#Conway game of life question simulator#

Try playing with a Life simulator set to max speed to get a feel for how remarkably intricate can be the evolution of even simple initial states. On the surface of it, I think that constructing a pattern within Life that solves the control question looks very difficult. See further discussion in the brief appendix below. More generally, as Charlie Steiner points out, what happens if there are patterns in the randomly initialized region that are trying to control the eventual configuration of the whole universe just as we are? To deal with this, we might amend the control question to require a pattern that 'works' for at least 99% of configurations of the randomly initialized area, since most configurations of that area will not be adversarial. Since the initial state is symmetric, all future states will be symmetric, which rules our creating a non-rotationally-symmetric smiley face. Richard Kennaway points out that for any pattern that attempts to solve the control question, we could consider the possibility that the randomly initialized region contains the same pattern rotated 180 degrees in the diagonally opposite corner, and is otherwise empty. Now there are actually some ways that we could get trivial negative answers to this question, so we need to refine things a bit to make sure that our phrasing points squarely at the spirit of the control question. The control question is: Can we use this small initial region to set up a pattern that will eventually determine the configuration of the whole system, to any reasonable degree of accuracy? Our goal is to pick an initial configuration for the controllable region in such a way that, after a large number of steps, the on/off configuration of the whole grid resembles a smiley face. The initial on/off configuration of the remaining cells will be chosen randomly. We are given power to control the initial on/off configuration of the cells in a square region that is a tiny fraction of the whole grid. To repeat that: we have a large grid of cells that will evolve over time according to the laws of Life. The control question is: Can this goal be accomplished? The cells outside the top-left corner will be initialized at random, and you do not get to see what their initial configuration is when you decide on the initial configuration for the top-left corner. Now suppose that I give you control of the initial on/off configuration of a region of size 10 20 by 10 20 in the top-left corner of this grid, and set you the goal of configuring things in that region so that after, say, 10 60 time steps the state of the whole grid will resemble, as closely as possible, a giant smiley face. Suppose that we are working with an instance of Life with a very large grid, say 10 30 rows by 10 30 columns. Take a look at this awesome video of a Universal Turing Machine operating within Life. It is possible to build logic gates and combine them together into a computer that can simulate any Turing machine, all by setting up a particular elaborate pattern of 'on' and 'off' cells that evolve over time according to the simple rules above. It turns out that these simple rules are rich enough to permit patterns that perform arbitrary computation. Over time, the cells switch between on and off according to a simple set of rules:Ī cell that is 'on' and has fewer than two neighbors that are 'on' switches to 'off' at the next time stepĪ cell that is 'on' and has greater than three neighbors that are 'on' switches to 'off' at the next time stepĪn cell that is 'off' and has exactly three neighbors that are 'on' switches to 'on' at the next time step In Conway’s Game Life, which I will now refer to as just 'Life', there is a two-dimensional grid of cells where each cell is either on or off. In this post I am going to discuss a celular autonoma known as Conway’s Game of Life: I propose the AI hypothesis, which is that any pattern that solves the control question does so, essentially, by being an AI. I argue that the permissibility or impermissibility of AI is a deep property of our physics. This question is then connected to questions of agency and AI, since one way to answer this question in the positive is by constructing an AI within Conway’s Game of Life. This post asks whether it is possible, in Conway’s Game of Life, to arrange for a certain game state to arise after a certain number of steps given control only of a small region of the initial game state.

I welcome financial support to make further posts like this possible.Įpistemic status: I have been thinking about these ideas for years but still have not clarified them to my satisfaction. Financial status: This is independent research.

Conway game of life question