Reference Material:
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.
- Macroscopic behavior/structure – Emergent phenomena are behaviors or structures that are identifiable at a macroscopic level of analysis but seem not to be present at a microscopic level. A glider in Life is not apparent in any single cell, only in the behavior of a very specific arrangement of 5 cells. An ESS is not apparent in any instance of 2 individuals playing a single game, only many individuals playing many games over time.
- Criticality – There is an element of criticality to many emergent phenomena. Criticality is immediately apparent in examples like Boolean networks and sandpiles, but it also exists in systematic examinations of all cellular automata. Make the rules too simple and the results are boring. Make the rules too complex and chaos reigns. Somewhere in between, stable but interesting macroscopic structures and behavior emerge. ESS’s also exhibit a kind of criticality – adjust an ESS in any way, and by definition, it will be susceptible to invasion by a mutant strategy.
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