April 15, 2004
What is Emergence?
Answer: Something Emerges
This implies two things:
1) There has to be a lower level from which the
"something" can emerge
2) The "something" may be considered a
higher level of organization and/or structure. I am agnostic as
to whether this higher level is "real" or the result
of our perception. The point is that we would not categorize a
phenomenon as emergent if it did not have a higher level.
A) Canonical Emergence
1) The lower level is populated by many agents who
follow simple rules. The agents interact with one another locally
and have only local knowledge of their environment. They have
no understanding of the "something" that they are creating.
Examples: Social insects, neurons, genes in evolution
2a) The "something" that emerges comes
as a surprise to the observer precisely because nothing about
the agents at the lower level would lead one to believe that they
would create the "something". I don't want to overemphasize
the uniqueness of surprise for emergence (though I will use it
several times in what follows). More generally, surprise is simply
the hallmark of learning something: you know you have learned
something new when you are surprised by it.
"It is not from the benevolence of the butcher,
the brewer, or the baker, that we expect our dinner, but from
their regard to their own interest.
The individual only intends his own gain, and he
is in this, as in many other cases, led by an invisible hand to
promote an end which was no part of his intention... By pursuing
his own interest he frequently promotes that of society more effectually
than when he really intends to promote it."
Adam Smith, The Wealth of Nations, 1776.
2b) The "something" that emerges may or
may not have optimality properties. For an emergent process to
have optimality properties, two additional characteristics must
i. There must be a diversity generator - something
that generates divergent behavior or characteristics in the agents.
ii. There must be a grim reaper (there you are Paul) which acts
as an editor and eliminates some agents based on fitness criteria.
The classic examples of emergent processes that
generate optimal outcomes are competitive markets and evolution.
Models without such properties include segregation, stock market
bubbles, and epidemics.
B) Is Canonical Emergence the only kind of emergence?
Agents and the Lower Level:
1) Are the agents only allowed to have knowledge
of their immediate environment?
No: Cells in a maturing embryo interact locally,
but contain the entire genome; economic agents can have knowledge
of the overall economy. While agents can have global knowledge
and they can act on that knowledge, they cannot base their actions
on an attempt to create the "something"; otherwise,
there really aren't two distinct levels and no real surprises.
2) Do there have to be a lot of agents?
Yes. A big part of what defines the two levels is
that there are many 'things" at the lower level, but one
"something" that emerges.
3) Do the agents have to follow the same rules?
4) Do the rules have to be simple?
No, but they cannot be so complex as, Go build the
Structure and the Higher Level:
My conclusion up front: To some degree, structure
is always going to be in the eyes of the beholder. It may not
be useful to attempt a full definition, or a complete description,
of what constitutes structure. Still, something (ie. some classes
of "something") need to be ruled out; otherwise, everything
1) "Somethings" to rule out:
Statistical regularities do not qualify as structures:
i) In many competitive environments, various outcomes
follow a power law. Examples: income, wealth, hits to web pages.
Should this statistical regularity qualify as a "something"?
I am dubious. If you look hard enough, you may be able to find
patterns in most anything.
ii) While emergenauts have focused on power laws,
a much more ubiquitous and fundamental distribution is the normal
distribution which was specifically derived as the outcome of
many small errors. Should anything that follows a normal distribution
be classified as emergent?
I would say that the normal distribution itself
can be considered an emergent phenomenon, but not the things that
fit it. So, for example, the height of a group of people is not
an emergent phenomenon just because it follows a normal distribution.
But, the fact, discovered by Gauss, that a very specific distribution
categorizes any linear combination of independent random variables
is an emergent phenomenon.
2) "Somethings" not to rule out:
Ted Wong says: "When a rough stone wheel is
worn smooth and efficient by use, is the smoothness an emergent
phenomenon? I say no". I say yes. Think of a smooth oblong
stone worn smooth by a stream: the first time you saw one, it
came as a complete surprise that a stone could look like this.
It was the result of a gazillion water molecules, each of which
had no knowledge of, or intention to create, a smooth stone.
C) The System as a whole (System is understood
to mean both the lower level and the structure that emerges):
What role does randomness play?
This is a complex and interesting question :
1) Cellular automata illustrate that emergence does
not require randomness - agents can follow completely deterministic
2) A common view is that in emergence the structure
that emerges is more "organized" - less random - than
the behavior of the agents at the lower level. In this view, self-organization
is synonymous with emergence. So, in the segregation model, while
you may not like it, the agents cluster, self-organize, into like
"minded" groups following an initial random placement.
