| In
Context #7 (Spring,
2002, pp. 19-23); copyright 2002 by The Nature Institute
(This is the second part of a two-part essay. The first part appeared
in our Fall, 2001 issue and is available here.
Anyone who lives in an earthquake zone knows that mild earthquakes are
much more common than powerful, devastating ones. What you might not expect,
however, is that a simple, straight-line mathematical relationship known
as a "power law" tells you what percentage of earthquakes will exceed
any given energy. Even more surprisingly, you can derive the same sort
of law showing what percentage of cities will be larger than a given size.
Or what percentage of fjords in Norway will exceed a given length. Other
power laws occur when you look at word-usage patterns in texts, global
temperature variations, the occurrence of traffic jams, stock market performance,
and (as discussed in part 1) avalanches in artificially constructed sand
piles.
In each of these domains any attempt at causal analysis leads you to
the complex, nearly unanalyzable interplay of countless factors. (Try
to tabulate all the reasons why individuals migrate to and from any particular
city!) And yet, in every case this interplay yields an elegant, straight-line
power law. This is the kind of thing that appeals to so many complexity
theorists, convincing them that they are on the track of a grand, unified
theory of nearly everything.
Seeking Universality
A planet in motion, obeying Newton's laws, does not present a picture
of complexity. By contrast, the geological, biological, and evolutionary
realities of a landscape (such as a fjord or region of earthquake faults)
are complex. This, at least, is the thought Per Bak expresses when
he says, "we do not live in a simple, boring world consisting only of
planets orbiting other planets, regular infinite crystals, and simple
gases or liquids." He goes on: "Crystals and gases and orbiting planets
are not complex, but landscapes are" (Bak 1996, pp. 4-5).
Bak, who is a pioneer of complexity theory, rejoices in the challenges
of the landscape. But note the slight oddity here. A planet is, after
all, the bearer of its landscapes, so it must be at least as complex as
any one of those landscapes. Only when we think away all the planet's
rich detail, reconceiving it abstractly as little more than a mathematical
point in Newtonian motion, does its complexity fall from view. We should
keep in mind that "boring" simplicity characterizes a way of theorizing
about phenomena, not the phenomena themselves.
And the irony is that, in embracing landscapes and other complex phenomena,
complexity theorists such as Bak rely on their own abstract simplifications,
along with a fierce resolve to "shear away detail." So they end up merely
repeating, on this new front, the astronomer's sacrifice of the world's
fullness. Where celestial mechanics reduces the planet to a locus for
interaction of a few simple mathematical laws, these researchers now reduce
the landscape to a locus for interaction of a few—rather different
and more statistical—mathematical laws. The landscapes that, in their
qualitative and particular reality, are so invisible to the astronomer
plotting a planet's Newtonian trajectory in space seem to be nearly as
invisible to the complexity theorist looking for deep, context-free truths.
All too often the study of complexity begins to look like an abandonment
of the phenomena the researchers originally set out to investigate.
Bak wants a general theory of life so profound that it "cannot have
any specific reference to actual species"—a theory that doesn't get
sidetracked by "utterly accidental details ... such as the emergence of
humans" (Bak 1996, p. 10). Likewise, speaking of the various power laws,
he observes that "since these phenomena [that is, statistical patterns]
appear everywhere, they cannot depend on any specific detail whatever."
And again: theorists who are going after fundamental principles must "avoid
the specific details, such as the next earthquake in California." Rather,
Our strategy is to strip the problem of all the flesh until we are
left with the naked backbone and no further reduction is possible. We
try to discard variables that we deem irrelevant. In this process we
are guided by intuition. In the final analysis, the quality of the model
relies on its ability to reproduce the behavior of what it is modeling.
(Bak 1996, p. 42)
But, just as Bak refers to "phenomena" when he is really speaking only
of statistical patterns, so, too, the "behavior" he alludes to here is
hardly the behavior of any particular thing. The particulars—such
as the individual character of the fault line that will produce California's
next earthquake—have been ruled out of the picture in advance. So
the behavior at issue is, again, a matter of highly abstract, statistical
generalities.
