David's Blague

Here's a 1983 Definition of Cellular Automata that I don't like:

Cellular automata are mathematical idealizations of physical systems in which space and time are discrete, and physical quantities take on a finite set of discrete values. A cellular automaton consists of a regular uniform lattice (or “array”), usually infinite in extent, with a discrete variable at each site (“cell”). The state of a cellular automaton is completely specified by the values of the variables at each site. A cellular automaton evolves in discrete time steps, with the value of the variable at one site being affected by the values of variables at sites in its neighborhood on the previous time step. The neighborhood of a site is typically taken to be the site itself and all immediately adjacent sites. The variables at each site are updated simultaneously (“synchronously”), based on the values of the variables in their neighborhood at the preceding time step, and according to a definite set of “local rules.”

My reasons for not liking it have to do not only with the metaphors used (space, time, physical quantities), but also with the overall approach as signified by phrases like "mathematical idealizations of physical systems." Not only is that not necessarily the case, but also it obfuscates the usefulness of these models.

I've tried writing a hundred different short definitions of cellular automaton, and never gotten it quite right. Here's a recent not-quite-right:

A cellular automaton is a model. It consists of a grid, with a discrete variable in each location on the grid. This is called a cell. The state of a cellular automaton is completely specified by the value of each cell. The neighborhood of a cell is all those cells adjacent to it on the grid. A cell is updated based upon the values of its neighborhood, according to a set of rules.

Still working on making it shorter and clearer.