Randomness

Recent article from NPR on "randomness" here:


http://www.npr.org/templates/story/story.php?storyId=125993584

Not For Math-Phobes

First, an interesting (lengthy) article on problems with statistics in research here:

http://tinyurl.com/ydfvaqj

On a related and slightly less-technical note, just finished reading Jason Rosenhouse's wonderful 2009 volume, "The Monty Hall Problem," devoted entirely to the "Monty Hall" problem from mathematics (one of the most intriguing, well-covered/debated probability problems oft-presented to lay audiences), and highly recommend it to all who have a general interest in mathematics or probability theory. I think the first 3 chapters, that cover the meat of the problem, and last 3 chapters that delve into more philosophical or epistemological elements, are especially good; in-between are some more over-the-top chapters dealing with variations on the basic problem, that require more mathematics and won't suit everyone's taste. Still, the complexities and intricacies of the deceptively-simple dilemma are really quite fascinating, and Rosenhouse admits at the end he has enough material left over to write yet a 2nd book on the topic!

Finally, a new volume I haven't read yet but that looks interesting, is "Dude, Can You Count," from Christian Constanda. More on it here:

http://www.springer.com/mathematics/book/978-1-84882-538-3

Meanwhile, I've received a copy of the new book, "The Genius In All of Us" (by David Shenk) from the publisher, and it will be next up for a fuller review here.

Another Approach To Prime Numbers

If you like prime numbers this website may keep you occupied for awhile:


http://www.sievesofchaos.com/

Mind-boggling

For those who want to compute the circumference of a circle with outrageous accuracy ;-) ....
Pi computed to 2.7 trillion digits (..."trillion" with a "tr"):


http://tinyurl.com/yhhb9fk

(....Daniel Tammet really has his work cut out for him now!)

Geometric Patterns in the Mind

Math and hallucinations of the psychedelic sort:


http://plus.maths.org/issue53/features/hallucinations/index.html

New Math Book

New math book, "The Princeton Companion to Mathematics," reviewed very favorably here:


http://tinyurl.com/y9vnc5y

The Golden Ratio

Human affinity for the 'Golden Ratio' of mathematics now explained by an engineer in terms of unification of "vision, thought and movement under a single law of nature's design":


http://www.labspaces.net/101235/Mystery_of_golden_ratio_explained

A Classic

 Classic Eugene Wigner paper here on the "unreasonable effectiveness of mathematics":

http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

The Polymath Project

The Polymath Project uses the 'Net to prove complex mathematical theorems (faster than they could be solved by individuals working apart). Fascinating concept... read all about it:

http://www.physicsgroupie.com/2009/11/polymath-project.html

Cantor and Infinity

Possibly nothing in math is more mind-blowing than infinity theory, as originally established by Georg Cantor. Here, for the Friday video, an introduction to infinity from a couple of YouTube offerings :

Math Conundrum

I was surprised to read over at another blog that there is no precise solution to this math problem; seems simple enough there would be one, but appearances can be deceptive.
It turns out there is an answer (to what is known as "Mrs. Miniver's problem") but it involves a transcendental number, and thus is only approximate.

Huhhh?

Just a simple fun math diversion today that I've adapted from another blog:


-- Proof --

Suppose:

a + b = c.

This can then be equivalently written as:

(4a – 3a) + (4b – 3b) = 4c – 3c

After reorganizing (adding/subtracting from both sides):

4a + 4b – 4c = 3a + 3b – 3c

Take the constants out of the brackets:

4(a + b – c) = 3(a + b – c)

Remove the same term left and right:

4 = 3

Ta-daaaaaaa!!

Origami and Math

The Friday video: Great TED talk by Robert Lang on the remarkable intricacy of modern-day origami:

"The Drunkard's Walk"

Randomness in our lives...


I generally like Leonard Mlodinow's writing (previous volumes include "Feynman's Rainbow" and "Euclid's Window"), and his 2008 offering, "The Drunkard's Walk: How Randomness Rules Our Lives," is no exception. I read it over a year ago, but it is newly out in paperback and making the bookstore rounds again, so worth a mention.

