At Home in the Universe by Stuart Kauffman (1995)
I now plan to devote several posts to the concept of emergence, as it arises both in science generally and its underpinnings in the philosophy of science. The concept seems to be a great spring board into related topics in the philosophy of science, and there are also interesting ties to determinism. Those explorations may come in the future, but for now I just want to attempt to form a decent conceptual understanding.
Emergence is a notoriously slippery concept. The basic idea is this – some systems, when described at a macroscopic level, exhibit behavior, patterns, or properties that in some sense don’t exist at a microscopic level. In such cases, the macroscopic behavior, patterns, or properties are deemed emergent. The conceptual vagueness enters in two main ways. First, the claim that a certain macroscopic behavior is or is not emergent seems open to interpretation. More importantly, the actual content of such a claim is the subject of much philosophical debate. A quip in the “Emergent Properties” Stanford Encyclopedia of Philosophy article sums up the situation nicely – “emergence encompasses whatever striking macroscopic phenomena the theorist in question is interested in”. To get a conceptual foothold on such slippery terrain, I’ll borrow a method from Julia Galef at the Rationally Speaking podcast. Let’s describe what is meant by emergence by cataloging several examples of claims of emergent behavior. Certain commonalities among the claims can then form the basis of a conceptual understanding.
A famous example of a kind of emergence (not from the reference material) is Conway’s Game of Life, a special case of a cellular automaton. Life, as it’s known, consists of an infinite 2-D grid of cells that are in 1 of 2 states, on or off, alive or dead. Each cell “evolves” from its current state to the next state by “interacting” with its neighbors via a set of rules – an example: evolve from on to off (“die”) if fewer than 2 of your neighbors are on (“alive”). A “game” of Life then consists of an initial grid state and its evolution according to the rules. This level of the game, with alive and dead cells, neighborhood interaction rules, and simple time evolution, might be termed the microscopic level. Systematic study of Life reveals various types of structures when the grid is viewed at a more macroscopic level, in say, 5x5 or 10x10 grids. A classic structure is a “glider”, an isolated cluster of 5 alive cells that shifts diagonally by 1 cell after 4 iterations, thus seeming to move. At a still higher level, Gosper’s glider gun is a stable oscillating structure of roughly 10v40 size from which gliders emanate every 30 iterations. Many other higher-level structures (puffers, rakes, breeders, etc.) have been discovered and catalogued. Somewhat needless to say, the existence and/or behavior of these higher-level structures is deemed emergent.
Let’s introduce a similar computational system, this time from Kauffan’s book. Boolean networks are collections of nodes with Boolean-valued states. Each node receives input from and sends output to some number of other nodes. Like Life, a Boolean network evolves iteratively. A node’s present value is determined by applying a Boolean-valued function to the node’s inputs from the previous iteration. A key parameter in defining a Boolean network is the parameter K, the number of inputs per node. When Boolean networks are studied parametrically with respect to K, emergent behavior is found at some critical value Kc. For K < Kc, a Boolean network is stable – all nodes reach an unchanging state after an initial transient period. For K > Kc, extremely chaotic, effectively random behavior is observed. But around K = Kc, the network settles down into a recurring sequence of some relatively small number of states, a so-called state cycle. The apparent emergence in this system is that cyclical behavior occurs in a system that exhibits both banal order and effective randomness.
Now for another example – sandpiles. Drop grains of sand (real ones or computational ones, as in the Bak-Tang-Wiesenfeld model) onto a horizontal surface to form a sandpile. Keep adding grains, and eventually the slope of the pile’s sides will reach the angle of repose. The pile will have reached a so-called critical state, where adding one additional grain could do anything: cause an avalanche of grains cascading across half the pile, nothing at all, or anything in between. At the critical state, it turns out to be basically impossible to predict the effect an additional grain will have. The critical state also exhibits a kind of stability – once criticality is reached, the sandpile will remain there as grains are added. That the sandpile has, absent external guidance, reached this critical state is termed self-organized criticality. This type of self-organization is considered an emergent phenomenon.
A final example, discussed by Kauffman but also widely known, is an evolutionarily stable strategy, or ESS. An ESS is a Nash equilibrium in a game-theoretic environment that is evolutionarily stable, meaning that if all individuals in a population adopt the strategy, an alternate strategy arising via mutation will not be evolutionarily favored. ESS’s are widely discussed and I needn’t expand on them here – a great popularizer of the concept was Dawkins’ The Selfish Gene. The point here is their status as emergent. At one level, you have the dynamics of classic game theory. A level above, you have a population of individuals, each continuously interacting with the game-theoretic environment. One more level up (temporally), the population is subject to the forces of natural selection. It is only at this third level that ESS’s emerge.
There are so many other examples of emergent phenomena – a single blog post can barely scratch the surface. Simply scrolling through the Wikipedia article gives you a glimpse at the variety of phenomena in question: crystals, snowflakes, temperature, termite mounds, swarming behavior, traffic jams, stock markets, life itself, and perhaps most controversially, mind. Is there anything that ties these disparate phenomena together, that identifies them as emergent? Based on my reading, three broad characteristics of emergent phenomena are apparent:
- Multiple levels of analysis – Descriptions of emergent phenomena involve identifying behavior, patterns, or structure at one level of analysis, (the “macroscopic” level), where there exists at least one other level of analysis (the “microscopic” level) “below” the macroscopic level. The levels are distinguished by one or several characteristics:
- Spatial extent – Life’s gliders are only apparent when the game is viewed from at least the 5v5 grid scale. You need to “zoom out” from an individual sand grain to be able to identify self-organized criticality.
- Temporal extent – Boolean networks must be monitored over many iterations to observe cyclical behavior. ESS’s are only apparent when Nash equilibria are analyzed in populations over time.
- Number of components – the self-organized criticality of sand piles is only apparent at the level of many, many sand grains.