The Competitiveness of Nations in a Global Knowledge-Based Economy

Stuart A. Kauffman

At Home in the Universe

Chapter 12 An Emerging Global Civilization

Oxford University Press, 1995, 273-304





Technological Coevolution

Random Grammars

Eggs, Jets, and Mushrooms

Technological Coevolution and Economic Takeoff

Global Civilization

Reinventing the Sacred


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


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-


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


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


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


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-


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.


Technological Coevolution

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


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


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


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.


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


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.

Random Grammars

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.


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,


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


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.

Eggs, Jets, and Mushrooms

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.


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


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


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-


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


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,


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


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.

Indeed, if we tie together the potential implications of the parallels between the coevolution of organisms and of artifacts that we have discussed in the previous chapters, something of a new, perhaps useful, framework concerning aspects of economic growth begins to emerge.

We have already seen that it is characteristic of optimization of conflict-laden problems that improvement is rapid initially, and then slows exponentially.  This well-known feature of technological learning curves implies that after a major innovation, there can be an early period of in-


creasing returns.  A given investment in the technology increases productivity greatly.  Later, as improvement slows exponentially, further investment faces diminishing returns.  This suggests that capital and credit will flow into the new sector in the early stages, during the increasing-returns phase.  If so, then major innovations drive capital formation and growth in the sector they create.  Just this is occurring in biotechnology today.  Later, as the learning curve is climbed and as markets saturate, growth in the mature sector dwindles.

But as the economic activities alter, the coevolutionary economic landscape deforms.  A family of new, “neighboring” technologies will proliferate, climbing uphill on the deformed landscapes.  As aircraft design and engine power increased, the fixed-blade propeller became less useful than a new innovation, the variable-pitch propeller.  Like branching speciation on a deforming landscape where the newly formed species may initially be relatively unfit, the newly invented variable-pitch propeller opened a modest new era of learning how to create better variable-pitch propellers.  So as nearby products and technologies are called forth by the deforming landscapes, each generates a new burst of rapid learning, and a burst of increasing returns can attract capital and credit, driving further growth in that sector.  In addition, the learning-by-doing that occurred with fixed-pitch propellers spills over to the neighboring new technologies.  The human capital, the learned skills, are naturally accumulated on a wider basis than the individual and his family, or even than a single narrow technology.

On a larger scale, persistent innovation in an economy may depend fundamentally on its supracritical character.  New goods and services create niches that call forth the innovations of further new goods and services.  Each may unleash growth both because of increasing returns in the early phase of improvement on learning curves or new open markets.  Some of these are truly triggers of Schumpeterian “gales of creative destruction,” ushering out many old technologies, ushering in many new ones in vast avalanches.  Such avalanches create enormous arenas of increasing returns because of the massive early improvements climbing learning curves along the novel technological trajectories, as well as major new markets.  So such large avalanches drive significant capital formation and growth.  Other new technologies come and go with hardly a ripple.  These differences presumably reflect, in part, how central or peripheral the new technology or product is in the current web and in its future evolution.  The automobile and the computer were central. The hula hoop was peripheral.

We have only sketched some obvious ideas, but they may be worth serious investigation.  Diversity begets diversity, driving the growth of


complexity.  Such ideas might eventually have policy implications.  If diversity matters, then helping Third World countries might be better accomplished by fostering cottage industries that create a local web that is mutually reinforcing and can take root and grow, rather than by creating the Aswan Dam.  But such conclusions lie in the future.  At best, I hope you will find grammar models an intriguing way to think about technological evolution and its roles in economic growth.

Before concluding our discussion of economic webs, I ask you to imagine yourself living in the world just sketched.  If such systems forever unfold with technological innovations, then what is wise?  If the side products of the technologies have unforeseeable long-term consequences for the planet, what is wisdom?  Bell South needs to decide whether to invest billions in fiber-optic technologies.  Should Bell South do so?  What if, in two years, some bright kid thinks up a way to toss tin cans into the sky held up by fans placed at strategic intervals in such a way that fiber-optics is less useful.  Billions down the tube.  Can Bell South management be sure of what to do, given the unfolding technological frontier?


