The Competitiveness of Nations in a Global Knowledge-Based Economy

Stuart A. Kauffman

At Home in the Universe

Chapter 9 Organisms and Artifacts

Oxford University Press, 1995, 191-206




Jumping Across Landscapes

The Cambrian Explosion

Technological Evolution on Rugged Landscapes

Learning Curves


Organisms arise from the crafting of natural order and natural selection, artifacts from the crafting of Homo sapiens.  Organisms and artifacts so different in scale, complexity, and grandeur, so different in the time scales over which they evolved, yet it is difficult not to see parallels.

Life spreads through time and space in branching radiations.  The Cambrian explosion is the most famous example.  Soon after multicelled forms were invented, a grand burst of evolutionary novelty thrust itself outward.  One almost gets the sense of multicellular life gleefully trying out all its possible ramifications, in a kind of wild dance of heedless exploration.  As though filling in the Linnean chart from the top down, from the general to the specific, species harboring the different major body plans rapidly spring into existence in a burst of experimentation, then diversify further.  The major variations arise swiftly, founding phyla, followed by ever finer tinkerings to form the so-called lower taxa: the classes, orders, families, and genera.  Later, after the initial burst, after the frenzied party, many of the initial forms became extinct, many of the new phyla failed, and life settled down to the dominant designs, the remaining 30 or so phyla,  Vertebrates, Arthropods, and so forth, which captured and dominated the biosphere.

Is this pattern so different from technological evolution?  Here human artificers make fundamental inventions.  Here, too, one witnesses, time after time, an early explosion of diverse forms as the human tinkerers try out the plethora of new possibilities opened up by the basic innovation.  Here, too, is an almost gleeful exploration of possibilities.  And, after the party, we settle down to finer and finer tinkering among a few dominant designs that command the technological landscape for some time - until an entire local phylogeny of technologies


goes extinct.  No one makes Roman siege engines any more.  The howitzer and short-range rocket have driven the siege engine extinct.

Might the same general laws govern major aspects of biological and technological evolution?  Both organisms and artifacts confront conflicting design constraints.  As shown, it is those constraints that create rugged fitness landscapes.  Evolution explores its landscapes without the benefit of intention.  We explore the landscapes of technological opportunity with intention, under the selective pressure of market forces.  But if the underlying design problems result in similar rugged landscapes of conflicting constraints, it would not be astonishing if the same laws governed both biological and technological evolution.  Tissue and terra-cotta may evolve by deeply similar laws.

In this chapter, I will begin to explore the parallels between organism and artifact, but the themes will persist throughout the remainder of the book.  I will explore two features of rugged but correlated landscapes.  The first feature accounts, I believe, for the general fact that fundamen­tal innovations are followed by rapid, dramatic improvements in a variety of very different directions, followed by successive improvements that are less and less dramatic.  Let’s call this the “Cambrian” pattern of diversification.  The second phenomenon I want to explore is that after each improvement the number of directions for further improvement falls by a constant fraction.  As we saw in Chapter 8, this yields an exponential slowing of the rate of improvement.  This feature, I believe, accounts for the characteristic slowing of improvement found in many technological “learning curves” as well as in biology itself.  Let’s call this the “learning-curve” pattern.  Both, I think, are simple consequences of the statistical features of rugged but correlated landscapes.

Jumping Across Landscapes

In our current efforts, I will continue to use the NK model of correlated fitness landscapes introduced in Chapter 8.  It is one of the first mathematical models of tunably rugged fitness landscapes.  I believe, but do not know, that the features we will explore here will turn out to be true of almost any family of rugged but correlated landscapes.  As we have seen, the NK model generates a family of increasingly rugged landscapes as K, the number of “epistatic” inputs per “gene,” increases.  Recall that increasing K increases the conflicting constraints.  In turn, the increase in conflicting constraints makes the landscape more rugged and multipeaked.  When K reaches its maximal value (K = N - 1, in which every gene is dependent on every other), the landscape becomes fully random.


