Tuesday, March 23, 2004

Perfect Ideas

Perfect Ideas

The human mind likes symmetry and perfection. The heliocentric model of the solar system, proposed by Copernicus, putting the Sun as the center of the known universe, displacing Earth, was revolutionary for its time. It was difficult for people to belief then that the Earth was just one (and an even unremarkable one) of many objects revolving around the Sun. But the heliocentric universe was the only model that conformed to scientific observations. It had to be accepted, even though it didn't appeal to our sense of perfection.

For some time after the Sun was accepted as the center of the solar system, we still thought that the planets revolved around the Sun in perfect circles. How could they not be circles? It is only logical to assume that God created the universe with a certain geometrical perfection in mind and circles seemed like perfect shapes.

Johannes Kepler was also driven by a sense of perfection. He figured that if planets revolved in perfect circles around the Sun, there must also be a certain relationship between their orbits; there must be a certain harmony associated with their movements around the Sun. During his time, only six planets (Mercury, Venus, Earth, Mars, Jupiter, Saturn) were known to be in existence. But why only six? Again there must be some underlying reason behind it.

Ancient Greek geometers have long known that there are only five perfect solids--the so-called Pythagorean Solids. Each Pythagorean solid comprises of sides made from perfect shapes: for example, a cube is a perfect solid because it is built from six perfect squares. Similarly a tetrahedron is made up of four perfect triangles. Twelve pieces of pentagons would fit nicely together to make a perfect dodecahedron.

One can experiment with all types of perfect shapes--triangles, squares, pentagons, hexagons--and try to build solids with them; but somehow only five are possible. There is a beautiful mathematical prove to show why this is so. To the ancient geometers, these five uniquely perfect solids must be sacred--God somehow favours them over others.

Kepler tried to associate these Pythagorean solids with the orbits of the six planets. He believed that there were only six planets because the six orbits (perfect circles) would perfectly nest the five Pythagorean solids between them; these five solids must be God's invisible structure that hold the orbits of the planets in the heavens. It was a beautiful idea, seemingly perfect.

Kepler spent years trying to fit the existing astronomical data to his model. But somehow empirical data betrayed his idea of what perfection ought to be. He later found out that the orbits were not even circles--they were elongated in shape--ellipses. Why did God favour an ellipse over a "perfect" circle?

Newton later showed that movement of the planets, and in fact any object with mass, is governed by the universal force of gravity which can be described using a simple mathematical equation, based on the inverse square law. God apparently has a grander idea of perfection: planets and other celestial objects actually "attempt" to move in straight lines--it is only because they attract one another that they assume that trajectories that we see now. Their elliptical orbits are but a natural consequence of them moving under the influence of gravitational attraction.

Decades later, it was Einstein who showed us that even this explanation did not capture God's idea of perfection. Gravity, according to Einstein's General Theory of Relativity is nothing but a geometrical property of the four-dimensional space-time continuum. Any object with mass will "warp" the space-time around it. Planets move the way they do because their paths are "curved" by the mass of the Sun. God loves geometry after all.

Human beings have a natural fondness for the intellectually-pleasing idea. We have a tendency to latch on to a pet idea that appeals to our sense of perfection and stop exploring further, believing that we have found the Ultimate Truth. Far from it. Science has time and again shown how infantile is our understanding the universe. Thus far, we have only been granted glimpses of God's mind. And sometimes our seemingly "perfect" ideas are our greatest obstacles towards understanding.

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