Who would have dreamed, a decade ago, that today we would be faxing from home to home?  Recently, I was invited to an intriguing meeting in Colorado, a few hundred miles from my home in Santa Fe.  I had lost the detailed instructions, so called a friend, Joan Halifax, who was going.  Joan was not at home.  I left word on her answering machine.  Ten minutes later, she called from the northern reaches of Vancouver Island, where she was hoping to spy a few whales.  I explained my confusion.  Within minutes, a fax arrived from Vancouver Island with instructions.  Good grief.

Global positioning systems (GPS), now allow you, for a few hundred dollars, to buy a widget that locks into a few satellites and locates you on the surface of the earth within a few dozen feet.  It is possible to locate to within a few inches or less, but the U.S. military apparently keeps the precision lower for civilian uses.  Today I heard a rumor that the Japanese, properly concerned with earthquakes, are setting up such systems at fixed points on their islands.  Small changes in the distances between these points would foretell changes that might themselves foretell an earthquake.  I don’t know if the rumor is true, but it is plausible.  So we measure location on the earth and changes in location to guess the behavior of magma down there, by tossing signals up to satellites we tossed up before the signals.  And Columbus thought himself lucky to have a lodestone.  The web does unfold.

It is not merely that we must imagine what it would be like to live in


our model untolding grammar world.  We do live in such a world.  We live on a self-organized sandpile that sheds avalanches down the critical slopes with each footstep.  We have hardly a clue what will unfold.


Global Civilization

What is to become of our patchwork of civilizations, ancient and new, drawn ever more tightly into one another’s embrace?  Like it or not, some form of global civilization will emerge.  We are at that particular time in history when population, technology, economics, and knowledge spin us together.  I write with no particular wisdom, but I, like you, am a member of this emerging civilization.  I wonder if we really understand very much of what we are creating, of the plausible foundations such a way of being must have to hold us all with some modicum of tolerance and forgiveness of one another.  I wonder if the political structures we have created will continue to serve us.

When Western culture touched the Inuit culture, the latter was soon vastly transformed.  When Western culture touched traditional Japanese culture, the latter was soon vastly transformed.  When Rome touched Athens, Rome was transformed and so was Athens.  When the Hellenistic and Hebraic worlds collided, the cornerstones of Western civilization fell together in some new way.  When the Spaniards touched the Aztecs, a new cultural mixture was formed in the crucible.  Ferocious gods glower from frescos painted with Spanish skills.  Guatemalan patterns linger in tapestries woven in Western styles.

Now all our cultures are in collision.  At the small meeting in Nambe, New Mexico, where I met N. Scott Momaday, Lee Cullum, and Walter Shapiro, where we were asked by an organization called the Gihon Foundation to be presumptuous enough to think about the major problems confronting the world, my own overwhelming concerns focused on this emerging world civilization, the cultural dislocations it would engender, and the issue of whether we could find a cultural and political framework that would work for us.

Somehow, the string images we have discussed press themselves on me.  The swirl of transformations of ideologies, fashions begetting fashions begetting fashions, cuisines begetting novel cuisines, legal codes and precedents begetting the further creation of law, seem similar in as yet unclear ways to model grammar worlds with their eggs, jets, and mushrooms.  If a new symbol string is tossed casually into Fontana’s silicon pot, a swarm of novel symbol strings might form.  The small perturbation can yield a vast transformation in the future of the string systern - or nothing at all.


When Mikhail Gorbachev began speaking of glasnost, we knew that something big might happen.  We knew that a move to open the closed Soviet society to its own people’s concerns might unlock a revolution.  We knew that the small steps might lead to vast transformations.  Yet while we knew this intuitively, and the pundits pummeled us with their insights, we do not really know what we intuited.  We do not understand how the logs of the logjam fit together, such that removing one particular log will cause the logjam to shift only slightly, while another, innocuous in its position, will unleash the whole mass to swarm downriver.  We do not understand the functional couplings among the elements - political, economic, cultural - of our public world.

When the Chinese government tragically decided to kill the young students on Tiananmen Square, those leaders feared the particular log that was being tugged by the students.  Yet none of us really have much insight into the structure of that logjam either.

We lack a theory of how the elements of our public lives link into webs of elements that act on one another and transform one another.  We call these transformations “history.”  Hence with all the accidents of history, biological and human, one must engage in a renewed debate: Is there a place for law in the historical sciences?  Can we find lawlike patterns - cultural, economic, and otherwise - such as subcritical and supracritical behavior, or patterns of speciation and extinction?

