The Competitiveness of Nations
in a Global Knowledge-Based Economy
May 2005
The Sciences of Complexity
and “Origins of Order”
Philosophy of Science Association,
Vol. Two: Symposia and Invited Papers
1990, 299-322.
Index
2. The Origin of Life and its Progeny
4. Closing Remark: A Place for Laws in Historical
Sciences
A new science, the science of
complexity, is birthing. This science
boldly promises to transform the biological and social sciences in the
forthcoming century. My own book, Origins
of Order: Self Organization and Selection in Evolution, (Kauffman, 1992),
is at most one strand in this transformation. I feel deeply honored that Marjorie Grene undertook organizing a session at the Philosophy of
Science meeting discussing Origins, and equally glad that Dick Burian, Bob Richardson and Rob Page have undertaken their
reading of the manuscript and careful thoughts. In this article I shall characterize the book,
but more importantly, set it in the broader context of the emerging sciences of
complexity. Although the book is not yet
out of Oxford press’s quiet womb, my own thinking has moved beyond that which I
had formulated even a half year ago. Meanwhile, in the broader scientific
community, the interest in “complexity” is exploding.
A summary of my own evolving hunch
is this: In a deep sense, E. coli and IBM know their respective worlds in the
same way. Indeed, E. coli and IBM have
each participated in the coevolution of entities
which interact with and know one another. The laws which govern the emergence of knower
and known, which govern the boundedly rational,
optimally complex biological and social actors which have co-formed, lie at the
core of the science of complexity. This
new body of thought implies that the poised coherence, precarious, subject to
avalanches of change, of our biological and social world is inevitable. Such systems, poised on the edge of chaos, are
the natural talismen of adaptive order.
The history of this emerging
paradigm conveniently begins with the “cybernetic” revolution in molecular
biology wrought by the stunning discoveries in 1961 and 1963, by later Nobelists Francoise Jacob and Jacques Monod
that genes in the humble bacterium, E. coli, literally turn one another on and
off (Jacob and Monod, 1961, 1963). This discovery laid the foundation for the
still sought solution of the problem of cellular differentiation in embryology.
The embryo begins as a fertilized egg,
the single cell zygote. Over the course
of embryonic development in a human, this cell divides about 50 times, yielding
the thousand trillion cells which form the newborn. The central mystery of developmental biology
is that these trillions of cells become radically different from one another,
some forming blood cells, others liver cells, still other nerve, gut, or gonadal cells. Previous work had shown that all the cells of
a
*
University of Pennsylvania
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human body contain the same
genetic instructions. How, then, could
cells possibly differ so radically?
Jacob and Monods’
discovery hinted the answer. If genes
can turn one another on and off, then cell types differ because different genes
are expressed in each cell type. Red
blood cells have hemoglobin, immune cells synthesize
antibody molecules and so forth. Each
cell might be thought of as a kind of cybernetic system with complex genetic-molecular
circuits orchestrating the activities of some 100,000 or more genes and their
products. Different cell types then, in
some profound sense, calculate how they should behave.
My own role in the birth of the
sciences of complexity begins in the same years, when as a medical student, I
asked an unusual, perhaps near unthinkable question. Can the vast, magnificent order seen in
development conceivably arise as a spontaneous self organized property of
complex genetic systems? Why
“unthinkable”? It is, after all, not the
answers which scientists uncover, but the strange magic lying behind the
questions they pose to their world, knower and known, which is the true impulse
driving profound conceptual transformation. Answers will be found, contrived, wrested,
once the question is divined. Why “unthinkable”? Since Darwin, we have viewed organisms, in
Jacob’s phrase, as bricolage, tinkered together
contraptions. Evolution, says Monod, is “chance caught on the wing”. Lovely dicta, these, capturing the core of the
Darwinian world view in which organisms are perfected by natural selection
acting on random variations. The tinkerer is an opportunist, its
natural artifacts are ad hoc accumulations of this and that, molecular Rube Goldbergs satisfying some spectrum of design constraints.
In the world view of bricolage, selection is the sole, or if not sole, the
preeminent source of order. Further, if
organisms are ad hoc solutions to design problems, there can be no deep
theory of order in biology, only the careful dissection of the ultimately
accidental machine and its ultimately accidental evolutionary history.
