A Moebius Ballet

I learned about it from Science News Online (here), but evidently it has been on its way to becoming a mini-phenomenon since it was posted on YouTube in June, 2007.

It’s a short animation of some mathematical concepts, called “Moebius Transformations Revealed“. To quote from the creators’ website (here):

Möbius Transformations Revealed is a short video by Douglas Arnold and Jonathan Rogness which depicts the beauty of Möbius transformations and shows how moving to a higher dimension reveals their essential unity.

It does do what it claims it does, although it doesn’t go so far as to suggest what we learn from understanding their essential unity, nor what we might do with our new understanding. Perhaps I’ll have that “aha!” later on.

Nevertheless, it’s a very pretty little film (2:32 long), and the music (Robert Schumann, a movement from Kinderscenen, for piano) seems unusually well suited.

But it’s better that you just have a look rather than listen to me talk about it.

More Undular Bores

For those who enjoyed the pictures a few days ago of undular bores — atmospheric waves visible in clouds — here are a few more treats via NASA’s Earth Observatory project.

This time the waves are in the atmosphere off the west coast of Africa, in a couple of satellite photos captured by the Moderate Resolution Imaging Spectroradiometer (MODIS) on NASA’s Terra and Aqua satellites on October 9, 2007. Take a few moments to read the informative text on the page, too.

(While you’re there, you might want to look at the dramatic satellite photos of the wildfires in Southern California.)

Undular Bores

Here is “Science @ NASA” again, sending me another interesting story with pretty pictures. This one — they say for shock value — is about “undular bores”. What they’re talking about is waves in the atmosphere that show up dramatically in cloud patterns.

I have a personal interest in all things waves because they were one of the things I studied in my former life as a physicist. They were waves in many forms that interested me, too, since I studied fluid motions, in which one can find physical waves, and field phenomenon, in which the waves are mathematically abstract but still represent real phenomenon.

In looking at these wave pictures coming up, it might be fun to know that in the ocean — or on any water surface — waves come in two types, call them “waves” (the big ones) and “ripples” (the little ones). Ripples are about finger sized, while waves are more body sized. Both are caused by disturbances, generally wind, but they undulate for different reasons. Ripples ripple because of the surface tension of the water; waves wave because of gravity, or buoyancy, in the water. Most water waves in the ocean, and those that break on shorelines, are generated by strong winds associated with storms that can be thousands of miles away.

Anyway, air also has buoyancy (remember: hot air rises, cool air sinks — the hot air is buoyant relative to the cool) and can sometimes show some very large scale waves, with wavelengths of about a mile. When there are clouds around they can make the waves dramatically visible. They can be caused by storms moving about as high-pressure centers collide with low-pressure centers and hot-air masses encounter cool-air masses.

Here’s Tim Coleman of the National Space Science and Technology Center (NSSTC) in Huntsville, Alabama:

“These waves were created by a cluster of thunderstorms approaching Des Moines from the west,” he explains. “At the time, a layer of cold, stable air was sitting on top of Des Moines. The approaching storms disturbed this air, creating a ripple akin to what we see when we toss a stone into a pond.”

Undular bores are a type of “gravity wave”—so called because gravity acts as the restoring force essential to wave motion. Analogy: “We’re all familiar with gravity waves caused by boats in water,” points out Coleman. “When a boat goes tearing across a lake, water in front of the boat is pushed upward. Gravity pulls the water back down again and this sets up a wave.”

[excerpt from "Giant Atmospheric Waves Over Iowa", Science @ NASA for 11 October 2007.]

There are two gorgeous visuals to see by clicking the link. The first is a video of the undular bores over Iowa. I’d suggest watching the animated gifs rather than the video because the gifs extract just the interesting parts between 9:25 and 9:45, and it keeps playing.

Then, just below that, don’t miss the radar photograph, which shows the train of waves with stunning clarity.

Now, as if that weren’t enough, I found this cool video on YouTube, intended to demonstrate “Gravity Waves” in the atmosphere, of which it is a beautiful example. But wait! Incredibly, this video also shows undular bores, over Iowa (but Tama, rather than Des Moines), as recorded by the same television station, KCCI!

Titanic Lakes

This just in from “Science @ NASA”:

Newly assembled radar images from the Cassini spacecraft are giving researchers their best-ever view of hydrocarbon lakes and seas on the north pole of Saturn’s moon Titan, while a new radar image reveals that Titan’s south pole also has lakes.

