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Sunday, April 28, 2013

Happy Birthday To You, Happy Axiomatic Birthday To You...


(via WikimediaCommons)
 A Happy Birthday today to Kurt Gödel (...wherever you are)!

In his honor I'll link once again to the logician George Boolos' clever explication, using only monoysllabic words(!), of Gödel's Second Incompleteness Theorem... always makes me grin:

http://www2.kenyon.edu/Depts/Math/Milnikel/boolos-godel.pdf

ADDENDUM: for those with a deep interest in Gödel the "Gödel's Lost Letter..." blog has just put up a wonderful ranging post also in honor of the birthday today:

http://rjlipton.wordpress.com/2013/04/28/happy-birthday-kurt-gdel/

Friday, April 26, 2013

This Is Not the Title of a Blogpost


Just a little self-referential humor today (not the same as self-deferential humor!), as I'm reading Douglas Hofstadter's latest book ("Surfaces and Essences"), which gets me thinking about such things again (or perhaps, thinking about thinking about such things...).
Also, earlier in week I enjoyed spying this bumper sticker on the car in front of me:


…which led me in turn eventually to the following webpage of self-referential humor:

http://web.maths.unsw.edu.au/~jim/selfref.html
(some good ones here… and, some not so good)

By the way, I've read elsewhere that "In order to understand recursion, one must first understand recursion." Seems about right.

And so it goes....

Wednesday, April 24, 2013

But Are Insurance Salesman This Clever? ;-)


Put your thinking caps on....
A classic sort of logic/math puzzle recently from Plus.maths.org:

http://plus.maths.org/content/unusual-sales-pitch

(if the answer eludes you, it can be found in the comments section below the puzzle)

Tuesday, April 23, 2013

Economics 101?


"The mystery of irreproducible results," and overselling of "austerity" (the Reinhart-Rogoff fiasco)… i.e., math gone awry (Excel miscoded) in the "dismal science"… from Paul Krugman:

http://tinyurl.com/crnc5p7

Monday, April 22, 2013

Monday Morning Buffet


Catching up on a few math links today:

1) Interesting view on how the trendy interest in "data science" or "big data" is different from academic statistics… and is that for good or ill:

http://simplystatistics.org/2013/04/15/data-science-only-poses-a-threat-to-biostatistics-if-we-dont-adapt/

2) Story on elite school, Amherst, rejecting affiliation with MOOC promoter EdX:

http://tinyurl.com/cqtbbh5

I'm curious how many, if any other, elite institutions have rejected outright invitations to participate in MOOC programs???

3) A nice introduction to limits from the "Better Explained" site here:

http://betterexplained.com/articles/an-intuitive-introduction-to-limits/

4) Have to admit I'd never heard of prodigy and lightning calculator Shakuntala Devi, an Indian math genius and astrologer(!), but apparently she was well-known to many. She passed away yesterday at 83. Learn about her interesting life and prowess at Wikipedia (which has additional links):

http://en.wikipedia.org/wiki/Shakuntala_Devi

5) …and lastly, I've put up an overview of Jim Holt's 2012 "Why Does the World Exist" volume over at my MathTango blog:

http://mathtango.blogspot.com/2013/04/from-whence.html

ADDENDUM: haven't had a chance to listen yet, but just realized Sol Lederman has a new podcast up with Ken Fan of "Girls' Angle," an organization specifically devoted to improving girls' experience with high school math:

http://wildaboutmath.com/2013/04/21/ken-fan-inspired-by-math-29/

Friday, April 19, 2013

Chillin'

  
All the darkness in the world cannot extinguish the light of a single candle.” 
-- St. Francis of Assisi 

....After the excruciating events of this extraordinary week not feeling very mathy at the moment, so once again just chilling out with some meditative music headed into the weekend.
Have a restful couple of days folks, and back to math on Monday...:





Thursday, April 18, 2013

A Post, a Rant, and a Video


A few more links today in case you've missed them:

Evelyn Lamb continues the recent spate of commentary on pi with her take on pi and big (I mean B-I-I-I-G) numbers here:

http://blogs.scientificamerican.com/roots-of-unity/2013/04/17/big-numbers-are-big/

Wonderful rant from Grant Wiggins on the never-ending-wrangle over teaching high-school algebra:

http://grantwiggins.wordpress.com/2013/04/10/my-100th-post-so-why-not-bash-algebra/

And Keith Devlin weighs in, as well, on the teaching of algebra, in this 4-minute video:




Wednesday, April 17, 2013

FBI Profiling... and Math

Timely….

