The Competitiveness of Nations
in a Global Knowledge-Based Economy
May 2005
Stuart A. Kauffman
At Home in the Universe
Chapter 12 An Emerging Global Civilization
Oxford
University Press, 1995, 273-304
Index
Technological Coevolution and Economic Takeoff
Hard rain had started. Brian Goodwin and I dodged under low-hanging
brush into a squat rectangular opening in a low concrete structure buried into
the crest of a hillside overlooking Lago di Lugano in northern Italy, a few
kilometers from the Swiss border. We
found ourselves in a World War I bunker peering though a horizontal slot made
for machine guns as the rain pelted the lake. We were able to see the imagined route where
the hero of Hemingway’s A Farewell to Arms made his way across the lake
to the Swiss shore a scant three kilometers away. I had traversed the same route in a small
rented sailboat with my young children, Ethan and Merit, two days before and
bought them hot chocolate as fortification for our return crossing. Brian was visiting us at the home of my
mother-in-law, Claudia, in Porto Ceresio, set on the lake’s edge. He and I figured we would think through the
implications of autocatalytic sets and functional organization.
Brian Goodwin is a close friend, a Rhodes Scholar from
Montreal years ago, and a wonderful theoretical biologist. I first met him in the office of Warren
McCulloch, one of the inventors of cybernetics, at the Research Laboratory of
Electronics at MIT in 1967. Brian, and
several years later my wife, Elizabeth, and I, had had the privilege of being
invited to live with Warren and his wife, Rook, for several months. When he had visited McCulloch, Brian was
working on the first mathematical model of large networks of genes interacting
with one another to control cell differentiation. I still remember the mixture of awe and dread
that crossed my heart when, as a young medical student stumbling forward with
my own first efforts at the Boolean network models I have described, I fell
upon Goodwin’s book, The Temporal Organization of Cells, in a bookstore
in San Francisco. Every young scientist,
at one point or another, faces this moment: “Oh, God, someone has already
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done it!” Typically,
someone hasn’t quite done what you have set out to do, so your entire life,
about to vanish into an abyss of lost dreams, can find a narrow passage forward
toward some upland pasture. Brian had
not done quite what I was trying to do, although the spirit was similar. We have been fast friends for years. I deeply admire his sense of the unseen deep
issues in biology.
“Autocatalytic sets,” mused Brian as we watched rain
turn to hail and spatter down, “those autocatalytic sets are absolutely natural
models of functional integration. They
are functional wholes.” Of course, I
agreed with him. Some years before, two
Chilean scientists, Humberto Maturana, himself a close colleague of McCulloch,
and Francisco Varela, had formulated an image of what they called autopoesis. Autopoetic systems -are those with the power
to generate themselves. The image is
older than Maturana, who I later met in India, and Varela, who has become a
good friend. Kant, writing in the late
eighteenth century, thought of organisms as autopoetic wholes in which each
part existed both for and by means of the whole, while the whole existed for
and by means of the parts. Goodwin and
his colleague Gerry Webster had written a clean exposition of the intellectual
lineage leading from Kant to contemporary biology. They had noted that the idea of an organism as
an autopoetic whole had been replaced by the idea of the organism as an expression
of a “central directing agency.” The
famous biologist August Weismann, at the end of the nineteenth century, developed
the view that the organism is created by the growth and development of specialized
cells, the “germ line,” which contains microscopic molecular structures, a
central directing agency, determining growth and development. In turn, Weismann’s molecular structures
became the chromosomes, became the genetic code, became the “developmental
program” controlling ontogeny. In no
small measure, the intellectual lineage is straight from Weismann to today. In this trajectory, we have lost an ealier
image of cells and organisms as self-creating wholes. The entire explanatory burden is placed on the
“genetic instructions” in DNA - master molecule of life - which in turn is
crafted by natural selection. From there
it is a short step to the notion of organisms as arbitrary, tinkered-together
contraptions. The code can encode any
program, and hence any tinkered bric-a-brac that selection may have cobbled
together.
Yet, as we saw in Chapter 3, it is not implausible
that life emerged as a phase transition to collective autocatalysis once a
chemical minestrone, held in a localized region able to sustain adequately high
concentrations, became thick enough with molecular diversity. A collectively autocatalytic set of molecules
- at least in silico, as we have seen - is capable of reproducing
itself, dividing into two “blobs” capa-
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ble of heritable variation, and hence, following Darwin’s argument, capable
of evolution. But in a collectively autocatalytic
set, there is no central directing agency. There is no separate genome, no DNA. There is a collective molecular autopoetic
system that Kant might have been heartened to behold. The parts exist for and by means of the whole;
the whole exists for and by means of the parts. Although not yet achieved in a laboratory
beaker, an autocatalytic set is not mysterious. It is not yet a true organism. But if we stumbled on some evolving or even
coevolving autocatalytic sets in a test tube or hydrothermal vent, we’d tend to
feel we were looking at living systems.
Whether or not I am right that life started with
collective autocatalysis, the mere fact that such systems are possible should
make us question the dogma of a central directing agency. The central directing agency is not necessary
to life. Life has, I think, an
inalienable wholeness. And always has.
So Brian and I actually had a large agenda in the
background as we squatted, wondering at the origins of life and the regularity
of war and death spewing out the concrete machine-gun slot before us. We could see that collectively autocatalytic
sets of molecules such as RNA or peptides announce their functional wholeness
in a clear, nonmystical way. A set of
molecules either does or does not have the property of catalytic closure. Catalytic closure means that every molecule in
the system either is supplied from the outside as “food” or is itself
synthesized by reactions catalyzed by molecular species within the
autocatalytic system. Catalytic closure
is not mysterious. But it is not a
property of any single molecule; it is a property of a system of molecules. It is an emergent property.
