decades to come.
"Target's pregnancy predictions were much more accurate than random guessing, though of course not 100 percent certain. A few wrong guesses were acceptable. The awkward exception is when a customer gets really, really upset by a wrong prediction.
"A few days later, the manager called back the irate customer to apologize a second time.
" 'I had a talk with my daughter,' the customer said. 'It turns out there's been some activities in my house I haven't been completely aware of. She's due in August. I owe you an apology.'"
"Witness the new human condition. A department store's software can guess that a woman is having a child; her own father can't. Should we marvel at how clever our algorithms are, or at how bad we are at listening to and understanding our fellow beings?"

-- from "Rock Breaks Scissors" by William Poundstone

...and I now have an interview up with Mr. Poundstone over at MathTango

[…If you have a favorite math-related passage that might make a nice Sunday morning reflection here let me know (SheckyR@gmail.com). If I use one submitted by a reader, I'll cite the contributor.]


Friday, September 26, 2014

Sampling Simply


One of the first things learned in intro statistics class is the importance of a "random" (supposedly "representative") sample for any scientific study. You don't even really need to "learn" it, since it's such an obvious necessary requisite to attaining useful, meaningful data. So I was dismayed early on in academia when I realized how many "studies" were being done with say 25 psyche101 students, or maybe with 50 college freshman, or a sample from any number of college students… or hey, maybe even 100 Americans -- i.e., not in any way, an actual random human sample.
Despite being a psychology major, I couldn't put much faith in most behavioral psychology studies. Along the way, I noticed epidemiology too often suffered the same sort of problem, so it was no wonder that one week a study might show coffee was good for you, and the following week, with a different sample, coffee was bad for you; even "meta" studies that combine other studies, have sampling problems. It would be 35 years after I left college before the problem got some widespread journal attention when the notion of "WEIRD" samples was put forth -- study samples being based on subjects who were primarily "Western, Educated, Industrial, Rich and Democratic." And this extends to most routine studies (behavioral, psychological, medical) involving humans.
Perhaps it is because political pollsters have become so good at predicting election outcomes based on small samples (although even there glaring mistakes happen), that so many people readily accept the results of publicized scientific "studies" as widely true.

In fact, truly random samples in human studies are a virtual impossibility (or even if you had a random sample, there'd be no way to know it for sure), which is why most such studies ought be taken with a grain of salt, instead of broadcast to the world in simplistic press headlines.
I've written before that 'skepticism' needs to extend to most scientific studies that involve human subjects -- there's plenty of junky science in reputable journals, and funded by NIH -- and that's not a slam against science, but just an honest recognition of how difficult and rare really excellent science is (especially behavioral and medical science -- although even moving outside the realm of human studies, other writers have bemoaned the near metaphysical or pseudo-scientific gloss that some current-day theoretical physics has taken on).

Anyway, I mention all of this simply because today Cathy O'Neil tackles a similar area of concern, focusing on the prevalence of males specifically in clinical studies (...sheeesh, next thing you know, females will be wanting equal opportunities in STEM fields ;-)). Give her a read here:

http://mathbabe.org/2014/09/26/women-not-represented-in-clinical-trials/

[on a side-note, Sunday I should have a new interview up at MathTango]



Wednesday, September 24, 2014

Tuesday, September 23, 2014

Geometry and Ancient Dance

George Hart (perhaps better known these days as Vi Hart's father ;-)) brings us an introduction to the mathematical aspects of the ancient art form of "long sword dancing":

http://tinyurl.com/kn8ckat

Combines dance/movement, geometry, structure, and sheer gee-whizness! Fun to watch.

Sunday, September 21, 2014

Sunday View (the nature of proof)


"What mathematics accomplishes with its reasoning may be more evident from an analogy. Suppose a farmer takes over a tract of land in a wilderness with a view to farming it. He clears a piece of ground but notices wild beasts lurking in the wooded area surrounding the clearing who may attack him at any time. He decides therefore to clear that area. He does so but the beasts move to another area. He therefore clears this one. And the beasts move to still another spot just outside the new clearing. The process goes on indefinitely. The farmer clears away more and more land but the beasts remain on the fringe. What has the farmer gained? As the cleared area gets larger the beasts are compelled to move farther back and the farmer becomes more and more secure at least as long as he works in the interior of his cleared area. The beasts are always there and one day they may surprise and destroy him but the farmer's relative security increases as he clears more land. So, too, the security with which we use the central body of mathematics increases as logic is applied to clear up one or another of the foundational problems. Proof, in other words, gives us relative assurance."

