History [of emergence of order] The fact that despite initial randomness processes like friction can make systems settle down into definite configurations has been the basis for all sorts of engineering throughout history. … But almost all work in the field of statistical mechanics concentrated on systems in or very near thermal equilibrium—in which in a sense there is almost complete disorder.

In example (a), the canonical form is all elements black; in (b) it is a single black element, and in (c) all elements are black, except the last one, which is white if there were any initial white elements.

And so, for example, the various models of atoms from the end of the 1800s and beginning of the 1900s were all based on familiar mechanical systems. … For if an ultimate model is going to be simple, then in a sense it cannot have room for all sorts of elements that are immediately recognizable in terms of everyday known physics.

In most places in the space of all possible field configurations, the value of s will vary quite quickly between nearby configurations. … In cases like QED and QCD the most obvious solutions to the classical equations are ones in which all fields are zero. … And indeed in other situations it seems likely that there will be all sorts of other solutions to the classical equations that become important.

If one starts with a priori probability distributions for all parameters, then Bayes's Theorem on conditional probabilities allows one to avoid the arbitrariness of methods such as maximum likelihood and explicitly to work out from the observed data what the probability is for each possible choice of parameters in the model.

Given a list of all steps in the evolution of the tag system, Cases[list, {__s}] picks out successive steps in the cellular automaton evolution.

But I suspect that enough computational irreducibility usually remains to make unprovability common when one asks about all possible forms of behavior of the program.

For large n roughly 1/4 of all n -input functions are universal.

It appears that digits 0, 1, 2 are sufficient to represent uniquely all numbers between 1 and 2.

One version posed as a problem by John Myhill in 1957 consists in setting up a rule in which all cells in a region go into a special state after exactly the same number of steps.