Laura Laing of "Math For Grown Ups" re-posted today an interview she did awhile back with an FBI profiler, discussing how math enters into their work. The current post is here:

http://www.mathforgrownups.com/boston-marathon-how-fbi-profilers-use-math/

…and it links back to the earlier full interview here:

http://www.mathforgrownups.com/math-at-work-monday-mary-ellen-the-fbi-profiler/

A bit therefrom:
"I learned all of the basic math I needed to do my job while in school, but profiling itself requires a lot of analytical thinking, especially reasoning and logic. You get better at both of those over time and with experience.
Math tends to have absolute answers. It’s usually more of a black and white field. It’s about finding the one number or answer. Profiling, on the hand, requires you to live in the gray area of human behavior. This can be difficult for people who prefer to have things more absolute."
 

Tuesday, April 16, 2013

Two for Tuesday


1) Here's a very good, informative commentary on Keith Devlin's math MOOC course (now at the 6-week point), from one of those enrolled in it; especially good read for anyone contemplating taking the course:

http://tinyurl.com/bqe9jck

(Keith is traveling right now, but it's probably close to time for him to weigh in as well with another update on the course at his MOOC blog.)

2) Overlapping a bit the Matt Springer piece I referenced a few days ago, here's another interesting post on the randomness of pi, this time from Huffington Post:

http://www.huffingtonpost.com/david-h-bailey/are-the-digits-of-pi-random_b_3085725.html

Speaking of pi, I'll leave you with this wonderful question wafting in your brain (...David Wees recently tweeted it as coming from his nephew, and I of course love its self-referential aspect):

"If Pi contains every possible sequence of numbers, does it contain itself?"

(...I think the answer is pretty clearly 'no,' but still a marvelous question from a nephew.)


Saturday, April 13, 2013

Saturday Potpourri...


A few sundry items for your artful attention and possible perusal ;-):

1) Lance Fortnow, computer scientist and author of "The Golden Ticket," (which I reviewed a bit ago), all about P vs. NP, is Sol Lederman's latest podcast guest at Wild About Math:

http://wildaboutmath.com/2013/04/12/lance-fortnow-inspired-by-math-28/

2) A nice little primer on the nature of real numbers and pi from physicist Matt Springer here:

http://scienceblogs.com/builtonfacts/2013/04/12/everything-in-pi-maybe/

3) An interesting-looking list here of 24 video lectures in number theory:

http://www.infocobuild.com/education/learn-through-videos/mathematics/introduction-to-number-theory.html

4) Just a heads-up that E.O. Wilson is scheduled to be on NPR's Sunday "Weekend Edition" (tomorrow). I assume there will be some discussion of his recent much-debated commentary asserting that scientists need not know advanced mathematics to be successful.

5) Finally, a site I only recently learned of called "Ideas Roadshow" which looks interesting and includes this recent 5-minute clip by philosopher James R. Brown on Platonism in mathematics:

http://www.ideasroadshow.com/issues/james-robert-brown-2013-04-12


Friday, April 12, 2013

Ideas... The Stuff of Math

Seymour Papert via Wikipedia

Math teacher David Wees today posted on 8 ideas pertinent to math as taken from Seymour Papert's 1980 work "Mindstorms":

http://davidwees.com/content/powerful-ideas-math

He also tweeted a link to this 4-minute clip of Papert explaining that math education too often deals with rote skills, and not IDEAS:



Good stuff!


Thursday, April 11, 2013

Research, Statistics, Oy veyyy


via NIH/WikimediaCommons

Almost 40 years ago in grad school I railed a bit about the non-random and small sample sizes of so many journal-published studies, particularly in the social and medical sciences… I felt like a lone wolf in the wilderness though.
Eventually, in 2005 these sorts of concerns became center-stage when John Ioannidis published his oft-cited paper, "Why Most Published Research Findings Are False."

