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Monday, February 28, 2011

The Internet and Us

Off on a non-math tangent today....

John Brockman's Edge group puts out a question each year to be answered succinctly by a multitude of cutting-edge scientists/thinkers. The resultant responses (and books) always make for interesting reading. The 2010 question was "Is the internet changing the way you think?" All (~170) sometimes redundant, but also diverse, responses are here (or you can buy the book):

http://www.edge.org/q2010/q10_index.html#responses

Among the most interesting responses to me are these (in no particular order):

Alun Anderson

Clay Shirky

David Eagleman

Jaron Lanier

Robert Sapolsky

Emanuel Derman

Stanislas Dehaene

The main Edge website is here: http://www.edge.org
And the 2011 question is already posted here: http://www.edge.org/q2011/q11_index.html
Finally, all their prior year questions can be found here: http://www.edge.org/questioncenter.html

The question of what the internet is doing to the human brain and thought is a fascinating one with a wide spectrum of varying opinions. Mathematics is one of the areas where the collaborative nature of the Web (call it "hive mind," "wisdom of large groups," "crowd-sourcing," or any number of other terms) is already proving its efficacy... of course there can also be such a thing as the "madness of crowds!"
My own view is that the intrinsic social and cognitive power that the internet wields will ultimately bulldoze over any of the potential negative effects that may come along with it. Politically, we may already be seeing the benefits in the deposition of long-entrenched autocracies, by populations (digitally) conjoined and organized for the first time in human history. Time will tell... but it is certainly an interesting era (and possibly even inflection point) to be alive, observing human civilization evolve!

Saturday, February 26, 2011

Thursday, February 24, 2011

'Bite-size' Reading





There are a lot of 'bite-size' books out now that introduce readers to a range of key mathematical ideas without getting too technical or too deep (but not too simplistic either). Thought I'd just mention two of the ones I particularly like for anyone not already familiar with them (feel free to mention your own favorite short intros to mathematics for the non-professional, in the comments section):

"Mathematics: A Brief Insight" by Timothy Gowers:

http://tinyurl.com/4gtcmpo 

and, "50 Mathematical Ideas You Really Need To Know" by Tony Crilly:

http://tinyurl.com/4jzbx79 
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Wednesday, February 23, 2011

Graph Fun

Just some more humor today... even those of you that never liked graphs in school should get a smile out of some of these "Graphjam" graphs courtesy of "SquareCircleZ" blog:

http://www.squarecirclez.com/blog/more-funny-graphjam-graphs/5624

http://www.squarecirclez.com/blog/funny-graphs-from-graphjam/5611

...enjoy!

Addendum: now I've found this prior post also from SquareCircleZ with hilarious math "equations" drawn from Morenewmath.com:

http://www.squarecirclez.com/blog/morenewmath-funny-equations-about-life/3676

...okay, enough fun for one day! 

Monday, February 21, 2011

More On Complexity...

A great introduction (with several links) today to complexity theory and chaos, from RJ Lipton here:

http://rjlipton.wordpress.com/2011/02/21/butterflies-and-complexity-theories/

...and I learned that the "Butterfly Effect" actually goes all the way back to a Ray Bradbury novel... (since I don't read science fiction, or any fiction for that matter, I never knew that... or, did the notion come to Bradbury from yet someone or something else... who got it from.....?!)

Saturday, February 19, 2011

Contemplation...

Long-time readers here know I enjoy recursive or self-reference elements in language and/or numbers. Below, a link to a cartoon that turns such into some humor:

http://tinyurl.com/4cxbfqk

Now, a computer could no doubt be made to generate such a sentence as included therein, but could a computer ever recognize the humor in it???

(... and I ask that, because a recent commentator on NPR, contemplating IBM's "Watson" victory over humans in the "Jeopardy" game show, asked aloud if computers, that can certainly match and exceed human mental capacities, could ever possess a 'sense of humor'!?)

Friday, February 18, 2011

What Next From IBM?

RJ Lipton's commentary stemming from the recent win by IBM's "Watson" computer in the recent "Jeopardy" face-off:

http://rjlipton.wordpress.com/2011/02/17/are-mathematicians-in-jeopardy/

...in which Lipton essentially asks whether the invention of an expert trivial-pursuit robot is a step toward the creation of an expert robot mathematician.

Thursday, February 17, 2011

Caltech TED Talk

Here a talk by computer scientist Scott Aaronson, author of the popular blog "Shtetl Optimized," in which he entertainingly  addresses P vs. NP, and quantum computing, among other things (...all in 15 minutes):

http://www.youtube.com/watch?v=SczraSQE3MY

This is from a recent TED Talk Symposium held at Caltech in honor of Richard Feynman, and you may find some of the other presentations worth checking out as well.

