The steady unfolding of cosmic order has led to the formation of complex structures on all scales of size. Astronomically speaking, the smallest structures are to be found in the solar system. It is a curious thought that although the motions of the planets have long provided one of the best examples of the successful application of the laws of physics, there is still no proper understanding of the origin of the solar system.
It seems probable that the planets formed from a nebula of gas and dust that surrounded the Sun soon after its formation about five billion years ago. As yet scientists have only a vague idea of the physical processes that were involved. In addition to gravitation there must have been complex hydrodynamic and electromagnetic effects. It is remarkable that from a featureless cloud of swirling material, the present orderly arrangement of planets emerged. It is equally remarkable that the regimented motion of the planets has remained stable for billions of years, in spite of the complicated pattern of mutual gravitational forces acting between the planets.
The planetary orbits possess an unusual, even mysterious, degree of order. Take, for example, the famous Bode's law (actually due to the astronomer Titius) which concerns the distances of the planets from the Sun. It turns out that the simple formula rn — 0.4 + 0.3 x 2n, where rn is the orbital radius of planet number n from the Sun measured in units of the Earth's orbital radius, fits to within a few per cent all the planets except
Neptune and Pluto. Bode's law was able to correctly predict the existence of the planet Uranus, and even predicts the presence of a 'missing' planet where the asteroid belt is located. In spite of this success, there is no agreed theoretical basis for the law. Either the orderly arrangement of the planets is a coincidence, or some as yet unknown physical mechanism has operated to organize the solar system in this way.
Several of the outer planets possess miniature 'solar systems' of their own, in the form of multiple moons and, more spectacularly, rings. The rings of Saturn, to take the best-known example, have aroused the fascination and puzzlement of astronomers ever since their discovery by Galileo in 1610. Forming a huge planar sheet hundreds of thousands of kilometres in size, they give the superficial impression of a continuous solid, but, as remarked in Chapter 5, the rings are really composed of myriads of small orbiting particles.
Close-up photography by space probes has revealed an astonishing range of features and structures that had never been imagined to exist. The apparently smooth ring system was revealed as an intricately complex superposition of thousands of rings, or ringlets, separated by gaps. Less regular features were found too, such as 'spokes', kinks and twists. In addition, many new moonlets, or ringmoons, were discovered embedded in the ring system.
Attempts to build a theoretical understanding of Saturn's rings have to take into account the gravitational forces on the ring particles of the many moons and moonlets of Saturn, as well as the planet itself. Electromagnetic effects as well as gravity play a part. This makes for a highly complicated non-linear system in which many structures have evidently come about spontaneously, through self-organization and cooperative behaviour among the trillions of particles.
One prominent effect is that the gravitational fields of Saturn's moons tend to set up 'resonances' as they orbit periodically, thereby sweeping the rings clear of particles at certain specific radii. Another effect is caused by the gravitational perturbations of moonlets orbiting within the rings. Known as shepherding, it results in disturbances to ring edges, causing the formation of kinks or braids.
There is no proper theoretical understanding of Saturn's rings. In fact, calculations repeatedly suggest that the rings ought to be unstable and decay after an astronomically short duration. For example, estimates of the transfer of momentum between shepherding satellites and the rings indi cates that the ring-ringmoon system should collapse after less than one hundred million years. Yet it is almost certain that the rings are billions of years old.
The case of Saturn's rings illustrates a general phenomenon. Complex physical systems have a tendency to discover states with a high degree of organization and cooperative activity which are remarkably stable. The study of thermodynamics might lead one to expect that a system such as Saturn's rings, that contains a vast number of interacting particles, would rapidly descend into chaos, destroying all large-scale structure. Instead, complex patterns manage to remain stable over much longer time scales than those of typical disruptive processes. It is impossible to ponder the existence of these rings without words such as 'regulation' and 'control' coming to mind.
An even more dramatic example of a complex system exercising a seemingly unreasonable degree of self-regulation is the planet Earth. A few years ago James Lovelock introduced the intriguing concept of Gaia. Named after the Greek Earth goddess, Gaia is a way of thinking about our planet as a holistic self-regulating system in which the activities of the biosphere cannot be untangled from the complex processes of geology, climatology and atmospheric physics.
Lovelock contemplated the fact that over geological timescales the presence of life on Earth has profoundly modified the environment in which that same life flourishes. For example, the presence of oxygen in our atmosphere is a direct result of photosynthesis of plants. Conversely, the Earth has also undergone changes which are not of organic origin, such as those due to the shifting of the continents, the impact of large meteors and the gradual increase in the luminosity of the Sun. What intrigued Lovelock is that these two apparently independent categories of change seem to be linked.
Take, for example, the question of the Sun's luminosity. As the Sun burns up its hydrogen fuel, its internal structure gradually alters, which in turn affects how brightly it shines. Over the Earth's history the luminosity has increased about 30 per cent. On the other hand the temperature of the Earth's surface has remained remarkably constant over this time, a fact which is known because of the presence of liquid water throughout; the oceans have neither completely frozen, nor boiled. The very fact that life has survived over the greater part of the Earth's history is itself testimony to the equability of conditions.
Somehow the Earth's temperature has been regulated. A mechanism can be found in the level of carbon dioxide in the atmosphere. Carbon dioxide traps heat, producing a 'greenhouse effect'. The primeval atmosphere contained large quantities of carbon dioxide, which acted as a blanket and kept the Earth warm in the relatively weak sunlight of that era. With the appearance of life, however, the carbon dioxide in the atmosphere began to decline as the carbon was synthesized into living material. In compensation, oxygen was released.
This transformation in the chemical make-up of the Earth's atmosphere was most felicitous because it matched rather precisely the increasing output of heat from the Sun. As the Sun grew hotter, so the carbon dioxide blanket was gradually eaten away by life. Furthermore, the oxygen produced an ozone layer in the upper atmosphere that blocked out the dangerous ultra-violet rays. Hitherto life was restricted to the oceans. With the protection of the ozone layer it was able to flourish in the exposed conditions on land.
The fact that life acted in such a way as to maintain the conditions needed for its own survival and progress is a beautiful example of self-regulation. It has a pleasing teleological quality to it. It is as though life anticipated the threat and acted to forestall it. Of course, one must resist the temptation to suppose that biological processes were guided by final causes in a specific way. Nevertheless, Gaia provides a nice illustration of how a highly complex feedback system can display stable modes of activity in the face of drastic external perturbations. We see once again how individual components and sub-processes are guided by the system as a whole to conform to a coherent pattern of behaviour.
The apparently stable conditions on the surface of our planet serves to illustrate the general point that complex systems have an unusual ability to organize themselves into stable patterns of activity when a priori we would expect disintegration and collapse. Most computer simulations of the Earth's atmosphere predict some sort of runaway disaster, such as global glaciation, the boiling of the oceans, or wholesale incineration due to an overabundance of oxygen setting the world on fire. The impression is gained that the atmosphere is only marginally stable. Yet somehow the inte-grative effect of many interlocking complex processes has maintained atmospheric stability in the face of large-scale changes and even during periods of cataclysmic disruption.
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