The genomic system linking the
activity of thousands of genes stands at the summit of four billion years of an
evolutionary process in which the specific genes, their regulatory intertwining
and the molecular logic have all stumbled forward by random mutation and
natural selection. Must selection have
struggled against vast odds to create order? Or did that order lie to hand for selection’s
further molding? If the latter, then
what a reordering of our view of life is mandated!
Order, in fact, lies to hand. Our intuitions have been wrong for thousands
of years. We must, in fact, revise our
view of life. Complex molecular
regulatory networks inherently behave in two broad regimes separated by a third
phase transition regime. The two broad
regimes are chaotic and ordered. The
phase transition zone between these two comprises a narrow third complex regime
poised on the boundary of chaos (Kauffman 1969, 1989; Fogleman-Soülie
1985; Derrida and Pomeau 1986; Langton
1991; Kauffman 1991, 1992). Twenty five
years after the initial discovery of these regimes, a summary statement is that
the genetic systems controlling ontogeny in mouse, man, bracken, fern, fly,
bird, all appear to lie in the ordered regime near the edge of chaos. Four billion years of evolution in the
capacity to adapt offers a putative answer: Complex adaptive systems achieve,
in a lawlike way, the edge of chaos.
Tracing the history of this
discovery, the discovery that extremely complex systems can exhibit “order for
free”, that our intuitions have been deeply wrong, begins
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with the intuition that even
randomly “wired” molecular regulatory “circuits” with random “logic” would
exhibit orderly behavior if each gene or molecular variable were controlled by
only a few others. Notebooks from that
period mix wire-dot diagrams of organic molecules serving as drugs with wire
dot models of genetic circuitry. The
intuition proved correct. Idealizing a
gene as “on” or “off’, it was possible by computer simulations to show that
large systems with thousands of idealized genes behaved in orderly ways if each
gene is directly controlled by only two other genes. Such systems spontaneously lie in the ordered
regime. Networks with many inputs per
gene lie in the chaotic regime. Real
genomic systems have few molecular inputs per gene, reflecting the specificity
of molecular binding, and use a biased class of logical rules,
reflecting molecular simplicity, to control the on/off behavior of those genes.
Constraint to the vast ensemble of
possible genomic systems characterized by these two “local constraints” also inevitably
yields genomic systems in the ordered regime. The perplexing, enigmatic, magical order of
ontogeny may largely reflect large scale consequences of polymer chemistry.
Order for free. But more: The spontaneously ordered features
of such systems parallels a host of ordered features seen in the ontogeny of
mouse, man, bracken, fern, fly, bird. A
“cell type” becomes a stable recurrent pattern of gene expression, an “attractor”
in the jargon of mathematics, where an attractor, like a whirlpool, is a region
in the state space of all the possible patterns of gene activities to which the
system flows and remains. In the
spontaneously ordered regime, such cell type attractors are inherently small,
stable, and few, implying that the cell types of an organism traverse their
recurrent patterns of gene expression in hours not eons, that homeostasis,
Claude Bernard’s conceptual child, lies inevitably available for selection to
mold, and, remarkably, that it should be possible to predict the number of cell
types, each a whirlpool attractor in the genomic repertoire, in an organism. Bacteria harbor one to two cell types, yeast
three, ferns and bracken some dozen, man about two hundred and fifty. Thus, as the number of
genes, called genomic complexity, increases, the number of cell types
increases. Plotting cell types
against genomic complexity, one finds that the number of cell types increases
as a square root function of the number of genes. And, outrageously, the number of whirlpool
attractors in model genomic systems in the ordered regime also increase as a
square root function of the number of genes. Man, with about 100,000 genes should have
three hundred seventy cell types, close to two hundred and fifty.
A simple alternative theory would
predict billions of cell types.
Bacteria, yeast, ferns, and man,
members of different phyla, have no common ancestor for the past 600 million
years or more. Has selection struggled
for 600 million years to achieve a square root relation between genomic
complexity and number of cell types? Or
is this order for free so deeply bound into the roots of biological organization
that selection cannot avoid this order? But if the latter, then selection
is not the sole source of order in biology. Then Darwinism must be extended to embrace
self organization and selection.
