Solar

According to this article in Der Spiegel, parabolic solar energy collection covering the largest red square would be sufficient to supply the world with electricity.

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Stasis

Jack Handey on How Things Even Out:

"Still don't believe things even out? Try this simple test: Flip a coin, over and over again, calling out 'Heads!' or 'Tails!' after each flip. Half the time people will ask you to please stop."

Note: Either the captchas are getting harder or I'm turning into a machine.

Take that, Minotaur!

10 miles to go...

Song: 10 Miles To Go On A 9 Mile Road
Artist: Jim White
Disc: No Such Place
Year: 2001

Superheavy?

If true, a fascinating discovery...

The physics Arxiv:

"The hunt for superheavy elements has focused banging various heavy nuclei together and hoping they’ll stick. In this way, physicists have extended the periodic table by manufacturing elements 111, 112, 114, 116 and 118, albeit for vanishingly small instants. Although none of these elements is particularly long lived, they don’t have progressively shorter lives and this is taken as evidence that islands of nuclear stability exist out there and that someday we’ll find stable superheavy elements.

But if these superheavy nuclei are stable, why don’t we find them already on Earth? Turns out we do; they’ve been here all along. The news today is that a group led by Amnon Marinov at the Hebrew University of Jerusalem has found the first naturally occuring superheavy nuclei by sifting through a large pile of the heavy metal thorium."

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Update: Chemistry Blog is skeptical.

Life on Mars

The Ukulele Orchestra of Great Britain...

I see a different you

Song: I see a different you
Artist: Koop
Disc: Koop Islands
Year: 2006

"Koop, the duo of Oscar Simonsson and Magnus Zingmark, seem to grasp what many other trip-hop production units never did -- that, no matter which instruments are used in your productions, digital or acoustic or electric, a sense of place is what should never be lost." - All Music Guide

Purls

A periodic roundup of a few interesting things..



From a design perspective, what can we learn from nature? A longtime subject of interest, National Geographic recently published a new piece, Biomimetics.

Is a longevity pill just around the corner? Technology Review: Longevity Pill Tested in Humans.

National Geographic chronicles discoveries of strange and bizarre critters in Antarctica. (Men without Hats sing Antarctica.)

Rising commodity prices... Krugman: Deja vu all over again. Soros says a commodity bubble is still in the growth phase as noted at The Big Picture.

None of the standard platinum-iridium cylinders defining the kilogram weigh the same anymore, The International Kilogram Conundrum.

Since plants absorb energy in sunlight, I've often wondered why plants aren't black. What's the point of rejecting green? SciAm: The Color of Plants on Other Worlds.

You know when you hang out with a friend, have a few drinks, take the bus home, have a snack, take a nap and your wife wakes you up because you have a knife sticking out of your back? I hate when that happens! BBC News: Drunk Russian sleeps off knifing.

This Flash game is addicting: Bloxorz

Perfect Way

One more 80's tune...



Song: Perfect Way (mp3)
Artist: Scritti Politti
Disc: Cupid & Psyche 85
Year: 1985

Ahead

Been busy...

Obscure, vintage video...



Song: Ahead (mp3)
Artist: Wire
Disc: The Ideal Copy
Year: 1986

The Village

Song: The Village
Artist: David Potts
Video: Holger von Törne
Disc: Community 2: A New Order Online Tribute
Year: 2006

Delayed Reaction

Interesting. I created this collage demonstrating the similarities of expression between John McCain and BSG's Col. Tigh over a year ago, but lately, due to McCain's rising popularity, it's been spreading like crazy, and today it made the front page of Reddit.

Same Old Drag

Song: Same Old Drag (mp3)
Artist: The Apples in Stereo
Disc: New Magnetic Wonder
Year: 2007

Pulitzer: Editorial Writing

In a time desperately calling for moral outrage, wisdom, prudence, the moment has come for Pulitzer to raise the banner and offer a hearty congratulations to:

No one!