Once we have autocatalytic sets, we can see that such
systems could form an ecology of competitors and mutualists. What you “squirt” at me may poison or abet
some reaction of mine. If we help one
another, we may have advantages of trade. We can evolve toward close coupling,
symbiosis, and the emergence of higher-ordered entities. We can form a molecular “economy.” Ecology and economy are already implicit in coevolving
autocatalytic sets. Over time, Brian and
I imagined, such an ecology of autocatalytic systems interacting with one
another, coevolving, would explore an increasing domain of molecular
possibilities, creating a biosphere of expanding molecular diversity in some as
yet unclear way. A kind of molecular
“wave front” of different kinds of molecules would propagate across the globe.
Later, the same image would begin to appear dimly like
a wave front of technological innovations and cultural forms, like an emerging
global civilization created by us, the descendants of Homo habilis. who
may
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have first wondered at his origins and destiny around some sputtering
fire. Perhaps it was on the shore of
Lago di Lugano one night. Perhaps hard rain fell.
The rain stopped; we crawled out of the bunker and
headed down to Claudia’s house, hoping that she and Elizabeth had made polenta
and funghi as well as minestrone. We
felt that our vision was promising. But
we knew we were stuck. We hadn’t a clue
how to generalize from an image of proteins or RNA molecules acting on one
another to a broader framework. We would
have to wait six years until Walter Fontana invented a candidate for the
broader framework.
Walter Fontana is a young theoretical chemist from
Vienna. His thesis work, with Peter
Schuster, concerned how RNA molecules fold into complex structures, and how
evolution of such structures might occur. Fontana and Schuster, like Manfred Eigen, like
me, like others, were beginning to consider the structure of molecular fitness
landscapes of the type discussed in Chapter 8.
But Fontana harbored more radical aims. Visiting Eigen’s group at Göttingen, Fontana
found himself in conversation with John McCaskill, an extremely able young
physicist engaged in theory and experiments evolving RNA molecules. McCaskill, too, had a more radical aim.
Turing machines are universal computational devices
that can operate on input data, which can be written in the form of binary
sequences. Referring to its program, the
Turing machine will operate on the input tape and rewrite it in a certain way. Suppose the input consisted of a string of
numbers, and the machine was programmed to find their average value. By changing 1 and 0 symbols on the tape, the
machine will convert it into the proper output. Since the Turing machine and its program can themselves
be specified by a sequence of binary digits, one string of symbols is
essentially manipulating another string. Thus the operation of a Turing machine on an
input tape is a bit like the operation of an enzyme on a substrate, snipping a
few atoms out, adding a few atoms here and there.
What would happen, McCaskill had wondered, if one made
a soup of Turing machines and let them collide; one collision partner would act
as the machine, and the other partner in the collision would act as the input
tape. The soup of programs would act on
itself, rewriting each other’s programs, until... Until what?
Well, it didn’t work.
Many Turing machine programs are able to
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enter infinite loops and “hang.” In such a case, the collision partners become
locked in a mutual embrace that never ends, yielding no “product” programs. This attempt to create a silicon
self-reproducing spaghetti of programs failed. Oh well.
On the wall at the Santa Fe Institute hangs a cartoon.
It shows a rather puzzled fuzzy-headed
kid pouring fluid into a beaker, a mess all over a table, and feathers flying
all over the room. The caption reads: “God
as a kid on his first try at creating chickens.” Maybe before the Big Bang, the chief architect
practiced on some other universe.
Fontana arrived at the institute, full of RNA
landscapes, but like most inventive scientists, found a way to follow his more
radical dream. If Turing machines “hung”
when operating on one another, he would move to a similar mathematical
structure called the lambda calculus. Many
of you know one of the offspring of this calculus, for it is the programming
language called Lisp. In Lisp, or the
lambda calculus, a function is written as a string of symbols having the
property that if it attempts to “operate” on another string of symbols, the
attempt is almost always “legitimate” and does not “hang.” That is, if one function operates on a second
function, there is almost always a “product” function.
More simply, a function is a symbol string. Symbol strings operate on symbol strings to
create new symbol strings! Lambda
calculus and Lisp are generalizations of chemistry where strings of atoms - called
molecules - act on strings of atoms to give new strings of atoms. Enzymes act on substrates to give products.
Naturally, since Fontana is a theoretical chemist, and
since lambda and Lisp expressions carry out algorithms and since Fontana wanted
to make a chemical soup of such algorithms, he called his invention algorithmic
chemistry, or Alchemy.
I think Fontana’s Alchemy may be an actual alchemy
that begins to transform how we think of the biological, economic, and cultural
world. You see, we can use symbol
strings as models of interacting chemicals, as models of goods and services in
an economy, perhaps even as models of the spread of cultural ideas - what the
biologist Richard Dawkins called “memes.” Later in the chapter, I will develop a model
of technological evolution in which symbol strings stand for goods and services
in an economy - hammers, nails, assembly lines, chairs, chisels, computers. Symbol strings, acting on one another to
create symbol strings, will yield a model of the coevolution of technological
webs where each good or service lives in niches afforded by other goods or
services. In a larger context,
symbol-string models may afford a novel and useful way to think about cultural
evolution and the emergence of a global civilization, as we deploy ideas,
ideals, roles, memes to act on one another in a
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never-ending unfolding rather like the molecular “wave front” expanding
outward in a supracritical biosphere. Walter created our first mathematical language
to explore the cascading implications of creation and annihilation that occurs
in “soups” of these symbol strings as they act on and transform one another.
What happened when Fontana infected his computer with
his Al-chemical vision? He got
collectively autocatalytic sets! He
evolved “artificial life.”