The pattern of questions posed here
is novel in biology since Darwin. In the
NeoDarwinian world view, where organisms are ad
hoc solutions to design problems, the answers lie in the specific details
wrought by ceaseless selection. In
contrast, the explanatory approach offered by the new analysis rests on
examining the statistically typical, or generic, properties of an entire class,
or “ensemble” of systems all sharing known local features of genomic systems. If the typical, generic, features of ensemble
members corresponds to that seen in organisms, then explanation of those
features emphatically does not rest in the details. It rests in the general laws governing the typical
features of the ensemble as a whole. Thus an “ensemble” theory is a new kind of
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statistical mechanics. It predicts that the typical properties of
members of the ensemble will be found in organisms. Where true, it bodes a physics of biology.
Not only a
physics of biology, but beyond, such a new statistical mechanics demands
a new pattern of thinking with respect to biological and even cultural
evolution:
Self
organization, yes, aplenty. But
selection, or its analogues such as profitability, is always acting. We have no theory in physics, chemistry,
biology, or beyond which marries self organization and selection. The marriage consecrates a new view of life.
But two other failures of Darwin,
genius that he was, must strike us. How
do organisms, or other complex entities, manage to adapt and learn? That is, what are the conditions of “evolvability”. Second, how do complex systems coordinate
behavior, and more deeply, why are adaptive systems so often complex?
Consider “evolvability”
first. Darwin supposed that organisms
evolve by the successive accumulation of useful random variations. Try it with a standard computer program. Mutate the code, scramble the order of
instructions, and try to “evolve” a program calculating some complex function. If you do not chuckle, you should. Computer programs of the familiar type are not
readily “evolvable”. Indeed the more
compact the code, the more lacking in redundancy, the more sensitive it is to
each minor variation. Optimally
condensed codes are, perversely, minimally evolvable. Yet the genome is a kind of molecular
computer, and clearly has succeeded in evolving. But this implies something very deep:
Selection must achieve the kinds of systems which are able to adapt. That capacity is not Godgiven,
it is a success.
If the capacity to evolve must
itself evolve, then the new sciences of complexity seeking the laws governing
complex adapting systems must discover the laws governing the emergence and
character of systems which can themselves adapt by accumulation of successive
useful variations.
But systems poised in the ordered
regime near its boundary are precisely those which can, in fact, evolve by
successive minor variations. The behavior of systems in the chaotic regime are so drastically
altered by any minor variation in structure or logic that they cannot
accumulate useful variations. Conversely, systems deep in the ordered regime
are changed so slightly by minor variations that they adapt too slowly to an
environment which may sometimes alter catastrophically. Evolution of the capacity to adapt would be
expected, then, to achieve poised systems.
How can complex systems coordinate
behavior? Again, complex adaptive
entities achieve the edge of chaos because such systems can coordinate the most
complex behavior there. Deep in the chaotic
regime, alteration in the activity of any element in the system unleashes an
avalanche of changes, or “damage”, which propagates throughout most of the
system (Stauffer 1987). Such spreading
damage is equivalent to the “butterfly effect” or sensitivity to initial
conditions typical of chaotic systems. The
butterfly in Rio changes the weather in Chicago. Crosscurrents of such avalanches unleashed
from different elements means that behavior is not controllable. Conversely, deep in the ordered regime,
alteration at one point in the system only alters the behavior of a few
neighboring elements. Signals cannot
propagate widely throughout the system. Thus, control of complex behavior cannot be
achieved. Just at the boundary between
order and chaos, the most complex behavior can be achieved.
Finally, computer simulations
suggest that natural selection or its analogues actually do achieve the edge of
chaos. This third regime, poised between
the broad ordered regime and the vast chaotic regime, is razorblade thin in the
space of systems.
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Absent other forces, randomly assembled systems will
lie in the ordered or chaotic regimes. But let such systems play games with one
another, winning and losing as each system carries out some behavior with
respect to the others, and let the structure and logic of each system evolve by
mutation and selection, and, lo, systems do actually adapt to the edge of
chaos! No minor point this: Evolution
itself brings complex systems, when they must adapt to the actions of other, to
an internal structure and logic poised between order and chaos, (Kauffman
1991).