Now, Katherine Button, Ioannidis, and others have published "Power failure: why small sample size undermines the reliability of neuroscience," further delineating such problems, as specific to up-and-coming neuroscience:
http://www.guardian.co.uk/science/sifting-the-evidence/2013/apr/10/unreliable-neuroscience-power-matters

A few lines therefrom:
"There is growing interest in the need to improve reliability in science… Many of the most hyped scientific discoveries eventually cannot be replicated...
"A major factor that influences the reliability of science is statistical power. We cannot measure everyone or everything, so we take samples and use statistical inference to determine the probability that the results we observe in our sample reflect some underlying scientific truth."
The article goes on to discuss various problems with statistical samples, false positives, and false negatives, and also making mention of publication bias, before concluding, "The current reliance on small, low-powered studies is wasteful and inefficient, and it undermines the ability of neuroscience to gain genuine insight into brain function and behaviour. " And from the research article's abstract: "Improving reproducibility in neuroscience is a key priority and requires attention to well-established but often ignored methodological principles."

Anyway, read the whole Guardian piece, or if you have access, the original journal article in Nature Neuroscience.


Tuesday, April 9, 2013

Jacob's Genius


Over a year ago I put up a brief post about the phenomenal math/science autistic prodigy Jacob (Jake) Barnett (I.Q. 170) after he'd appeared on a "60 Minutes" segment:

http://math-frolic.blogspot.com/2012/01/autistic-prodigy-1-in-10-million.html

I hadn't really followed his story since then (he's 14 years-old now, studying astrophysics at college), but noticed this week in the bookstore that his mother has authored a new book about raising him, entitled "The Spark."
From briefly flipping through pages and early reviews, looks to be a very interesting volume (though don't know when I'll have a chance to read all the way through). Anyway, passing it along for any, who like me, have a fascination with the linkages between math, language, music, and cognition/savantism. So hard to comprehend where this kind of genius or brain-wiring derives from, or alternatively, since it does exist, why it is so rare.

Many YouTube clips of young Jacob in action here:

http://www.youtube.com/user/mathboysmom

An older newspaper piece about him here:

http://tinyurl.com/4oa599v  

And a more recent piece here:

http://www.usatoday.com/story/news/nation/2013/04/08/indiana-boy-genius-book/2064921/


Monday, April 8, 2013

Mandelbrot in 3-D

from Ondřej Karlík via WikimediaCommons

Everyone is by now familiar with the (2-dimensional) fractal Mandelbrot set... Jennifer Ouellette writes about a 3-dimensional extension of it called a "Mandelbulb" fractal here and the difficulty that was involved in creating a computer generation of it (at left):

http://blogs.scientificamerican.com/cocktail-party-physics/2013/04/08/meet-the-mandelbulb/

(oh, and she ends with another video clip employing Jonathan Coulton's "Mandelbrot Set" song, which I can never hear too many times.)

 ...Meanwhile, many more folks across the Web have responded to E.O. Wilson's piece which I referenced yesterday. Of course it's a debate full of nuances on both sides, so I won't pursue it further, except to possibly give it a little further context by offering the (16-min.) 2012 TEDTalk where Wilson originally put forth his somewhat rebel view:



Sunday, April 7, 2013

E.O. Wilson's Secret

via WikimediaCommons

No less than the prolific, award-winning E.O. Wilson writes in the Wall Street Journal that math is NOT a necessity for becoming an outstanding scientist:

http://online.wsj.com/article/SB10001424127887323611604578398943650327184.html

He starts this way: "For many young people who aspire to be scientists, the great bugbear is mathematics. Without advanced math, how can you do serious work in the sciences? Well, I have a professional secret to share: Many of the most successful scientists in the world today are mathematically no more than semiliterate."

He goes on to explain that he took up math relatively late in his academic career and "was never more than a C student," but then continues to describe how he was always able to collaborate with mathematicians or statisticians as needed.
...Should offer some encouragement to those who struggle with math, yet are still interested in the sciences. Wilson admits that math aptitude may be more crucial to some sciences, like physics and chemistry, than for many areas of biology, and ends with, "For every scientist, there exists a discipline for which his or her level of mathematical competence is enough to achieve excellence."