Here is what Walter did in his early numerical
experiments. He created a “chemostat” on
the computer that maintained a fixed total number of symbol strings. These strings bumped into one another just
like chemicals. At random, one of the
two strings was chosen as the program; the other, as the data. The symbol-string program acted on the
symbol-string data to yield a new symbol string. If the total number of symbol strings exceeded
some maximum, say 10,000, Fontana randomly picked one or a few and threw them
away, maintaining the total at 10,000. By
throwing away random symbol strings, he was supplying a selection pressure for
symbol strings that were made often. By
contrast, symbol strings that were rarely made would be lost from the
chemostat.
When the system was initiated with a soup of randomly
chosen symbol strings, at first these operated on one another to create a
kaleidoscopic swirl of never-before-seen symbol strings. After a while, however, one began to see the
creation of strings that had been encountered before. After a while, Fontana found that his soup had
settled down to a self-maintaining ecology of symbol strings, an autocatalytic
set.
Who would have expected that a self-maintaining
ecology of symbol strings would come popping out of a bunch of Lisp expressions
colliding and “rewriting” one another? From
a random mixture of Lisp expressions, a self-maintaining ecology had
self-organized. Out of nothing. What had Fontana found?
He had stumbled into two types of self-reproduction. In the first, some Lisp expression had evolved
as a general “copier.” It would copy
itself, and copy anything else. Such a
highly fit symbol string rapidly reproduced itself and some hangers-on and took
over the soup. Fontana had evolved the
logical analogue of an RNA polymerase itself made of RNA, hence a ribozyme RNA
polymerase. Such an RNA would be able to
copy any RNA molecule, including itself. Remember, Jack Szostak at Harvard Medical
School is trying to evolve just such a ribozyme ENA polymerase. It would count as a kind of living molecule.
But Fontana found a second type of reproduction. If he “disallowed” general copiers, so they
did not arise and take over the soup, he found that he evolved precisely what I
might have hoped for: collectively auto-
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catalytic sets of Lisp expressions. That is, he found that his soup evolved to
contain a “core metabolism” of Lisp expressions, each of which was formed as
the product of the actions of one or more other Lisp expressions in the soup.
Like collectively autocatalytic sets of RNA or protein
molecules, Walter’s collectively autocatalytic sets of Lisp expressions are
examples of functional wholes. The holism
and functionality are entirely nonmystical. In both cases, “catalytic closure” is
attained. The whole is maintained by the
action of the parts; but by its holistic catalytic closure, the whole is the
condition of the maintenance of the parts. Kant would, presumably, have been pleased. No mystery here, but a clearly emergent level
of organization is present.
Fontana called copiers “level-0 organizations” and
autocatalytic sets “level-1 organizations.” Now working with the Yale biologist Leo Buss, he
hopes to develop a deep theory of functional organization and a clear notion of
hierarchies of organizations. For
example, Fontana and Buss have begun to ask what occurs when two level-1
organizations interact by exchanging symbol strings. They find that a kind of “glue” can be formed
between the organizations such that the glue itself can help maintain either or
both of the participating level-1 organizations. A kind of mutualism can emerge naturally. Advantages of trade and an economy are already
implicit in coevolving level-1 autocatalytic sets.
The car comes in and drives the horse out. When the horse goes, so does the smithy, the
saddlery, the stable, the harness shop, buggies, and in your West, out goes the
Pony Express. But once cars are around,
it makes sense to expand the oil industry, build gas stations dotted over the
countryside, and pave the roads. Once
the roads are paved, people start driving all over creation, so motels make
sense. What with the speed, traffic
lights, traffic cops, traffic courts, and the quiet bribe to get off your
parking ticket make their way into the economy and our behavior patterns.
The economist Joseph Schumpeter had spoken of gales of
creative destruction and the role of the entrepreneur. But this was not the august Schumpeter
speaking; it was my good friend, Irish economist Brian Arthur, hunched over
seafood salad at a restaurant called Babe’s in Santa Fe. Defying any theorem about rational choice, he
always chose Babe’s seafood salad, which, he said, tasted absolutely awful. “Bad restaurant,” he vowed each time. “Why do you keep ordering their seafood
salad?” I asked. No answer. It was the only time I had stumped
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him in seven years. Brian, among
other things, has become deeply interested in the problem of “bounded
rationality,” why economic agents are not actually infinitely rational, as
standard economic theory assumes, although all economists know the assumption
is wrong. I suspect Brian is interested
in this problem because of his own incapacity to try Babe’s hamburgers, which
are fine. Good restaurant.
“How do you economists think about such technological
evolution?” I asked. From Brian and a
host of other economists, I have begun to learn the answer. These attempts are fine and coherent. Work initiated by Sidney Winter and Dick
Nelson and now carried on by many others center on ideas about investments
leading to innovations and whether firms should invest in such innovations or
should imitate others. One firm invests
millions of dollars in innovation, climbing up the learning curve of a
technological trajectory, as we discussed in Chapter 9. Other firms may also invest in innovation
themselves, or simply copy the improved widget. IBM invested in innovation;
Compaq cloned and sold IBM knock-offs. These
theories of technological evolution are therefore concerned with learning
curves, or rate of improvement of performance of a technology as a function of
investment, and optimal allocation of resources between innovation and
imitation among competing firms.
I am not an economist, of course, even though I have
now enjoyed listening to a number of economists who visit the institute. But I cannot help feeling that the economists
are not yet talking about the very facts that Brian Arthur first stressed to
me. The current efforts ignore the fact
that technological evolution is actually coevolution. Entry of the car drove the smithy to
extinction and created the market for motels. You make your living in a “niche” afforded by
what I and others do. The
computer-systems engineer is making a living fixing widgets that did not exist
50 years ago. The computer shops that
sell hardware make a living that was impossible to make 50 years ago.
