Playing a Mandelbrot Set - Hum a Few Iterations and I'll Fake It

Eventually by Sergio Lazo

In the annals of how-to songs one will find everything from delicate interactions with a weapon of mass destruction - e.g. How to Dismantle an Atomic Bomb by U2 - to an even more dangerous and potentially deadly situation - How to Handle a Woman from Camelot comes to mind.

(Yes I know that How to Dismantle an Atomic Bomb is not the name of an actual song! So suggest a better title to match up with How to handle a Woman.)

And now comes the ultimate how-to for the fractally-minded: Mandelbrot Set by Jonathan Coulton, the Contributing Troubadour for Popular Science Magazine and composer of "well-crafted geek folk-pop. Hilarious but heartbreaking songs about mad scientists, robot armies and self-loathing giant squids." His is the voice of "every one of us who has ever sat despairingly on the floor, surrounded by parts of an Ikea endtable, weeping over our Allen wrenches.

Coulton's work is truly unique. Check out his site for all of his tunes. And there are plenty of them: In 2005-2006 he recorded and published a new song podcast every week. All of the lyrics are there, as well as guitar tabs and videos.

Mandelbrot Set is funny, incredibly clever, and mathematically correct! Some excerpts...

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M.C. Escher: Chaos and Order and Back Again

Order and Chaos. Click to enlarge.

In an earlier post I commented on the ability of M.C. Escher to capture the infinity of time and space in his woodcuts, drawings, and lithographs.

Another common thread in many of Escher's works is the sense of order arising out of chaos - or is it chaos out of order? A master of graphic puns that simultaneously emphasize and blur the demarcation between figure and ground, Escher does seem to lean more in the direction of order out of chaos. In The Magic of M.C. Escher , a fabulous compendium of Escher's works that includes unpublished sketches from his workbooks and excerpts from his correspondence with family and colleagues, this direction is clear:

The consistency of the phenomena around us, order, regularity, cyclical repetitions and renewals, have started to speak to me more and more strongly all the time. The awareness of their presence brings me repose and gives me support. In my pictures I try to bear witness that we are living in a beautiful, ordered world, and not in a chaos without standards, as it sometimes seems.

For a very good intro to a broad selection of Escher's most famous works, visit the M.C. Escher - Life and Work on-line tour at the National Gallery of Art. From the program notes for the Order and Chaos lithograph pictured in this post:

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Modeling Acts of God, Part 1

Hurricane structure. Click to enlarge.

This post is the first in a series of the state of modeling very powerful, nasty natural phenomena such as hurricanes, earthquakes, and tsunami.

Depending on where you live you may have trouble acquiring or affording insurance protection form these so-called "acts of God. "  Whatever these AOG's might be, they are often home- and life-threatening.  Can these AOG's be modeled successfully, i.e. how well are they understood and can their generation, properties, and behavior be predicted with any accuracy?

Along with the understanding and prediction provided by standard models for these event, it is natural to wonder how global warming contributes to these phenomena. Do models for these AOG's compensate for GW's effect? This is a very pressing question. Anecdotally, many claim that the events are both more frequent and more severe, with natural tendency to assign blame to global warming.

Consider hurricanes. Hurricanes are pretty well "understood" in terms of how they start and move. Proto-hurricanes start as small tropical vortices , which themselves originate because of rotational effects of the earth on atmospheric gases. Kerry Emanuel, Professor of atmospheric sciences at MIT explains this in Hurricanes: Tempests in a Greenhouse:

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As the World Turns - Foucault's Eco

Feb. 3rd marked the 156th anniversary of Léon Foucault's demonstration that the earth revolved on its axis. The experiment was brilliantly simple: let a large pendulum swing back and forth over the course of a day, with a sharp tip hanging off of the pendulum bob making patterns in a bed of sand below it. As the pendulum bob moves back and fort in a vertical plane the earth rotates beneath it, and this rotation can be measured by the marks in the sand. (For a nice intro to Foucault's Pendulum, check out the scriptographic booklet on the subject at the California Academy of Sciences.)

