Magic or emergence

by Marcus Loane


In the World Views article I sketched a hierarchy where each level is derived from a lower level, with everything ultimately coming from physics. This way of explaining phenomena in terms of something simpler, or by breaking components into ever smaller parts (eg. organs, cells, DNA, molecules, atoms, quarks) is called reductionism.

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B i o l o g y


Physics: Theory of everything

However it can be misleading. Biology may indirectly depend on physics but if the theories of physics change that does not mean biology has to change. There are appropriate levels of explanations. For example we could explain how a car engine works by describing the motions and interactions of every subatomic particle that it is composed of. That would be theoretically possible but it would be hopelessly obscure to human brains - it is too fine a level of detail. We need an explanation at the level of pistons, spark plugs and combustion. We can usually ignore the details at the lower levels. If our understanding of those details change it may have no effect on the higher levels.

If a theory of everything is devised it may have little impact on the higher levels. The work in biology and neuroscience and many other subjects will go on, discovering features and rules at the higher levels, that somehow transcend or appear to "float free" from the fine level detail that causes them. For example rules about ecosystems may be impossible for us to derive from rules about subatomic interactions even if we know that there is a chain of causes from the subatomic level all the way up to ecosystems.

The rules describing behaviour at higher levels just seem to emerge (emergent properties). It may be that they can be derived from the rules at lower levels, the rules that describe subatomic particles, but it seems difficult for human brains to see exactly how. Maybe some day this will change. The new science of complexity is attempting to tackle these questions.

I use the term "emergence" in a completely non-mystical sense. The Game Of Life detailed below gives an example of how emergent properties of systems arise from dynamics of interacting components.


Conway's Game Of Life is a toy universe with its own physics. Usually it is set up in a computer program. The program is freely available on the internet. The toy universe is two dimensional. It is a grid of squares which can be either white or black. Time in the toy universe goes forward in discrete instants. Each instant the colour of a square depends on the colour of its eight neighbours in the previous instant.

The toy universe's Theory Of Everything (its physics) consists of this law:

Each square "asks" how many of its neighbouring squares are black. If the answer is two, the square stays the same colour in the next instant. If the answer is three, the square will be black in the next instant. Any other answer and the square will be white in the next instant.

Everything that happens in the toy universe is derived from that one law. The toy universe has a starting condition with some squares white and some black but we can use any starting condition we like. We then let the computer apply the toy universe physics and the patterns of black and white squares will change each instant according to the rules. The state of the toy universe at any instant depends on the state of it at the previous instant. Events unfold like clockwork.

Gliders, eaters, puffers

Now what is interesting is that this toy universe has emergent properties. Certain shapes of black squares appear that have properties of their own. Some shapes never change (still lifes) like a square made of four black squares. Other shapes shrink and die - any diagonal will lose its end squares each instant until it vanishes. There are shapes that flash on and off. The still life shown below is easy to understand. It does not change because each square has three black squares next to it so according to the rule, it stays black. The flasher switches between three horizontal squares and three vertical squares. By examining each square it is fairly easy to see how its behaviour arises from the rule. More complicated arrangements become progressively difficult to understand.


A simple still life


A flasher

There are shapes that move around. One of these has been named a glider. There are "eaters" that destroy everything in their path. There are puffer trains, oscillators and guns which shoot off a steady stream of gliders. There are shapes that combine with each other to create new shapes. All these "creatures" (or "molecules" - it depends on your analogy) with their own properties and behaviour have emerged from one simple law of physics. They didn't necessarily exist in the mind of the programmer. All the programmer did was set up the physics and an initial configuration of squares, a "Big Bang" of sorts, and see what happened.

A glider appears to move through space

Note this is not some magic emerging from a computer. The whole setup can be enacted, albeit more slowly, on a piece of paper with a square grid, on which we place counters. We could painstakingly apply the rules to each square by hand and make the appropriate changes to the counters. We would need to photograph it each "instant" and then use each photograph as a frame in a movie to observe the higher level behaviour.

However it is much easier to let the computer apply the rules for us.

The gliders, eaters and puffer trains can be thought of as objects in their own right even though they are "just" conglomerations of squares. It is the same way we regard a skateboard or a bacteria as an object even though they are "just" a conglomeration of atoms. Skateboards have their own properties, like running down hills or amusing children, which seem far removed from the atomic physics that they ultimately depend on for their existence. Conway's Game Of Life creatures also have their own peculiarities which seem distant from the underlying Game Of Life physics.

An oscillator with a period of 9 instants

Conway's Game Of Life illustrates the concept of emergence. Complicated, unexpected (to us) things happen as the result of very simple underlying laws.

A computer inside the toy universe

It has been mathematically proven that a functioning computer (a Turing machine, for those in the know) can be created in Conway's Game Of Life universe. The various objects like gliders and flashers can be put together to make a "tape" and a "tape reader" and a memory and so on. The whole construction needs a very large grid. It could be done with counters on a real grid but it would need to be several miles wide. Now this two dimensional computer which is still "just" lots of little squares obeying the toy universe's simple physics, can be programmed to play chess at world champion level. Remember this has been proven to be possible. A 2d universe whose only rule is the simple law described earlier, can contain an entity capable of playing chess. It seems counter intuitive but it is true.

Now to understand a chess player you do not worry about the underlying physics, even though the chess player would not exist without it. In Conway's Game Of Life, if playing the chess computer, we would think about chess moves and strategies and we could forget the underlying toy universe physics. We now have at least three levels in the Game Of Life hierarchy of knowledge, the low level physics of individual squares, the level of gliders and puffers with their derived rules of behaviour, and the level of intentionality in the chess playing computer. There are probably more levels between the gliders level and the chess computer level, since simple objects are built into more complicated ones like tape streamers which have their own rules and which in turn can be built into even more complicated components. The theme is that different levels of explanation are appropriate depending on the context, even if all the levels are derived from those below them.

In both our Universe and Conway's Game Of Life universe, different rules/laws occur at different levels. The higher level rules are derived from the lower level rules but it is often very difficult for us to see how. That is not because there is some magic gap between levels. It is difficult because documenting all the little micro causes at a low level is such a huge task. Describing a car engine in terms of atoms would require enormous amounts of data and processing and it would not be particularly useful (I would guess).

Examples of emergent properties in our Universe are replication (necessary for life), periodic behaviour of some ecosystems, periodic behaviour of some chemical reactions, intelligence and consciousness. Developments in physics are beginning to show that the laws of physics themselves are emergent properties (results of "symmetry breaking"). That leaves us with spontaneous, in a non-mystical sense, creation of the laws of physics, and order from primeval chaos emerging naturally.

Marcus Loane