Fri, 12 Jan 2007
Out of the Matrix
In the Matrix Neo is trapped in a computer simulation that he mistakes for reality until he's given a red pill that takes him out of the simulation. (By blocking his i/o ports.) What most people don't recognize is that they're trapped in a different sort of matrix: the belief that the laws of physics are a description of reality and that we live in that reality. Descartes invented coordinate geometry and Newton based his laws of mechanics upon it. Since then physics has described reality as a three dimensional continuum. (Four dimensional since Einstein.)
Practically everyone considers this a description of reality, but it can't possibly be so. The reason why is simple: the continuum has paradoxical properties that reality does not have. For example, a sphere in a three dimensional continuum can be cut into a finite number of pieces and reassembled into two spheres of equal size to the first. (This is the Banach-Tarski theorem.)
In the continuum there is always an interval between any two points that do not coincide. This means two objects can never touch, because the concept of touching has no meaning in a continuum. You may not be trouble by giving up the concept of touching, but are you willing to give up the concept of causation? Our idea of causation is that the cause must precede the effect. If the effect exists at the same time as its supposed cause, then it could not have been the cause. But if the cause no longer exists at the time of its effect, there must be a gap during which the cause has ceased and the effect has not yet arisen. Our concept of causation rests on the idea of two events touching, which cannot happen if time is a continuum.
It's not that there's a problem with physics that needs to be fixed. Physics provides a good model of reality, but it is not that reality itself. Once you see that, you've stepped out of the matrix.