-- Morris Kline in "Mathematics: The Loss of Certainty"


[…If you have a favorite math-related passage that might make a nice Sunday morning reflection here let me know (SheckyR@gmail.com). If I use one submitted by a reader, I'll cite the contributor.]



 

Friday, September 19, 2014

Whether 'tis Nobler To Get a Prize... or Not



Well, sadly (…or, maybe not) for the third year in a row there was no Ig Nobel Prize given out for pure mathematics last evening at Harvard's annual gala awards ceremony. Last year there was at least an Ig Nobel for "Probability" work, granted for this piece of Scottish research on cows:

http://www.appliedanimalbehaviour.com/article/S0168-1591%2810%2900054-7/abstract?cc=y

The Ig Nobel citation says the paper makes "two related discoveries: First, that the longer a cow has been lying down, the more likely that cow will soon stand up; and Second, that once a cow stands up, you cannot easily predict how soon that cow will lie down again."
And thus science marches onward!...

To all the pure mathematicians out there, start upping your game (or more likely tamping it down)… and better luck next year! (...actually, the last time a mathematics award was given out, in 2011, it went to 6 non-math individuals who wrongly predicted the world was coming to the end... so maybe we're better off without this prize, and just sticking with those humble MacArthurs, Fields, Abels, Breakthroughs, etc.)

You can visit all the past Ig Nobel winners here: http://www.improbable.com/ig/winners/#ig2014

And finally here's a search for math-related articles in "The Annals of Improbable Research" (which created the Ig Nobels):
http://tinyurl.com/nnkhfny

Wednesday, September 17, 2014

The Mathematical MacArthurs


The 21 MacArthur Fellows for 2014 have been announced:

http://www.macfound.org/fellows/class/class-2014/ 

http://tinyurl.com/mdg4csr  (NPR coverage)

As usual quite a motley group, but including at least three with mathematical connections:

Danelle Bassett is a physicist, using mathematics to study the complex networking of the brain.

Yitang Zhang, the suddenly-famous mathematician who showed there were finite bounds to the prime gap problem.

and Jacob Lurie, a 36-year-old Harvard pure mathematician shown below:

 


Tuesday, September 16, 2014

A Threshold Reached...


Interesting little story of how "network theory" (via social media) underlied the solution to a 13-year-old mystery photograph from the 9/11 tragedy:

http://tinyurl.com/luhnov8

a blurb:

"...when information moves through a social network, it doesn’t move at random: The information pings from one 'node,' or person, to another, and the relationships between all those thousands of nodes create an intricate geography of influence and power"....
"...there’s a reason the photo went viral this year, when it didn’t go viral all the long years before. For the first time, it hit what information scientists call the epidemic threshold — the point at which a thing reaches enough nodes in the network that it can’t easily die out."

 


Monday, September 15, 2014

Calculus Going Viral?… Could It Be


Forbes Magazine reports on Ohio State professor Jim Fowler taking calculus to the Web via Coursera (and getting rave reviews):
http://tinyurl.com/lz2smt2

And he's on YouTube, if you don't want to sign up for Coursera without getting a sampling first:
https://www.youtube.com/user/kisonecat

here's his intro to the course:




Sunday, September 14, 2014

Sunday Reflection


From Philip Davis and Reuben Hersh's "The Mathematical Experience":
(I don't necessarily agree with this sentiment, but do find it interesting)
" We maintain that:

1)  All the standard philosophical viewpoints rely in an essential way on some notion of intuition.
2)  None of them even attempt to explain the nature and meaning of the intuition which they postulate.
3)  A consideration of intuition as it is actually experienced leads to a notion which is difficult and complex, but it is not inexplicable or unanalyzable. A realistic analysis of mathematical intuition is a reasonable goal, and should become one of the central features of an adequate philosophy of mathematics….

"Mathematics does have a subject matter, and its statements are meaningful. The meaning, however, is to be found in the shared understanding of human beings, not in an external nonhuman reality. In this respect, mathematics is similar to an ideology, a religion, or an art form; it deals with human meanings, and is intelligible only within the context of culture. In other words, mathematics is a humanistic study. It is one of the humanities."

[…If you have a favorite math-related passage that might make a nice Sunday morning reflection here let me know (SheckyR@gmail.com). If I use one submitted by a reader, I'll cite the contributor.] 