Almost all of us make livings in ways that were not
possible for Homo habilis, squatting around his fire, or even
Cro-Magnon, crafting the magnificent paintings in Lascaux in the Perigord of
southern France. In the old days, you
hunted and gathered to get dinner each day.
Now theoretical economists scratch obscure equations on whiteboards, not
blackboards any longer, and someone pays them to do so! Funny way to catch dinner, I say.
(I was recently in the Perigord and purchased a flint
blade made using upper Paleolithic techniques from a craftsman in Les Eyzies,
near the Font-de-Gaume cave. In his
mid-forties, with a horned callus half an inch thick on his right hand from
hefting his hammer, an elk leg bone, he may be the singular member of our
species who has made the
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largest number of flint artifacts in the past 60,000 years. But even he is making his living in a new
niche - hammering flint for sale to the tourists awestruck by the Cro-Magnon
habitat of our ancestors.)
We live in what might be called an economic web. Many of the goods and services in a modern
economy are “intermediate goods and services,” which are themselves used in the
creation of still other goods and services that are ultimately utilized by some
final consumers. The inputs to one
intermediate good - say, the engine for a car - may come from a variety of
other sources, from toolmakers to iron mines to computer-assisted engine design
to both the manufacturer of that computer and the engineer who created the
software to carry out computer-aided design. We live in a vast economic ecology where we
trade our stuff to one another. A vast
array of economic niches exist.
But what creates those niches? What governs the structure of the economic
web, the arrangement by which jobs, tasks, functions, or products connect with
other jobs, tasks, functions, or products to form the web of production and
consumption?
And if there is an economic web, surely it is more
complex and tangled now than during the upper Paleolithic when Cro-Magnon
painted. Surely it is more complex now
than when Jericho first built its walls. Surely it is more complex than when the
Anasazi of New Mexico created the Chacoan culture 1,000 years ago. If the economic web grows more tangled and
complex, what governs the structure of that web? And the question I find most fascinating: If
the economy is a web, as it surely is, does the structure of that web itself
determine and drive how the web transforms? If so, then we should seek a theory of the
self-transformation of an economic web over time creating an ever-changing web
of production technologies. New
technologies enter (like the car), drive others extinct (like the horse, buggy,
and saddlery), and yet create the niches that invite still further new
technologies (paved roads, motels, and traffic lights).
The ever-transforming economy begins to sound like the
ever-transforming biosphere, with trilobites dominating for a long, long run on
Main Street Earth, replaced by other arthropods, then others again. If the patterns of the Cambrian explosion,
filling in the higher taxa from the top down, bespeak the same patterns in
early stages of a technological trajectory when many strong variants of an
innovation are tried until a few dominant designs are chosen and the others go
extinct, might it also be the case that the panorama of species evolution and
coevolution, ever transforming, has its mirror in technological coevolution as
well? Maybe principles deeper than DNA
and gearboxes underlie biological and technological coevolution, principles
about the kinds of complex
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things that can be assembled by a search process, and principles about
the autocatalytic creation of niches that invite the innovations, which in turn
create yet further niches. It would not
be exceedingly strange were such general principles to exist. Organismic evolution and coevolution and
technological evolution and coevolution are rather similar processes of niche
creation and combinatorial optimization. While the nuts-and-bolts mechanisms underlying
biological and technological evolution are obviously different, the tasks and
resultant macroscopic features may be deeply similar.
But how are we to think about the coevolving web
structure of an economy? Economists know
that such a structure exists. It is no
mystery. One did not have to be a
financial genius to see that gas stations were a great idea once cars began to
crowd the road. One hustled off to one’s
friendly banker, provided a market survey, borrowed a few grand, and opened a
station.
The difficulty derives from the fact that economists
have no obvious way to build a theory that incorporates what they call
complementarities. The automobile and
gasoline are consumption complementarities. You need both the car and the gas to go
anywhere. When you tell the waitress,
“Make it ham and eggs, over easy,” you are specifying that you like ham with
your eggs. The two are consumption
complements. If you went out with your
hammer to fasten two boards together, you would probably pick up a few nails
along the way; hammer and nails are production complements. You need to use the two together to nail
boards together. If you chose a
screwdriver, you would feel rather dumb picking up some nails on your way to
your shop to make a cabinet. We all know
screws and screwdrivers go together as production complements. But nail and screw are what economists call
production substitutes. You can usually
replace a nail with a screw and vice versa.
The economic web is precisely defined by just these
production and consumption complements and substitutes. It is just these patterns that create the
niches of an economic web, but the economists have no obvious way to build a
“theory” about them. What would it mean
to have a theory that hammer and nail go together, while car and gasoline go together?
What in the world would it mean to have
a theory of the functional connections between goods and services in an
economic web? It would appear we would
have to have a theory of the functional couplings of all possible kinds of
widgets, from windshield wipers to insurance policies to “tranches” of
ownership in bundled mortgages, to laser usage in retinal surgery. If we knew the “laws” governing which goods and
services were complements and substitutes for one another, we could predict
which niches would emerge as new goods were created.
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We could build a theory about how the technological web drives its own
transformation by persistent creation of new niches.
Here is a new approach. What if we think of goods and services as
symbol strings that we humans can use as “tools,” “raw materials,” and
“products?” Symbol strings act on symbol
strings to create symbol strings. Hammer
acts on nail and two boards to make attached boards. A protein enzyme acts on two organic molecules
to make two attached molecules. A symbol
string, thought of in Lisp light, is both a “tool” and a “raw material” that
can be acted on by itself or other tools to create a “product.” Hence the Lisp laws of chemistry implicitly
define what are production or consumption complements or substitutes. Both the “enzyme” and the “raw-material”
symbol strings are complements used in the creation of the product
symbol string. If you can find another
symbol-string “enzyme” that acts on the “raw-material” string to yield the same
product, then the two enzyme strings are substitutes. If you can find a different raw-material
string that, when acted on by the original enzyme string, yields the same final
product, then the two raw-material strings are substitutes. If the outputs of one such operation yield
products that enter into other production processes, you have a model of a webbed
set of production functions with complementarities and substitutes defined
implicitly by Lisp logic. You have the
start of a model of functionally coupled entities acting on one another and
creating one another. You have, in
short, the start of a model of an economic web where the web structure drives
its own transformation.
