Context #6 (Fall,
2001, pp. 15-19); copyright 2001 by The Nature Institute
In April, 1999, the prestigious journal, Science, informed its
readers that "shortfalls in reductionism are increasingly apparent ....
The much-used axiom that scientists 'know more and more about less and
less' may have an element of truth .... Another problem is oversimplification.
Witness the 'gene-for' syndrome (as in 'gene for intelligence' or 'gene
for sexual preference'), in which genes that contribute to human traits
are instead taken to specify that trait" (Gallagher and Appenzeller 1999,
These remarks occur in a special issue of Science devoted to
complex systems. A news article in that issue carries the point
about genes further:
"The expression of individual genes is not being regulated
by one, two, or five proteins but by dozens," says Shirley Tilghman, a
molecular biologist at Princeton University. Some regulate specific genes;
others work more broadly. Some sit on DNA all the time, while others bind
temporarily. "The complexity is becoming mind numbing," says Tilghman.
"When we get to a certain network complexity," adds Adam Arkin, a physical
chemist at Lawrence Berkeley National Laboratory, "we completely fail to
understand how it works" (Service 1999, p. 81).
In recent years the study of complex systems, or complexity, has been
widely proclaimed a scientific revolution. The revolution lends new currency
to the idea of holism, and has popularized terms such as "self-organization,"
"complexity," and "chaos." Many might take the aspirations of the complexity
theorists as a fulfillment of the hope, often expressed in our Nature
Institute publications, for a new and revitalized science. But it is a
live question whether the current developments are indeed a renewal of
science or instead represent a retrenchment and strengthening of the most
serious limitations of traditional science.
In any case, we think readers of In Context will want to know
something about this ongoing "revolution." Unfortunately, a summary is
not easy. There is no consensus definition of complexity studies, and
its researchers seem to understand what they are doing more in terms of
a style of theorizing than a specific subject matter. Indeed, the subject
matter is often taken to be scarcely distinguishable from "everything,"
which is perhaps why the disciplines at issue have so far yielded a richer
harvest in vague hunches than concrete results.
Vagueness, however, has not made for shyness. Rarely, if ever, have
the advocates of a new science been so effective at advertising the fundamental,
"paradigm-shifting" importance of their own work before they had much
to show for it. In addition to a new holism, the advertisements promise
a rejection of reductionism, the discovery of almost mystical-sounding
"emergent" and "self-organizing" properties of physical systems, and the
overcoming of narrow specialization.
Here I present a brief sketch of the new work, with this caveat: In
what follows you will find a strange mixture of high aspirations and the
crassest dismissal of nature you could possibly imagine. I try to present
a sympathetic description, but you should not think that the views summarized
here are those of the researchers at The Nature Institute. These views
are, however, powerfully symptomatic of the scientific thinking of our
day, and we would all do well to come to terms with such thinking.
First, then, three "classic" pictures invoked in many complexity studies:
First Picture. If you drop grains of sand onto
the middle of a table, you will eventually form a pile reaching all the
way to the table's edges. As you continue dropping the grains, some of
the avalanches they provoke will send little sand cascades off the table.
But, over time (and up to a point), the pile will continue to grow, with
the sides getting steeper, and with some of the avalanches getting larger
and larger. During the later stages the pile becomes susceptible to catastrophic
collapse; as far as you can know, the next grain of sand may (and likely
will) have only a tiny, local effectbut it may also trigger an avalanche
that sends much of the pile cascading onto the floor. Nothing about the
local collection of grains near the point of the next grain's impact can
tell you whether a catastrophic shift will occur. The necessary information
is distributed throughout the pile as a whole.
Second Picture. You and an acquaintance are
in prison, being separately interrogated about a crime the two of you
may or may not have committed. The prosecutor gives you this choice: if
you deny the crime and your acquaintance implicates you, you will get
life in prison and he will go free.
If you both deny the crime, you will receive a minimum sentence. If
you both confess, you will receive a medium sentence. The same choice
is offered to your acquaintance, so if he denies the crime and you implicate
him, he will be the one sentenced to life and you will go free.
This is known as the Prisoner's Dilemma. The scenario is truly devilish,
for even if you and your partner previously agreed to maintain silence
(therefore assuring yourselves of a light sentence), you both also know
that the other may be tempted to get off scott-free by confessing. So
holding to your agreement could very possibly land you in prison for life.
Can you risk that? Wouldn't it be better to confess, knowing that you
just might gain your freedom, while at worst you would be slapped with
a medium sentence? And one further question: is evolution an iterative
playing of the Prisoner's Dilemma game, through which one organism continually
seeks an advantage over the others?
