Rambling

A scientific law is not a law unless it holds true at every point. Whether one prefers relativity (special or general), quantum mechanics, classical mechanics, or some of the more avant-garde theories such as the GUT, ToE, or M-theory, they all seem to break down at one point: the big bang. Dr. Hawking has stated everything from the early conditions having a temperature of ten billion degrees and a probable density of a trillion trillion trillion trillion trillion trillion (1 with 72 zeros after it) tons per cubic inch to the big bang itself being a point of infinite temperature and density...however neither of these sound very likely.

First we'll tackle the really big number scenario. Science tells us that what we perceive as empty space is really filled with gases and particles that are too <insert random sensory adjective here> to detect. However, it appears empty space is all around us. i have heard things from "imagine an atom is a baseball stadium, the dense nucleus making up over 99.9% of the mass is a mere pea sitting on home plate, the rest of the stadium is the electron clouds" to "there is more empty space inside each atom as there is atoms in the universe." I'm not sure of what the exact scientific measurement is, but it is a lot. This also means the vast majority of what we consider our solid bodies is nothing but empty space. If some gravitational force was large enough, it could conceivably squish these empty electron clouds and nuclei together into a density of trillions upon trillions of tons per cubic inch. This is probly where matter "disappears" to in a black hole, another singularity in the spacetime continuum. Perhaps every black hole contains a universe just waiting to explode.

The infinity thing is a little bit trickier. But first a little metaphysical tangent. There is talk here about infinity and mathematical points, neither of which exist in real life. No matter how small one gets, that point has a length, width, and height, and point in time for you 4 dimensional sticklers. I'm finally going to use that blasted anthropic principal to my benefit for once and say that a single mathematical point could only exist in a zero-dimensional universe, and then there wouldn't be any dimensions for the big bang to explode into and we wouldn't be here talking about this right now, or even existing for that matter (hmmm, maybe we don't...) But the beauty (or magic depending on how you choose to look at it) of calculus has allowed us to do the next best thing: calculate the limit of that temperature and density as the universe approaches that single point.
Using the theory from the last entry that energy is spontaneously contracting into matter by E=mc^2, as we follow this back to the big bang more and more of the universe exists as energy rather than matter. But the problem with calculating limits is that there is still that exact point where the equation is undefined. There is no solution, just a big empty asymptote or other point of discontinuity. Then again mathematics often predicts things which don't happen or work in real life. An interesting fact to note here, energy has no mass (however, energy does have a measurable momentum, which is directly related to mass. Logic tells us that it must then also have a measurable mass, but my physics text book disagrees. Until i gain some higher understanding, i'm going to again chalk this one up to that "magic" (my higher intuition however tells me that scientists just aren't looking hard enough or don't have sensitive enough instruments to detect this mass. After all, it's been "proven" light is bent by gravity. How could something without mass be affected by gravity?) From this lack of mass, we can conclude that as the universe approaches the big bang and more and more of its matter converts to energy, its mass approaches zero. This solves the problem of infinite density quite well. Something with zero mass must also have zero density. An infinite amount of energy can be condensed into one mathematical point as it takes up no space, and would be certain to generate an infinite amount of heat.

To my regrets this still doesn't generate a smooth continuous equation (is one really necessary?) but it does make the function defined at every point. For every value of X we now have a Y.