Now all of this may sound fine, philosophically speaking, but in practice, surely we, ourselves, can’t just be part of a mathematical structure? Equations don’t think! Well, yes, that’s true, if a little glib. By us being purely mathematical structures, or substructures, I don’t mean that we’re like programmed robots. What I mean is that, at the most fundamental level, there are no particles, only patterns, and by patterns, I mean the essence of the patterns, not the physical arrangement of things. In this scenario, the arrangement of particles and forces into chemical elements and stars and planets and people is no different from our current understanding of how things are put together, except that, ultimately, these particles and forces are purely mathematical structures. If our constituent parts are purely mathematical structures at the most fundamental level, then so are we!

An analogy may help: if you haven’t heard of it, let me introduce you to the Game of Life. The Game of Life (or simply “Life” to the afficionados) is not a competitive game; rather, it is played out on a two-dimensional grid of squares called cells, and displayed on a computer monitor screen. Once you have decided on the initial configuration of cells in the grid, you press the start button and see what happens to the cells you have chosen. A cell can be either alive or dead – typically, live cells are coloured black and dead ones white. The configuration of a cell – alive or dead – is determined by its eight neighbours. (Think of nine cells arranged in a square three cells wide by three cells high; then, with respect to the central cell, the remaining eight are its neighbours.)

The rules are simple:

1. If a cell is dead and exactly three of its neighbours are alive, then that cell will come alive at the next time-step.

2. If a cell is alive, it will die at the next time-step unless exactly two or three of its neighbours are also alive, in which case it will remain alive at the next time-step.