I begin by describing a simple, idealized kind of adaptive walk - long-jump adaptation - on a correlated but rugged landscape.  We have already looked at adaptive walks that proceed by generating and selecting single mutations that lead to fitter variants.  Here, an adaptive walk proceeds step-by-step in the space of possibilities, marching steadfastly uphill to a local peak.  Suppose instead that we consider simultaneously making a large number of mutations that alter many features at once, so that the organism takes a “long jump” across its fitness landscape.  Suppose we are in the Alps and take a single normal step.  Typically, the altitude where we land is closely correlated with the altitude from which we started.  There are, of course, catastrophic exceptions; cliffs do occur here and there.  But suppose we jump 50 kilometers away.  The altitude at which we land is essentially uncorrelated with the altitude from which we began, because we have jumped beyond what is called the correlation length of the landscape.

Now consider NK landscapes for modest values of K, say N 1,000 and K = 5-1,000 genes whose fitness contributions each depends on 5 other genes.  The landscape is rugged, but still highly correlated.  Nearby points have quite similar fitness values.  If we flip one, five, or 10 of the 1,000 genes, we will end up with a combination that is not radically different in fitness from the one with which we began.  We have not exceeded the correlation length.

NK landscapes have a well-defined correlation length.  Basically, that length shows how far apart points on the landscape can be so that knowing the fitness at one point still allows us to predict something about the fitness at the second point.  On NK landscapes, this correlation falls off exponentially with distance.  Therefore, if one jumped a long distance away, say changing 500 of the 1,000 allele states - leaping halfway across the space - one would have jumped so far beyond the correlation length of the landscape that the fitness value found at the other end would be totally random with respect to the fitness value from which one began.

A very simple law governs such long-jump adaptation.  The result, exactly mimicking adaptive walks via fitter single-mutant variants on random landscapes is this: every time one finds a fitter long-jump variant, the expected number of tries to find a still better long-jump variant doubles!  This simple result is shown in Figure 9.1 (HHC: figure not reproduced).  Figure shows the results of long-jump adaptation on NK landscapes with K = 2 for different values of N.  Each curve shows the fitness attained on the y-axis plotted against the number of tries.  Each curve increases rapidly at first, and then ever more slowly, strongly suggesting an exponential slowing.  (If the slowing is, in fact, exponential, reflecting the fact that at each im-


HHC: Figure not reproduced

Figure 9.1  Taking long leaps.  NK landscapes can be traversed by taking long jumps - that is, mutating more than one gene at a time.  But on a correlated landscape, each time a fitter long-jump variant is found, the expected number of tries to find an even better variant doubles.  Fitness increases rapidly at first, and then slows and levels off.  (a) This slowing is shown for a variety of K = 2 landscapes.  “Generation” is the cumulative number of independent long-jump trials . Each curve is the mean of 100 walks.  (b) Logarithmic scales are used to plot the number of improvements against the number of generations.

provement the number of tries to make the next improvement really doubles, then if we replot the data from Figure using the logarithm of the number of tries, we should get a linear relation.  Figure shows that this is true.  The expected number of improvement steps, S = 1nG.)

The result is simple and important, and appears nearly universal.  In adaptation via long jumps beyond the correlation lengths of landscapes, the number of times needed to find fitter variants doubles at each improvement step, hence slowing exponentially.  It takes 1,000 tries to find the first 10 fitter variants, then 1 million tries to find the next 10, then 1 billion to find the next 10.

(Figure also shows another important feature: as N increases, enlarging the space of possibilities, long-jump adaptation attains ever poorer results after the same number of tries.  From other results we know that the actual heights of peaks on NK landscapes do not change as N increases.  Thus this decrease in fitness is a further limit to selection that, in my book The Origins of Order, I called a complexity catastrophe.  As the number of genes increases, long-jump adaptations becomes less and less


fruitful; the more complex an organism, the more difficult it is to make and accumulate useful drastic changes through natural selection.)