3) In Stephen Wolfram's world view (see last section),
deterministic rules can lead to randomness. For Wolfram, the interesting
rules are the ones that lead to a "structure" that is
more random than the behavior of the underlying agents.
This appears to be the polar opposite of 2) above.
4) Information theory (which I know virtually nothing
about), may, in a loose sense, support Wolfram's view. According
to information theory, a message is most dense (ie. has maximal
information) when it is indistinguishable from randomness. So,
one could say that the most complex systems will appear random.
5) A resolution of this paradox may be to distinguish
between two different types of emergent processes :
a) Type 1 has disordered agents, perhaps behaving
randomly, at the lower level, but generates a more organized structure
at the higher level. Most of the work in emergence seems to concentrate
on this type.
b) Type 2 processes start with orderly agents, perhaps
completely deterministic as in cellular automata, and generates
randomness. This seems to be the paradigm that Wolfram is working
Is it turtles (emergence) all the way down?
Ants exhibit emergent behavior, but the ants' brains
have neurons which exhibit emergent behavior, so is it emergence
all the way down? While it is certainly possible to build emergent
systems on top of one another, to conclude that it is emergence
all the way down, is to make everything emergent.
"To a little boy with a hammer, the whole world
is a nail"
Let's avoid that (Sorry Doug and Paul).
To what degree can the levels be separated?
By this I mean, can meaningful laws exist that relate
only to the structure without making reference to the rules that
the underlying agents at the lower level follow? Wolfram and Doug
Blank say no, they believe in what I will call irreducible complexity.
I, however, hope yes. Upper level laws not based on the rules
followed by the underlying agents will not be a complete description
of the reality, but they can still be true and useful.
Example: Boyle's Law accurately describes the behavior
of the volume of a gas under different temperatures and pressures
without making reference to the underlying gas molecules.
To me, this is a critical, maybe THE critical, question.
If the levels cannot be separated, then there is no way to understand
the behavior of the system without replaying all of the individual
interactions that generated the structure. While this is a full
employment guarantee for intellectuals and computers, to me it
would be a sad outcome.
It may be useful to briefly explain Wolfram's rationale
for believing in irreducible complexity. So here is Wolfram's
1) Everything is a computation.
2) The complexity of a system is determined by the complexity
of the computations that it can perform.
3) Systems that can perform equivalent computations are of equivalent
4) There is an upper bound to the kind of computations that can
be performed, and this upper bound is reached very quickly in
nature. Therefore, most systems in the natural and social world
are already at maximal complexity.
5) To be able to predict the outcome of a system, you have to
be able to "outcompute" it.
6) Since most systems in nature, including the human brain and
the biggest theoretical computer, are already at the upper bound
of complexity, it is impossible for the human brain to outcompute
most systems in nature Therefore, prediction is impossible
In a sense, this is where chaos and emergence meet.
While both fall under the rubric of complexity, to me they are
very different, except:
a) The hallmark of chaos theory is that the outcomes
of the equations that govern the system are so sensitive to initial
conditions, that in practice one cannot predict the outcomes (since
you will never have exact enough knowledge of the initial conditions).
b) If the levels of emergent systems cannot be separated, then
emergence shares this unpredictability. The only way that one
could predict things would be to replay all of the lower level
interactions, and in practice this would be impossible.
My conclusion: emergent phenomena may fall into
1) Reducible - those for whom the levels can be
separated and laws can be established that govern the structure
without reference to the agents at the lower level.
2) Irreducible - those that cannot be understood
except with reference to the entire past history of the underlying
It would be interesting to know if this dichotomization
maps directly into the Type 1 and Type 2 processes discussed in
the section on randomness. The irreducible processes do seem to
fit nicely into Wolfram's generation of randomness from deterministic
rules. The Type 1 processes, however, may not all be reducible.
So, for example, in the segregation model, the exact
pattern of segregation can only be determined by running the model,
so, in this sense, the model is Type 1 (the generation of organization
from disorderly underlying behavior) but also irreducible. Still,
there may be general laws that can be formulated about the segregation
model that predict the degree of segregation from the underlying
preferences of the agents, the percent of empty spaces, and the
initial distribution of agents. Such a law would in my view illustrate
that the levels can be meaningfully separated, since the exact
pattern of segregation (as opposed to the percentage of segregation)
may not be of importance to us.
Additions, revisions, extensions are encouraged
in the Forum
and/or at emergent.brynmawr.edu
Participants for April 15.2004: Mark, Al, Karen, Deepak, Mike,
Will, Ted, Anne, Doug, Alan, Tim, Jim, Jim, Paul (14)