Several books in recent years, like this one, have made the point that despite our intuitive notions of order and scientific predictability in our lives, randomness actually plays a far more significant role. Mlodinow, a former Cal Tech physicist/mathematician is skilled at explaining probability and statistics to a lay audience in an engaging, even humorous manner. The author shows how our basic instinct to perceive patterns and order in the world around us often leads us astray, while a more clear understanding of statistics will often account for seeming anomalies. He covers most of the popular and entertaining topics in this arena, as well as some less-widely covered ones, with clear explanations that can be readily followed by even the non-mathematically-inclined. Again, I won't do a full review here, but pass along an "A-" rating, and refer readers to these other reviews on the Web:

NY Times review
The Guardian review

Mathematics In 10 Lessons

"Mathematics In 10 Lessons: The Grand Tour" by Jerry King

Just a brief review since I can't recommend this offering to a general readership, and only give it an overall "C" rating. Browsing the volume in a bookstore it looked intriguing to me, as it touched upon many math topics of interest to me: infinity, number theory, probability, calculus, paradox, imaginary numbers, and "truth and beauty."

The book claims that it does not require much math background to be enjoyed, and several mathematicians endorse the book heartily on the back cover (although I noticed none of them are major math popularizers who's names would be readily recognized). However, I think a math novice or lay reader might have some difficulty with the material, while those more well-read in math may find the material dull or boring --- the writing is likely too dry and pedantic for a lay reader and too basic or simplistic for those more sophisticated in math. Some math fans may find the content elucidative, but I suspect they may be a small subset of all readers. Much of the material is on math underpinnings and/or proofs that may appear intuitively obvious --- and while there is some benefit in this explication, it can also be somewhat tedious. Generally speaking, the most interesting aspects of math are probably those that are counter-intuitive, and thusly in need of step-by-step rendering. I think the author here has made a very sincere attempt to bring many fundamentals of math to a general audience, but this is actually one of the most difficult tasks in all of science-writing, and so most attempts, as in this case, fall short.

A book that covers at least some of the same type material, which I found much more engaging and do strongly recommend is William Byers' 2007 volume "How Mathematicians Think."

The Monty Hall Problem

One of the most interesting popular math problems of recent times:







And on the same topic, Jason Rosenhouse's new book, entirely on this puzzle,"The Monty Hall Problem," is now available at Amazon HERE.

Mathematical Curiosities Indeed!

Number Fun...

The latest volume from prolific British mathematician Ian Stewart is "Professor Stewart's Cabinet of Mathematical Curiosities," an entertaining compendium (he calls it "a miscellany") of "amusing and intriguing" puzzles, tales, factoids, and interesting tidbits from recreational mathematics; actually quite an amazing range and variety of short offerings (180+ entries). All the common mathematical recreations are found here, and a great many less familiar ones. Discussion tends to be brief, but not overly so, although in a few cases greater elucidation might've been helpful.

Obviously, one needs to enjoy math to enjoy this volume, but one doesn't need an advanced grasp of mathematics to comprehend most of the content (although for some entries it WILL definitely help). For the math aficionados out there I definitely give this book a "B+"; it is a wonderful addition to this genre. One recreational math work I probably like better (and would rate an "A") is Martin Gardner's "The Colossal Book of Mathematics," but then it's pretty hard to top Martin Gardner! And for math-inclined lay readers who especially enjoy this genre I'll mention three other volumes I'm fond of:

"Math Charmers" by Alfred Posamentier, and
"A Passion For Mathematics" by Clifford Pickover
"Wonders of Numbers" also Clifford Pickover

Lastly, another review of Stewart's book HERE.

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Euler's Equation

This is the month of Leonhard Euler's birth; Euler was one of the most prolific, productive mathematicians of all time. His so-called "Euler's Equation" or "Euler's Identity" is considered by many to be hands-down the most beautiful equation in all of mathematics. In his honor this older essay from Keith Devlin:

http://www.maa.org/devlin/devlin_10_04.html

Happy Pi Day!

This is March 14, otherwise known as "Pi Day" (3.14)
Math enthusiasts are celebrating.
So if you're looking for an excuse to celebrate, a few pertinent websites here:

http://www.joyofpi.com/thebook.html

http://www.exploratorium.edu/pi/

http://tinyurl.com/adjvyx (excellent book)

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

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For Math Junkies

For a Friday video offering, this zoom-in of the marvelous Mandelbrot Set to a "6th level mini-set" with Jonathan Coulton's "Mandelbrot Set" musical accompaniment:

(and if you know of a video or graphic link on the Web that might be interesting, inspiring, or educational for science/nature folks please send it along to me via email for possible use as a Friday post)



(there are many other zooms of the Set available on YouTube)

Addendum:

Below, strictly for math aficionados, are the lyrics to the Jonathan Coulton music:

"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 "

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