Foucault did not stop with simply showing that the earth rotates. He was able to predict how fast the pendulum would appear to rotate because of the fact that the rate at which the marks carve out a pattern depends on the latitude of the pendulum. So, for example, at one of the poles the earth will spin once in 24 hours, while at the equator the earth does not spin with respect to the plane of the pendulum. Anywhere in between the amount of time it takes for the pendulum to make one complete rotation is given by

T = 24/sin L

Here T is the time for the pendulum to return to its original position (in hours), and L is the latitude at which the experiment is carried out.

The pendulum demonstration was a huge success, showing as it did in a very simple way what could not be felt by earthly inhabitants - the rotation of the earth they were standing on. (It was also a majestic demonstration, being conducted in the the Panthéon in Paris.) The fact that Foucault could actually predict the exact timing of the rotation made him akin to the explorers who mesmerized remote villagers with abilities to predict eclipses, and he achieved physics rock-star status - maybe the most until Einstein.

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When Scientists Argue About Religion and Science

God the GeometerIn his July 2006 Addressing the public about science and religion opinion piece for Physics Today,  Murray Peshkin - a theoretical physicist at Argonne national Lab - argues passionately about the benefits of scientists addressing the boundary between religion and science in a public forum. Peshkin describes how his public appearances have led to some interesting give-and-take - learning experiences for him and his audiences.

Peshkin's position is summarized by the title and opening line of an essay published in the Chicago Tribune magazine:

SCIENCE AND RELIGION: CAN THEY LEARN TO LIVE WITH EACH OTHER?
The answer is that they can and they must, or we will all suffer the consequences.

Given the nature of the polarized debates surrounding Intelligent Design, and particularly the Dover court case, it's clear that two topics need a good deal of elaboration: describing how a scientist uses the word theory, and the need for a theory to be falsifiable in order to count as science.

Peshkin uses an interesting, and effective hypothetical situation to drive home the falsifiable idea, which leads to his main point about the inherent differences between a scientific and religious world view:

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The 10th Carnival of Art

Carnival by Elaine Normandy , who uses Gnofract 4D - freeware fractal software for Linux.I found out earlier today that my post on Art and Science Transvergence: Glowing Bunnies was listed in the latest Carnival of Art, a blog carnival that has been hosted by Australian artist Jennie Rosenbaum since June 2006.

I really appreciate the link there - so thank you Jennie!

I urge all readers here to check out Carnival of Art - #10 . With categories in Art History, Art News, Art Philosophy, Artworks, Creating Art, and The Biz, there are a lot of intriguing, compelling, beautiful, and informative posts.

And don't stop there - read the Carnivals of Art #1 through #9.

This is my first experience with a blog carnival, and I am very impressed with the ability to reach more readers, and find more amazing blog posts than I can imagine finding by other routes, including Technorati.

For more on blog carnivals, including how to find them, submit a post, or even host one, check out BlogCarnival.com.

For a detailed analysis of the ability of blog carnivals to be important engines of social networks, and their potential to "become online equivalents of not just TIME magazine, but also GQ, Vogue, Parenting, National Geographic, People, and, why not, Science and Nature" see Blog Carnivals And The Future Of Journalism, an excellent post by Bora Zivkovic in his Science and Politics blog.

Luminiferously Aethereal Dark Matter and Energy

Star Traveler from Angelbert Metoyer's Dark Energy Splitting the Universe . Click to enlarge.At the end of the 19th Century century many physicists were still searching for the luminiferous aether - the mysterious, invisible substance that permeated the universe - the medium that (it was presumed) needed to exist in order to support light waves.

At that time, waves were understood to be mechanical disturbances in a medium - in effect, shapes that propagate through the medium transporting energy from source to receiver with a speed dependant on the medium itself . Water waves, waves on a string, sound waves in a column of air - all of these phenomena relied on matter to support these moving shapes.

The Aether was supposed to be the invisible stuff that somehow oscillated as the shapes of light waves passed from point A to point B. It had to be really odd stuff - invisible, for one thing, and also incredibly resilient, because it had to support an unbelievable speed - the speed of light.