Wednesday, February 16, 2011

The Geometry of The Universe

An international team of mathematicians is creating a "periodic table" of 3-, 4-, and 5-dimensional "shapes" composing the Universe:
"As these building block shapes are revealed, the mathematicians will work out the equations that describe each shape and through this, they expect to develop a better understanding of the shapes' geometric properties and how different shapes are related to one another."
creating "...a directory that lists all the geometric building blocks and breaks down each one's properties using relatively simple equations."

" ...a computer modelling programme... should enable the researchers to pinpoint the basic building blocks for these multi-dimensional shapes from a pool of hundreds of millions of shapes...The researchers calculate that there are around 500 million shapes that can be defined algebraically in four dimensions and they anticipate that they will find a few thousand building blocks from which all these shapes are made."

"In our project we are looking for the basic building blocks of shapes. You can think of these basic building blocks as 'atoms', and think of larger shapes as 'molecules.' The next challenge is to understand how properties of the larger shapes depend on the 'atoms' that they are made from. In other words, we want to build a theory of chemistry for shapes," added Dr Coates.
One of the many reports on the study is here:

http://www.gizmag.com/periodic-table-of-shapes/17895/

Saturday, February 12, 2011

Weekend Chuckle...

"The difference between an introvert and extrovert mathematician is: An introvert mathematician looks at his shoes while talking to you. An extrovert mathematician looks at your shoes."

...just one of the many light-hearted take-aways from Michael O'Brien over at his most recent Equalis Community Blog post:

http://www.equalis.com/members/blog_view.asp?id=565749&post=119636

Thursday, February 10, 2011

Book Recommendations (from elsewhere)

"Math-blog" has now compiled its list of recommended math books, as suggested by its readers (a very diverse list indeed, ranging from fairly basic to somewhat provocative to rather technical):

http://tinyurl.com/462bxyx

Wednesday, February 9, 2011

Math, Language, Cognition

An NPR piece this morning talks about language and math here:

http://tinyurl.com/4mqgdg7

And an older discussion of the cognitive relationship between mathematics and language from plus.maths.org here:

http://plus.maths.org/content/evolutionary-maths

Tuesday, February 8, 2011

Favorite Math Books...

"Math-blog" is doing a survey to compile a list of people's 'favorite math books' (using that term broadly). If you have one that comes to mind, go fill out their simple form. The more that take part, the merrier:

http://tinyurl.com/489hdvm

Sunday, February 6, 2011

Chaotic Chaos

Quote... unquote....

Been tied up with other things lately, but will put up for contemplation this passage from chapter 9 of Michael and Ellen Kaplan's book "Chances Are...," wherein they're discussing the work of Edward Lorenz, chaos theory, and deterministic systems:
"The mathematics of chaotic systems produces the same effect at every scale. Tell me how precise you want to be, and I can introduce my little germ of instability one decimal place further along; it may take a few more repetitions before the whole system's state becomes unpredictable, but the inevitability of chaos remains. The conventional image has the flap of a butterfly's wings in Brazil causing a storm in China, but even this is a needlessly gross impetus. The physicist David Ruelle, a major figure in chaos theory, gives a convincing demonstration that suspending the gravitational effect on our atmosphere of one electron at the limit of the observable universe would take no more than two weeks to make a difference in Earth's weather equivalent to having rain rather than sun during a romantic picnic."

Tuesday, February 1, 2011

Devlin Delivers... and so do the Kaplans

Another great post (...he says "rant" in this case) from Keith Devlin, regarding the Body-Mass Index (BMI), forensic DNA profiling, and emperors with or without garments:

http://www.maa.org/devlin/devlin_02_11.html

Here's a bit therefrom to wet your appetite:
"The fact is, in the era of DNA identification, judges and juries simply cannot avoid getting to grips with the relevant math. Identification hinges on those calculations. There may be no way of avoiding bringing mathematicians into court to explain how the calculations are done. But for that to be effective, those judges and juries need first to learn (and accept) that human intuitions about probabilities are hopelessly unreliable."
There is a lot more information around the Web about the statistics of DNA forensics and common misperceptions (...sometimes by people who should know better).

On a pertinent side-note, I'm currently reading "Chances Are..." by Michael and Ellen Kaplan. It's a slightly older volume (2006), so I probably won't write a full review of it, but I have already read enough to say I'm very much enjoying it (one of the best books I've seen on probabilities for a mass audience), and so recommend it to all who have an interest in the topic. Here's a NY Times review of the volume:

http://www.nytimes.com/2006/03/31/books/31book.html