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.
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.