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This is: Agency in Conway’s Game of Life, published by Alex Flint on the AI Alignment Forum.
Financial status: This is independent research. I welcome financial support to make further posts like this possible.
Epistemic status: I have been thinking about these ideas for years but still have not clarified them to my satisfaction.
Outline
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.
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.
I argue that the permissibility or impermissibility of AI is a deep property of our physics.
I propose the AI hypothesis, which is that any pattern that solves the control question does so, essentially, by being an AI.
Introduction
In this post I am going to discuss a celular autonoma known as Conway’s Game of Life:
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. Over time, the cells switch between on and off according to a simple set of rules:
A cell that is "on" and has fewer than two neighbors that are "on" switches to "off" at the next time step
A cell that is "on" and has greater than three neighbors that are "on" switches to "off" at the next time step
An cell that is "off" and has exactly three neighbors that are "on" switches to "on" at the next time step
Otherwise, the cell doesn’t change
It turns out that these simple rules are rich enough to permit patterns that perform arbitrary computation. 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. Take a look at this awesome video of a Universal Turing Machine operating within Life.
The control question
Suppose that we are working with an instance of Life with a very large grid, say
10
30
rows by
10
30
columns. 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.
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.
The control question is: Can this goal be accomplished?
To repeat that: we have a large grid of cells that will evolve over time according to the laws of Life. 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. The initial on/off configuration of the remaining cells will be chosen randomly. 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 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?
[Updated 5/13 following feedback in the comments] 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. Richard Kennaway points out that for any pattern that attempts to solve the control question, we ...
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