Wednesday, June 30, 2010

Gathering For Gardner

Some photos from the 9th "Gathering For Gardner" get-together that took place in March in Atlanta (in honor of Martin Gardner, just recently passed away) here:

http://luceoimages.com/2010/06/g4g9-for-new-scientist/

more on the conference here:

http://g4g4.com/

...and here is blogger Jason Rosenhouse's account of this year's conference:

http://tinyurl.com/yk4ck95

Finally, a recent hour-long podcast with John Conway addressing his long-time friendship with Gardner:
http://mathfactor.uark.edu/2010/06/ha-conway-on-gardner/


Addendum: speaking of Conway, check out this recent post at another site:
 
http://tinyurl.com/2c4hnnr 

Tuesday, June 29, 2010

A Demonstration

Try this exercise, I've copied directly from another book:

"Answer the following questions as fast as you can:

-2 + 2 = ?

-4 + 4 = ?

-8 + 8 = ?

-16 + 16 = ?


Now quick! Pick a number between 12 and 5. Got it?
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The number you picked is 7, isn't it?"


...I succumbed to this piece of 'mindreading' when I read it in Stanislas Dehaene's 1997 "The Number Sense: How the Mind Creates Mathematics." Did you?
He calls this a "demonstration of the automaticity of arithmetic memory" and explains it thusly:
"How did I read your mind? The mere presentation of the numbers 12 and 5 seems enough to trigger an unconscious subtraction 12 - 5 = 7. This effect is probably amplified by the initial addition drill, the reversed order of the numbers 12 and 5, and the ambiguous phrase 'between 12 and 5' that may incite you to compute the distance between the two numbers. All these factors conspire to enhance the automatic activation of 12 - 5 up to a point where the result enters consciousness. And you believed that you were exercising your 'free will' when selecting a digit!"

I'm not sure I find Dehaene's explanation completely satisfactory... but, I can't argue with the effect, which I did fall for.
  

Monday, June 28, 2010

Science Blogger Obsessed With a Puzzle

Lifelong interest in a certain geometric puzzle described here:

http://tinyurl.com/23el8m6

(correct solution is given in the blogger's comments section)

Saturday, June 26, 2010

"The Geometry Junkyard"

If you're particularly geometry-inclined, check out this wonderful and expansive site (of links), just added to the "Misc. Resources" list in right-hand column:

http://www.ics.uci.edu/~eppstein/junkyard/all.html

Friday, June 25, 2010

Human Calculator Extraordinaire

Frenchman Alex Lemaire holds the world record for calculating the 13th root of a 200 digit number (yeah, you read that right!) in little over a minute, earning him the title of world's fastest human calculator, or "mathlete."

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

http://news.bbc.co.uk/2/hi/uk_news/magazine/6913236.stm

Wednesday, June 23, 2010

Recursivity...

In the next sentence, the number of occurrences of 0 is 1, of 1 is 7, of 2 is 4, of 3 is 1, of 4 is 1, of 5 is 1,of 6 is 1, of 7 is 1, of 8 is 2, and of 9 is 1.

In the previous sentence, the number of occurrences of 0 is 1, of 1 is 8, of 2 is 2, of 3 is 1, of 4 is 2, of 5 is 1,of 6 is 1, of 7 is 2, of 8 is 1, and of 9 is 1.

...see some related efforts here:

http://www.fatrazie.com/EWpangram.html

Monday, June 21, 2010

Simple Riddle

The 3 jungle spiders.... a riddle lifted directly from chapter 9 of Clifford Pickover's "Wonders of Numbers":

"Dr. Googol was in a Peruvian rain forest, 15 miles south of the beautiful Lake Titicaca, when he dreamed up this tortuous brain boggler. A month later, while in Virginia, Dr. Googol gave this puzzle to all CIA employees to help them improve their analytical skills.

"  Three spiders named Mr. Eight, Mr. Nine, and Mr. Ten are crawling on a Peruvian jungle floor. One spider has 8 legs; one spider has 9 legs; one spider has 10 legs. All of them are usually quite happy and enjoy the diversity of animals with whom they share the jungle. Today, however, the hot weather is giving them bad tempers.
"   'I think it is interesting,' says Mr. Ten, 'that none of us have the same number of legs that our names would suggest.'
"  'Who the heck cares?' replies the spider with 9 legs.

