Loveliness is Rare

by Eric Steinhart

Order, complexity, regularity, patterning, are all examples of features that I’ll just refer to as lovely. It’s a term of art, and it’s a lovely term.

Within many familiar systems, loveliness is very very rare. It’s very rare within the models of simple physical theories and even more rare within the models of complex physical theories (e.g. the solutions to the equations of string theory). This can be illustrated with the cellular automaton known as the game of life. You can read lots about the game of life on the web. I’ll just give a very quick presentation of the relevant points.

The game of life is played on a grid composed of square cells, like a chessboard. A clock is ticking (all cells can hear it). A cell is either ON or OFF (alternatively, LIVE or DEAD, or 1 and 0). Cells blink ON and OFF like lightbulbs, according to a rule each cell computes every time the clock ticks: (1) a cell counts its ON neighbors; (2) if it is ON and has 2 or 3 ON neighbors, then it stays ON, else it turns OFF; if it is OFF and has 3 ON neighbors, then it turns ON, else it stays OFF.

The figure below illustrates how cells change according to the life rule.

The game of life supports regular patterns, such as the glider, which appears to move across the space of the life grid. The glider is shown below.

It’s even possible to construct universal Turing machines and self-reproducing patterns in the game of life. But the game of life is rare within the class of similar cellular automata.

The rule for the game of life can be expressed in a small table. The table is shown in the figure below.

Since there are 16 slots in this table, and each can take the value 0 or 1, there are 2^16 different variants of the game of life. That’s 65536 variants. These are all the possible classes of life-like universes. Some of these variants are shown below.

Out of these, very few support any physical content at all. Perhaps a dozen or so support moving patterns. And only one is known to support patterns that compute and that reproduce (namely, the game of life itself). Within an extremely large number of physical systems, or purely mathematical systems, loveliness is vanishingly rare. Hence, that any actual universe is lovely, when almost all possible universes are not, is extremely surprising.

To say a fact is “surprising’ is far from merely subjective. Surprising facts almost always carry information. That’s because carrying information is itself a lovely feature. And that’s why our brains are highly sensitive to loveliness: when, out of the endless background of noise, you are given a signal carrying information, you’d better pay attention. It’s a good rule to follow in any uncertain environment.

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