The germane issue is this: the “universal law” governing long-jump adaptation suggests that adaptation on a correlated landscape should show three time scales - an observation that may bear on the Cambrian explosion.  Suppose that we are adapting on a correlated, but rugged NK landscape, and begin evolving at an average fitness value.  Since the initial position is of average fitness, half of all nearby variants will be better.  But because of the correlation structure or shape of the landscape, those nearby variants are only slightly better.  In contrast, consider distant variants.  Because the initial point is of average fitness, again half the distant variants are fitter.  But because the distant variants are far beyond the correlation length of the landscape, some of them can be very much fitter than the initial point.  (By the same token, some distant variants can be very much worse.)  Now consider an adaptive process in which some mutant variants change only a few genes, and hence search the nearby vicinity, while other variants mutate many genes, and hence search far away.  Suppose that the fittest of the variants will tend to sweep through the population the fastest.  Thus early in such an adaptive process, we might expect the distant variants, which are very much fitter than the nearby variants, to dominate the process.  If the adapting population can branch in more than one direction, this should give rise to a branching process in which distant variants of the initial genotype, differing in many ways from one another as well, emerge rapidly.  Thus early on, dramatically variant forms should arise from the initial stem.  Just as in the Cambrian explosion, the species exhibiting the different major body plans, or phyla, are the first to appear.

Now the second time scale: as distant fitter variants are found, the universal law of long-jump adaptation should set in.  Every time such a distant fitter variant is found, the number of mutant tries, or waiting time, to find still another distant variant doubles.  The first 10 improvements may take 1,000 tries; the next 10 may take 1 million tries; the next 10 may take 1 billion tries.  As this exponential slowing of the ease and rate of finding distant fitter variants occurs, then it becomes easier to find fitter variants on the local hills nearby.  Why?  Because the fraction of fitter nearby variants dwindles very much more slowly than in the long-jump case.  In short, in the mid term of the process, the adaptive branching populations should begin to climb local hills.  Again, this is what happened in the Cambrian explosion.  After species with a number of major body plans sprang into existence, this radical creativity slowed and then dwindled to slight tinkering.  Evolution concentrated its sights closer to home, tinkering and adding filigree to its inventions.


In the long term, the third time scale, populations may reach local peaks and stop moving or, as shown in Chapter 8, may drift along ridges of high fitness if mutation rates are high enough, or the landscape itself may deform, the locations of peaks may shift, and the organisms may follow the shifting peaks.

Recently, Bifi Macready and I decided to explore the “three time scale” issue in more detail using NK landscapes.  Bifi carried out numerical studies searching at different distances across the landscape as walks proceeded uphill.  Figure 9.2 shows the results (HHC: figure not reproduced).

What we wanted to know was this: as one’s fitness changes, what is the “best” distance to explore to maximize the rate of improvement? Should we look a long way away, beyond the correlation length when

HHC: Figures 9.2 (a), (b) & (c) not reproduced

Figure 9.2  As fitness increases, search closer to home. On a correlated landscape, nearby positions have similar fitnesses.  Distant positions can have Fitnesses very much higher and very much lower. Thus optimal search distance is high when fitness is low and decreases as fitness increases. (a) to (c).  The results of sending 1,000 explorers with three different initial fitnesses to each possible search distance across the landscape.  The distribution of fitnesses found by each 1,000 explorers is a bell-shaped, Gaussian curve.  Crossmarks on the bars show plus or minus one standard deviation for each set of 1,000 explorers, and hence correspond to the best or worse one in six fitnesses they find.



fitness is average, as I argued earlier?  And, as fitness improves, should we look nearby rather than far away?  As Figure 9.3 shows, summarizing the results in Figure 9.2, the answers to both questions are yes.  Fitness is plotted on the x-axis, and the optimal distance to search to improve fitness is plotted on the y-axis.  The implication is this: when fitness is average, the fittest variants will be found far away.  As fitness improves, the fittest variants will be found closer and closer to the current position.  Therefore, at early stages of an adaptive process, we would expect to find dramatically different variants emerging.  Later, the fitter variants that emerge should be ever less different from the current position of the adaptive walk on the landscape.

