The Game of Life is Turing complete. And therefore a complete analysis of how to write programs in it would imply a solution to the Halting problem. Which is impossible.
With finite state, one could theoretically brute force search every possible 1D sequence to find a glider shorter than the one discovered here.
Obviously that's impractical, but turns the whole thing into a search problem - find the best/a good solution in a huge search space.
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The Game of Life is Turing complete. And therefore a complete analysis of how to write programs in it would imply a solution to the Halting problem. Which is impossible.