And in the case shown here the slow growth of the region visited by the active cell in the underlying evolution is reflected in rapid growth of the corresponding causal network.

And in most cases this is presumably best achieved by avoiding differences in densities of certain local features.

And in general, in any system with definite rules that only ever visits a limited number of states, it is With each cell at each step having a gray level that is the average of its predecessor and its two neighbors the total amount of black is conserved, but eventually becomes spread uniformly throughout the system.

Things appear somewhat simpler with boiling points, and as noticed by Harry Wiener in 1947 (and increasingly discussed since the 1970s) these tend to be well fit as being linearly proportional to the so-called topological index given by the sum of the smallest numbers of connections visited in getting between all pairs of carbon atoms in an alkane molecule.

And in my experience many of the intellectually most interesting aspects of technology emerge only when one actually tries to build technology for real—and they are often in a sense best captured by the technology itself rather than by a book about it.

With this procedure, evolution from any initial condition can visit every possible configuration, so that the configurations which satisfy the constraints will at least eventually be reached.

What is usually said is that prices are in fact determined not by true value, but rather by the best estimates of that value that can be obtained at any given time.

The relevance of theorems Following traditional mathematical thinking, one might imagine that the best way to be certain about what could possibly happen in some particular system would be to prove a theorem about it.

Which fit should be considered best in any particular case must ultimately depend on external considerations.

Physical randomness generators It is almost universally assumed that at some level physical processes must be the best potential sources of true randomness.