Nevertheless, by this point the mechanical qualities of the aether had become more and more magical: it had to be a fluid in order to fill space, but one that was millions of times more rigid than steel in order to support the high frequencies of light waves. It also had to be massless and without viscosity, otherwise it would visibly affect the orbits of planets. Additionally it appeared it had to be completely transparent, non-dispersive, incompressible, and continuous at a very small scale. (wikipedia)

In other words, aether couldn't be seen, weighed, touched or tasted, but it was stronger than anything known to man. And it was everywhere - in your shoes, hair, mouth, nose, and subway tunnels. A really strange thing for physicists to believe in.

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One Degree of Separation - Global Hot Air

Sterling Hot-Air Engine. Click to enlarge.The world, and especially all of blogville has exploded with the release of the IPCC's executive summary of its 2007 Climate Change: The Physical Basis. A web search for anything to do with global warming seems to yield just as many blogs that talk about the "myths" of global warming (e.g. see JunkScience) as there are "myths about myths" about global warming (e.g. see The Environmental Defense Fund site). How can anyone navigate through this stream of flotsam/jetsam? How do these blogs do anything but attract those who already believe in that point of view, or are leaning heavily that way?

Not even political persuasion is a good predictor of what you'll find out there. For example, read Facts and Myths about Global Warming: A Conservative Perspective at the The Green Elephant site. Green Elephant being the Republicans for Environmental Protection, of course.

Then there is the godfather of the anti-warming crowd - none other than the king of science fact/fiction media success - Michael Crichton (see my previous post on Crichton's role in the GW debate). His recent lecture The Impossibility of Prediction is a good example of why Crichton is listened-to and often quoted, especially by members of the Bush administration who,

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Coping with Chaotic Climate Models

Model prediction of Arctic sea ice loss - 2000 (L) vs. 2040 (R). From BBC news. Click to Enlarge.Now that the IPCC has released the summary of it's upcoming study report Climate Change 2007: The Physical Science Basis , strongly stating that global warming is man-made, it is still important for scientists to clearly enumerate any issues surrounding the accuracy and reliability of their models.

Because if they don't, global warming deniers, or those who believe that we need still more time for convincing proof will focus on the slightest inaccuracy in a model's prediction in classic red herring fashion. (In a way similar to anti-evolutionists, they will neglect the hundreds of accurate predictions and claim that the one that doesn't quite fit calls for total abandonment of a theory.)

Climate models are by their very nature prone to chaotic behavior. This behavior must be accounted for when using climate models for any type of prediction.  An excellent article on how chaotic models are handled has been provided recently by Cecilia Bitz of the Univ. of Washington. In her Real Climate article Arctic Sea Ice decline in the 21st Century, Bitz describes work she did with colleagues Marika Holland and Bruno Tremblay, which culminated in a paper for the Dec. 2006 Geophysical Research Letters. I want to focus on two aspects of Bitz's commentary: the presence of chaos in the climate models, and the overall accuracy of the modeling process. Bitz recounts:

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Pi-Brained Schemas & Savants: Who's Normal Now?

Meesh Pi. Click to enlargeA most peculiar feat was reported in yesterday's Philadelphia Inquirer:  Marc Umile, a filing clerk from the Philly area, was able to recite the first 12,887 digits of π from memory - an American record. (The current verified world record is for 43,000 digits by Krishan Chahal of India.)

In an odd twist, Umile performed his prodigious feat at a law office, and not for the Guiness Book folks. In these litigious times, it is obviously prudent to be prepared for intellectual property infringement in any activity such as this, which in this case comes under the heading of π's and torts ...

While Umile's feat is incredible, I am more intrigued by the physical/mental issues involved in the data entry, storage and retrieval of these digits. The actual amount of data is not the issue - 12,000 is a very small number of single digits when compared to the potential of the human brain.  Data entry is not hard to comprehend, either, with Umile spending two-plus years memorizing the digits. (I am not commenting on motivation or sanity here.  See the Inquirer piece for this!)

How in the world are the values recalled/retrieved?

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