Important criteria for this in my experience include specifying processes directly rather than through constraints, the explicitness in the representation of input and output, and the existence of small, memorable, examples.

In quantum theory the quantization of particle spin implies that any photon hitting a polarizing filter will always either just go through or be absorbed—so that in effect its spin measured relative to the orientation of the polarizer is either +1 or -1. … The approach I discuss in the main text is quite different, in effect using the idea that in a network model of space there can be direct connections between particles that do not in a sense ever have to go through ordinary intermediate points in space.

From the Pythagoreans around 500 BC through Ptolemy around 150 AD to the early work of Johannes Kepler around 1595 there was the notion that the planets might follow definite geometrical rules like the elements of a mechanical clock.

In fact, it was really only through the development of rigorous mathematical analysis in the late 1800s that this confusion finally began to clear up.

For a long time it was assumed that the magnitude of the complexity was so great that it could never have arisen from any ordinary natural process, and therefore must have been inserted from outside through some kind of divine plan.

Sequences of states in any shift register must correspond to paths through a network of the kind shown on page 941 .

So for example, it must in some sense be either true or false that a given Turing machine halts with given input—but according to the Principle of Computational Equivalence there is no finite procedure in our universe through which we can guarantee to know which of these alternatives is correct.

In the mid-1960s David Raup used early computer graphics to generate pictures for various ranges of parameters, but perhaps because he considered only specific classes of molluscs there emerged from his work the belief that parameters of shells are greatly constrained—with explanations being proposed based on optimization of such features as strength, relative volume, and stability when falling through water.

Examples (a) through (c) below have this property; (d) does not.

Among the 256 elementary rules, the total numbers that have conserved quantities involving at most blocks of lengths 1 through 10 are {5, 38, 66, 88, 102, 108, 108, 114, 118, 118} .