Math, Randomness, and Omega
Yesterday I came across a stunning article entitled Omega and why maths has no TOEs. “TOE” stands for “Theory of Everything“, a grand unified theory capable of explaining everything about everything. Such a formula is the holy grail of physics and mathematics, and of the type Einstein spent the later half of his life searching for.
Anyway, there’s a few very interesting things in this article. Perhaps one that really intrigued me is “How do you define Random?”. Any piece of data has a pattern, but the pattern may be just as large as the data itself. In the example they use they essentially revert to the old math standby of fitting a line through a cloud of points. You can make a perfect fit by using a formula with as many polynomials as you have points, but what does that really prove? Therefore, a truly “random” piece of data is one that cannot be compressed, or expressed through simpler means. Up to a point, Randomness = Complexity. He then uses this nugget of information and some studies of Turing’s Halting Problem to prove that math is incapable of a Theory of Everything, because it cannot precisely define his probabilistic number “Omega”.
On the other hand, I look at it another way. If Randomness = Complexity, then Randomness is a approachable point. As we get smarter & computers grow in power, the complexity of problems drops. Essentially, as we have more time & power to look at data, we start to realize that some of it isn’t as random as we thought. You hear about it every day on the news as new scientific studies bring things like Quarks & Quantum Theory closer to reality. Whether or not we’ll ever be able to comprehend “infinite complexity” is tough to say, but is anything actually infinitely complex? Could stuff that seems infinite today, just be seen as really large tomorrow?
[tag:math][tag:omega][tag:random]
