And by 500 BC the Pythagoreans had come to believe that all natural phenomena should somehow be reducible to relationships between numbers. … But despite the vast range of phenomena in nature that have never successfully been described in mathematical terms, it has become quite universally assumed that, as David Hilbert put it in 1900, "mathematics is the foundation of all exact knowledge of natural phenomena". There continue to be theories in science that are not explicitly mathematical—examples being continental drift and evolution by natural selection—but, as for example Alfred Whitehead stated in 1911, it is generally believed that "all science as it grows toward perfection becomes mathematical in its ideas".

This means that same rules should apply if one not only reverses the direction of time (T), but also simultaneously inverts all spatial coordinates (P) and conjugates all charges (C), replacing particles by antiparticles. … Originally it was assumed that C, P and T would all separately be invariances, as they are in classical mechanics.

So if they have simple underlying rules, do all cellular automata started from random initial conditions eventually settle down to give stable states that somehow look simple?

When the initial density of black cells is less than 50%, all regions of black eventually disappear, and the system becomes completely white.

In the case shown here, all the replacements found to fit in a left-to-right scan are carried out at each step.

For small numbers, all these approaches yield representations that are at least somewhat longer than the explicit sequences shown in picture (a).

The cellular automata shown here all have 3-color totalistic rules.

And in the early 1940s Mary Cartwright and John Littlewood noted that van der Pol's equation could exhibit solutions somehow sensitive to all digits in its initial conditions. … In the late 1960s there began to be all sorts of simulations of differential equations with complicated behavior, first mainly on analog computers, and later on digital computers. … By the early 1980s at least indirect signs of chaos in this sense (see note below ) had been seen in all sorts of mechanical, electrical, fluid and other systems, and there emerged a widespread conviction that such chaos must be the source of all important randomness in nature.

But at least at first, I suspect that huge simplifications will be made, with the result that all sorts of misleading conclusions will probably be reached, perhaps in some cases even seemingly contradicting the principle.

History [of universal objects] There are various precedents in philosophy and mysticism for the idea of encoding all possible knowledge of some kind in a single object.