Emergence and Free Will
Emergence and Free Will
Emergence and Free Will
RICHARD CRAIB
Emergence: Definition and Characteristics
Classic Examples
The Problem with the Classics
The Game of Life Rules
Simple Examples in The Game of Life
Emergence in The Game of Life
More Cellular Automata with Stephen Wolfram
Irreducible Computations
Free Will Emerges
References
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Definition and Characteristics
According to Wikipedia, “emergence is the way complex systems and patterns arise out of a
multiplicity of relatively simple interactions” (Wikipedia, 2009). I take the liberty of referencing
Wikipedia because Wikipedia itself is a great example of emergence! And for the purposes of this
Also helpful, are Goldstein’s characteristics of emergence as summarized by Corning. These are
“(1) radical novelty (features not previously observed in systems); (2) coherence or correlation
(meaning integrated wholes that maintain themselves over some period of time); (3) A global or
macro "level" (i.e. there is some property of "wholeness"); (4) it is the product of a dynamical
process (it evolves); and (5) it is "ostensive" (it can be perceived)” (Corning, 2002)
The concept of emergence has been in use since at least Aristotle in Metaphysics; in it he says,
“anything that has a plurality of parts but is not just the sum of these, like a heap... exists as a whole
beyond its parts” (Aristotle, n.d.) i.e. the whole is greater than the sum of its parts.
Classic Examples
Observe Figure 1 below (Aristotle’s “heap” should spring to mind); this is a photograph of a termite
cathedral -- a classic example of emergence in nature. Here, the “simple interactions” are those of
the termites following their simple instincts and what ‘emerges’ is a beautiful structure - built grain
by grain - complete with spires. Although it appears designed (because of the observed
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Figure 1: A termite cathedral Source: Wikimedia
There are hundreds of examples of emergence in nature. Evolution is one giant example. In The
Origin of Species Darwin proposed the idea that the relatively simple interactions of variation,
heritability, and natural selection could produce the extreme complexity of life.
Unfortunately, the standard examples of emergence - the ones given above - are not good examples.
As discussed, emergence is concerned with simple interactions producing complexity. Yet, with the
termites, it is not obvious that their interactions are simple. They are living organisms; their
behavior is extremely complex and cannot be described with simple rules. Evolution as well
involves extreme complexity even at its fundamental level; there is no specific set of simple rules
governing variation in populations. In a sense, these examples require a prior belief belief in
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In order to convince the reader of the power of emergence (and how something like free will might
just be an example of emergence) we need a strong example, an example with extremely simple
rules and extremely complex emergent properties. John Conway’s1 Game of Life is such an
The Game of Life is a zero-player game that is played on a two dimensional infinite grid. Cells in
the grid can either be black (representing a life form) or white (representing emptiness). It is a zero-
player game in the sense that the game just takes some initial configuration of black and white
squares on the grid and then the rules are applied indefinitely.
Adapted from: bitstorm.org
1 John Conway proved The Free Will Theorem which states that if humans have free will then so to do certain
elementary particles! That result alone should make you not want to believe in free will.
2 We spell it ‘neighbours’ out of respect for the British inventor, John Conway.
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Consider the state above, we have three live (black) cells and the rest empty (white). We will call
this state the first generation3. We apply the rules simultaneously. (1) The top and bottom live cells
each have no neighbors, and therefore they die. (2) There is no overpopulation concern. (3) The
middle live cell survives because it has two neighbors. (4) There are two white cells with three
neighbours (diagonal neighbours count) so they become live cells. The resulting second generation
Observe the similarities between Figure 2 and Figure 3. One is merely the horizontal version of the
other. A keen reader might notice that Conway’s rules do not ‘care’ about vertical or horizontal
orientation and therefore generation three will be exactly the same as generation one (if you’re not
convinced, just apply the rules again to Figure 3). So this structure ‘blinks’ from vertical to
horizontal or horizontal to vertical in each generation, the structure is known as ‘the blinker’. For
generation n we can tell if it will be vertical or horizontal based on whether n is odd (vertical) or
even (horizontal). The blinker is a structure in Conway’s Game of Life which never grows and
never dies. It would not have been easy to predict that such a structure would exist on first glance
of the rules.
Clearly, there are structures in The Game of Life that do perish (for example, one live cell with no
neighbours will die in one generation). There are also structures that grow surprisingly large but
then taper off at some finite maximum. The ‘acorn’ structure, depicted in Figure 4, is a great
example. The acorn starts off with just seven live cells but after 5 206 generations it has produced
3 A ‘generation‘ passes in The Game of Life after every simultaneous iteration of the rules.
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633 live cells (Koenig, 2005). Here, we get the first glimpse of emergent properties of Conway’s
We have that some structures die out, that some structures remain stable, and that some grow to a
finite maximum. The curious mathematician would then ask, if there are any structures that grow
indefinitely without ever reaching a maximum. John Conway, the inventor himself, conjectured
(guessed but did not prove) that no such structure could exist in his game, and in 1970 he offered a
$50 prize to anyone who could prove or disprove the conjecture by the end of the year (Silver,
2009). By November that year, a team led by Bill Gosper at MIT disproved the conjecture with a
counterexample, and won the $50. The counterexample is known as ‘Gosper’s Glider Gun’, and the
reason it disproves the conjecture is that every 15th generation of the structure produces a new
‘glider’ (shown within each broken circle in Figure 5). A glider is a structure that always has
precisely 5 live cells, never dies, and continues to move outward. So every 15 generations there are
5 more live cells, which means that there cannot be maximum number of live cells.
