Late Night Philosophy

Godel's Incompleteness

I read the other day about Godel's Incompleteness theory. Before I state what it is, I'd like to point out that Godel is spelled with the two-dot accent over the 'o', but I'm limited to an English keyboard....

But Godel's Incompleteness is a property of mathematics and, when you think about it, the universe, as a whole. It basically states that in any system of mathematics (aka, a collection of mathamatical axioms), there will always be statements that are unproveable and, therefore, there will aways be new theorems to discover.

The basic proof of this is the theorem, P, that states "P has no proof". If P is false, there is a proof that P is true, which is a contradiction. Therefore, in that mathematical system, P cannot be determined to be true or false.

Alternatly, for every previously unsolveable statement or theorem in a mathematical set that is finally proven to be either true or false, a new unproveable statement or theorem will be found at or near the bounderies of the previous unsolveable. And so, there is always more to know.

The unfortunate thing about this Incompleteness is that we are finite beings. The universe is also finite. Energy is also finite (being that mass and energy all the same). Even information, seemingly intangable, as an energy density.

It takes an certian amount of energy to write a bit of information to a storage medium (be it our brains or a computer disk), store that information over time, and then to recall it at a later time.

So with Godel's Incompleteness in mind, it follows that there is an infinite amount of knowledge in the universe, put a limited capacity to store it. The only solution to this problem is that there are an infinite number of degress of construction in the universe (quarks to sub-atomic particles to atoms to molecules, etc) so that values can be assigned on an ever decreasing scale. Of course, that theory is not proveable, so I'm forced to assume that the unvierse has a finite number of particles and, therefore, a finite data capacity.

This is another reason for the human race not to stick around in this universe. It's just another restriction against our existence. Even as we burn calories to keep as alive, we burn unused data capacity we may never get back.... but that's all entropy and thernodynamics, isn't it?
That's another point isn't it? Even if we used every last available particle as a storage medium, entropy would always corrupt the data over time. That's life in the universe, isn't it? We see infinite potential for learning only to find that it will all evaporate before our eyes over time.

"I can't imagine a God who would care."
"Every moment we are alive is a moment that we have cheated Death."
Myself
Please read my journal "Late Night Philosophy"