The Universe as a Fixed Point

More random silliness. The common model of a the universe at a point of time seems to be based on the prevalent technology. So, in the mechanical past the universe is 'like clockwork'. Nowadays there is a bit more thought of the universe algorithmically - leading to things like Tiplerian nuttiness, The Matrix and Wolfram's New Kind of Science (I think - I've not read that tome).

A more general view is of the universe as the solution of equations. In some ways, this is not entirely dissimilar to the algorithmic view. For example, you can solve a PDE abstractly, or treat it as some kind of grid-based evolution of state. However, the equation solution approach is more powerful.

For example, you can be very silly, and extend the Tipler view. If the universe has infinite computational capability, it can simulate, say, the universe. Moreover, the universe we're in could be the result of some simulation. But we can go further than that, and have the universe simulate itself. That is, have the universe be a simulation running inside itself. This is obviously rubbish, if you treat the universe as a naive algorithm.

Another way of looking at it, though, is as a Y combinator attached to the world. That is, the universe is the fixed point of an equation of 'things that simulate themselves'. It simulates itself into existence. It's turtles all the way down. :p

Posted 2011-04-13.