I'm glad Wilson offers this reassurance to those scientifically-minded who may be self-conscious about their weakness in math. Still, one also can't help but note that Wilson is almost 84 years old… he grew up at a time and worked throughout decades when a scientist could probably more easily succeed without a good math background. I suspect this may prove more difficult (though not impossible) for scientists of the future just now being currently trained.
So, interesting advice... but might yet require a grain of salt.

ADDENDUM: Looks like another blogger has taken Wilson's piece with a big grain of salt... and offers a longish response here (with interesting debate in comments):

http://dynamicecology.wordpress.com/2013/04/07/e-o-wilson-vs-math/




Saturday, April 6, 2013

97th Carnival of Mathematics


Usually the 'Carnival of Mathematics' is more inspiration than perspiration… but this go-around I'm not so sure (check it out to see what I mean):

http://www.flyingcoloursmaths.co.uk/carnival-of-mathematics/

(...a panoply of perceptive pieces to pick from)


Friday, April 5, 2013

Bobby Fischer Would Be Pleased

via Alan Light/Wikimedia

A bit tangential to math, but I dare say a lot of math enthusiasts also enjoy the game of chess...

Forget about last year's debate over algebra in high school, the below essay argues that CHESS ought be a mandatory class in the U.S. school system:

http://www.realclearscience.com/blog/2013/04/chess-should-be-required-in-us-schools.html

One quotation from within the article reads as follows:
"Chess trains logical thinking. It teaches how to make decisions, trains memory, strengthens will power, motivates children to win and teaches them how to deal with defeat. It's the only school subject that can do all this."
I was actually led to this piece by a Jason Rosenhouse post, which included another quote toward the end that I liked:
“The ability to play chess is the sign of high intellect. The ability to play chess well is the sign of high intellect gone wrong.” ;-)
(...makes us rank amateurs feel a tad better)

ADDENDUM: interestingly, just as I was completing this post 'All Things Considered' on NPR was running a story on "The Final Four" of college chess competition coming up this very weekend:

http://www.npr.org/2013/04/05/176368227/the-other-final-four-trades-in-courts-for-chess-boards?ft=1&f=1003





Thursday, April 4, 2013

33,550,336 is a Perfect Number


...It is one of just 48 that are known (the last one just discovered a couple months ago). Are there any odd ones? Are there an infinite number of them? No one knows for sure.

Read about 'perfect numbers' from this Mario Livio post for Huffington Post Science:

http://www.huffingtonpost.com/mario-livio/perfect-numbers_b_2998917.html

Tuesday, April 2, 2013

Monday, April 1, 2013

Riemann Hypothesis Appears Proven


NO, NO, NO, not THAT Riemann Hypothesis… but rather Shecky Riemann's hypothesis that there might be a review of Lance Fortnow's book, "The Golden Ticket," appearing somewhere on the internet today ;-):

http://mathtango.blogspot.com/2013/04/of-p-and-np.html

...But seriously (or, I guess not-so-seriously) there have been some wonderful April Fool's jokes from mathematicians over the years, as indicated by this American Mathematical Society post:

http://www.ams.org/samplings/this-math-month/april-fools

And here is Erik Dermaine presenting at an MAA meeting a couple years back, also employing the Riemann Hypothesis as his foil:




But the classic mathematics April Fool's example is certainly (for those old enough to remember) the Scientific American piece from April 1975 by prankster/essayist/author/philosopher/commentator/and-oh-yes-mathematician Martin Gardner (referenced in the above AMS posting). Unfortunately, so far as I'm aware, that old article is not freely available in its entirety anywhere on the Web, but his black-and-white map creation purportedly requiring five colors and disproving the "four-color theorem," is shown on a wolfram.com page here (with a 4-color solution):

http://mathworld.wolfram.com/Four-ColorTheorem.html

(at the time, the four-color theorem was still an open question, though it has since been proven)

…anyway, my advice is don't trust anything you read on the Web today between now and midnight (…but of course some might say that advice holds for ANY day! ;-)