Third Picture. Imagine a pot with numerous
"symbol strings" floating around in it. A symbol string is, in the simplest
case, just an ordered group of zeroes and onesfor example, here
are three strings:
Imagine further that these strings randomly "collide" with one another
and that some of the collisions result, according to a set of "grammar
rules," in the transformation of one of the strings. For example, a rule
If part of one colliding string consists of 011, and if part
of the other string is 100, then the latter sequence of digits is changed
You may, if you like, think of the first string as an "enzyme" that facilitates,
or catalyzes, the transformation of the second string. The assumption is
that the pot contains an adequate provision of zeroes and ones to supply
any additional digits required for a catalytic reaction.
It is easy to simulate a given initial pot of strings and a given set
of grammar rules by using a computer. The program simply selects pairs
of strings at random and "collides" them by applying the grammar rules.
In this way, the pot of strings can evolve. For example, given the right
initial conditions, you might find that you get an "autocatalytic set"that
is, a set of symbol strings that proves stable, continually producing
more of the very same strings it itself consists of. Such a set is self-regenerating,
and is thought by some to provide crucial insight into life's development
from a primordial "soup pot" containing molecular "strings" of atoms.
Each of these "pictures" has figured in the work of complexity theorists
over the past few decades. We can use them to help us grasp several fundamental
characteristics of the new work, as it is seen by its practitioners:
"The convergence of chemistry, physics, biology, and engineering
is upon us," according to Stanford University biologist, Lucy Shapiro
(quoted in Service 1999, p. 80). Complexity theorists are looking for
the underlying laws governing such diverse phenomena as the fragile edge
along the crest of a sand dune, the collective action of networks of neurons
in the brain, ecologies of living organisms, and the behavior of financial
markets. These theorists commonly express a yearning for "deep" truthsdeep
because possessed of the greatest possible generality.
For example, the Santa Fe Institute's Stuart Kauffman is intrigued by
the similarities between an E. coli bacterium and the IBM corporation.
"Organisms, artifacts, and organizations are all evolved structures ....
What are the laws governing the emergence and coevolution of such structures?"
(Kauffman 1995, p. 246). Referring to the pot of symbol strings and their
"grammars," Kauffman reflects,
Somehow the string images we have discussed press themselves
on me. The swirl of transformations of ideologies, fashions begetting
fashions begetting fashions, cuisines begetting cuisines, legal codes
and precedents begetting the further creation of law, seem similar in
as yet unclear ways to model grammar worlds .... (Kauffman 1995, p. 298)
Similarly reaching across disparate domains, the influential philosopher
Daniel Dennett asks why trees in the forest expend so much energy growing
tall. He answers: "For the very same reason that huge arrays of garish
signs compete for our attention along commercial strips .... Each tree
is looking out for itself and trying to get as much sunlight as possible."
Invoking the Prisoner's Dilemma, he goes on:
If only those redwoods could get together and agree on some
sensible zoning restrictions and stop competing with each other for sunlight,
they could avoid the trouble of building those ridiculous and expensive
trunks, stay low and thrifty shrubs, and get just as much sunlight as
But, like the prisoners, the trees cannot get together, and therefore
"defection from any cooperative 'agreement' is bound to pay off if ever
or whenever it occurs." Such agreements would be "evolutionarily unenforceable"
(Dennett 1995, pp. 253-55).
This drive toward generalitytoward principles that can be applied
to the development of cuisines and laws and brains and redwoods and commercial
street signsleads, as we will see, to most of the other key themes
in complexity theory.
"A general theory of complex systems," says Danish scientist Per Bak,
"must necessarily be abstract." Bak, who pioneered the investigation
of sandpile models, believes that a general theory of life "cannot have
any specific reference to actual species. The model may, perhaps, not
even refer to basic chemical processes, or to the DNA molecules that are
integral parts of any life form that we know." After all, he wonders,
what might life forms on Mars be like?
We must learn to free ourselves from seeing things the way
they are! A radical scientific view indeed! If, following traditional
scientific methods, we concentrate on an accurate description of the details,
we lose perspective. A theory of life is likely to be a theory of process,
not a detailed account of utterly accidental details of that process,
such as the emergence of humans. (Bak 1996, p. 10)
The demand for abstraction is a demand for sharp-edged, unambiguous,
precise terms, ridded as far as possible of qualitative or phenomenal
content. Numbers and the terms of logic are perhaps the primary abstractions,
and Bak observes further that theories "must be statistical"like
the laws governing sandpile avalanches. John Holland, the University of
Michigan theorist and "father of genetic algorithms," speaks a great deal
about the necessity for the scientist to "strip away details," noting
that "numbers go about as far as we can go in shearing away detail."