The web of technologies expands because novel goods
create niches for still further new goods. Our symbol-string models therefore become
models of niche creation itself. The molecular
explosion of supracritical chemical systems, the Cambrian explosion, the
exploding diversity of artifacts around us today - all these drives toward
increased diversity and complexity are underpinned by the ways each of these
processes creates niches for yet further entities. The increase in diversity and complexity of
molecules, living forms, economic activities, cultural forms - all demand an
understanding of the fundamental laws governing the autocatalytic creation of
niches.
If we do not have the real laws of economic
complementarity and substitutability, why hammers go with nails and cars with
gasoline, what’s the use of such abstract models? The use, I claim, is that we can discover the
kinds of things that we would expect in the real world if our “as if” mock-up
of the true laws lies in the same universality class. Physicists roll out this term, “universality
class,” to refer to a class of models all of which exhibit the same robust
behavior. So the behavior in question
does not depend on the details of the model. Thus a variety
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of somewhat incorrect models of the real world may still succeed in
telling us how the real world works, as long as the real world and the models
lie in the same universality class.
At about the same time as Alonzo Church developed the
lambda calculus as a system to carry out universal computation and Alan Turing
developed the Turing machine for the same purpose, another logician, Emil Post,
developed yet another representation of a system capable of universal
computation. All such systems are known
to be equivalent. The Post system is
useful as one approach to trying to find universality classes for model
economies.
On the left and right sides of the line in Figure 12.1
are pairs of symbol strings. For example, the first pair has (111) on the left
and (00101) on the right. The second
pair has (0010) on the left and (110) on the right. The idea is that this list of symbol strings
constitutes a “grammar.” Each pair of
symbol strings specifies a “substitution” that is to be carried out. Wherever the left symbol string occurs, one is
to substitute the right symbol string. In Figure 12.2, I show a “pot” of symbol
strings on which the grammar in Figure 12.1 is supposed to “act.” In the simplest interpretation, you apply the
grammar of Figure 12.1 as follows. You
randomly pick a symbol string from the pot. Then you randomly choose a pair of symbol
strings from the figure. You try to
match the left symbol string in the figure with the symbol string you chose. Thus if you picked the first pair of symbol
strings in the figure and you find a (111) in the symbol string you chose from
the pot, you are to “snip” it out and substitute the right symbol string from
the same row of Figure 12.1. Thus (ill)
is replaced by (00101).
Obviously, you might continue to apply the grammar
rules of Figure 12.1 to the symbol strings in the pot ad infinitum. You might continue
Figure 12.1 A Post grammar. Instances of the left
symbol string are to be replaced by the corresponding right symbol string.
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Figure 12.2 When the Post grammar in Figure 12.1 is
applied to a “pot” of symbol strings, a succession of new symbol strings
emerges.
to randomly pick up symbol strings in the pot, choose a row from the
figure, and apply the corresponding substitution. Alternatively, you might define precedence
rules about the order in which to apply the rows to any symbol string. And you might notice that sometimes the application
of a substitution in Figure 12.1 to a symbol string in Figure 12.2 would create
a new “site” in the symbol string, which was itself a candidate for application
of the rule that just created it. To
avoid an infinite loop, you might decide to apply any row substitution from
Figure 12.1 to any site only once before all the other rows had been chosen.
Any such set of decisions about application of the
substitutions in Figure 12.1 plus decisions about the order of applying the rules
to the symbol strings yields a kind of algorithm, or program. Starting with a set of initial symbol strings
in the pot, you would keep applying the substitutions and derive a sequence of
symbol strings. Like a Turing machine
converting an input tape to an output tape, you would have carried out some
kind of computation.
Now the next step is to remove you, the reader, from
the action, and allow the symbol strings in the pot to act on one another, like
enzymes do on substrates, to carry out the substitutions “mandated” by the
“laws of substitution” in Figure 12.1. An
easy way to do this is to define “enzymatic sites.” For example, the first row of Figure 12.1
shows that (111) is to be transformed to (00101). Let us think of a symbol string in the pot of
Figure 12.2 with a (111) sequence somewhere in it as a substrate. An “enzyme” might be a symbol string in the
same pot with a “template matching” (000) site somewhere in it. Here the “enzyme match rule” is that a 0 on
the enzyme matches a 1 on the substrate,
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rather like nucleotide base-pairing. Then given such a rule for “enzymatic sites,”
we can allow the symbol strings in the pot to act on one another. One way is to imagine two randomly chosen
symbol strings colliding. If either
string has an “enzymatic site” that matches a “substrate site” on the other,
then the enzymatic site “acts on” the substrate site and carries out the
substitution mandated in the corresponding row of Figure 12.1.
That’s all there is to it. Now we have an algorithmic chemistry specified
by a specific “grammar.” The symbol
strings in the pot transform one another into new symbol strings, which again
act on one another, ad infinitum. This persistent action will generate some flowering
of symbol strings. It is the behavior of
this florescence of symbol strings over time that is of interest now. For the patterns of flowering are to become
our models of technological coevolution. To accomplish this, we will have to add a few
ideas.
