We kind of have a grasp of patterns and abstractions now; the last piece of that particular puzzle is the way such things emerge. Patterns and abstractions are not guaranteed to arise in any particular system (in particular, any apparent emergence in a purely stochastic system is likely to be nothing more than Poisson clumping) but as we have seen with gliders in Conway’s Game of Life, emergence does happen.
There are a few different ways emergence has been described, though for my purposes I will take my own stab at it. I shall say that:
Emergence is when the operation of the rules of a system produces a set of patterns in the system which form an abstraction whose inaccuracies (e.g. the case of colliding gliders from Monday’s example) are sufficiently contained that the abstraction can still be used as a reasonable model to predict the future state of the underlying system.
That’s rather long-winded, I know. To elaborate slightly on what I mean by “sufficiently contained inaccuracies”, consider the glider case. As long as the gliders don’t collide (and there are no other cells active) our abstract system of gliders perfectly models the underlying system of Life: starting in the same state and following the appropriate rules will produce the same subsequent state (if Life had probabilistic rules, the additional caveat would be needed that we assume the same random choices as well). However, in the corner cases of colliding gliders (or when the initial state has non-glider cells active) then the glider system diverges slightly from the underlying Life system. This is still an emergent model though, both because the divergence between the abstraction and the underlying system is relatively small in most cases, and because it is easy to catch; even if we don’t have rules for handling it, we can easily notice when two gliders collide and consequently know that the abstraction is no longer necessarily correct.