"How many legs does Mr. Nine have? Amazingly, it is possible to determine the answer, despite the little information given."

answer below:
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.
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Mr Nine has 10 legs... (Mr. Ten CAN'T have 10 legs, same as his name, and can't have 9, since the spider with 9 replies to him; therefore he must have 8 legs... from there you can likely solve the rest.)

Sunday, June 20, 2010

Friday, June 18, 2010

Terence Tao on Prime Numbers

Mathematical prodigy and MacArthur Fellow Terence Tao gives a talk (~50 mins.) on prime numbers:


Wednesday, June 16, 2010

The Savant Mind At Work

"Embracing the Wide Sky" by Daniel Tammet (book review)....


Autistic savant Daniel Tammet's first book, "Born On A Blue Day" was an international best-seller as an engaging autobiographical overview of his fascinating life and talents. His second book (2009), "Embracing The Wide Sky" is a more scientific look at the way his mind works, and provocatively covers a range of cognitive issues.
Tammet's perspective is utterly unique, as an articulate, thoughtful savant who can introspectively analyze his own mind workings. The book actually includes a lot of references to more standard journal literature as well, but Tammet never blindingly accepts the conclusions of academic researchers when his own intuitive understanding of how the brain operates runs counter to the party-line of academics. Plenty of outside-the-box thinking here on subjects where outside-the-box thinking is welcome, and sometimes difficult to come by.

Although he doesn't go into great depth in any given area, Tammet touches upon a smorgasbord of cognitive subjects including brain plasticity and re-wiring, intelligence testing, memory, language acquisition and processing, number instinct, perception, and creativity. And interestingly, he believes many of the talents of savants are not as special as they appear, in some cases even being accessible to non-savants. He winces at the notion of savant skills as almost machine-like aberrations in the human family. Tammet sees humanity as more of a continuous broad-spectrum of abilities and talents, with savant skills as rare, but not abnormal outliers.

The mathematical capabilities of autistic savants are often among the most difficult parts of their repertoire to understand or explain. These may include lightening-fast calculation or other feats of computation. And oftentimes, as in Daniel Tammet's case, their description of numbers as having color and texture or shape is likewise difficult to grasp. Tammet is famous for reciting pi accurately to over 22,000 digits from memory, a virtually inconceivable accomplishment, that is aided by his sense of pi as not just a number, but a 'landscape' so-to-speak.

Interestingly, in this volume Tammet hypothesizes that his math prowess stems from "abnormal cross-communication" between areas of the brain that govern math skill and those that govern language (and specifically syntactic rules), which normally are separate. He points out that the two areas (left parietal lobe and left frontal lobe) lay physically next to each other in the brain, and that his "numerical abilities are rapid, intuitive, and largely unconscious" very much like the way most people produce and process language. Further, he notes that along with his mathematical talents he has already learned a dozen languages, and very easily picks up new languages to a conversational level. By his own admission he is a lover of words and language, as well as numbers.

Savantism is one of those topics which is so inherently captivating (and rare) that almost anything written on it is automatically fascinating, and several researchers have dealt with it previously. Still, there is something even more entrancing when you have the savant himself calmly, analytically peering into his own mind and communicating what he finds. I don't know if any parts of Tammet's books are ghostwritten or if Tammet composes all the words himself, but if the latter than he can add communicating and educating to his many talents. One hopes to hear much more from him as his life progresses.

More on Tammet here:
http://www.guardian.co.uk/theguardian/2005/feb/12/weekend7.weekend2/

His record-breaking 2004 pi performance/recitation reported here:

http://www.pi-world-ranking-list.com/lists/details/tammet.html

And lastly, a couple more articles on the relationship between savantism and mathematics:

http://discovermagazine.com/2002/feb/featsavant/

  http://www.centreforthemind.com/publications/integerarithmetic.cfm     

Monday, June 14, 2010

New Books...

Brand new book out by Alex Bellos looking at "the wow factor" in mathematics, titled "Here's Looking at Euclid: A Surprising Excursion Through the Astonishing World of Math."
Looks good:

http://tinyurl.com/29c2amb

Amazon link: http://tinyurl.com/2utajtd

And moving over to the quantum realm, another new volume that looks excellent:

"Absolutely Small: How Quantum Theory Explains Our Everyday World," by Michael Fayer, here:

http://tinyurl.com/2dyywh2

Friday, June 11, 2010

In Further News...

