"One of the most brilliant mathematicians of the last and current century is John Horton Conway. Near the middle of the last century he formalized a notion of game in terms of a certain recursive data structure. He went on to show that every notion of number that has made it into the canon of numerical notions could be given representations in terms of this data structure. These ideas are documented in his delightful On Numbers and Games. Knuth popularized some of these ideas in his writings on surreal numbers."
Rudy Rucker on cellular automata: "I was first hooked on modern cellular automata by [Wolfram84]. In this article, Wolfram suggested that many physical processes that seem random are in fact the deterministic outcome of computations that are simply so convoluted that they cannot be compressed into shorter form and predicted in advance. He spoke of these computations as "incompressible," and cited cellular automata as good examples."
"What need we know, Wittgenstein asked, in order that we apply terms
like 'chair', or 'leaf', or 'game' unequivocally and without provoking
That question is very old and has generally been answered by saying
that we must know, consciously or intuitively, what a chair, or a leaf,
or game _is_. We must, that is, grasp some set of attributes that all
games and only games have in common. Wittgenstein, however, concluded
that, given the way we use language and the sort of world to which we
apply it, there need be no such set of characteristics. Though a
"Consider for example the proceedings that we call `games'. I mean board games, card games, ball games, Olympic games, and so on. What is common to them all? Don't say, "There must be something common, or they would not be called `games' " - but look and see whether there is anything common to all. For if you look at them you will not see something common to all, but similarities, relationships, and a whole series of them at that. To repeat: don't think, but look! Look for example at board games, with their multifarious relationships.