We are lead to a bold hypothesis:
Complex adaptive systems achieve the edge of chaos.
The story of the “edge of chaos” is
stronger, the implications more surprising. Organisms, economic entities, nations, do not
evolve, they coevolve. Almost miraculously, coevolving systems,
too, mutually achieve the poised edge of chaos. The sticky tongue of the frog alters the
fitness of the fly, and deforms its fitness landscapes that is, what changes in
what phenotypic directions improve its chance of survival. But so too in technological
evolution. The automobile
replaced the horse. With the automobile
came paved roads, gas stations hence a petroleum industry and war in the Gulf,
traffic lights, traffic courts, and motels. With the horse went stables, the smithy, and
the pony express. New goods and services
alter the economic landscape. Coevolution is a story of coupled deforming “fitness
landscapes”. The outcome depends jointly
on how much my landscape is deformed when you make an adaptive move, and how
rapidly I can respond by changing “phenotype”.
Are there laws governing coevolution? And how
might they relate to the edge of chaos? In startling ways. Coevolution, due to a selective “metadynamics”
tuning the structure of fitness landscapes and couplings between them, may
typically reach the edge of chaos (Kauffman 1992). E.coli and IBM not
only “play” games with the other entities with which they coevolve.
Each also participates in the very definition
or form of the game. It is we who
create the world we mutually inhabit and in which we struggle to survive. In models where players can “tune” the mutual
game even as they play, or coevolve, according to the
game existing at any period, the entire system moves to the edge of chaos. This surprising result, if general, is of
paramount importance. A simple view of
it is the following: Entities control a kind of “membrane” or boundary
separating inside from outside. In a kind
of surface to volume way, if the surface of each system is small compared to
its volume it is rather insensitive to alterations in the behaviors of other
entities. That is, adaptive moves by
other partners do not drastically deform one partner’s fitness landscape. Conversely, the ruggedness of the adaptive
landscape of each player as it changes its “genotype” depends upon how
dramatically its behavior deforms as its genotype alters. In turn this depends upon whether the adapting
system is itself in the ordered, chaotic, or boundary regime. If in the ordered, the system itself adapts on
a smooth landscape. In the chaotic
regime the system adapts on a very rugged landscape. In the boundary regime the system adapts on a
landscape of intermediate ruggedness, smooth in some directions of “genotype”
change, rugged in other directions. Thus, both the ruggedness of one’s own fitness
landscape and how badly that landscape is deformed by moves of one’s coevolving
partners are themselves possible objects of a selective “metadynamics”.
Under this selective metadynamics, tuning landscape structure and
susceptibility, model coevolving systems which mutually know and interact with
one another actually reach the edge of chaos. Here, under most circumstances, most entity
optimizes fitness, or payoff, by remaining the same. Most of the ecosystem is frozen into a percolating
Nash equilibrium, while coevolutionary changes
propagate in local unfrozen islands within the ecosystem. More generally, alterations in circumstances
send avalanches of changed optimal strategies propagating through the
coevolving system. At the edge of chaos
the size distributions
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of those avalanches approach
a power law, with many small avalanches and few large ones. During such coevolutionary
avalanches, affected players would be expected to fall transiently to low
fitness, hence might go extinct. Remarkably, this size distribution comes close
to fitting the size distribution of extinction events in the record. At a minimum, a distribution of avalanche
sizes from a common size small cause tells us that small and large extinction
events may reflect endogenous features of coevolving systems more than the size
of the meteor which struck.
The implications are mini-Gaia. As if by an invisible hand, coevolving complex
entities may mutually attain the poised boundary between order and chaos. Here, mean sustained payoff, or fitness, or
profit, is optimized. But here
avalanches of change on all length scales can propagate through the poised system.
Neither Sisyphus, forever pushing the
punishing load, nor fixed unchanging and frozen, instead E.coli
and its neighbors, IBM and its neighbors, even nation states in their collective
dance of power, may attain a precarious poised complex adaptive state. The evolution of complex adaptive entities
itself appears lawful. How far we come from Darwin’s genius.
