Cosmologists are a whiney bunch. They often moan about how we - blobs of organic matter that we are - are utterly insignificant, which presumably includes the cosmologists themselves. They moan and bitch that nobody understands them and in the very next breath, they will wax lyrical about seeing the mind of god in the paper printouts beamed down from the hubble telescope.

They are certainly right to wax lyrical because cosmology rests on the equations of Generaly Relativity, and these equations are very beautiful. But insignificance? Well, it turns out that when you look into it closely, the epistemological assumptions of cosmology already have insignficance built right into them. In this essay, I hope to show how this existential crisis is really a case of looking at a glass half-empty rather than half-full. But more importantly, I want to sketch out some of the beautiful ideas in General Relativity that allow cosmologists to think about the universe. So bear with me.

Cosmology is an ambitious discipline - it claims to study the physics of the entire universe. Despite the universe being very much older than we are, current science estimate 6.5 billion years old, cosmology itself is a very young scientific discipline. The reason why it's so young is that the age of the universe could not be articulated physically until Einstein came up in 1918 with the General Theory of Relativity. The Universe before Albert Einstein - as described by Isaac Newton

Before General Relativity, we had what physicists call the Newtonian (or Classical) universe. In the Newtonian universe, there was space, and there was time, and they were independent. That means if it takes you 8 minutes to boil an egg, then no matter where you were, or how fast you were travelling, it would still take 8 minutes to boil an egg. Time flows the same, no matter where you were. Another way to say this is that things in a Newtonian universe tend to travel in a straight line.

In the Newtonian universe, even though everything travels in a straight line, everything is also pulled around by the universal force of gravity. It is because of gravity that when you throw a baseball into the sky, the baseball gets pulled back down to earth. Now saying that things fall back on the ground would be a trivial statement except that Newton showed that gravity could be described exactly with an inverse square law - the justly celebrated Law of Universal Gravitation. A straightforward calculation using this law would tell you that a baseball falls back down in a perfect parabola. Such a precise description of a law of nature was unprecedented.

Yet, in some ways, it was a bit of a black eye for Newton that he could find no deeper reason why gravity takes the form of the inverse square. Indeed, Newton was accused by jealous critics of being an alchemist because he believed in something called gravity that was a mystical thing, like the Force in Star Wars. They had a point but in the end, the ability to calculate things directly with the inverse square law was so immensely powerful that questions about ultimate causes was politely brushed aside.

The Theory of General Relativity - Making all the pieces fit together

Fast forward to 1918, where the world's most celebrated physicist, Albert Einstein, had decided to wrestle with all the loose ends left over from the Newtownian revolution - where does the inverse square come from? Why is the gravitational mass the same as the inertial mass?

In one of the greatest pieces of lateral thinking ever, Einstein realised that the reason that a thrown baseball traces out a parabola was not due to a force called gravity, but because space is warped. The curved parabola that the baseball traces out is, in fact, the "straightest" possible path seen in the light of some higher dimension. Space is warped, and we didn't even realise it.

What the hell was Einstein smoking? Harking back to the Russian mathematician Riemann, Einstein had stumbled onto a system of geometry where lines did not have to be straight. Riemann found that you could have a geometry where the straightest line you draw is in fact, curved. These geometries are not as esoteric as you think. Essentially, Riemann was thinking about the problem of drawing lines on a beach-ball. Try as you might, a straight line on a beach ball never looks as straight as a straight line drawn on a flat piece of paper. A "straight" line on a beach-ball has unusual properties. For instance, a line drawn on a beach ball can wrap-around and meet the beginning of the line again. Try that on a flat piece of paper!

Riemann invented a new mathematics to describe geometries where lines can be curved. He defined a mathematical object, known as the Riemann tensor, that exactly describes the curvature at any given point.

The long and short of it is that Einstein eventually came up with an elegant equation that had the Riemann tensor on the left hand side, and mass on the right. Having mass in a point in space will warp the curvature of the space. After some herculean calculations, Einstein showed that near a point of mass, the Riemann tensor can be split into 3 parts. There is a straight line part, an inverse square part, plus an extra bit.

With one fell swoop, Einstein showed how the idea of curvature will give you a geometry that has straight lines far away from a mass, an inverse square law near a mass, and a tiny correction factor for things that are jammed right up close to a large mass. That extra little bit turned out to be really important. With the extra bit, Einstein calculated a little wobble in the orbit of Mercury because Mercury is jammed right up closer to the sun than all the other planets. This wobble had remained inexplicable to astronomers using plain old Newtonian gravity. As well Einstein had finally explained the origin of Newton's Law of Gravitation and why inertial masses are the same as gravitational masses. Deriving the consequences of the General Theory of relativity is one of the greatest achievements of the scientific imagination.

Even more exciting, Einstein realized he could apply General Relativity to the universe without violating the Cosmological Principle.

How General Relativity Put a Shape to the Universe

The Theory of General Relativity allowed one to think geometrically about the universe as a whole. Think back to the beach ball. An ant crawling along the beach-ball will think that its travelling in a straight line. But if the ant is smart, it may realize that it ends up back in the place whilst travelling around the ball back, and eventually the ant will realize that the surface is curved. The ant could determine the curvature by studying straight lines on a beach ball. And from this curvature, the ant could figure out size to the beach-ball.

Taking this analogy by the scruff of the neck, Einstein applied it to our universe. According to the equations of General Relativity, if you have a constant mass-density throughout the universe then the universe must be curved eveywhere. A constant curvature puts a size on the universe, where if you keep traveling in the same direction, you wil eventually end up back where you started, thus defining the radius of the universe. The Cosmological Principle

One of the great virtues of this model of the universe is that it satisfies the Cosmological Principle. The Cosmological Principle should really be called the principle of maximum boringness. It says that space must be isotropic, a rather ugly word that means everything must look the same no matter where you were, and no matter which direction you turn.

By applying the Cosmological Principle, Einstein assumed that the universe was bland and featureless, which simplified his calculations enormously. And thus Cosmology was born.

Einstein thus got three solutions to his equations: the universe was either expanding, or contracting, or hovering unstably. Expansion in General Realtivity is a little bit subtle. Expansion of the universe means that everyone is running away from everyone else, much like blowing up the beach-ball makes every point on the beach-ball stretch away from each other. Another way to interpret expansion is that everything is shrinking as the universe expands, because the space between us stretching.

Einstein didn't like expansion one little bit. In a move that Einstein would later regret as the 'biggest mistake of my life,' Einstein added an artificial constant into his equations that would stop the universe from expanding or contracting.

What Cosmologists Think

Today's cosmologists have vastly expanded the original calculation of Einstein and the state-the-art theory have names such as the Inflation Model. Most of them fall under the rubric of Big Bang Theories in which the Universe started off as a compact ball of energy that exploded and has been expanding at a maddening rate ever sense. Cosmologists believe that this cataclysmic birthing can be heard by our radio telescopes in the background radiation at 3.1K. This is the dying echo of the scream at the birth of our universe, which has criss-crossed our universe ever since the beginning, but getting fainter as the universe ages along.

But no matter how refined the theory, all our theories of the universe assumes the Cosmological Principle. And much as cosmologists may claim that these are commonsensical assumptions, they are in reality, absolutely crucial in thinking about the universe, because without these comforting assumptions, it would be impossible to make any calculations. So when cosmologists moan about how insignificant we are in the vast scheme of things, it is simply because cosmology is fundamentally founded on the assumption that the universe is a bland uniform homgenous material. Where then, is there room for the messy, complicated things we call human beings, beings who sometimes try to imagine the very universe that they had been born in?