Eccentric, reclusive mathematician/genius Grigori Perelman was (not-too-unexpectedly) a no-show in Paris this week to pick up his $1 million Millennium Prize for proving the Poincare Conjecture. Read all about it:

http://tinyurl.com/y9gcxrq

http://www.math.columbia.edu/~woit/wordpress/?p=3005

Off-Topic...

Okay, this is actually off-topic, dealing more with physics, cosmology, and the like, than with pure mathematics, but just too funny not to pass along... "submissions" to snarXiv.org :

http://snarxiv.org/

And to understand more of what it's all about, check here:
(helps if you're already familiar with arxiv.org...)

http://davidsd.org/2010/03/the-snarxiv/

Tuesday, June 8, 2010

In Our Lifetime?

In 2009, when John Brockman asked his "Edge" thinkers' group what scientific development they expected to see "change everything" in their lifetime, the response from polymath Clifford Pickover was that the Riemann Hypothesis (one of math's most enduring unsolved problems involving prime numbers), would be proven:

http://www.edge.org/q2009/q09_3.html#pickover

Monday, June 7, 2010

Math Chuckle and More

Lifted directly from "Math Jokes 4 Mathy Folks" blog:

A farmer was showing his fields to a mathematician and his wife. The mathematician made continual attempts to impress with his intellect, referencing arcane formulas and then doing computations mentally. Frustrated by this, the farmer decided to teach him a lesson. He took them to a field packed with hundreds of cows and said to the mathematician, “If you can guess the exact number of cows in this field, you can have all of them! But if you get it wrong, I get to sleep with your wife!”

The mathematician thought for a moment, his eyes quickly scanning the entire field. Finally he said, “228.”

The farmer was stunned. “How on Earth did you do that?” he asked. ”There’s no way you could have counted all those cows so quickly!”

“You’re right,” the mathematician replied. “‘I counted their legs and then divided by 4.”

(...r-r-r-rrimshot)

And check out the rest of the latest "Carnival of Mathematics" HERE.

Friday, June 4, 2010

Mandelbrot Set To Music

Video of Mandelbrot Set with Jonathan Coulton's lyrics below:



lyrics:

Pathological monsters! cried the terrified mathematician
Every one of them is a splinter in my eye
I hate the Peano Space and the Koch Curve
I fear the Cantor Ternary Set And the Sierpinski Gasket makes me want to cry
And a million miles away a butterfly flapped its wings
On a cold November day a man named Benoit Mandelbrot was born

His disdain for pure mathematics and his unique geometrical insights
Left him well equipped to face those demons down
He saw that infinite complexity could be described by simple rules
He used his giant brain to turn the game around
And he looked below the storm and saw a vision in his head
A bulbous pointy form
He picked his pencil up and he wrote his secret down

Take a point called Z in the complex plane
Let Z1 be Z squared plus C
And Z2 is Z1 squared plus C
And Z3 is Z2 squared plus C and so on
If the series of Z's should always stay
Close to Z and never trend away
That point is in the Mandelbrot Set

Mandelbrot Set you're a Rorschach Test on fire
You're a day-glo pterodactyl
You're a heart-shaped box of springs and wire
You're one badass f**king fractal
And you're just in time to save the day
Sweeping all our fears away
You can change the world in a tiny way

Mandelbrot's in heaven, at least he will be when he's dead
Right now he's still alive and teaching math at Yale
He gave us order out of chaos, he gave us hope where there was none
And his geometry succeeds where others fail
If you ever lose your way, a butterfly will flap its wings
From a million miles away, a little miracle will come to take you home

Just take a point called Z in the complex plane
Let Z1 be Z squared plus C
And Z2 is Z1 squared plus C
And Z3 is Z2 squared plus C and so on
If the series of Z's should always stay
Close to Z and never trend away
That point is in the Mandelbrot Set
Mandelbrot Set you're a Rorschach Test on fire
You're a day-glo pterodactyl
You're a heart-shaped box of springs and wire
You're one badass f**king fractal
And you're just in time to save the day
Sweeping all our fears away
You can change the world in a tiny way
And you're just in time to save the day
Sweeping all our fears away
You can change the world in a tiny way
Go on change the world in a tiny way
Come on change the world in a tiny way

Wednesday, June 2, 2010

Monty Hall Redux

Jason Rosenhouse's delectable volume devoted entirely to the 'Monty Hall problem':

http://tinyurl.com/y927aou

(I think the first three, and last three chapters are especially good.)