This strand in the birth of
complexity theory, here spun, has its history. The first stages were set in the mid 1960s by
the discovery of spontaneous order, as well as the expected chaos, in complex
genomic systems. The discovery was not
without attention among scientists the day. Warren McCulloch, patriarch of cybernetics,
author with Pitts of “The Logical Calculus of Ideas Imminent in the Mind”,
step-child of Bertrand Russell’s logical atomism, and ancestor to today’s
neural connectionist flowering, invited me to share his home with his
remarkable wife Rook. “In pine tar is. In oak none is. In mud eels are. In clay none are”, sang this poet of neural
circuitry, demonstrating by dint of a minor Scots accent that no hearer could
unscramble four simple declarative sentences. Mind, complex, could fail to classify. “All Cambridge excited about your work”, wrote
McCulloch to this medical student who, thrilled, was yet to decode Warren’s
style.
Yet the time was not ripe. McCulloch had said twenty years would elapse
before biologists took serious note. He
was right, almost to the hour. And for
good reason had he made his prediction. The
late 1960s witnessed the blunderbuss wonderful explosion of molecular biology. Enough, far more than enough, to thrill to the
discovery of the real molecular details: How a gene is transcribed to RNA, translated
to protein, acts on its neighbors. What
is the local logic of a bacterial genetic circuit controlling metabolism of
lactose? Of a
bacterial virus, or phage? What
of the genes in a higher organism like the heralded but diminutive fruit fly? What of mouse and man? Enveloped by the Darwinian world view, whose
truths run deep, held in tight thrall by the certainty that the order in
organisms resides in the well wrought details of construction and design,
details inevitably ad hoc by virtue of their tinkered origins in the
wasteland of chance, molecular biologists had no use for heady, arcane,
abstract ensemble theories. The birth of
complexity theory, or this strand of it, though noted, received no sustaining
passion from its intended audience.
Twenty years, indeed. Rebirth of
this strand was midwifed by the physicists. An analogue ensemble theory, called “spin
glasses”, had been developed starting in the mid 1970s by solid state
physicists such as Philip Anderson, Scott Kirkpatrick, Bernard Derrida, Gerard
Toulouse, were struggling with an odd kind of dilute magnet material. Unlike the familiar ferromagnet,
captured in the famous Ising model, where magnetic
spins like to orient in the same direction as their neighboring spins, hence
the magnetized state with all spins oriented in the same direction arises, in
these bewildering spin glasses, adjacent spins might like to orient in the same
or in the oppo-
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site direction, depending sinusoidally on the distance between the spins. What a mess. Edwards and Anderson started an industry among
their brethren, and legitimized the new class of ensemble theories, by building
mathematical models of spin glasses on two or three dimensional lattices. Here each vertex houses a spin. But, to capture the bizarre logic of their
magnetic materials, Edwards and Anderson assumed that each adjacent pair of
spins “chose”, once and forever, whether they wanted to point in the same or
opposite direction, and how much they cared, given by an energy for that bond. Such messy models meant two major things. First, since couplings are assigned at random,
any one model spin glass is a member of a vast ensemble governed by the same
statistics. This is an ensemble theory
averaging, not over the states of one system as in the familiar statistical
mechanics of gases, but over billions of systems in the same ensemble. One seeks and characterizes the typical, or generic features of these systems. Second, such systems have tortuous and rugged
“energy landscapes”. This is due to
“frustration”. Consider four spins
around a square, where three pairs wish to point in the same direction, the
fourth does not. All cannot be
satisfied. Each configuration of the
many spins in the lattice of a spin glass has a total energy. The distribution of energies over the
configurations is the energy landscape, the analogue of a fitness landscape. Frustration implies that the landscape is
rugged and multipeaked.
Later, the structures of these spin
glass landscapes would provide new models of molecular evolution over rugged multipeaked fitness landscapes. Molecular evolution turns out to be much like
an electron bouncing on a complex potential surface at a small temperature. At too low a temperature, the electron remains
trapped in poor potential wells. At too
high a temperature, the electron bounces all over the potential surface and has
a high, unhappy, average energy. On any
defined time scale, energy is minimized at a specific fixed temperature at
which the electron is just “melting” out over the energy landscape, sliding
gracefully over low saddles in the surface separating wells such that it finds
good potential wells rather easily, then does not hop
out of them too rapidly. The analogue in
molecular evolution or other biological evolution over a fixed fitness
landscape, or one deforming at a given mean rate, is to tune the parameters of
adaptive search over the space such that an adapting population is just
“melting” out of local regions of the space. Again: The edge of Chaos!
