Defining emergence takes a moment to set up for the uninitiated, so let’s try this in two phases. First, a simple, formal definition:
The appearance of novel properties, patterns or behaviors at a “higher level” of organization that are not obviously present and cannot be easily predicted from the properties of the individual parts of a given system.
(As with the definition of entropy, pedants can nitpick and argue about “strong” vs “weak” emergence, but that sort of tedium focuses on the finger and misses the point.)
The idea of ordered “levels” appears and so does the idea of a system. “Levels” here are easy to understand if we think of what happens in a board game. The rules of a board game are usually simple and few in number. These rules define the “low level” of the game. Each move made in the game, in isolation of the broader context of whatever is going on among the players, can be evaluated for validity according to the rules in a simple manner. But now what we’ve done is mention “whatever is going on among the players” and here we are already touching on the “higher level” and are implicitly leaning on the idea that there is a higher level.
The rule set of a game is the low level, the gameplay that emerges from them is the high level, and all of this taken together is the system that the defines the game overall.
The techniques, strategies, and “meta” of the game as played among the players is always emergent. That is, there are the rules of the game, and then what emerges is the way the players actually play it. Many games have simple rules but the gameplay that emerges from those rules is rarely obvious.
The most important maxim in game design is: “You don’t know what game you have created until you watch other people play it.” This hits home more strongly the more experience you have in game design.
Similarly, in computer programming we typically have a relatively simple set of physical computer instructions available, but we program the computer in terms of a “higher level” set of languages that are translated to the simpler computer instructions by a compiler. Each higher level computer language is itself a relatively simple set of limited instructions, just structured more comfortably for human reasoning, but the programs we write using those languages can be arbitrarily complex in nature. There are essentially a limitless set of novel properties that can emerge in this context, as simulations of arbitrary rule sets can be emulated in programs themselves. It is even the case that very often the machines we are writing code against are themselves virtual machines which are nothing more than programs that emulate a machine instruction set that exists nowhere in the world of real hardware.
So now let’s return to the definition of emergence again:
The appearance of novel properties, patterns or behaviors at a “higher level” of organization that are not obviously present and cannot be easily predicted from the properties of the individual parts a given system.
The laws of physics are relatively few in number, each individually simple. The way in which they interact is complex. The structures that emerge from those few laws are arbitrarily complex at a higher level, and at each level a new possibility is created for yet another level of emergence to occur. In fact, we’re not quite sure we’ve discovered the deeper underlying rules at the simplest levels, nor have we fully understood how high the levels of emergent behavior in the universe go.
That it is generally impossible to predict emergent behavior is central to understanding why it is so counterintuitive that life would ever be an emergent property of the laws of physics, or that consciousness could ever be an emergent property of life, or that moral systems could ever be an emergent property of consciousness.
As a closing side note, the title image of this post displays the rules for “Conway’s Game of Life”. This is a little game system with a tiny number of rules, but from which arbitrary emergence can occur. It is, in fact, Turing complete, and even processor architectures have been emulated within it. I strongly encourage anyone with the time and interest to look into this further. A vast wealth of resources, discussions and books on the subject can be easily found with a search for “Conway’s Game of Life”.