We had best attempt to understand such processes, for the global civilization is fast upon us.  We will live through its birth, ready or not.

Modern democracy as we encapsulate it, as we tell ourselves the story of ourselves, is so much a product of the Enlightenment.  Newton and Locke.  The United States Constitution, which has served so well for more than 200 years, is a document built on an image of balancing political forces holding an equilibrium.  Newton and Locke.  Our political system is built to be flexible enough to balance political forces and allow the polity to evolve.  But our theory of democracy takes little account of the unfolding, evolving nature of cultures, economies, and societies.  In the nineteenth century, the idea of historical science came to the fore.  Hegel gave us thesis, antithesis, and synthesis.  Marx stood Hegel on his idealist head to create dialectical materialism.  These ideas now stand discredited.  Yet thesis, antithesis, synthesis sounds more than a little bit like the evolution of the hundreds of millions of species that have come and gone, or the evolution of technologies that have come and gone.

John Maynard Smith, at a meeting at the Santa Fe Institute in the summer of 1992, startled me by telling a group gathered together, “Perhaps you all are embarking on some kind of post-Marxist analysis of social evolution.”  I did not know what he meant.  Marxism has such a bad


reputation that I wasn’t certain I was at all happy with whatever it was he might have meant.  Yet might we be beginning to develop the conceptual tools that may help us to understand a bit more of the historical evolution of societies?  Historians do not think of themselves as merely recounting the record, but as looking for the web of influences that kaleidoscopically interact with one another to create the patterns that unfold.  Is there, in fact, a place for “law” in the historical sciences?  Is the Industrial Revolution, with its explosion of technologies, an example of assembling a critical diversity of goods and services, of new production technologies, such that the diversity fed on itself autocatalytically?  What of cultural revolutions such as the Renaissance and the Enlightenment?  Do these somehow reflect a web of collectively self-reaffirming ideas, norms, and agencies?

Richard Dawkins, an evolutionary biologist at Oxford, popularized the word meme.  In the simplest image, a meme is a bit of behavior that is replicated in a population.  Women now wear sunglasses perched on top of their heads.  I suspect that this was spawned by Audrey Hepburn playing Holly Golightly in the movie Breakfast at Tiffany’s many years ago.  In this limited sense, memes are “replicators,” which are invented and then imitated in complex patterns of cultural transmission.  But this sense of meme is too limited.  It is like one of Fontana’s level-0 organizations, a mere replicator that may spread in a population.  Are there collectively autocatalytic sets, level-1 organizations of memes?  Can cultural patterns be thought of as self-sustaining and mutually defining sets of beliefs, behaviors, roles?

Perhaps at present, the analogy is loose, more of a metaphor than the start of a real theory.  But might we not be members of a variety of such cultural entities?  We invent concepts and categories that we use to carve up the world.  Those categories are mutually defined in a complex reaffirming circle.  How could it be otherwise?  Having invented the categories, we carve the world into them and find ourselves categorized as well.  Due to the creation of a legal system, I am able to enter into contracts.  Because we can both do so, you and I can create a person that may live forever, the corporation, which takes on aims that survive and can even harm the interests of many of those who founded it.  Thus the modern corporation is a collectively self-sustaining structure of roles and obligations that “lives” in an economic world, exchanges signals and stuffs, and survives or dies in ways at least loosely analogous to those of E. coli.  E. coli is collectively autocatalytic and sustains itself in its world.  The modern corporation also seems collectively autocatalytic.  Both E. coli and IBM coevolve in their respective worlds.  Both participate in the creation of the ecosystem each inhabits.  As the recent diffi-


culties of massive IBM show, even the mighty can find their world vastly transformed.

So a global civilization is emerging.  At the small meeting in Nambe, Walter Shapiro (a political writer for Time) and Lee Cullum (a writer for the Dallas Morning News) focused on the implications of the advent of a McDonald’s in the corner of an ancient castle in Heidelberg, a German university town.  Good business?  Probably.  Unsettling, certainly.  Maria Verela is a MacArthur Fellow living 50 miles north of Santa Fe, near Chama.  She is struggling to help a local Hispanic community preserve a long heritage by keeping the weaving craft alive.  We can be in the world only by being in a culture.  The local Hispanic culture is under assault.  While watching the movie The Milagro Beanfield War, one laughs and cries at the same time.  There are heroes and villains in the story, of course, but in the real world of New Mexico and elsewhere much of the transformation seems the near inevitable consequence of cultures entwining and transforming one another.  Fajitas, it seems, were invented in Texas, not Mexico.  In New York, Chinese who fled Cuba have created Cuban-Chinese cuisine.