We need to recall one further point.  When fitness is low, there are many directions uphill.  As fitness improves, the number of directions uphill dwindles.  Thus we expect the branching process to be bushy initially, branching widely at its base, and then branching less and less profusely as fitness increases.

Uniting these two. features of rugged but correlated landscapes, we

HHC: Figures 9.3 not reproduced

Figure 9.3  The best distance to search.  As one’s fitness changes, what is the best distance to explore to maximize the rate of improvement?  In this graph, as fitness increases, optimal search distance shrinks from halfway across the space to the immediate vicinity.  When fitness is average, it is best to look a long way, as fitness improves, it is better to search nearby.


should find radiation that initially both is bushy and occurs among dramatically different variants, and then quiets to scant branching among similar variants later on as fitness increases.

I believe that these features are just what we see in biological and technological evolution.


The Cambrian Explosion

From the first chapter of this book I have regaled you with images of the Cambrian explosion and the profound asymmetry of that burst of biological creativity compared with that following the later Permian extinction.  In the Cambrian, over a relatively short period of time, according to most workers in the field, a vast diversity of fundamentally different morphological forms appeared.  Since Linnean taxonomy has been with us, we have categorized organisms hierarchically.  The highest categories, kingdoms and phyla, capture the most general features of a very large group of organisms.  Thus the phylum of vertebrates - fish, fowl, and human - all have a vertebral column forming an internal skeleton.  There are 32 phyla today, the same phyla that have been around since the Ordovician, the period after the Cambrian.  But the best accounts of the Cambrian suggest that as many as 100 phyla may have existed then, most of which rapidly became extinct.  And as we have seen, the accepted view is that during the Cambrian, the higher taxonomic groups filled in from the top down: the species that founded phyla emerged first.  These radically different creatures then branched into daughter species, which were slightly more similar to one another yet distinct enough to become founders of what we now call classes.  These in turn branched into daughter species, which were somewhat more similar to one another yet distinct enough to warrant classifying them as founders of orders.  They in turn branched and gave off daughter species distinct enough to warrant being called founders of families, which branched to found genera.  So the early pattern in the Cambrian shows explosive differences among the species that branch early in the process, and successively less dramatic variation in the successive branchings.

But in the Permian extinction some 245 million years ago, about 300 million years after the Cambrian, a very different progression unfolded.  About 96 percent of all species became extinct, although members of all phyla and many lower taxa survived.  In the vast rebound of diversity that followed, very many new genera and many new families were founded, as was one new order.  But no new classes or phyla were formed.  The higher taxa filled in from the bottom up.  The puzzle is to


account for the vast explosion of diversity in the Cambrian, and the profound asymmetry between the Cambrian and the Permian.

A related general phenomenon is this: during postextinction rebounds, it appears to be the case that most of the major diversification occurs early in the branching process of speciation.  Paleontologists call such a branching lineage a clade.  They speak of “bottom-heavy” clades, which are bushy at the base, or oldest time, and note that genera typically diverge early in the history of their families, while families diverge early in the history of their orders.  In short, the record seems to indicate that during postextinction rebounds most of the diversity arises rather rapidly, and then slows.  Thus while the Cambrian filled in from the top down and the Permian from the bottom up, in both cases the greatest diversification came first, followed by more conservative experimentation.

Might it be the case that the general features of rugged fitness landscapes shed light on these apparent features of the past 550 million years of evolution?  As I have suggested, the probable existence of three time scales in adaptive evolution on correlated rugged landscapes, summarized in Figure 9.3, sounds a lot like the Cambrian explosion.  Early on in the branching process, we find a variety of long-jump mutations that differ from the stem and from one another quite dramatically.  These species have sufficient morphological differences to be categorized as founders of distinct phyla.  These founders also branch, but do so via slightly closer long-jump variants, yielding branches from each founder of a phylum to dissimilar daughter species, the founders of classes.  As the process continues, fitter variants are found in progressively more nearby neighborhoods, so founders of orders, families, and genera emerge in succession.