But first, how should we pick our grammar, as
exemplified by Figure 12.1? No one knows
“the right way” to specify the choice of pairs of symbol strings in the “laws
of substitution” figure. Worse, there is
an infinity of possible choices! In
principle, the number of pairs of symbol strings might be infinitely long. Moreover, no one is limiting us to single
symbol strings as “enzymes” acting on single symbol strings as “substrates” to
yield single symbol strings as “products.” We can perfectly well think about an ordered
set of symbol strings as an “input bundle” and an ordered set of symbol strings
as a “machine.” Push the input bundle
into the machine, and you get some “output bundle.” The “machine” would be like an assembly line,
doing a series of transformations on each input symbol string.
If we want to allow input bundles and machines, and if
each can be any subset of the symbol strings, then a mathematical theorem says
that the number of possible grammars is not just infinite, but is second-order
infinite. That is, the number of
possible grammars, like the real numbers, is uncountably infinite.
Since we cannot count the possible grammars, let’s
cheat. Let’s just sample grammars at
random from the infinity of possible grammars and find out what grammars in
different regions of “grammar space” do. Let’s imagine that we can find regions of
grammar space within which the resulting behavior of our pot of symbol strings
is insensitive to the details. Let’s
look, in short, for universality classes.
One way to define classes, or ensembles, of grammars
in regions of grammar space is by the number of pairs of symbol strings that
can occur in the grammar, the distributions of their lengths, and the way the
longer and shorter symbol strings are distributed as the left or right
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member of the pair. For example,
if all the right members are smaller than the left members, substitution will
eventually lead to very short symbol strings, which are too short to match any
“enzymatic site.” The “soup” will become
inert. In addition, the complexity of
allowed “input bundles,” “machines,” and “output bundles” can be defined in
terms of the number of symbol strings in each. As these parameters defining grammars are
systematically altered, different regions of grammar space can be explored. Presumably, different regions will give rise
to different characteristic behaviors. These
different regions and behaviors would be the hoped-for universality classes.
This systematic study has not yet been done. If we could find a region of “grammar space”
that gave us models of technological coevolution that look like real
technological coevolution, then perhaps we might have found the right
universality class and the correct “as if” model of the unknown laws of
technological complementarity and substitutability. Here, then, is a program of research.
The program has begun, for my colleagues and I have
actually made a few small models of economies that are already yielding
interesting results.
Before we turn to economic models, let us consider
some of the kinds of things that can happen in our pot of symbol strings as
they act on one another, according to the laws of substitution we might happen
to choose. A new world of possibilities
lights up and may afford us clues about technological and other forms of
evolution. 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. Bear in mind that grammar models
give us, for the first time, kinds of general “mathematical” or formal theories
in which to study what sorts of patterns emerge when “entities” can be both the
“object” acted on and transformed and the entities that do the acting, creating
niches for one another in their unfolding. Grammar models, therefore, help make evident
patterns we know about intuitively but cannot talk about very precisely.
One might get a symbol string that copied itself or
any other symbol string, a kind of replicase.
One might get a collectively autocatalytic set of
symbol strings. Such a set would make
itself from itself. In The Origins of
Order, I used a name I thought of late one night. Such a closed self-creating set is a kind of
“egg” hanging in the space of symbol strings.
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Suppose that one had a perpetually sustained “founder
set” of symbol strings. Such a sustained
founder set of symbol strings might create new symbol strings, which in turn
acted on one another to create still new strings - say, ever longer symbol
strings - in a kind of “jet.” A jet
would squirt away from the founder set out into the space of possible strings.
The jet might be finite or infinite. In the latter case, the founder set would
squirt out a jet of ever-increasing diversity of symbol strings.
An egg might be leaky and squirt out a jet. Such an egg object would hang like some
bizarre spaceship, spraying a jet of symbol strings into the inky blackness of
the far reaches of string space.
A sustained founder set might create a jet whose
symbol strings were able to “feed back” to create symbol strings initially
formed earlier by alternative routes. In
my late-night amusement, I called these “mushrooms.” A mushroom is a kind of model for
“bootstrapping.” A symbol string made by
one route can later be made by another route via a second symbol string that
the first one may have helped create.
Stone hammers and digging tools became refined, eventually led to mining
and metallurgy, which led to the creation of machine tools, which now manufacture
the metal tools used to make the machine tools.
Hmm. Bootstrapping. Think, then, about how common mushrooms must
be in our technological evolution since the lower Paleolithic. The tools we make help us make tools that in
turn afford us new ways to make the tools we began with. The system is autocatalytic. Organisms and their collectively autocatalytic
metabolisms built on a sustained founder set of exogenously supplied food and
energy are kinds of mushrooms, as is our technological society. Mushroom webs in ecosystems and economic systems
are internally coherent and “whole.” The
entities and functional roles that each plays meet and match one another
systematically.
A sustained founder set of symbol strings might make
an infinite set of symbol strings, but there may be a certain class of symbol
strings that will never be made from that founder set. For example, it may be the case that no symbol
string starting with the symbols (110101...) will ever be made. While an infinite set is made, an infinite
number are never made. Worse, given the
initial set of symbol strings and the grammar, it can be formally impossible to
prove or disprove that a given symbol string, say (1101010001010), will never
be produced. This is called formal
undecidability in the theory of computation and is captured in Kurt Gödel’s
famous incompleteness theorem.
In a moment, we’re going to imagine that we live in
such a world. Formal undecidability
means that we cannot, in principle, predict certain things about the future. Perhaps we cannot predict, for example, if
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we lived in the world in question, that (11010100001010) will never be
formed. What if (1101010000l010) were
Armageddon? You’d never know.
What if it is true that the technological, economic,
and cultural worlds we create are genuinely like the novel string worlds we are
envisioning? After all, string worlds
are built on the analogy with the laws of chemistry. If one could capture the laws of chemistry as
a formal grammar, the stunning implication of undecidability is this: given a
sustained founder set of chemicals, it might be formally undecidable whether a
given chemical could not possibly be synthesized from the founder set! In short, the underlying laws of chemistry are
not mysterious, if not entirely known. But if they can be captured as a formal
grammar, it is not unlikely, and indeed is strongly urged by Gödel’s theorem,
that there would remain statements about the evolution of a chemical reaction
system that would remain impossible to prove or disprove.
