And this implies that if one knew all of the underlying details of the network that makes up our universe, it should always be possible to work out the result of any measurement.

But it does not mean that threads can have no effect at all.

One might imagine that one could always just try running all programs with progressively longer descriptions, and see whether any of them ever generate what one wants.

But despite some confusion in the past it is certainly not true that just checking equality of frequencies of blocks of colors—even arbitrarily long ones—is sufficient to ensure that no regularities at all exist.

Given a set of raw data the procedure for finding which model in this class is best—according, say, to the criterion of maximum likelihood—is extremely straightforward: all one does is to compute what fraction of squares in the data are black, and this value then immediately gives the value of p for the best model.

all its development over the past few thousand years mathematics itself has continued to concentrate only on rather specific types of abstract systems—most often ones somehow derived from arithmetic or geometry.

But so where in all of this would the actual content of our memory reside?

There has in the past been a great tendency to assume that given all its apparent complexity, human thinking must somehow be an altogether fundamentally complex process, not amenable at any level to simple explanation or meaningful theory.

For it potentially allows one to get a large number of different kinds of components without ever needing to increase the complexity of the underlying rules at all.

In the case of the 19-color universal cellular automaton on page 645 it turns out that encodings in which individual black and white cells are represented by particular 20-cell blocks are sufficient to allow the universal cellular automaton to emulate all 256 possible elementary cellular automata—with one step in the evolution of each of these corresponding to 53 steps in the evolution of the original system.