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Figure 5: Gosper’s Glider Gun Source: Wikimedia
Going back the definition of emergence, it is clear that The Game of Life involves a “multiplicity of
relatively simple interactions” -- way more simple than the interactions of termites and populations.
And it is clear that a “complex system” -- like Gosper’s Glider Gun -- can arise out of these
interactions.
The significance of Gosper’s Glider Gun is that it grows indefinitely within Conway’s rules; simple
rules which do not give any hints that such a structure might emerge from a simple starting
configuration. In this way, the Glider Gun demonstrates Goldstein’s characteristic of “radical
novelty”. If the rules were just that every live cell turns into two live cells then obviously any
Running through, Corning’s other characteristics for Gosper’s Glider Gun we also observe
“coherence and correlation”, the property of “wholeness”, “ostensiveness”, and finally that it is the
“product of a dynamical process”. These would be especially apparent to the reader if you could
watch the glider progress through each generation on one of the online Game of Life demonstrators
(see References).
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More Cellular Automata with Stephen Wolfram
It turns out, Conway’s Game of Life is actually just a special case of a discrete mathematical model
called cellular automata. Every different cellular automata is like The Game of Life but with
different rules describing the behavior of the live cells within their neighborhoods.
Stephen Wolfram, another genius British mathematician, literally wrote the book on Cellular
Automata, and he called it Cellular Automata and Complexity. In a series of papers the book
elaborates on the surprising emergence complexity in these simple programs. Wolfram’s twenty
year fascination and work with cellular automata stretched many disciplines and finally culminated
in his master work titled A New Kind of Science. In the preface of the book Wolfram claims in his
signature style (where clarity trumps modesty), “I have discovered vastly more than I ever thought
possible, and in fact what I have done now touches almost every existing area of science, and quite
Irreducible Computations
In A New Kind of Science, Wolfram defines the concept of an ‘irreducible computation’, which we
“For if the evolution of a system corresponds to an irreducible computation then this means that the
only way to work out how the system will behave is essentially to perform this computation--with
the result that there can fundamentally be no laws that allow one to work out the behavior more
The blinker is a good example of a reducible computation, and we already discovered a law for
predicting its behavior: in the nth generation the blinker is vertical if n is odd and horizontal if n is
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even. By following our law we have made made performing the actual computation totally
An irreducible computation is then one where we can find no such simple law, and the simplest way
to determine what happens in the nth generation is to compute it. The following is just one of many
of Wolfram’s pathological examples of cellular automata, which (I think you’ll find) appear to be
very irreducible.
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Free Will Emerges
When you watch cellular automata in a computer program iterating relatively fast through each
generation, and you try to explain the behavior you will find yourself saying things like “look what
it’s doing”, “it just branched left”, “now, it decided to branch right”. As Wolfram notes in
describing the behavior in this way, “[you are] thereby effectively attributing to it some sort of free
If there is some apparent free will in simple cellular automata, is it really a stretch to argue that
human free will is merely apparent and that the perception of free will is just an example of
emergence?
Presumably the neurons and synapses in our brains follow definite laws. The laws may be
complicated but even proponents of free will agree that locally, on the micro level, these laws are
definite. We can now begin to think of neighborhoods of neurons and synapses with cellular
automata-esque rules describing their interactions. There could be thousands of rules, and they will
surely be more complicated than the rules in The Game of Life but they will still be relatively
simple. But through the multiplicity of their simple interactions over a number of generations
Wolfram argues that apparent free will not only an example of emergence but also an example of an
simple and definite rules yet “[their] overall behavior ends up being sufficiently complicated that
many aspects of it seem to follow no obvious laws at all” (Wolfram, 2002). This is exactly the case
with free will too. We can get all the complexity we need for apparent free will from simple rules
governing neighborhoods of neurons and synapses, and even though the rules are simple there is no
way to predict someone’s decision without having that person compute the decision.
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References
Books
Aristotle (n.d.) “Metaphysics” translated by W. D. Ross, New York, NY: Cosmo Publications
Papers
Koenig, H. (February 21, 2005). "New Methuselah Records". Retrieved January 24, 2009
Stephen A. Silver. "Gosper glider gun". The Life Lexicon. Retrieved July 12, 2009
Other
Gospers_glider_gun.gif
Termite_Cathedral_DSC03570.jpg
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