When we talk of numbers, nothing is left of shape, or color,
or mass, or anything else that identifies an object, except the very fact
of its existence. (Holland 1998, pp. 23-24)
The quest for generality dictates this resort to abstraction. To arrive
at generalizations regarding phenomena, we have to strip away all the
differences between the phenomena, looking only for what they have in
common. This stripping away makes it possible to assign different things
to the same class (for example, street signs and redwoods), and once we
have done this we can, without ambiguity, count and measure the members
of the classes we have formed and reason mathematically about them (for
example, formulating laws about their height).
As mentioned above, no information about local regions of the sandpile
can tell you whether the next grain added to the pile will trigger a catastrophic
collapse. The necessary information is distributed throughout the whole
of the pile. It is a matter of the interlinked balances of force upon
every grain in the pile, the shape of every grain, and so on. Therefore,
the theorists of complexity say, understanding must proceed on a holistic
"The whole is greater than the sum of its parts," says Kauffman, repeating
a common refrain (Kauffman 1995, p. 24). As a news item in Science
reports, "understanding how parts of a biological systemgenes or
moleculesinteract is just as important as understanding the parts
themselves. It's a realization that's beginning to spread" (Service 1999,
p. 80). The editors of Science, in their special issue devoted
to complexity, note that "we have taken a 'complex system' to be one whose
properties are not fully explained by an understanding of its component
parts" (Gallagher and Appenzeller 1999). In the same spirit, Kauffman
we have lost an earlier image of cells and organisms as self-creating
wholes. The entire explanatory burden is placed on the "genetic instructions"
in DNAmaster molecule of lifewhich in turn is crafted by natural
selection. From there it is a short step to the notion of organisms as
arbitrary, tinkered-together contraptions.
He adds: "Life has, I think, an inalienable wholeness" (Kauffman 1995,
The difficult and rather obscure notion of emergence is close companion
to holism. If the whole is greater than the sum of its parts, then (as
these theorists seem to view the matter) somewhere along the way from
parts to whole something in addition to the parts must have emerged.
Holland tells us that emergence "occurs only when the activities of the
parts do not simply sum to give activity of the whole." He also
says that "the hallmark of emergence is this sense of much coming from
Holland's examples of emergent phenomena may help to explain this. He
speaks of ant colonies where, "despite the limited repertoire of the individual
agentsthe antsthe colony exhibits a remarkable flexibility
in probing and exploiting its surroundings. Somehow the simple laws of
the agents generate an emergent behavior far beyond their individual capacities.
It is noteworthy that this emergent behavior occurs without direction
by a central executive."
In the same way, he speaks of collections of neurons, the immune system,
the Internet, and the global economy as systems where the emergent "behavior
of the whole is much more complex than the behavior of the parts." Likewise,
the complex dynamics of the solar system and galaxy would hardly have
been foreseeable if we had merely been given Newton's laws of motion to
contemplate, and are therefore emergent (Holland 1998, pp. 1-12). In a
similar vein, Bak remarks that "the emergence of the [complex avalanche
dynamics] of the sandpile could not have been anticipated from the properties
of the individual grains" (Bak 1996, p. 51).
All this makes clear that the holism we spoke of above does not refer
to wholes independent of, or antecedent to, the parts. The term "emergence"
testifies to a bottom-up conception of the whole: it is not that the whole
generates, and manifests itself through, its parts, but rather that the
parts, by interacting, generate the complex behavior of the whole that
"emerges." It is hardly clear, from the current literature, what this
emergent whole is thought to be, beyond the sum of its parts.
Science magazine introduced its special issue on complex systems
with the heading, "Beyond Reductionism." The claim to have escaped reductionism
is common (though not universal) among investigators concerned with complexity.
The idea is that if higher-level properties really do emerge in complex
systems, yielding wholes that are more than the sum of their parts, then
explanations of these systems must refer to the higher-level properties.
Everything cannot be "reduced" to descriptions of lower- level parts.
As Bak puts it, when the growing sandpile reaches the state where it is
subject to catastrophic collapse, the pile itself "is the functional unit,
not the single grains of sand. No reductionist approach makes sense."
To predict a catastrophic avalanche in traditional, reductionist terms,
one would have to measure everything everywhere [in the pile]
with absolute accuracy, which is impossible. Then one would have to perform
an accurate computation based on this information, which is equally impossible.
(Bak 1996, pp. 60-61)
These researchers therefore accept, for example, that there can be a
legitimate science of economics, whose explanations need not be reduciblecertainly
not in any practical senseto the motions of atoms. Humans and societies
and commercial activities have all emerged in the course of evolution,
and in order to understand them we have to speak directly of their emergent
featuresthings like rational agents, markets, prices, interest rates,
and so onnot just the lower-level entities from which they emerged.
Depending on what we are trying to explain, we must resort to different
levels of explanation, or descriptionto use a phrase that
often turns up.