But why, then, was the flowering after the Permian extinction so different from the explosion during the Cambrian?  Can our understanding of landscapes afford any possible insight?  Perhaps.  A few more biological ideas are needed.  Biologists think of development from the fertilized egg to the adult as a process somewhat akin to building a cathedral.  If one gets the foundations wrong, everything else will be a mess.  Thus there is a common, and probably correct, view that mutants affecting early stages of development disrupt development more than do mutants affecting late stages of development.  A mutation disrupting formation of the spinal column and cord is more likely to be lethal than one affecting the number of fingers that form.  Suppose this common view is correct.  Another way of saying this is that mutants affecting early development are adapting on a more rugged landscape than mutants affecting late development.  If so, then the fraction of fitter neighbors


dwindles faster for mutants affecting early development than those affecting late development.  Thus it becomes hard to find mutants altering early development sooner in the evolutionary process than to find mutants affecting late development.  Hence if this is correct, early development tends to “lock in” before late development.  But alterations in early development are just the ones that would cause sufficient morphological change to count as change at the phylum or class level.  Thus as the evolutionary process continues and early development locks in, the most rapid response to ecological opportunity after a mass-extinction event should be a rebound with massive speciation and radiation, but the mutations should affect late development.  If this is true, no new phyla or classes will be found.  The radiation that occurs will be at the genus and family level, corresponding to minor changes that result from mutations affecting late development.  Then the higher taxa should fill in from the bottom up.

In short, if we imagine that by the Permian early development in the organisms of most phyla and classes was well locked in, then after 96 percent go extinct, only traits that were more minor, presumably those caused by mutations affecting later stages of an organism’s ontogeny, could be found and improved rapidly.

If these views are correct, then major features of the record, including wide radiation that fills taxa from the top down in the Cambrian, and the asymmetry seen in the Permian, may find natural explanations as simple consequences of the structure of fitness landscapes.  In the same vein, notice that bushy radiation should generally yield the greatest morphological variation early in the process.  Thus one might expect that during postextinction rebounds, genera would arise early in the history of their families and families would arise early in the history of their orders.  Such bottom-heavy clades are just what is observed repeatedly in the evolutionary record.


Technological Evolution on Rugged Landscapes

At first glance, the adaptive evolution of organisms and the evolution of human artifacts seem entirely different.  After all, Bishop Paley urged us to envision a watchmaker to make watches and God the watchmaker to make organisms, and then Darwin pressed home his vision of a “blind watchmaker” in his theory of random variation and natural selection.  Mutations, biologists believe, are random with respect to their prospective significance.  Man the toolmaker struggles to invent and improve, from the first unifacial stone tools some 2 or more million years ago, to


the bifacial hand axes of the lower Paleolithic, to the superbly crafted flint blades hammered free from prepared cores and then pressure-flaked to stunning perfection.  What in the world can the blind process of adaptive evolution in biological organisms have to do with technological evolution?  Perhaps nothing, perhaps a great deal.

Despite the fact that human crafting of artifacts is guided by intent and intelligence, both processes often confront problems of conflicting constraints.  Furthermore, if Darwin proposed a blind watchmaker who tinkered without foreknowledge of the prospective significance of each mutation, I suspect that much of technological evolution results from tinkering with little real understanding ahead of time of the consequences.  We think; biological evolution does not.  But when problems are very hard, thinking may not help that much.  We may all be relatively blind watchmakers.