"For distinguished editorial writing, the test of excellence being clearness of style, moral purpose, sound reasoning, and power to influence public opinion in what the writer conceives to be the right direction, in print or in print and online, Ten thousand dollars ($10,000).

No Award"

link

Ha!

Breathe

Song: Breathe (mp3)
Artist: Télépopmusik
Disc: Genetic World
Year: 2003

SVD for the Vertically Challenged

If you haven't noticed, this blog can be a bit random, and I never know what will garner interest on the Net. One surprisingly popular offering has been the little SVD calculator I created by porting the JAMA SVD code from Java to JavaScript.

Today, I found an obvious bug in my applet and fixed it. In the process, I discovered a number of people querying the Net about the issue leading to the bug. The problem was that the JAMA code only calculated the SVD in cases where m >= n; i.e., it could only calculate the SVD on matrices with more rows (m) than columns (n).

This is easily fixed, if you consider the matrix transpose and corresponding transpose of its SVD.

A^T = (U*S*V^T)^T

The basic rule of matrix algebra to consider: The transpose of a matrix product is equal to the reverse product of the individual matrix transposes (cf. The Matrix Cookbook).

In other words:

(U*S*V^T)^T = V*S^T*U^T

Bottom line: If you can only calculate the SVD of A where m >= n, all you need to do is calculate the SVD of A^T and swap the resulting U and V matrices.

Advice for the Thirsty Triangle

A picture is worth a thousand words, but when it comes to comprehending algorithms, I think a decent visualization applet is worth even more--maybe ten thousand words--but I'll be happy if the following helps elucidate a concept for a single curious soul.

The applet du jour demonstrates the Nelder-Mead method, also called the downhill simplex method, the simplex method or the amoeba algorithm.

Suppose you're a triangle and you're thirsty. Knowing water runs downhill, you seek the lowest point you can, but what rules will you apply in finding this thirst-quenching minimum?

Let's refer to your two lowest vertices as your feet and your highest vertex as your head. Here are some of your possible power moves:

1. Stretch to twice your height and flip on your feet.
2. Flip on your feet.
3. Shrink to half your height.
4. Shrink to half your size.

Try each each move in order. If a move puts your head in a lower position, start over and keep doing it until you've shrunk yourself down to a point. Note: which vertex is your head may change after each round.

Try it here: Nelder-Mead applet

This simple algorithm is useful in finding minimums of functions when you have no information about derivatives (i.e., the slope of the surface at a given point). The value of the function at each point is all that's required. The triangle is easily extended to a simplex in higher dimensions (in 4D, it's a flipping tetrahedron, etc.), and the algorithm can be applied to find minimums in n-dimensional space.

In practice, I've used Nelder-Mead to simultaneously optimize the weighted sum of a collection of polynomial models. Because the algorithm finds local minimums, it's best to run a number of trials from random starting points--especially when the underlying space contains a lot of hills and valleys.

A competing method that is said to converge faster is Powell's method. I may see if I can come up with an applet for it in the future, but I had to do Nelder-Mead first, because I think it makes for a much more interesting animation.

fin

The New Frontier

Thanks to Warner Bros. for putting an excellent quality version of Donald Fagen's New Frontier on YouTube, a clip from his sardonic and wistful retrospective on coming of age in the Kruschev-fearing, Tomorrowland-embracing suburban America of the early 1960s. Love in a bomb shelter.



Artist: Donald Fagen
Song: New Frontier
Disc: The Nightfly
Year: 1982

The Tax Break Fairy Strikes Again

Looks like the pesky Tax Break Fairy has been at it again...*

"NEW YORK (CNNMoney.com) -- Lawmakers grilled executives from the world's five largest publicly traded oil companies Tuesday, criticizing them for taking tax subsidies and not investing in renewable resources amid record prices for oil and gasoline."

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*How else could those oil companies have gotten all those tax breaks and subsidies?