Will the emerging global civilization drift to homogeneity, as many suppose?  Will we all speak English because the United States was powerful when television became widespread?  Will we all love hamburgers?  God knows, I do.  But then I am a typical product of middle America.

Or will new cultural symbol strings sprout everywhere, created on every edge where two or more cultural traditions collide? Is the global civilization supracritical?  If we find Cuban-Chinese cuisine, what else will we invent - say, on the frontiers of Islam and hard rock?  Will we kill one another to preserve our ways of being in the world?  What does tolerance demand of us when our ways of being in the world are swept into a whirlwind of change by the touch of someone else’s memes beamed or e-mailed into our living rooms and studies?

For reasons I do not know, except perhaps that the image appeals to me, I find myself thinking about Per Bak and sandpiles again.  I find myself suspecting that we will ever invent new cultural solar flares at the frontiers of bits of old colliding cultures.  I find myself thinking about small and large avalanches of change propagating within and between the civilizations we have built in the past.  I deeply fear the social havoc of dying ways of being in the world.  People go to war for less.  But one does find the idea of Cuban-Chinese cuisine and whatever might emerge from Islam and hard rock at least interesting.  Maybe we need more of a sense of humor.  Maybe we will know we are on our way when we can tell one another ethnic jokes because the mutual respect is so deep and the tolerance is so clear that laughter helps heal the remaining tensions.


Having listened to all these concerns, Scott Momaday returned to his own core thesis: we must reinvent the sacred in the modern world.  Momaday’s vision elicited from the four of us a strange sense: if a global civilization is emerging, we may be entering its heroic age, its age of creation.  When Greek civilization collected itself on the Aegean shores, its early citizens constructed their own sustaining myths.  We four “thought leaders,” picked by some rather random process to assemble near Nambe New Mexico, found ourselves thinking that this emerging global civilization would have to invent its own new sustaining myths.

“Thought Leaders Gather on New Mexico Mountaintop and Advise World to Talk to Itself,” quipped Walter Shapiro, as we ended our little meeting of the Gihon Foundation and went outside for lunch overlooking Michael Nesmith’s gardens and the hills behind Nambe.

Reinventing the Sacred

Some 10,000 years ago, the last Ice Age began to falter.  The ice sheets slowly retreated to the poles.  In what later became the south of France, the Magdalenian culture - which had created the art in the caves of Font-de-Gaume and Lascaux, as well as upper Paleolithic flint blades, spears, and fishhooks of exquisite precision - faded.  The large herds drifted northward.  These ancestors drifted away, leaving the paintings that stun us today.

The bison and deer arched on these cave walls capture the sense of humanity’s harmony with, reverence for, and awe of nature.  No painting shows violence beyond images of hunting.  One painting depicts two deer nuzzling.  For some 14,000 years, these two have cared for each other on a stony curved wall in the Perigord.

Awe and respect have become powerfully unfashionable in our confused postmodern society.  Scott Momaday said that we must reinvent the sacred.  Our little meeting ended over a year ago.  I lack Momaday massive frame, deeply resonant voice, and uncanny authority.  Who am I to speak of these things?  Another small voice.  But has not our Baconian tradition, which celebrates science as the power to predict and control, also brought us a secular loss of awe and respect?  If nature were truly ours to command and control, then we might well afford the luxury of contempt.  Power corrupts, after all.

Friend, you cannot even predict the motions of three coupled pendula.  You have hardly a prayer with three mutually gravitating objects.  We let loose pesticides on our crops; the insects become ill and are eaten by birds that sicken and die, allowing the insects to proliferate in


increased abundance.  The crops are destroyed.  So much for control.  Bacon, you were brilliant, but the world is more complex than your philosophy.