What seems never to occur to Bak and many of his fellow researchers
is that the grand unifying theory they are stalking may be grand in scale,
and may be unifying, but for this very reason promises to be more or less
trivial. Don't get me wrong, however. There are doubtless interesting
ways to elucidate the power laws we can abstract from diverse phenomena.
It's just that the act of abstraction here has been so severe—so
many aspects of the phenomena we were looking at have been left out—that
our discoveries, while interesting in their own right, will tell us almost
nothing about these particular phenomena. The scholar who is seeking to
understand the population growth of Cairo is much better advised to explore
the relevant cultural, social, political, economic, geographic, and ecological
realities bearing on this one place than to dwell on the elegance of a
straight-line graph showing the frequency of occurrence of cities with
different population levels. It's not clear who among students of particular
phenomena will find much use, or much revelation, in that graph.
Explanations that do not depend on specific details will fail to elucidate
those details. If, at the outset of our investigations, we strip away
every concrete particular we can, then we will hardly arrive at any profound
understanding of concrete, particular phenomena. But what else is there
to understand? It was the whole concern of the key figures of the Scientific
Revolution to shun the abstract cerebrations of the medieval schoolmen
and open their eyes to the world around them. Should science reject this
stance now, preferring (in Bak's words) "to free ourselves from seeing
things the way they are"?
The problem with a scientific method based on maximum generalization
and abstraction is that the more it succeeds—that is, the more general
and abstract its results become—the shallower they tend to be. They
tell us less and less about the particular contexts we wish to understand.
Look at it this way. If you let X represent anything at all and let
1 stand for "exists" and 0 for "does not exist," then it is true to say
of every existent thing (every X) in the universe: "X = 1". By the standard
of generality, abstraction, and precision, this must be just about the
deepest truth of all. And, perhaps in some sense worthy of meditation,
it really is. But as a scientific statement it is vacuous. Its vacuity
is directly related to its generality. Precisely because it tries to tell
us something about everything, it doesn't tell us much about anything
in particular.
In our drive toward generality and abstraction, we end up with what
we ask for. If, for example, we are determined to reckon only with what
is generally true of both living organisms and systems of inanimate, mineral
objects, we will end up seeing only the inanimate, mineral aspects of
living organisms. We will get a theory that "connects" diverse things,
but in the process loses the things we are connecting.
Flight from Phenomena
The abandonment of detail by complexity theorists sometimes begins to look
like an outright abandonment of phenomena. In the first part of this article
I mentioned Stuart Kauffman's pot of symbol strings. A symbol string is
just an ordered group of zeroes and ones—for example:
011
101011
11100
Kauffman asks us to imagine these strings floating around rather like
molecules in a pot of liquid, interacting with each other according to
a set of "grammar rules." That is, when strings "collide," zeroes and
ones may be appended to a string, or deleted, or changed (drawing as necessary
upon a reservoir of available digits). As the grammar rules are applied
to the colliding strings, the latter may "evolve" in interesting ways.
Now, you may well wonder just what sort of pot this is. How do numbers
interact in a pot? Kauffman describes the process almost as if it were
a matter of physics—a matter of real materials obeying real laws.
He speaks (albeit in quotation marks) of "enzymes" and "substrates" and
"strings" that "collide." And he considers his strings to be models:
Bear in mind that we can consider our strings as models of molecules,
models of goods and services in an economy, perhaps even models of cultural
memes such as fashions, roles, and ideas. (Kauffman 1995, p. 287)
Yet Kauffman shows no sign of reckoning with the stubborn realities
of an actual model that works. What excites him is an abstract set of
purely logical relations. Yes, his excitement quite evidently arises because
he imagines these relations to be applicable to real phenomena; but he
is not so much engaged in the study of the phenomena as in the elaboration
of his logical scheme.