Now, if formal undecidability can arise from the real
laws of chemistry, might the same undecidabiity not arise in technological or
even cultural evolution? Either we can
capture the unknown laws of technological complementarity and substitutability
in some kind of formal grammar or we cannot. If we can, then Gödel’s theorem suggests that
there will be statements about how such a world evolves that are formally
undecidable. And if we cannot, if there
are no laws governing the transformations, then surely we cannot predict.
Technological Coevolution and Economic Takeoff
In helping to build theories of technological
coevolution, I suspect that these toy worlds of symbol strings may also reveal
a new feature of technological evolution: subcritical and supracritical
behavior. A critical diversity of goods
and services may be necessary for the sustained explosion of further
technological diversity. Standard
macroeconomic models of growth are single-sector models - a single stuff is
produced and consumed. Growth is seen as
increasing amounts of stuff produced and consumed. Such a theory envisions no role for the growth
of diversity of goods and services. If
this growth in diversity is associated with economic growth itself, as is
supported by some evidence, then diversity itself may bear on economic take
off.
In Figure 12.3, I show an outline of France. Again, we are going to model goods and
services as symbol strings. We want to
think about how the “technological frontier” evolves as the French people
realize the unfolding potential of the raw materials with which we are about to
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Figure 12.3 The outline of France, showing
different products growing from the soil. These symbol strings represent the renewable
resources - wood, coal, wool, dairy, iron, wheat, and such - with which France is
endowed. As the people use the strings
to act on other strings, new, more complex products emerge.
endow them. Imagine that, each
year, certain kinds of symbol strings keep emerging out of the fertile soil of
France. These symbol strings are the
“renewable resources” of France, and might stand for grapes, wheat, coal, milk,
iron, wood, wool, and so forth. Now
let’s forget the values of any of these goods and services, the people who will
work with them, and the prices that must emerge and so forth. Let’s just think about the evolving
“technological possibilities” open to France, ignoring whether anyone actually
wants any of the goods and services that might be technically feasible.
At the first period, the French might consume all
their renewable resources. Or they might
consult the “laws of technological complement-
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tarity” engraved at the hotel de ville in each town and village,
and consider all the possible new goods and services that might be created by
using the renewable resources to “act” on one another. The iron might be made into forks, knives, and
spoons, as well as axes. The milk might
be made into ice cream. The wheat and
milk might be made into a porridge. Now
at the next period, the French might consume what they had by way of renewable
resources, and the bounty of their first inventions, or they might think about
what else they could create. Perhaps the
ice cream and the grapes can be mixed, or the ice cream and grapes mixed and
placed in a baked shell made of wheat to create the first French pastry. Perhaps the axe can be used as such to cut
firewood. Perhaps the wood and axe can
be used to create bridges across streams.
You get the idea. At each period, the goods and services previously
“invented” create novel opportunities to create still more goods and services. The technological frontier expands. It builds on itself. It unfolds. Our simple grammar models supply a way to talk
about such unfolding.
Economists like to think about at least slightly more
complex models that include consumers and their demands for the potential goods
and services. Imagine that each symbol
string has some value, or utility, to the one and only consumer in French
society. The consumer might be Louis
XIV, or Jacques the good hotelier, or actually a number of identical French
folks with the same desires. In this
simple model, there is no money and there are no markets. In their place is an imaginary wise social
planner. The task of the social planner
is this: she knows the desires of Louis XIV (or she had better), she knows the
renewable resources of the kingdom, and she knows the “grammar table,” so she
can figure out what the ever-evolving technological frontier will look like by
“running the projection” forward. All
she has to do is to try to optimize the overall happiness of the king, or all
the Jacques, over the future. At this
point, simple economic models posit something like this: the king would rather
have his pleasures today, thank you, than at any time in the future. Indeed, if he has to wait a year, he is
willing to trade X amount of happiness now for X plus 6 percent next year, and
6 percent more for each year he must wait. In short, the king discounts the value of
future utility at some rate. So does
Jacques. So do you.
So our infinitely wise social planner thinks ahead
some number of periods, say 10, called a planning horizon; thinks through all
the possible sequences of technological goods and services that might possibly
be created over these 10 periods; considers the (discounted) happiness of the
king for all these possible worlds; and picks a plan that makes his lordship as
pleased as possible. This plan specifies
how much of each
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technologically possible “production” is actually to be carried out
over the 10 periods and how much of what will be consumed when. These production activities occur in some
ratio: 20 times as much ice cream and grapes as axes, and such. The ratio actually is the analogue of price,
taking one of the goods as “money.” Not
all of the possible goods may be produced. They do not make the king happy enough to
waste resources on. Thus once we include
the utilities of the goods and services, the goods actually produced at any
moment will be a subset of the entire set of what is technologically possible.
Now the social planner implements the first year of
her plan, the economy cranks forward for a year with the planned production and
consumption events, and she makes a new 10-year plan, now extending from year 2
to year 11. We’ve just considered a
“rolling horizon” social planner model. Over
time, the model economy evolves its way into the future. At each period, the social planner plans ahead
10 periods, picks the optimal 10-year plan, and implements the first year.
Such models are vast oversimplifications, of course. But you can begin to intuit what such a model
in our grammar context will reveal. Over
time, novel goods and services will be invented, displacing old goods and
services. Technological speciation and
extinction events occur. Because the web
of technologies is connected, the extinction of one good or service can start a
spreading avalanche in which other goods and services no longer make sense and
lapse from view. Each represented a way
of making a living, come and gone, having strutted its hour. The set of technologies unfolds. The goods and services in the economy not only
evolve, but coevolve, for those present must always make sense in the context
of the others that already exist.
