| Two of the most fascinating open questions about the Game of Life are in my opinion: 1. What is the behavior of Conway's Game of Life when the initial position is random? Paraphrasing Boris Bukh's comment on the post linked below, the Game of Life supports self-replication and is Turing-complete, and therefore can support arbitrarily intelligent programs. So, will a random initial position (tend to) be filled with super-intelligent life forms, or will the chaos reign? There exist uncountably infinitely many particular initial configurations out of which a random one may be drawn, which makes this more difficult (a particular infinite grid configuration can be represented as the binary digits (fractional part) of a real number, spiraling outwards from a given center coordinate cell: 0.0000... represents an empty infinite grid, 0.1111... a fully alive infinite grid). https://mathoverflow.net/questions/132402/conways-game-of-li... 2. Relatedly, does a superstable configuration exist? One that continues to exist despite any possible external interference pattern on its border? Perhaps even an expanding one? https://mathoverflow.net/questions/132687/is-there-any-super... |
One of the chapters asks "what is life?". It considers (and rejects) various options, and finally settles upon a definition based on Von Neumann-style self-replicating machines using blueprints and universal constructors, and explains why this is the most (only?) meaningful definition of life.
Later, it talks about how one would go about creating such a machine in Conway's Game of Life. When the book was written in 1984, no one had actually created one (they need to be very large, and computers weren't really powerful enough then). But in 2010 Andrew J. Wade created Gemini, the first successful self-replicating machine in GoL, which I believe meets the criteria - and hence is "alive" according to that definition (but only in the sense that, say, a simple bacteria is alive). And I think it works somewhat like how it was sketched out in the book.
Another chapter estimated how big (and how densely populated) a randomly-initialized hypothetical GoL universe would need to be in order for "life" (as defined earlier) to appear by chance. I don't recall the details - but the answer was mind-boggling big, and also very sparsely populated.
All that only gives you life though, not intelligence. But life (by this definition) has the potential to evolve through a process of natural selection to achieve higher levels of complexity and eventually intelligence, at least in theory.