We have presumed to command, based on our best knowledge and even our best intentions.  We have presumed to commandeer, based on the availability of resources, renewable or not, that lay readily at hand.  We do not know what we are doing.  If Victorian England, standing astride an empire on which the sun never set, could in full good conscience see itself as the world’s leader in persistent progress, where science meant the ensured betterment of mankind, can we see ourselves in such a way today?

We suspect ourselves.  This is not new.  Faust made his bargain.  Frankenstein assembled his sad monster.  Prometheus let loose fire.  We have seen the fires we have lit spread beyond their intended hearth-stones.  We begin to know that proud humankind is still another beast, still embedded in nature, still spoken for by a larger voice.

If we find renewed concern about the untellable consequences of our own best actions, that is wise.  It is not as though we could find a stance with either moral or secular certainty.  We make our worlds together.  All we can do is be locally wise, even though our own best efforts will ultimately create the conditions that lead to our transformations to utterly unforeseeable ways of being.  We can only strut and fret our hour, yet this is our own and only role in the play.  We ought, then, play it proudly but humbly.

Why try if our best efforts ultimately transform to the unforeseeable?  Because that is the way the world is, and we are part of that world.  That is the way life is, and we are part of life.  We latter-day players are heritors of almost 4 billion years of biological unfolding.  If profound participation in such a process is not worthy of awe and respect, if it is not sacred, then what might be?

If science lost us our Western paradise, our place at the center of the world, children of God, with the sun cycling overhead and the birds of the air, beasts of the field, and fish of the waters placed there for our bounty, if we have been left adrift near the edge of just another humdrum galaxy, perhaps it is time to take heartened stock of our situation.

If the theories of emergence we have discussed here have merit, perhaps we are at home in the universe in ways we have not known since we knew too little to know to doubt.  I do not know if the stories of emergence we have discussed in this book will prove to be correct.  But these stories are not evidently foolish.  They are bits and pieces of a new arena of science, a science that will grow in the coming decades toward some new view of emergence and order in this far-from-equilibrium


universe that is our home.  I do not know if life began, as I have attempted to suggest, as an expected emergent collective property of the kinds of organic molecules that almost inevitably were formed on the early earth.  Yet even the possibility of such collective emergence is heartening.  I would rather life be expected in this unfolding since the Big Bang than that life be incredibly improbable in the timespan available.  I do not know if the spontaneous order in mathematical models of genomic regulatory systems really is one of the ultimate sources of order in ontogeny.  Yet I am heartened by a view of evolution as a marriage of spontaneous order and natural selection.  I am heartened by the possibility that organisms are not contraptions piled on contraptions all the way down, but expressions of a deeper order inherent in all life.  I am not certain that democracy evolved to achieve reasonable compromises between people with legitimately conflicting interests, but I am heartened by the possibility that our social institutions evolve as expressions of deep natural principles.  “The Lord is subtle, but not malicious,” said Einstein.  We have only begun to invent the science that will account for the evolving emergent order I see out my window, from spider weaving her web, to coyote crafty on the ridgetop, to my friends and me at the Santa Fe Institute and elsewhere proudly hoping that we are unlocking some kinds of secrets, to all of you making your ways by your own best efforts and own best lights.

We are all part of this process, created by it, creating it.  In the beginning was the Word - the Law.  The rest follows, and we participate.  Some months ago, I climbed to the first mountaintop I have been able to reach since my wife and I were badly injured in a car accident.  I climbed to Lake Peak with Phil Anderson, Nobel laureate in physics and good friend at the institute.  Phil is a dowser. I once was astonished to see him pull a forked twig off a tree and march across a hilltop holding it.  I pulled off a forked twig and followed him.  Sure enough, whenever his twig dipped toward the ground, so too did mine.  But then, I could see him ahead of me.  “Does it work?” I asked him.  “Oh, sure.  Half of all people can dowse.”  “Ever dig where your stick pointed?”  “Oh, no.  Well, once.”  We reached the peak.  The Rio Grande Valley spread below us to the west; the Pecos Wilderness stretched out to the east; the Truchas Peaks erupted to the north.

“Phil,” I said, “if one cannot find spirituality, awe, and reverence in the unfolding, one is nuts.” “I don’t think so,” responded my dowsing, but now skeptical, friend.  He glanced at the sky and offered a prayer:

“To the great nonlinear map in the sky.”