Emergence from complexity



(note this page is best read in conjunction with this one here).

Introductory Background

Emergence is the appearance of phenomena at a scale of system organisation that is not present at the lower scales within it. The idea is that all systems are made from relationships amongst component parts. If we begin with the most elemental components, these are related to one another by regulated* interactions to form, what at least appear to be, more complex units, which in turn may be related by (possibly other) regulated interactions to form higher-level units, and so on… producing a hierarchy. We may take elementary particles (electrons etc.) as the elemental components and the laws of physics that govern their behaviour as the restrictions for their interactions. We know that they interact to form atoms and that atoms interact in ways that seem different to those governing the elementary particles from which they are composed (chemistry seems to have some different rules to physics). It is important to realise here that the rules of physics are not replaced by, but added to by those of chemistry. We know that organisms are all made from chemical components, obeying the laws of chemistry, but it seems there are some very different and important laws that spontaneously ‘emerge’ to make life very special. That is when the right molecules interact in the right way to count as part of something living. Indeed, living can be defined as a network of chemical reactions that obey some particular rules which extend beyond inanimate chemistry: they appear to be special emergent rules of life.

* note - these are regulated in the sense that not any interaction is permitted if the system is to be at all organised: typically relationships between component parts have to be highly prescribed for the system to be even identifiable, let alone functional.


The essential message of scientific constructivism is that creation is composed of a nested hierarchy of phenomena in which new laws, laws that could not be foreseen by studying lower levels of the hierarchy, govern the workings of each level in turn. Thus, physics has its laws and chemistry has additional ones that cannot be understood at a level below chemistry. The same with biology: laws of life are new and unique to life, they cannot be derived from chemistry and physics. One reason this is an uncomfortable conclusion is that we know that physics, chemistry and biology are just categories of scientific enquiry, reflecting the historical divisions of research pursued by different people who’s interests were so divided. We might suspect that nature is not really made from distinct ‘Russian dolls’, each with its own governing principles. Whether or not this is true, rests on the question of whether the emergence of apparently new phenomena with each increasing level of complexity is genuine, or just an appearance. If it is genuine: each level really does introduce new rules as though from nothing, then it is called ‘hard emergence’ (sometimes 'strong emergence). If it is only an illusion, then the apparently new rules are really just a reworking of those already known from the more fundamental levels and we call that ‘soft emergence’ (sometimes 'weak emergence').

Soft Emergence in the Game of Life

A very good explanation which demonstrates soft emergence is provided by Russ Abbott in Emergence Explained’ (2006). It uses the computer-based cellular automaton called Conway’s ‘Game of Life’ (GoL).
The GoL is a very simple set of rules which govern transitions from ‘on’ to ‘off’ and back among a set of interconnected elements, best thought of as grid squares, for example on a chess board. Each element (grid square) has four neighbours with which it shares a side and four with which it shares a corner; all these together are its eight neighbours. If an element is on now, then in the next move (or time-step) it will stay on if and only if two or three of its neighbours is on, otherwise it will go off. If it is off now, it will stay off unless exactly three of its neighbours is now on, in which case it switches on in the next move. That’s it.
Famously, there are certain patterns of on and off which you can make on the grid that persist and move over the grid, looking almost like flat little creatures - the glider being the best known of these. Some people have created large ‘zoos’ of patterns that do interesting things in the grid, interact in fascinating ways, reproduce and generally amaze. If you watch these patterns performing their behaviours on the grid, they certainly seem to have a life of their own, but never forget that they are in fact just made from, and strictly obey, the simple elemental rules. Never the less, to describe the behaviour of the patterns, we have to refer to what appear to be new rules that describe the way different kind of pattern interact.

There is then, a higher level of abstraction, beyond and not including the elemental rules, where GoL ‘creatures’ can be described according to their behaviours and interactions. They can do a lot of things, for example they can represent even very complicated calculations, but one thing they are never able to do is change the elemental rules from which they are made. For this reason we refer to them as 'transendent' phenomena of the rules of the GoL. As scientists, we could be very reductionist and say there is nothing to see except the repeated application of a few rules, or we may be more synthesist and describe the diversity and behaviours of patterns we see within the GoL, without reference to the underlying causes. Both are valid, but incomplete.

One especially important and elaborate creation within the GoL is the ‘Universal Turing Machine’ (UTM): it really is astonishing that such a thing can be created within GoL, but you can see one working in this YouTube video: here. As well as giving you a good impression of the sort of dynamic patterns that can be created with the rules of GoL, the UTM is of special interest for us. The reason is that its author, the British mathematician Alan Turing, proved that it could, in principle, compute anything that is computable, because by definition a UTM can compute and can simulate any other Turing Machine, which in turn can compute anything that a ‘real’ computer can compute. In fact, the Turing Machine, and its more general relative the UTM, were devised as representations of computation in general and their study yielded fundamental insights for the development of all the computers used today. So, this universal computer, which can compute anything, can be made using the GoL (and this was established by John Conway himself - another British mathematician).

Now, to continue Abbott’s explanation, the UTM generated in a GoL is pure information and is a transcendent complex (explained here) of the patterns that comprise it as interacting component parts, these patterns themselves being transcendent complexes of the GoL rules. So far, then, we have two hierarchical levels of soft-emergence and it is important to realise that both are pure information: the first as it comprises nothing but patterns on the grid and the second, because it is computation, made from those patterns. This turns out to be a general feature of transcendent complexes: they are pure information. They are also (by definition) logically independent of the elemental components and rules from which they are built. This is because they can be built from more than one kind of elemental system. For example a Turing machine can be made from a digital computer program, or in a physical model, even made from plastic building components (e.g. Lego), as well as from the GoL. When we want to study and discuss the transcendent complexes (e.g. a UTM), it is not relevant to refer to the GoL, Lego, or computer with which it is formed.

Is it a large step to apply the same thinking to a living cell? Can all the workings of a cell (the process of living) be formed, not from biochemicals, but in a computer simulation, or on the GoL grid? This does not mean a computer model of the cell, it literally means the process of living, not ‘run on’ biochemistry, but rather in some other logical base-system. If the answer is yes, then we shall know that life is an transcendent phenomenon and that it is pure information.