Chaotic dinosaurs?

In the comic above, XKCD is objecting to Jurassic Park (21 years after the movie was released):

MALCOLM: You see? The tyrannosaur doesn’t obey set patterns or park schedules. The essence of Chaos.

ELLIE: I’m still not clear on Chaos.

MALCOLM: It simply deals with unpredictability in complex systems. The shorthand is the Butterfly Effect. A butterfly can flap its wings in Peking and in Central Park you get rain instead of sunshine.

No, Ian Malcolm, XKCD is right. That doesn’t really clear things up. And I’m pretty sure that topological mixing is actually more fundamental to the concept of Chaos:

Wired also has a piece on the anniversary of the film (concentrating on the special effects).


What your professor never told you about science: a review of Bellwether

Bellwether by Connie Willis

I recently re-read the classic science-fiction comedy Bellwether by Connie Willis. Bellwether, which is set in a fictional research company called “Hi-Tek,” is one of those books that reminds us how science really works:

People like to think of science as rational and reasonable, following step by step from hypothesis to experiment to conclusion. Dr. Chin, last year’s winner of the Niebnitz Grant, wrote, ‘The process of scientific discovery is the logical extension of observation by experimentation.’ Nothing could be further from the truth. The process is exactly like any other human endeavor—messy, haphazard, misdirected, and heavily influenced by chance. Look at Alexander Fleming who discovered penicillin when a spore drifted in the window of his lab and contaminated one of his cultures. Or Roentgen

Connie Willis keeps us laughing as she describes the ups and down of grant applications, staff interaction, chaos, confusion, recalcitrant laboratory animals, and management fads (I will always remember the ridiculous “1. Optimize potential. 2. Facilitate empowerment. 3. Implement visioning. 4. Strategize priorities. 5. Augment core structures.”).

The lead character’s own research project concerns the sociology of fads:

Coffeehouse (1450–1554) – Middle Eastern fad that originated in Aden, then spread to Mecca and throughout Persia and Turkey. Men sat cross-legged on rugs and sipped thick, black, bitter coffee from tiny cups while listening to poets. The coffeehouses eventually became more popular than mosques and were banned by the religious authorities, who claimed they were frequented by people ‘of low costume and very little industry.’ Spread to London (1652), Paris (1669), Boston (1675), Seattle (1985).

Bellwether contains some inaccuracies both in the discussion of chaos theory and the history of coffee. However, it is such a great comic novel that it was nominated for the Nebula Award in 1997, even though it is only science fiction in the sense that it is fiction about science, written by a science-fiction author. On the whole, a highly recommended book – one that is both funny and insightful.

* * * *
Bellwether by Connie Willis: 4 stars

Hyperion’s chaotic tumble

The Saturnian moon Hyperion, seen above in an image from Cassini, is known for its chaotic, tumbling rotation. The video below gives a sense of what this cosmic potato looks like, using the Celestia software (running at 100,000 times real time). Thanks to YouTube user “Beth F” for the video.


Lorenz and Chaos

In March 1963, Edward Lorenz founded chaos theory with his paper “Deterministic Nonperiodic Flow” (Journal of the Atmospheric Sciences, 20, 130–141). In honour of the anniversary, Physics Today has a survey paper, “Chaos at fifty.”

Lorenz’s classic paper described the Lorenz Attractor. The image above (by “XaosBits”) shows two orbits of the attractor. Microscopically different starting points give totally different trajectories. The image below (by “Wikimol”) gives another view of the attractor.

Lorenz’s paper was followed by the discovery of the Rössler attractor in 1976, and then what can only be called an avalanche of further work. Prior to Lorenz, signs of chaos had been seen in the logistic map, but Lorenz showed that the world itself (weather, specifically) was chaotic. Chaos also shows up in orbital motion, in turbulence, and in mixing. The image below (by “”) shows the result of simulating a magnetic pendulum.

Lorenz went on to coin the term “butterfly effect.” This effect, more formally known as “sensitivity to initial conditions,” is one of the key marks of chaos. Another is “topological mixing,” which means that the system will evolve over time so that any given region of its phase space will eventually overlap with any other given region. The image below (public domain) shows a circular region (blue) progressively being mapped (purple, pink, red, orange, yellow, and further iterations not shown) to a set of points which leaves no blank areas in the phase space.

Lorenz died on 16 April, 2008, at the age of 90. Physics Today also published an obituary when Lorenz died.