Among complexity theorists there is often a strange disregard of the
distinction between abstract thought structures and real-world phenomena,
including real models. But there is, after all, a radical difference between
a purely notional pot of symbol strings, conceived as a set of logical
relations, and any actual embodiment of these relations. You can see this
difference even if the embodiment takes form only as a computer simulation,
where the zeroes and ones are translated into electrical patterns in silicon
and light patterns on a screen.
Once you have such embodiment, your thought experiment comes under constraints
that were absent from the purely abstract logical relations. The abstract
relations just are what they are—eternally, you might say—but
the embodiment is an entirely different matter. To begin with, a computer
simulation of the symbol pot can be sustained only because a massive technical
infrastructure is in place and because engineers have carefully designed
the simulation hardware and software. And even once it is up and running,
the simulation might take an unexpected turn due to an electrical power
failure, or I might spill coffee into the computer's circuitry, or a bug
in the supporting software might supervene, or a giant meteor might strike
the earth, or the hardware might (and over time certainly will) succumb
to normal wear and tear. Contingencies of this sort are exactly what make
the difference between the purity of logic and the reality of the world.
This is the kind of reflection that seems wholly irrelevant to a person
enamoured of disembodied abstractions. But it is exactly what should matter
to anyone who, like Kauffman, takes the abstractions as key to understanding
the evolution of real (embodied) life forms.
This point is worth pressing further.
Physics or Fancy?
You may have heard of the Game of Life. It divides your computer screen
into a fine-meshed rectangular grid wherein each tiny cell can be either
bright or dark, on or off, "alive" or "dead." The idea is to start with
an initial configuration of bright or live cells and then, with each tick
of the clock, see how the configuration changes as the software applies
these simple rules:
- If exactly two of a cell's eight immediate neighbors are alive at
the clock tick ending one interval, the cell will remain in its current
state (alive or dead) during the next interval.
- If exactly three of a cell's immediate neighbors are alive, the cell
will be alive during the next interval regardless of its current state.
- And in all other cases—that is, if less than two or more than
three of the neighbors are alive—the cell will be dead during the
next interval.
You can, then, think of a cell as dying from loneliness if too few of
its neighbors are alive, and dying from over-crowding if too many of them
are alive.
Now, what interested the early students of this game in the 1960s was
the fact that, given well-selected initial configurations, remarkable
patterns are produced. A "glider" composed of lit cells might sail serenely
across the screen. A "glider gun" might produce an endless series of gliders.
Another entity might swallow up any glider that makes contact with it,
while itself remaining intact. There are static patterns, blinking patterns,
rotating patterns, and forms that can evolve and even reproduce themselves
in endlessly fascinating ways.
What is still more remarkable is the conclusion some researchers eventually
drew from all this. Full of excitement as they watched their enchanted
screens, they began to suspect that they were being initiated into the
deepest secrets of biological evolution, of reproduction, and of life
itself. (The complexity discipline known as Artificial Life grew out of
this work.)
Referring to the Game of Life and the three-part law governing its performance,
philosopher Daniel Dennett has remarked that "the entire physics of the
Life world is captured in that single, unexceptionable law" (Dennett 1995,
p. 167). Moreover, "our powers of prediction [regarding the Life world]
are perfect: there is no noise, no uncertainty, no probability less than
one" (Dennett 1991, p. 38).
But, as we have seen, the "unexceptionable law" is hardly a law of physics,
and it is a little odd to talk about our "powers of prediction" where
only thought relations are in view. If, on the other hand, we really are
talking about a physical machine equipped to represent the thought relations
in some embodied form—a machine whose activity we might now venture
to predict—then the problems of a sustainable power supply, spilled
coffee, and all the rest cannot be avoided. What we have, contrary to
Dennett, is noise, no certainty, and no probability equal to one.
It is not that brilliant thinkers such as Dennett would fail to recognize
this obvious truth. It's just that the truth doesn't seem to count for
much in their thinking. The "something else" that enables us to talk about
the phenomenal world instead of the pure thought relations of an assemblage
of abstractions draws no particular attention from them.