Self-organization. References to self-organization
abound in the literature on complex systems. The sandpile, says Bak, has
"organized itself" into the "critical state" where it is susceptible to
unpredictable avalanches of all sizes. Kauffman's pot of grammar-obeying
symbol strings spontaneously organizes itself into a self-regenerating
"autocatalytic set," suggesting to him that an oceanic soup of primordial
molecules could do the sameand this principle of self-organization,
he believes, underwrites the entire evolutionary drama:
I propose that much of the order in organisms may not be the
result of selection at all, but of the spontaneous order of self-organized
systems. Order, vast and generative, not fought for against the entropic
tides but freely available, undergirds all subsequent biological evolution.
(Kauffman 1995, p. 25)
Kauffman has practically made a mantra out of the phrase, "order for
free." Others are more modest; they do not say "for free" but only "somehow."
Speaking of the "spontaneous self-organization" through which individuals
form economies, cells form organisms, birds form flocks, and atoms form
molecules, Mitchell Waldrop observes:
In every case, groups of agents seeking mutual accommodation
and self-consistency somehow manage to transcend themselves, acquiring
collective properties such as life, thought, and purpose that they might
never have possessed individually. (Waldrop 1992, p. 11)
Again, this notion of self-organization is integral to the others we
have discussed. If a new and coherent whole emerges bottom-up from interacting
parts, then, somehow, it appears that the parts have transcended
themselves and "self-organized" so as to produce the whole.
Reliance on Models and Algorithms.
The drive toward simplicity dictating the goals of generality and abstraction
is also evident in an extreme reliance upon models. Holland (1998, p.
24) observes that "shearing away detail is the very essence of model building.
Whatever else we require, a model must be simpler than the thing
modeled." We are a long way here from Goethe's contention that the phenomenon,
rightly and fully understood, is the theory, and that there is
no need for an intervening model. Similarly, Bak writes,
The beauty of the model can be measured as the range between
its own simplicity and the complexity of the phenomena that it describes,
that is, by the degree to which it has allowed us to condense our descriptions
of the real world. (Bak 1996, p. 44)
The model offering this condensed description is, of course, a mechanical
one, and today this means more and more that the description is algorithmic,
or recipe-like, in the way that computer programs are algorithmic. More
likely than not, in fact, the model just is a computer simulation.
Daniel Dennett sees three key features in all algorithmic explanations:
- Substrate neutrality. It doesn't matter what sort of material
apparatus executes the algorithm as long as the logical structure of
the recipe is preserved.
- Underlying mindlessness. A dumb mechanism can do the job.
- Guaranteed results. Follow the recipe and the result is assured.
You can think of these three principles as representing the movements
toward abstraction, mechanism, and logical purity, respectivelywhich
are actually a single movement (Talbott 2000).
Those are some of the key themes and intellectual commitments guiding the
work on complex systems, as voiced by a number of the pioneers in the field.
In the next issue of In Context I will attempt an assessment of these
themes and commitments. Here I would like merely to suggest one question
that seems to me fundamental for any such assessment:
Are the rather obscure appeals to "emergence," "self-organization,"
and "holism" simply the result of reintroducing, magically and without
sufficient justification, some of the richness of the original phenomenarichness
that was "sheared away" in the drive toward generality and abstraction?
After all, if the complexity theorist's explanations are to explain real
phenomena, then somehow the qualitative phenomena that were sacrificed
to abstraction and mechanical modeling have to be regained at the end
of the explanatory process. But is saying that they just happened to "emerge"
a satisfactory way to get them back into the picture? Or should we instead
pursue a qualitative science that refuses to sacrifice the phenomena to
abstraction in the first place?
Go to the sequel of this
Bak, Per (1996). How Nature Works: The
Science of Self-Organized Criticality. New York: Springer-Verlag.
Dennett, Daniel C. (1995). Darwin's Dangerous
Idea: Evolution and the Meanings of Life. New York: Simon and Schuster.
Gallagher, Richard and Tim Appenzeller (1999). "Beyond
Reductionism." Science, vol. 284 (April 2), p. 79.
Holland, John H. (1998). Emergence: From Chaos
to Order. Reading MA: Addison-Wesley.
Kauffman, Stuart (1995). At Home in the Universe:
The Search for the Laws of Self-Organization and Complexity. Oxford:
Oxford University Press.
Service, Robert F. (1999). "Exploring the Systems
of Life." Science, vol. 284 (April 2), pp. 80-83.
Talbott, Stephen L. (2000). "The Ghostly Machine." In
Context (newsletter of The Nature Institute) #4 (Fall), pp. 2-3, 20.
Available at http://www.netfuture.org/ni/ic/ic4/ghost.html.
Waldrop, M. Mitchell (1992). Complexity: The
Emerging Science at the Edge of Order and Chaos. New York: Simon and
Original source: In Context (Fall, 2001, pp. 15-19); copyright
2001 by The Nature Institute
Steve Talbott :: The Lure of Complexity