Approximately 60 percent of Titan’s north polar region (north of 60o latitude) has been mapped by Cassini’s radar. About 14 percent of the mapped region is covered by what scientists believe are lakes filled with liquid methane and ethane:

The mosaic image was created by stitching together radar images from seven Titan flybys over the last year and a half. At least one of the pictured lakes is larger than Lake Superior.

[excerpt from "New Lakes Discovered on Titan", Science @ NASA, 12 October 2007.]

Isn’t that fascinating: “hydrocarbon lakes” filled with “liquid methane and ethane”!

The photograph accompanying the press release is really quite lovely — it’s what attracted my attention in the first place. Follow the link above to see the photomosaic.

The Brightest Supernova Ever

Here’s the lead from the NASA release about an observation with the Chandra X-Ray [orbiting] Observatory of “the brightest supernova ever“:

May 7, 2007: The brightest stellar explosion ever recorded may be a long-sought new type of supernova, according to observations by NASA’s Chandra X-ray Observatory and ground-based optical telescopes. This discovery indicates that violent explosions of extremely massive stars were relatively common in the early universe, and that a similar explosion may be ready to go off in our own galaxy.

“This was a truly monstrous explosion, a hundred times more energetic than a typical supernova,” said Nathan Smith of the University of California at Berkeley, who led a team of astronomers from California and the University of Texas in Austin. “That means the star that exploded might have been as massive as a star can get, about 150 times that of our sun. We’ve never seen that before.”

Astronomers think many of the first stars in the Universe were this massive, and this new supernova may thus provide a rare glimpse of how those first generation stars died. It is unprecedented, however, to find such a massive star and witness its death. The discovery of the supernova, known as SN 2006gy, provides evidence that the death of such massive stars is fundamentally different from theoretical predictions.

The photographs accompanying the release are extraordinary, showing that the supernova was as bright as the core of its galaxy — that’s bright! It seems this one was bright enough that some light even reached the mainstream press, as in this story from the L.A. Times.

As additional background, may I point out my own posting called “A Star Explodes in Slow Motion“, which feature an informative excerpt from Galileo’s Finger: The Ten Great Ideas of Science, by Peter Atkins.

Noctilucent Clouds

For those who fear that there may be nothing left in the world to discover (hardly a chance!), consider this item from Space Weather News for April 25, 2007:

NIGHT-SHINING CLOUDS: NASA’s AIM spacecraft left Earth Wednesday on a two-year mission to study mysterious noctilucent (night-shining) clouds. Hovering at the edge of space, these clouds were first noticed in the 19th century; they are remarkable for their electric-blue color and sharp, wavy ripples. In recent years noctilucent clouds have been growing brighter and spreading. What causes them? Theories range from space dust to global warming. For the next two years, AIM will scrutinize the clouds from Earth orbit to learn what they may be telling us about our planet. Visit http://spaceweather.com for more information about the AIM mission, pictures of noctilucent clouds and observing tips.

Earth from Saturn

This is a most unusual, beautiful, and evocative photograph — and it is an actual photographic image, albeit a composite. The photographer was the Cassini-Huygens spacecraft. On this occasion Saturn interposed itself between the Sun and the spacecraft, thus creating this beautifully backlit composition. Although it is hard to make out in this small version, the dot in the upper-left quadrant of the lower image, indicated by the text, is the Earth, seen through Saturn’s rings.

This version of what is sure to become a famous image came to my attention through NASA’s Earth Observatory website. Visit the original page (“A View of Earth from Saturn“) for larger versions of the image, and lots of information about the image and the Cassini-Huygens mission.

Here is a short excerpt from that page:

This beautiful image of Saturn and its rings looks more like an artist’s creation than a real image, but in fact, the image is a composite (layered image) made from 165 images taken by the wide-angle camera on the Cassini spacecraft over nearly three hours on September 15, 2006. Scientists created the color in the image by digitally compositing ultraviolet, infrared, and clear-filter images and then adjusting the final image to resemble natural color. (A clear filter is one that allows in all the wavelengths of light the sensor is capable of detecting.) The bottom image is a closeup view of the upper left quadrant of the rings, through which Earth is visible in the far, far distance.