Pi day, and Einstein's birthday

(Este post en español.)

Pi day is back! I shouldn't actually considered it as such, since we Spanish-speaking people write this day as 14/3, instead of 3/14... however, since the 3th day of the 14th month isn't likely to arrive anytime soon, I may as well jump on the wagon. My humble contribution is an applet (see below) for estimating Pi by picking random points in a square.

But additionally, today is the birthday of Albert Einstein, who was born in Ulm, Germany, 128 years ago. He was a giant like few others, and we are still waiting for someone big enough to stand on his shoulders and see further. Before the pi applet, here are some quotes from Einstein; Bora has some more.

Anyone who has never made a mistake has never tried anything new.

There are two ways to live: you can live as if nothing is a miracle; you can live as if everything is a miracle.

Space and time are modes by which we think, not conditions under which we live.

Underlying the seeming differences between science and magic are more similarities than you might imagine. Both disciplines rely on a process sparked by mystery and nurtured by curiosity.

After a certain level of technological skill is achieved, science and art tend to coalesce in aesthetic plasticity and form. The greater scientists are artists as well.

Do not worry about your problems with mathematics, I assure you mine are far greater

And now, let's estimate pi. What's the idea? It's simple: we have a circle (of a certain radius R) inscribed inside of a square. Since the radius of the circle is R, the side of the square is 2R. The area inside of the circle is πR², and the square's area, (2R)²=4R². Thus, if we randomly pick a point inside of the square, the probability that it will fall inside the circle (and hence, the frequency with which this will happen) is (πR²)/(4R²) = π/4. If we pick many points, and multiply by 4 the frequency with which we fall inside the circle, we will be increasingly close to the value of pi.

The applet is fairly intuitive; the points shown are the last 20 that have been picked (the fade away after 20 iterations), though the pi computation is done with the total accumulated points. With a few points, the "3" of pi shows up. Before 1000, the first decimal will converge to 1. Alas, maaaaany iterations are required to obtain (with a good probability) a good number of decimals; the 4th decimal will probably be beyond your patience.

Another method for estimating pi through probabilities (which is nicer, since there is no obvious circular thing in the setup) is through Buffon's needles.

Here is the applet; you can see the source code here:

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On a lighter note...

(Este post en español.)

Some other things I learned while perusing three months worth of blogs...

* Second Life is becoming more and more like a real country, and one that appears in the newspapers more than some of the traditional ones. Not surprisingly, Reuters opened a news agency there. Sweden has become the first country to open a virtual embassy in SL. There is even a terrorist movement in-world! Last but not the least, there is also science on display in SL; in my brief visit (yes, I joined, I'm curious!) I didn't manage to find any, but now I see that Paul Decelles provides some useful pointers. Rob Knop of Galactic Interactions gave a talk there, and promised to write about SL in the future.

* The truth came out.

* The nice Powers of 10 video was featured in a lot of blogs, but only in The Daily Transcript did I find Simpsons' version too.

* 17 was found to be the most random number. Though, of course, with randomness you can never be sure.

* There is some hope, after so many promises, that stem cells will finally start to deliver.

* I was really impressed by the story about chimps making spears (and I don't understand why the whole planet is not speaking about it). But how could this even more shocking discovery go almost unnoticed?

* Another bit of natural history which wasn't highlighted as it deserved: The march of the librarians (via Improbable Research). Forget penguins. Al Gore was lucky; this documentary should have been nominated and awarded instead of his talk.

* Via Digg: how would the creatures imagined by children look if they could draw just a little bit better? Perhaps like this?

* Of course, there where plenty of quizzes waiting for me in the feeds. Thus I learned that I'll die from an Unlikely Illness ("only to find out after death that eating more broccoli would have cured you"), that I'm Einstein ("a detached intellectual whose ideas saved/will destroy the world"), that my dominant intelligence is linguistic, that I'm Dr. Doom ("blessed with smarts and power but burdened by vanity"), that I know the Bible 95%, that I'm a mad King of France, that my brain falls exactly in the middle of the male-female continuum, that I'm William Gibson, and that I'm a loser (sorry about that, William).

During the last few months...

(Este post en español.)

After returning from a long trip and a couple of months mostly offline, I had (of course) to go through the 11000+ posts accumulated in bloglines; I still haven't finished the 10% I marked as "worth reading". So much stuff, so much. And the tables of contents of journals are lagging even behind that, a monstrous lump growing in my inbox. I just want to highlight some of the things I found when I reconnected to the blogosphere, and after that I hope to keep posting.

* Two new carnavals worth paying attention: Oekologie, "the blogosphere’s first ecology and environmental science carnival", and one that was long due: a carnival of mathematics, creatively called the Carnival of Mathematics. Three editions are already up, chez Alon, MarkCC, and the third since yesterday at Michi's. Editions will appear every other Friday, and the next one will be hosted by Jason Rosenhouse at EvolutionBlog. Lots of good stuff in each one.

* Anatol Rapaport passed away in January. He made great contributions to mathematical biology and mathematical social science, both through specific works and by organizing research areas and programmes.

* In February there was a Week of Science, where a number of science bloggers refrained from fighting crackpots, discussing politics and posting quizz results, and just wrote about science, one post per day. All entries (a looot of them) where crossposted at a Just Science blog, which will now be in stand-by until next year's edition.

* Some science bloggers have been writing posts on basic concepts in science; a list is being compiled and maintained by John Wilkins here. Extraordinary work.

* Also in the field of "blog aggregation", Bora of A Blog around the clock compiled and published a science blogging anthology, The Open Laboratory. The list of posts included is here, the book can be bought here, and John Dupuis has reviewed it (along with two other books). The idea grew out of a Science Blogging conference, and the next conference and anthology are already in the works.

* People, but specially the press, love to do reviews when a year ends and another begins, and 2006 didn't escape from that. If you still want to remember what happened last year besides Pluto's demotion (now reverted in New Mexico, by the way), Charles Daney at Science and Reason had links and comments to Nature's and Science's reviews, as well as a list of physics stories of the year. Nobel Intent, Ars Technica's science blog, reviewed the year in four posts, too. On the other hand, if you want to know what awaits us in 2007, see what some people told Seed magazine about it.

* Another New Year tradition: Edge.org published the answers of many clever people to a certain question. This time: What are you optimistic about?. They made me feel like Schopenhauer in a bad day.

* Two important memorial days. One was for Charles Darwin, and Clock's Bora compiled links to the many posts. The other was for Carl Sagan, and Joel Schlosberg has the list of the even more numerous blog tributes. I can only add links to this remembrance of Sagan as a skeptic, at the Skeptical Inquirer, and two reviews of his recent posthumous book, The Varieties of Scientific Experience. I'm sorry not to have blogged on those days; Darwin and Sagan were both important in my early interest in science. I remember how I bothered the librarian of my school until she managed to buy The Origin of Species, and how after that I never borrowed it (since I had also bothered my parents, and had received my own copy by then :-) ). And since I couldn't watch Sagan's Cosmos on TV (it was on a channel that didn't reach my city at the time), I bought and enjoyed the book as soon as my monthly allowances became worth saving.

* Bill Hooker completed a trilogy of guest posts at 3 Quarks Daily on Open Access, Open Science, and An Open Science World. Excelent.