Familiar features of technological evolution appear to bespeak search on rugged landscapes.  Indeed, qualitative features of technological evolution appear rather strikingly like the Cambrian explosion: branching radiation to create diverse forms is bushy at the base; then the rate of branching dwindles, extinction sets in, and a few final, major alternative forms, such as final phyla, persist.  Further, the early diversity of forms appears to be more radical, and then dwindles to minor tuning of knobs and whistles.  The “taxa” fill in from the top down.  That is, given a fundamental innovation - gun, bicycle, car, airplane - it appears to be common to find a wide range of dramatic early experimentation with radically different forms, which branch further and then settle down to a few dominant lineages.  I have already mentioned, in Chapter 1, the diversity of early bicycles in the nineteenth century: some with no handlebars, then forms with little back wheels and big front wheels, or equal-size wheels, or more than two wheels in a line, the early dominant Pennyfarthing branching further.  This plethora of the class Bicycle (members of the phylum Wheeled Wonders) eventually settled to the two or three forms dominant today: street, racing, and mountain bike.  Or think of the highly diverse forms of steam and gasoline flivvers early in the twentieth century as the automobile took form.  Or of early aircraft design, helicopter design, or motorcycle design.  These qualitative impressions are no substitute for a detailed study; however, a number of my economist colleagues tell me that the known data show this pattern again and again.  After a fundamental innovation is made, people experiment with radical modifications of that innovation to find ways to improve it.  As better designs are found, it becomes progressively harder to find further improvements, so variations become progressively more modest.  Insofar as this is true, it is obviously reminiscent of the claims


for the Cambrian explosion, where the higher taxa filled in from the top down.  Both may reflect generic features of branching adaptation on rugged, correlated fitness landscapes.


Learning Curves

A second signature that technological evolution occurs on rugged fitness landscapes concerns “learning curves” along technological trajectories.  There are two senses in which this occurs.  First, the more copies of an item produced by a given factory, the more efficient production becomes.  The general result, as accepted by most economists, is this: at each doubling of the number of units produced in a factory, the cost per unit (in inflation-adjusted dollars or in labor hours) falls by a constant fraction, often about 20 percent.  Second, learning curves also arise on what are called technological trajectories.  It appears common that the rate of improvement of various technologies slows with total industry expenditure; that is, improvement in performance is rapid at first, and then slows.

Such learning curves show a special property called a power-law relation.  A simple example of such a power law would be this: the cost in labor hours of the Nth unit produced is 1/N of the cost of the first unit produced.  So if you make 100 widgets, the last one costs only 1/100 as much as the first.  The special character of a power law shows up when the logarithm of the cost per unit is plotted against the logarithm of the total number of units produced.  The result is a straight line showing the cost per unit decreasing as the total number of units, N, increases.

Economists are well aware of the significance of learning curves.  So too are companies, which take them into account in their decisions on budgets for production runs, projected sales price per unit, and the expected number of units that must be sold before a profit is made.  In fact, the power-law shapes of these learning curves are of basic importance to economic growth in the technological sector of the economy: during the initial phase of rapid improvements, investment in the new technology yields rapid improvement in performance.  This can yield what economists call increasing returns, which attract investment and drive further innovation.  Later, when learning slows, little improvement occurs per investment dollar, and the mature technology is in a period of what economists call diminishing returns.  Attracting capital for further innovation becomes more difficult.  Growth of that technology sector slows, markets saturate, and further growth awaits a burst of fundamental innovation in some other sector.


Despite the ubiquity and importance of these well-known features of technological evolution and economic growth, no underlying theory seems to account for the existence of learning curves.  Do our simple insights into adaptive processes on landscapes offer any help?  Again, perhaps, and the story is a typical Santa Fe Institute adventure.  In 1987, John Reed (chairman of Citicorp) asked Phil Anderson (a Nobel laureate in physics) and Ken Arrow (a Nobel laureate in economics) to organize a meeting to bring economists together with physicists, biologists, and others.  The institute had its first meeting on economics and established an economics program, first headed by the Stanford economist Brian Arthur.  I, in turn, began trying to apply ideas about fitness landscapes to technological evolution.  Several years later, two young economics graduate students, Phil Auerswald of the University of Washington and José Lobo from Cornell, were taking the institute’s summer course on complexity, and asked if they might work with me on applying these new ideas about landscapes to economics.  José began talking with the Cornell economist Karl Shell, already a friend of the institute.  By the summer of 1994, all four of us began collaborating, helped by Bill Macready, a solid-state physicist and postdoctoral fellow working with me at the institute, and Thanos Siapas, a straight-A computer-science graduate student at MIT.  Our preliminary results suggest that the now familiar NK model may actually account for a number of well-known features of learning curves: the power-law relationship between cost per unit and total number of units produced; the fact that after increasingly long periods with no improvement, sudden improvements often occur; and the fact that improvement typically reaches a plateau and ceases.