Thus these grammar models afford us new tools to study
technological coevolution. In
particular, once one sees one of these models, the idea that the web itself
drives the ways the web transforms becomes obvious. We know this intuitively, I think. We just have never had a toy world that
exhibited to us what we have always known. Once one sees one of these models, once it
becomes obvious that the economic web we live in largely governs its own directions
of transformations, one begins to think it would be very important indeed to
understand these patterns in the real economic world out there.
These grammar models also suggest a possible new
factor in economic takeoff: diversity probably begets diversity; hence
diversity may help beget growth.
In Figure 12.4, I show, on the x-axis, the diversity
of goods and services that emerge from the French soil as renewable resources
each period. On the y-axis. I show the
number of pairs of symbol strings com-
Figure 12.4 The number of renewable goods with
which an economy is endowed is plotted against the number of pairs of symbol
strings in the grammar, which captures the hypothetical “laws of
substitutability and complementarity.” A
curve separates a subcritical regime below the curve and a supracritical regime
above the curve. As the diversity of
renewable resources or the complexity of the grammar rules increases, the
system explodes with a diversity of products.
posing the grammar, or laws, of complementarity and substitutability. And in this xy plane, I sketch the now
familiar curve separating the now familiar subcritical and supracritical
behaviors.
Imagine that the grammar laws had only a single pair
of symbol strings. Imagine that an
impoverished France sprouted only a single kind of symbol string from its soil
each spring. Alas, the grammar law might
be such that nothing at all could be done with the single renewable resource to
make anything new and interesting. All
the French could do is to consume that resource. No explosion of the technological frontier
could occur. If by dint of hard work,
the French saved excess amounts of this single resource, well that’s good. Nevertheless, no explosion of diverse goods
could occur. The system is subcritical.
But suppose the grammar laws have many pairs of symbol
strings, and the fertile soil of France sprouts many kinds of renewable resources.
Then the chances are overwhelming that a
large number of useful and interesting products can be created immediately from
these founder symbol strings by using them to transform one another. In turn,
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the enhanced diversity of goods and services can lead to a further explosion
of the technological frontier. If the
social planner deems them useful to the king, an unfolding subset of the
technically possible goods and services will actually arise and extinguish in
some complex progression. Economic takeoff
in diversity has occurred. The system is
supracritical.
If France were subcritical and so, too, were England
across the Channel, then trade between them might be sufficient to allow the
two to become technologically supracritical. So a larger, more complex economy may grow in
diversity because it allows the technological frontier to explode.
The behavior of our model economies also depends on
the “discount” factor and the social planner’s planning horizon. If the king does not want to wait for his happiness,
then the wise social planner does not put off drinking milk today. Ice cream is never created. The economy that might have blossomed into
diversity remains truncated, perhaps blissfully, in its initial Garden of Eden
state. Alternatively, whatever the king
might prefer, if the social planner does not think ahead, she never realizes
that ice cream can be created. Again,
the model economy truncates its diversification.
Models with social planners, while used by economists,
are far less realistic than models in which there are markets and economic
agents who buy and sell. In
social-planner models, all the problems of coordination of actions among the
agents, the invisible hand part of economics, is taken care of by the planner,
who simply commands the appropriate ratio of the different production and
consumption activities. In the real
world, independent agents make decisions and the market is supposed to
coordinate their behaviors. While the
social-planner model I have used ignores all the important issues concerning
the emergence of markets and behavior coordination among such agents, I have
done so to concentrate on the evolution of the web of technologies. Birth and extinction of technologies, and
subcritical and supracritical behaviors can occur. It seems reasonable, but remains to be shown,
that similar features will show up in more realistic versions of this kind of
model in which the social planner is replaced with markets and optimizing
agents.
Caveats. I am not an economist. These grammar models are new. You should at most take them as metaphors at
present. Yet even as metaphors, they
make suggestions that may be worth investigation. Among these, the possibility that diversity
may help drive economic growth.
Standard theories of economic growth appear not to
have taken into
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account the potential linkages between the diversity of economic sectors
in economic growth. Standard
macroeconomic theories often build models of economic growth based on an
economy producing a single stuff, a kind of aggregate of all our productions,
and talk in terms of aggregate demand, aggregate supply, money growth, interest
rate, and other aggregated factors. Long-term economic growth is typically attributed
to two major factors: technological improvements and growth in the productivity
and skill of workers, called human capital. Growth in technology is seen as occurring in
response to investments in research and development. Growth in human capital occurs because of
investments in education and on-the-job learning. Here the improvements accrue to the benefit
of the individual or his immediate family. How “technological improvements” and “human
capital” may be linked to the underlying dynamics of technological webs and
their transformation is not yet well articulated.
It is not that economists are unaware of the kinds of complementarities we have discussed. Indeed, enormous input-output matrices of economic interaction are studied. But lacking a formalizable framework, economists appear to have had no obvious way to build models of connections between various economic sectors and study their implications for further diversification and economic growth. Yet there is beginning to be evidence of the importance of these cross-connections. If this view is correct, then diversity should be a major predictor of economic growth. This is not a new idea. Canadian economist Jane Jacobs advanced the same idea on different grounds two decades ago. Recently, University of Chicago economist José Schenkman, also a Santa Fe Institute friend, reported work that strongly suggests that the rate of economic growth of cities is, in fact, strongly correlated with the diversity of the sectors within the cities. Schenkman and his colleagues carefully controlled for the aggregate capitalization of the industries and the specific sectors involved. Thus at least some clues support the rather obvious idea we discuss here: the web structure of an economic system is itself an essential ingredient in how that economic system grows and transforms.