Monday, September 8, 2014

"Why Study Paradoxes?"


Given my fondness for paradoxes… and, for Raymond Smullyan... I couldn't help but love this weekend post from Ray T. Cook on paradoxes (and why to study them) at Oxford University Press blog:

http://tinyurl.com/ppvg4cp

After offering his own example that he once posed to the master logician Smullyan, Cook goes on to talk about the mathematical complexity of paradoxes before ending thusly:
"...that's why I work on paradoxes: their surprising mathematical complexity and mathematical beauty. Fortunately for me there is still a lot of work that remains to be done, and a lot of complexity and beauty remaining to be discovered."
Fortunately for me, there is still a lot of work that remains to be done, and a lot of complexity and beauty remaining to be discovered. - See more at: http://blog.oup.com/2014/09/why-study-paradoxes/?utm_source=feedblitz&utm_medium=FeedBlitzRss&utm_campaign=oupblogmathematics#sthash.VxyOQRJg.dpuf
that’s why I work on paradoxes: their surprising mathematical complexity and mathematical beauty. Fortunately for me, there is still a lot of work that remains to be done, and a lot of complexity and beauty remaining to be discovered. - See more at: http://blog.oup.com/2014/09/why-study-paradoxes/?utm_source=feedblitz&utm_medium=FeedBlitzRss&utm_campaign=oupblogmathematics#sthash.VxyOQRJg.dpuf
that’s why I work on paradoxes: their surprising mathematical complexity and mathematical beauty. Fortunately for me, there is still a lot of work that remains to be done, and a lot of complexity and beauty remaining to be discovered. - See more at: http://blog.oup.com/2014/09/why-study-paradoxes/?utm_source=feedblitz&utm_medium=FeedBlitzRss&utm_campaign=oupblogmathematics#sthash.VxyOQRJg.dpuf
And that’s why I work on paradoxes: their surprising mathematical complexity and mathematical beauty. Fortunately for me, there is still a lot of work that remains to be done, and a lot of complexity and beauty remaining to be discovered. - See more at: http://blog.oup.com/2014/09/why-study-paradoxes/?utm_source=feedblitz&utm_medium=FeedBlitzRss&utm_campaign=oupblogmathematics#sthash.VxyOQRJg.dpuf
And that’s why I work on paradoxes: their surprising mathematical complexity and mathematical beauty. Fortunately for me, there is still a lot of work that remains to be done, and a lot of complexity and beauty remaining to be discovered. - See more at: http://blog.oup.com/2014/09/why-study-paradoxes/?utm_source=feedblitz&utm_medium=FeedBlitzRss&utm_campaign=oupblogmathematics#sthash.VxyOQRJg.dpuf
that’s why I work on paradoxes: their surprising mathematical complexity and mathematical beauty. Fortunately for me, there is still a lot of work that remains to be done, and a lot of complexity and beauty remaining to be discovered. - See more at: http://blog.oup.com/2014/09/why-study-paradoxes/?utm_source=feedblitz&utm_medium=FeedBlitzRss&utm_campaign=oupblogmathematics#sthash.VxyOQRJg.dpuf
that’s why I work on paradoxes: their surprising mathematical complexity and mathematical beauty. Fortunately for me, there is still a lot of work that remains to be done, and a lot of complexity and beauty remaining to be discovered. - See more at: http://blog.oup.com/2014/09/why-study-paradoxes/?utm_source=feedblitz&utm_medium=FeedBlitzRss&utm_campaign=oupblogmathematics#sthash.VxyOQRJg.dpuf
that’s why I work on paradoxes: their surprising mathematical complexity and mathematical beauty. Fortunately for me, there is still a lot of work that remains to be done, and a lot of complexity and beauty remaining to be discovered. - See more at: http://blog.oup.com/2014/09/why-study-paradoxes/?utm_source=feedblitz&utm_medium=FeedBlitzRss&utm_campaign=oupblogmathematics#sthash.VxyOQRJg.dpuf
that’s why I work on paradoxes: their surprising mathematical complexity and mathematical beauty. Fortunately for me, there is still a lot of work that remains to be done, and a lot of complexity and beauty remaining to be discovered. - See more at: http://blog.oup.com/2014/09/why-study-paradoxes/?utm_source=feedblitz&utm_medium=FeedBlitzRss&utm_campaign=oupblogmathematics#sthash.VxyOQRJg.dpuf