What's happening here is that the world has been reconceived as a machine,
the machine has been reconceived as a pure abstraction (for example, as
software—see Talbott 2000), and the theorists, taking up their stance
within this realm of abstraction, merrily spin out new thought relations
to "explain" the world. But since their method has instructed them to
avoid the real world as far as possible by shearing away detail, they
remain mostly in a kind of abstract never-neverland. The rules of the
Game of Life do not explain what I see on my computer screen even when
I am running the Game of Life. Any such explanation would have to reckon
with power supplies, programmers, and a great deal else.
The Consequences of Abandoning the World
I have restricted myself here largely to the problem of generality and abstraction.
However, I should offer at least these exceedingly brief remarks about some
of the other complexity themes I alluded to in Part 1.
Reductionism.
The claim by some complexity researchers to have moved "beyond reductionism"
is not justified by the facts. The decisive and damaging act of reduction
within conventional science has always been the reduction, in thought,
of the qualitative world of phenomena to abstract, machine-like models
devoid of qualities. Complexity theorists seem at least as committed to
this reduction as any other scientists. It is true that many of these
theorists want to grant "irreducible" status to higher-level orders of
reality such as economics, animal behavior, and human thinking. But this
hardly makes much difference if the concepts available for dealing with
these realities are as machine-like and as qualitatively emptied as the
concepts previously applied to atoms and photons.
Holism.
There can be no holism without the qualities that complexity researchers
strip from the world. It is the nature of qualities to interpenetrate
one another, and only through such mutual interpenetration can a whole
express itself through each of its parts. Without qualities, there are
featureless "particles" side by side in changing arrangements, but nothing
to make an integral unity of them—nothing to give the assemblage
the sort of distinctive, expressive character enabling us to recognize
a whole. Where theorists do speak of wholes, you will find that either
their terms do not justify such speaking, or else they have surreptitiously
imported qualitative considerations without acknowledging them and without
giving them a proper place in their method.
The literature of complexity presents us with countless references to
wholes that are "more than the sum of their parts." But those who speak
this way don't seem to take their own words seriously. If they did, they
would be forced to grant that the whole—the "something more than
the sum"—remains even after all the parts have been removed. They
would, for example, strive to grasp the generative idea, the productive
unity, of the rose—the unity that expresses itself through root,
leaf, and flower but is by no means a mere collection (sum) of roots,
leaves, and flowers. (See "Of Ideas and Essences" in this issue.)
Disciplinary convergence.
The loss of any foundation for holism within complexity studies suggests
that the hope for meaningful disciplinary convergence is probably misplaced.
Confusion on this point results from a failure to see the double aspect
of abstract generality. It is true, on the one hand, that we can homogenize
many disciplines by seeing only their projections upon the same abstract
grid. In this way, chemistry, biochemistry, genetics, botany, zoology,
evolutionary theory, and cosmology have increasingly come to be dominated
by the same sort of remote, non-experiencable "entities"—particles,
atoms, molecules, genes—that first colonized the physicists' imagination.
But the interdisciplinary unity being sought here, as I have been arguing,
is an emptied unity—the unity that comes from the one-sided urge
to strip away differences and refuse to consider them. The study of cities
and of earthquakes--or the study of plants and of minerals--become the
"same" studies.
By contrast, a true unity arises when we recognize differences while
at the same time bringing those very differences into meaningful
relationship—an essentially qualitative undertaking. We would not
see the expressive unity of Hamlet if we turned away from the uniqueness
of each character, looking only for what they had in common. There would
be nothing significant left to bring into unity.
So the other tendency of abstract generality—and this is what has
driven the fragmentation of science from the beginning—is to rob
the various disciplines of the distinctive elements through which they
might have entered into muscular relationship. An increasingly featureless
commonality replaces mutual illumination and complementation. One is left
with no scientific tools for relating the world's different phenomena
to each other (as opposed to obscuring their differences), so compartmentalism
remains a major affliction. How meaningfully can Artificial Life investigators,
on the one hand, and naturalists observing living frogs and trees, on
the other, relate their separate undertakings?
