Thursday, January 2, 2014

Irrational Numbers and Real Reality

The current dominant strain of "western" philosophical thought has roots in the occult, esoteric tradition. The quick and dirty version: man is a historically and culturally constructed being, and that there is no reality, only mental constructs. As I wrote before, this leads to a counter-intuitive result: though reality is understood in radically subjective and solipsistic terms, other beings are inexorably viewed as mere objects that lack their own internal reality. We see this strain of thought infecting economics and political philosophy, and the low become the high. For example, mere rhetoric in the pursuit of power becomes the highest art. (See: Gorgias for the very thorough 2,400 year old analysis and discussion.)

Kurt Goedel
In spite of this belief, reality remains. It might be possible to herd billions of people into a cave of nihilistic illusion but reality still shines through. My personal favorite example is the irrational numbers. The square root of 2, for example, can be interpreted in a number of different ways. The Pythagoreans, for example, regarded it as a deadly secret. Why? Perhaps they believed the human mind partakes in the cosmic mind and number is at minimum, proof of that, and perhaps the universe is number. However, you can't use numbers to express the length of the hypotenuse of a simple triangle with legs of length 1: sqrt(2), which seems to indicate that the mathematical bridge between the human mind and reality doesn't make it all the way. The Austrian logician Kurt Goedel showed, with the incompleteness theorem, that axiomatic systems are self referential.