Recall that on random landscapes, every time a step is taken uphill, the number of directions uphill falls by a constant fraction, one-half.  More generally, we saw that with the NK landscape model for K larger than perhaps 8, the number of fitter neighbors dwindles by a constant fraction at each step toward higher fitness.  Conversely, the number of “tries” to find an improvement increases by a constant fraction after each improvement is found.  Thus the rate of finding fitter variants - of making incremental improvements - shows exponential slowing.  The particular rate of exponential slowing depends, in the NK model, on K.  The slowing is faster when the conflicting constraints, K, are higher and the landscape is more rugged.  Finally, recall that adaptive walks on rugged landscapes eventually reach a local optimum, and then cease further improvement.

There is something very familiar about this in the context of technological trajectories and learning effects: the rate of finding fitter variants


(that is, making better products or producing them more cheaply) slows exponentially, and then ceases when a local optimum is found.  This is already almost a restatement of two of the well-known aspects of learning effects.  First, the total number of “tries” between finding fitter variants increases exponentially; thus we expect that increasingly long periods will pass with no improvements at all, and then rapid improvements as a fitter variant is suddenly found.  Second, adaptive walks that are restricted to search the local neighborhood ultimately terminate on local optima.  Further improvement ceases.

But does the NK model yield the observed power-law relationship?  To my delight, the answer appears to be yes.  We already know that the rate of finding fitter variants slows exponentially.  But how much improvement occurs at each step?  In the NK model, if the “fitness” values are considered instead as “energy” or “cost per unit,” and adaptive walks seek to minimize energy or “cost,” then it turns out that with each of these improvements the reduction in cost per unit is roughly a constant fraction of the improvement in cost per unit achieved the last time an improvement was made.  Thus the amount of cost reduction achieved with each step slows exponentially, while the rate of finding such improvements also slows exponentially.  The result, happy for us four, is that cost per unit decreases as a power-law function of the total number of tries, or units produced.  So if the logarithm of cost per unit is plotted on the y-axis, and the logarithm of the total number of tries, or units produced, is plotted on the x-axis, we get our hoped-for straight-line (or near straight-line) distribution.

Not only that, but to our surprise - and, at this stage of our work, healthy skepticism - not only does a power law seem to fall out of the good old NK model, but we find power laws with about the right slopes to fit actual learning curves.

You should not take these results as proof that the NK model itself is a proper macroscopic account of technological evolution.  The NK model is merely a toy world to tune our intuitions.  Rather, the rough successes of this first landscape model suggests that better understanding of technological landscapes may yield deeper understanding of technological evolution.

I am not an expert on technological evolution; indeed, I am also not an expert on the Cambrian explosion.  But the parallels are striking, and it seems worthwhile to consider seriously the possibility that the patterns of branching radiation in biological and technological evolution are governed by similar general laws.  Not so surprising, this, for all these forms of adaptive evolution are exploring vast spaces of possibilities on more or less rugged “fitness” or “cost” landscapes.  If the struc-


tures of such landscapes are broadly similar, the branching adaptive processes on them should also be similar.

Tissues and terra-cotta may indeed evolve in similar ways.  General laws may govern the evolution of complex entities, whether they are works of nature or works of man.


The Competitiveness of Nations

in a Global Knowledge-Based Economy

May 2005

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