So what you’re saying is that if we did define such a universe to contain only a single blank canvas and nothing else, our internal model of a grid with a glider would be a good example of a counterfactual?
(thus demonstrating that counterfactuals can, themselves, contain counterfactuals).
(thus demonstrating that counterfactuals can, themselves, contain counterfactuals).
Nice one.
I am trying to nail the definition of a counterfactual in a GoL universe. Clearly, if you define this universe as a blank canvas, every game is a counterfactual. However, if the GoL universe is a collection of all possible games (hello, Tegmark!!), then there are no counterfactuals of the type you describe in it. However, what army1987 suggested would probably still count as a counterfactual: given a realization of a game and a certain position in it, find whether another realization, with an extra glider, converges to the same position. The counterfactualness there comes from privileging one game from the lot, not from mapping it to our universe.
So what you’re saying is that if we did define such a universe to contain only a single blank canvas and nothing else, our internal model of a grid with a glider would be a good example of a counterfactual?
(thus demonstrating that counterfactuals can, themselves, contain counterfactuals).
Nice one.
I am trying to nail the definition of a counterfactual in a GoL universe. Clearly, if you define this universe as a blank canvas, every game is a counterfactual. However, if the GoL universe is a collection of all possible games (hello, Tegmark!!), then there are no counterfactuals of the type you describe in it. However, what army1987 suggested would probably still count as a counterfactual: given a realization of a game and a certain position in it, find whether another realization, with an extra glider, converges to the same position. The counterfactualness there comes from privileging one game from the lot, not from mapping it to our universe.