The universe is a fractal
Einstein famously wrote that “the most incomprehensible thing about the world is that it is comprehensible.” By this benchmark, one of the most amazing properties of our universe is the amount of self-similarity it contains, how the same phenomena occur on various scales of size, time, and in various forms of matter and non-matter. The laws of Nature seem designed to allow complex behaviour to be approximated by fundamental laws that appear also on smaller scales.
Mechanical waves (of water, sound, and so on), which are incredibly complex systems made up of a billion billion billion molecules, each made up of atoms made up of electrons and protons and neutrons made up of quarks, propagate in a fashion remarkably similar to the way individual photons do in an electromagnetic wave.
Even the familiar formula for a photon’s momentum, p = E/c readily approximates the momentum that a mechanical wave carries, when we substitute the wave’s velocity v for the speed of light c.
The waves of water in a pool interfere exactly like electromagnetic radiation does, but by entirely different processes! Photons interfere even when there is only one photon according to the laws of quantum mechanics. Comparatively, mechanical waves propagate and interfere for classical reasons, by the momentum carried from atom to atom in an unimaginably long chain, in order to mimic the behaviour of electromagnetic waves.
The gravitational force exerted by a planet 12,000 kilometers wide made up again of an enormous number of particles is approximately that exerted by a single point of the same total mass. And it is exactly into this shape that gravity tends to mold the matter in the universe, as if to make its effects as simple to analyze.
Combining the above two observations, we may analyze the mechanics of one billiard ball striking another by applying a much simpler model than the one seemingly required by reality.
This kind of approximately self-similar behaviour in Nature brings Microsoft’s Photosynth technology to mind. At an incredibly zoomed-out perspective, complex interactions average out and allow the billiard ball to be seen as a lone object, striking another ball and instantly transferring its kinetic energy into it. Only as we zoom in do we begin to see the detailed interactions inside the balls, and how the kinetic energy is transferred between them by means of a wave propagating through their matter. Zooming in further we see the balls’ individual atoms wiggling about and interacting, the cause of what previously appeared to be a wave.
If mankind one day decides to engineer an efficient universe, our own seems like a good model.