Andúnië :: the sky is (not) falling

17 july 2004

the sky is (not) falling

Many physical systems are periodic: the movement in the system repeats at regular intervals. Examples of such systems include Earth's diurnal rotation and the movement of pendulums. To be more precise, actual physical systems are only approximately periodic, as nothing can be perfectly isolated from its environment. Earth's rotation, for instance, is very gradually slowing, primarily because of gravitational interactions with our moon. But in practice such perturbations can often be ignored.

Yet often does not mean always. If the jolt from the outside is sufficiently large, the system may be bumped into a new mode of oscillation with a different maximum kinetic energy than in the original configuration. More interesting are those cases in which the disturbance is not a single jolt or push, but rather a continuous (though varying) driving or damping force; in such instances even the most simple of systems can exhibit very complex behavior.

One example is the chaotic pendulum:

In the motorised chaotic pendulum, a bar magnet is suspended at its middle from a string so that it can move in any direction. If such a device is given a known initial displacement from equilibrium then the resulting motion should be completely predictable.

In order to introduce a non-deterministic factor, we can set a second bar magnet spinning just underneath the suspended magnet. Then, when the suspended magnet passes equilibrium, it experiences a force from the spinning magnet and the interaction sends the suspended magnet off on a completely unpredictable path. In our exhibit, we have hidden the second magnet under a wooden base and used a motor to rotate it so that viewers can be quizzed on what they think is going on.

(Click here for a popup image.)

Without the second spinning magnet, this would be an ordinary pendulum, not unlike those in grandfather clocks. But with that addition, it becomes something else entirely. No matter how long power is supplied to the motor, the pendulum's motion will not repeat; or—as the site from which I took the diagram and quote above rather dramatically puts it—It could be said that the period of the motion is longer than the age of the universe.

(For more on chaotic pendulums, including a very cool java applet, go here.)

Note, however, that chaotic systems can exhibit behavior that at first blush looks periodic. A prime example is the so-called “11 year” solar sunspot cycle:

The solar cycle is a typical example for quasi-periodic behavior in a complex natural system. Although we talk about an 11-year cycle, the time between two adjacent maxima can be anything between 7 and 18 years. And, to make matters a little bit more challenging, the sunspot number in different maxima can vary by a factor of about 4. Sunspots even can vanish from the Sun for decades as during the second half of the 17th century. The unusual cold period in Europe during that time, called the Little Ice Age, is interpreted as a consequence of missing solar activity although the detailed coupling mechanisms are not understood yet. In the 1970s, Eddy combined climate proxies and indirect evidence for solar activity inferred from 14C records of the previous 5000 years and found a close correlation between high solar activity, a warmer climate and cultural growths while times of low solar activity were connected with cold periods and cultural depression. [Emphasis added.]

There will be more on the climate change aspects in the second part of this essay. But for now, note only that a truly periodic system will repeat its behavior after a fixed amount of time. Contrast this with a quasiperiodic chaotic system, which may return to its initial condition (or more properly, something sorta resembling its initial condition) repeatedly, although the time required for each such cycle can vary considerably.

So much for preliminaries. Time now to take a closer look at the NYT science article that Matt Drudge teased on Monday. Here's the lede:

read the rest »

The collapse of the Earth's magnetic field, which both guards the planet and guides many of its creatures, appears to have started in earnest about 150 years ago. The field's strength has waned 10 to 15 percent, and the deterioration has accelerated of late, increasing debate over whether it portends a reversal of the lines of magnetic force that normally envelop the Earth.

During a reversal, the main field weakens, almost vanishes, then reappears with opposite polarity. Afterward, compass needles that normally point north would point south, and during the thousands of years of transition, much in the heavens and Earth would go askew.

A reversal could knock out power grids, hurt astronauts and satellites, widen atmospheric ozone holes, send polar auroras flashing to the equator and confuse birds, fish and migratory animals that rely on the steadiness of the magnetic field as a navigation aid. But experts said the repercussions would fall short of catastrophic, despite a few proclamations of doom and sketchy evidence of past links between field reversals and species extinctions.

Some of this passage is just silly. If the transition indeed takes thousands of years, then astronauts will not likely be affected—for conditions will not change so rapidly that missions could not be adjusted accordingly.

Anyways:

No matter what the new findings, the public has no reason to panic, scientists say. Even if a flip is imminent, it might take 2,000 years to mature. The last one took place 780,000 years ago, when Homo erectus was still learning how to make stone tools.

Some experts suggest a reversal is overdue. “The fact that it's dropping so rapidly gives you pause,” said Dr. John A. Tarduno, a professor of geophysics at the University of Rochester. “It looks like things we see in computer models of a reversal.”

In an interview, Dr. Tarduno put the odds of an impending flip at more likely than not, adding that some of his colleagues were placing informal bets on the possibility but realized they would probably be long gone by the time the picture clarified.

Yes. As would those poor astronauts, of course.

The geodynamo—the generator of Earth's magnetic field—is a true quasiperiodic system, meaning that we cannot predict with any confidence when a polarity reversal might occur. The suggestion that a flip is “overdue” is merely an extrapolation from the geologic record; the sources I found by googling state that the average time between reversals is anywhere from 200,000 to 500,000 years. At least in the most recent periods: but during the Cretaceous, for instance, there was a stretch of some 35 million years without a single reversal. Moreover, there is evidence suggesting that magnetic field strength can at times vary considerably, though without leading to a polarity flip (same link). Hence the observations of recent field decay may not tell us all that much.

The Times article describes the geodynamo like so:

Deep inside the Earth, the magnetic field arises as the fluid core oozes with hot currents of molten iron and this mechanical energy gets converted into electromagnetism. It is known as the geodynamo. In a car's generator, the same principle turns mechanical energy into electricity.

Which, to be blunt, is rather lame. Here is a better, if not yet fully verified, description:

It is the motion of the fluid outer core that continuously generates Earth's magnetic field. Without the dynamo motion, the field would, once created, decay in about 20,000 years. Convection in the outer core is driven by both thermal and compositional buoyancy sources at the inner core boundary, produced as the planet slowly cools and iron in the fluid alloy solidifies onto the inner core. These buoyancy forces, together with the Coriolis forces due to Earth's rotation, orient the fluid flow in a cylindrical fashion, causing the complex fluid dynamics that result in Earth's large-scale, slowly changing magnetic field.

Finally, the Times piece does an adequate job of summing the geologic evidence for past polarity reversals, and discusses in some detail how the ecosystem might or might not be impacted by the next such flip.

But the main point remains: the sky is not falling, at least not on account of a fickle geodynamo. Nonetheless, there is another quasiperiodic phenomenon that warrants our attention, for its reappearance would make a magnetic polarity reversal seem by comparison like a May shower. And there are claims that its return is also overdue.