Emergence.
When your scientific work repeatedly brings you up against vaguely conceived
"emergent" phenomena—phenomena that seem to arise from out of nowhere—you
might reasonably wonder whether your models and explanatory mechanisms
have omitted something important. While most complexity theorists seem
undisturbed by this thought, I have been suggesting above that the omission
has in fact been as radical as it could possibly be: what the models tend
to leave out is the phenomenal world as such, with all its contingencies
and with all its causal, or generative, powers. To these investigators,
therefore, all actual phenomena are likely to appear emergent simply
because all phenomena present a qualitative fullness that has intentionally
been stripped from the theoretical apparatus employed to explain them.
What the situation requires is a fundamental reconsideration of method.
Most importantly, this means a reconsideration of the founding decision
within science to ignore qualities, since it turns out that to ignore
qualities is to ignore the world. There is no way to get from the sheer
abstractions of complexity theory back to the world of phenomena, except
by re-introducing qualities "through the back door" when no one is looking—and
then exclaiming about the "emergent" wonders that arise. It would be much
more sound scientifically to face qualities up front, wrestling through
to an understanding of their proper place in the scientific enterprise.
Looking for the Positive
I have left a huge amount out of my cursory survey, and this is the
place to acknowledge the fact. I have said nothing, for example, about
the promise of chaos theory (about which I hope to write in the future).
And I have not noted that some investigators, such as the Nobel prize-winning
chemist, Ilya Prigogine, avoid at least some of the excesses dominating
the field. (See Grégoire and Prigogine 1989; Prigogine and Stengers 1984.)
Let me conclude, then, on a somewhat more balanced note. It is certainly
arguable—as I have indeed argued—that the tools complexity researchers
bring to their work are even more severely constrained, more one-sidedly
abstract and quantitative, less tolerant of qualities, less relevant to
the richness of the world given through observation, than was the case
with much of the science they are trying to reform.
But it is also true that the students of complexity really are seeking
a better science. Their desire to overcome narrow compartmentalization
is genuine, and this means they are acknowledging broader contexts—they
are actually seeing nature's diversity—at least long enough
to wheel out the heavy artillery of abstraction with which they proceed
to level the newly acknowledged landscape. Moreover, the hunger for "emergent"
realities surely reflects a sense that we need to reckon scientifically
with a larger reality than the traditional "hard" sciences have addressed.
Researchers looking at earthquake faults or economic transactions or the
population growth of cities no longer accept the charge that they are
on secondary scientific ground whenever they speak, not of particles,
but of the phenomena they can actually observe.
This willingness to observe, for purposes of explanation, a much fuller
world is the main hope of complexity work. The problem, as we have seen,
is that the kinds of explanation employed immediately obscure the fuller
world the researchers are straining toward. This, of course, is where
Goethean scientists can play a helpful role by demonstrating the possibilities
of a qualitative science that honors the phenomena in all their richness.
References
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.
Dennett, Daniel C. (1991). "Real Patterns," Journal
of Philosophy, vol. 87, pp. 27-51.
Kauffman, Stuart (1995). At Home in the Universe:
The Search for the Laws of Self-Organization and Complexity. Oxford:
Oxford University Press.
Nicolis, Grégoire and Ilya Prigogine (1989). Exploring
Complexity: An Introduction. New York: W. H. Freeman.
Prigogine, Ilya and Isabelle Stengers (1984). Order
Out of Chaos: Man's New Dialogue with Nature. New York: Bantam.
Talbott, Stephen L. (2001). "The Trouble with Qualities,"
In Context #6 (Fall, 2001), pp. 3-4.
Talbott, Stephen L. (2000). "The Ghostly Machine," In
Context #4 (Fall, 2000), pp. 3-4, 20.
Original source: In Context (Spring, 2002, pp. 19-23); copyright
2002 by The Nature Institute
Steve Talbott :: The Lure of Complexity (Part 2)
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