By 1985 many of the physicists had
tired of their spin glasses. Some turned
to models of neural networks, sired by McCulloch, where neurons turn one
another on and off rather like genes, or like spins for that matter. Hopfield found further fame by modeling
parallel processing neural networks as spin systems, (Hopfield 1982). Attractors of such networks, rather than
modeling cell types as I had suggested, were taken to model memories. Each memory was an attractor. Memories were content addressable, meaning
that if the network were begun in the “basin of attraction” drained by one
whirlpool attractor, the system would flow to that attractor. Partial data, corresponding to an initial
state in a basin of attraction but not on the attractor itself, could be
reconstructed to the stored memory. (All
scientists regret the article not written. Jack Cowan and I had sketched an article in
1970 arguing against the logical atomism implicit in McCulloch and Pitts, an
atomism melted by Wittgenstein’s Investigations. In contrast, we wanted to suggest that
concepts were attractors in neural networks, hence a collective integrated
activity. From Wittgenstein we knew that
language games are not reducible to one another, law to human action to
physical phenomena. We wanted to argue
that new concepts, new language games, arose by bifurcations yielding new
attractors in the integrated activity of coupled neurons. One such attractor would not be reducible in
any obvious way to another attractor. Grandmother
cells be damned, concepts are collective properties.) Toulouse, brilliant as Hopfield, followed with
other spin glass like models whose basins of attraction were, he said, more
like French than English gardens. Many
have followed, to the field’s flowering.
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Not all the physicists who tired of
spin glasses turned to neurobiology. In
the way of these things, French physicist Gerard Weishbuch
was romantically involved with French mathematician Francoise Fogleman-Soulie. Francoise chose, as her thesis topic, the
still poorly understood order found in “Kauffman nets” (Fogleman-Soulie
1985). Many theorems followed. Gerard’s interest extended from Francoise and
spin glasses to this strange hint of order for free. Summers in Jerusalem and Haddasah
hospital with Henri Atlan, doctor, theoretical
biologist, author of Crystal and Smoke with its search for order and
adaptability, led to more results. Put
these bizarre genetic networks on lattices, where any good problem resides. See the order. Scale parameters. Find phase transitions and the scaling laws of
critical exponents. A
new world to a biologist. And
Gerard shared an office with Bernard Derrida, nephew of deconstructionist
Jacques. Bernard looked at these
“Kauffman nets”, the name is due to Derrida, and leaped to an insight no
biologist would ever dare. Let the
network be randomly rewired at each moment, creating an “annealed” model. Theorem followed theorem. No genome dances so madhatterly.
But the mathematics can. Phase transition assured. Order for free in networks
of low connectivity. Analysis of sizes of basins of attraction, and of overlaps between
attractors, (Derrida and Pomeau 1986). I lost a bottle of wine to Derrida, shared
over dinner, on the first theorem.
Even I chimed in with a few
theorems here and there: a mean field approach to attractors, the existence of
a connected set of elements which are “frozen” and do not twinkle on and off,
that spans or percolates across the system. This frozen component, leaving behind isolated
twinkling islands, is the hallmark of order. The phase transition to chaos occurs, as
parameters alter, when the frozen component “melts”, and the twinkling islands
merge into an unfrozen, twinkling, percolating sea, leaving behind small
isolated frozen islands. The third,
complex regime, the boundary between order and chaos, arises when the twinkling
connected, percolating sea is just breaking up into
isolated islands. Avalanches of changes
due to perturbations, which only propagate in the twinkling unfrozen sea, show
a characteristic “power law” distribution at the phase transition, with many
small avalanches and a few enormous ones (Kauffman 1989).
Now the reader can see why systems
on the boundary between order and chaos can carry out the most complex tasks,
adapt in the most facile fashion. Now
too, I hope, you can see the intrigue at the possibility that complex adaptive
systems achieve the edge of chaos in their internal structure, but may also coevolve in a selective metadynamics
to achieve the edge of chaos in the ecosystem of the mutual games they play! The edge of chaos may be a major organizing
principle governing the evolution and coevolution of
complex adaptive systems.
