Further to my other comment, how would one define a counterfactual in the Game of Life? Surely we should be able to analyze this simple case first if we want to talk about counterfactuals in the “real world”?
Say we have a blank grid. It would be reasonable to say “if this blank grid had a glider, the glider would move up and left” even if there is no actual glider on the grid. You can still make a mental model of what would happen in a changed grid, even if that grid isn’t instantiated. I chose the example of a glider to show that you don’t actually have to run a step-by-step simulation of the grid to predict behavior and thus emphasize that a counterfactual is a mental model, not an actual universe. Counterfactuals require a universe and a model that is isomorphic to that universe in some way, but the isomorphism doesn’t have to be perfect.
I like this example, and it counts as a counterfactual in our universe, where there is no actual glider drawn on an actual blank grid, but I am not sure it would count as a counterfactual in a GoL universe, unless you define such a universe to contain only a single blank canvas and nothing else.
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.
What you suggest is one type of a counterfactual: change the state. Erasing a glider is, of course, illegal under the rules of the game, so to make it a legal game, you have to trace it backwards from the new state, or else you are not talking about the GoL anymore. This creates an interesting aside.
Like the real life, the Game of Life is not well-posed when run backwards: infinitely many configurations are legal just one simulation step back from a given one. This is because objects in the Game can die without a trace, and so can appear without a cause when run backward. This is similar to the way the world appears to us macroscopically: there is no way to tell the original shape of a drop of ink after it is dissolved in a bucket of water. This situation is known as the reversibility problem in cellular automata.
This freedom to create life out of nothing when simulating GoL backwards does not help us, however, in constructing the same starting configuration as the one with the glider not erased, because GoL is deterministic in the forward direction, and you cannot arrive at two different configurations when starting from the same one. But it does let us answer the following hypothetical: would adding a glider have made a difference in the future? I.e. would the glider in question collide with another object and disintegrate without a trace after several turns?
This “butterfly effect” investigation is trivial in the GoL and similar irreversible automata with simple rules, but it is quite suggestive if we consider the original question:
If Lee Harvey Oswald hadn’t shot John F. Kennedy, someone else would’ve.
We can liken Oswald to your glider and see of removing it from the simulation (“counterfactual surgery”) still results in the same final configuration (JFK shot). If so, we can declare the above statement to be “true”, though not in the same sense as “Oswald shot JFK” is true, but in the same sense as a proved theorem is “true”: its statement follows from its premises.
Further to my other comment, how would one define a counterfactual in the Game of Life? Surely we should be able to analyze this simple case first if we want to talk about counterfactuals in the “real world”?
Say we have a blank grid. It would be reasonable to say “if this blank grid had a glider, the glider would move up and left” even if there is no actual glider on the grid. You can still make a mental model of what would happen in a changed grid, even if that grid isn’t instantiated. I chose the example of a glider to show that you don’t actually have to run a step-by-step simulation of the grid to predict behavior and thus emphasize that a counterfactual is a mental model, not an actual universe. Counterfactuals require a universe and a model that is isomorphic to that universe in some way, but the isomorphism doesn’t have to be perfect.
I like this example, and it counts as a counterfactual in our universe, where there is no actual glider drawn on an actual blank grid, but I am not sure it would count as a counterfactual in a GoL universe, unless you define such a universe to contain only a single blank canvas and nothing else.
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.
You go back to an earlier state of the grid, erase a glider, and resume the simulation from there.
A few thoughts on the matter.
What you suggest is one type of a counterfactual: change the state. Erasing a glider is, of course, illegal under the rules of the game, so to make it a legal game, you have to trace it backwards from the new state, or else you are not talking about the GoL anymore. This creates an interesting aside.
Like the real life, the Game of Life is not well-posed when run backwards: infinitely many configurations are legal just one simulation step back from a given one. This is because objects in the Game can die without a trace, and so can appear without a cause when run backward. This is similar to the way the world appears to us macroscopically: there is no way to tell the original shape of a drop of ink after it is dissolved in a bucket of water. This situation is known as the reversibility problem in cellular automata.
This freedom to create life out of nothing when simulating GoL backwards does not help us, however, in constructing the same starting configuration as the one with the glider not erased, because GoL is deterministic in the forward direction, and you cannot arrive at two different configurations when starting from the same one. But it does let us answer the following hypothetical: would adding a glider have made a difference in the future? I.e. would the glider in question collide with another object and disintegrate without a trace after several turns?
This “butterfly effect” investigation is trivial in the GoL and similar irreversible automata with simple rules, but it is quite suggestive if we consider the original question:
We can liken Oswald to your glider and see of removing it from the simulation (“counterfactual surgery”) still results in the same final configuration (JFK shot). If so, we can declare the above statement to be “true”, though not in the same sense as “Oswald shot JFK” is true, but in the same sense as a proved theorem is “true”: its statement follows from its premises.