Also, Ray has apparently written a short book entirely on Yablo's Paradox which I've mentioned here before (and which the above post is related to):
http://ukcatalogue.oup.com/product/9780199669608.do


Sunday, September 7, 2014

Complex Numbers (Sunday Reflection)


"…there is never a need to go beyond the complex numbers. No further numbers are needed. They suffice and so they bring to completion the very long effort at construction that over thousands of years yielded first the natural numbers, then the fractions, then zero and the negative numbers, and after that the real numbers. The complex numbers complete the arch.
"Beyond the theory of complex numbers, there is the much greater and grander theory of the functions of a complex variable, as when the complex plane is mapped to the complex plane, complex numbers linking themselves to other complex numbers. It is here that complex differentiation and integration are defined. Every mathematician in his education studies this theory and surrenders to it completely. The experience is like first love.
"I once mentioned the beauty of complex analysis to my great friend, the mathematician M.P. Schutzenberger. We were riding in a decrepit taxi, bouncing over the streets of Paris.
" 'Perhaps too beautiful,' he said at last.
"When I mentioned Schutzenberger's remarks to Rene' Thom, he shrugged his peasant shoulders sympathetically.
"This is one of the charms of the theory of complex numbers and their functions. It has broken men's hearts."


-- David Berlinski from "Infinite Ascent"


[…If you have a favorite math-related passage that might make a nice Sunday morning reflection here let me know (SheckyR@gmail.com). If I use one submitted by a reader, I'll cite the contributor.]

Thursday, September 4, 2014

Books For a Desert Island... (meme?)


First off, 3 new mathy-related books I've been looking at recently are:

"Mathematics and the Real World" by Zvi Artstein (a historical look at mathematics over time)  
"Standard Deviations" by Gary Smith (another popular take on how statistics get used and misused) 
and
"Rock Breaks Scissors" by William Poundstone (another probability-meets-the-real-world sort of offering)

I like almost everything Poundstone writes so suspect I'll enjoy his latest work, and the Smith book looks good as well (though somewhat redundant in content to several other recent works), but the only volume I've actually started is the Artstein book... and so far not particularly enamored of it; it has plenty of information, just a more mundane or pedantic writing style (perhaps because it is a translation, from Hebrew) than several recent popular math books -- Jordan Ellenberg has spoiled me ;-)  I'm liking the second half of the volume more than the first half and will withhold judgment 'til finished, but Publishers Weekly (where I rarely see negative reviews) appears even more disenchanted with the volume than I am:

http://www.publishersweekly.com/978-1-61614-091-5

(Even at that it may still fill a certain niche on your math bookshelf, depending on what historical volumes you already have.)
Anyway, I may say more about any/all of these books later.

Now, departing from the mathy-track once again....

via Mr.TinDC flickr

Blog memes don't seem to go around much anymore as they did at one time, but I did notice a meme bubbling in some Facebook circles, asking for 10 books that most moved you or changed/affected your life. I probably couldn't name 10 volumes that affected me at that level, but thought about 10 books that were important to me, and that I'd grab to take to a deserted island, if need be.

Might be interesting to hear from other math communicators what would make it onto THEIR list for a desert island… if for no other reason than to show that math buffs are less nerdy and more diverse than some people might imagine!! (…although my list, admittedly, is somewhat nerdy, especially since I don't read fiction :-((

Anyway, with no annotations and in no particular order, here are my 10:

1)  "The Night Is Large"  -- Martin Gardner
2)  "Pilgrim At Tinker Creek"   -- Annie Dillard  
3)  "Metamagical Themas" (and "Gödel, Escher, Bach" as well)  -- Douglas Hofstadter
4)  "The Outer Limits of Reason"  -- Noson Yanofsky
5)  "Natural Prayers"    -- Chet Raymo
6)  "The Pleasure of Finding Things Out"  -- Richard Feynman
7)  "The Black Swan"   -- Nassim Taleb
8)  "Language In Thought and Action"    -- S.I. Hayakawa
9)  "Beyond the Hoax"   -- Alan Sokal
10)  "How Mathematicians Think"    -- William Byers

There are lots of other books I'd want along for sheer entertainment value (including, off to the side somewhere, book-compendiums of either "Dilbert," "New Yorker," or "Far Side" cartoons), but above are ones I'd want along to exercise my mind.

I, for one, would be interested to hear of other math bloggers'/writers' lists (post at your own blog or in the comments here).