Other themes, again spawned by
physicists, arose in America, and lead quasi-independently, quasi-conversing,
to the growth of interest in complexity. “Kauffman nets”, where the wiring diagram
among “genes” or binary elements, is random, and the
logic governing each element is randomly assigned, hence differs for different
“genes”, are versions of a mathematical structure called “cellular automata”. Cellular automata were invented by von Neuman, whose overwhelming early work, here and on the
existence of self reproducing automata, filters down through much that follows.
The simplest cellular automata are lines
or rings of on/off sites, each governed by the same logical rule which
specifies its next activity, on or off, as a function of its own current state
and those of its neighbors to a radius, r. Enter young Stephen Wolfram, quick, mercurial,
entreprenurial. The youngest MacArthur
Fellow, Wolfram had begun publishing in high energy physics at age 16. While a graduate student at Cal Tech, he
earned the mixed admiration and enmity of his elders by inventing computer code
to carry out complex mathematical calculations. Cal Tech did not mind his
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mind. It minded his marketing the products of his
mind. Never mind. Thesis done, Wolfram packed off to the
Institute for Advanced Study and fell to the analysis of cellular automata. He amazed his audiences. The world of oddball mathematicians, computer
scientists, wayward physicists, biologists soon twiddled with CA rules. Four classes of behavior
emerged, stable, periodic, and chaotic, of course. And between them, on the
edge between order and chaos, capable of complex computation, perhaps universal
computation? A
third “complex class”. Among the
most famous of these CA rules is Conway’s “Game of Life”, provably capable of
universal computation, demonstrably capable of capturing gigabits of memory and
gigaseconds of time among amateurs and professionals
world wide. The game of life, like true
life itself according to our bold hypothesis, also lies at the edge of chaos.
Paralleling Derrida is the lineage
flowing from Chris Langton. Langton, a computer
scientist and physicist, elder graduate student, survivor of early hang gliding
and an accident relieving him of most unbroken bone structure in his
mid-twenties body, thought he could improve on von Neuman.
He invented a simple self reproducing automaton
and littered computer screens from Los Alamos to wherever. Then Langton,
following von Neuman again, and fired up by Wolfram,
began playing with cellular automata. Where I had shown that the transition from
order to chaos was tuned by tuning the number of inputs per “gene” from 2 to
many, Langlon reinvented Derrida’s approach. Derrida, like Langton
after him, in turn reinvented a classification of logical rules first
promulgated by Crayton Walker. This classification marks the bias, P, towards
the active, or inactive state, over all combinations
of activities of the inputs to an element. Derrida had shown that the phase transition
occurred at a critical value of this bias, Pc. At that bias, frozen components emerge. Langton found the
same phase transition, but measured in a different way to focus on how complex
a computation might be carried out in such a network. This complexity, measured as mutual information,
or what one can predict about the next activity of one site given the activity
of another site, is maximized at the phase transition (Langton
1991).
The poised edge reappears, like a new second law of thermodynamics,
everywhere hinted, but, without Carnot, not yet
clearly articulated, in the recent work of physicist Jim Crutchfield. “Symbolic dynamics” is a clever new tool used
to think about complex dynamical systems. Imagine a simple system such as a pendulum. As its swings back and forth, it crosses the
midpoint where it hangs straight down. Use
a 1 to denote times when the pendulum is to the left of the midpoint, and 0 to
denote times when the pendulum swings to the right. Evidently, the periodic pendulum gives rise to
an alternating sequence of 1 and 0 values. Such a symbol sequence records the dynamics of
the pendulum by breaking its state space into a finite number of regions, here
two, and labeling each region with a symbol. The flow of the system gives rise to a symbol
sequence. Theorems demonstrate that,
with optimally chosen boundaries between the regions, here the midpoint, the
main features of the dynamics of the real pendulum can be reconstructed from
the symbol sequence. For a periodic
process, the symbol sequence is dull. But link several pendulums together with weak
springs and again denote the behavior of one pendulum by 1 and 0 symbols. Now the motion of each pendulum is influenced
by all the others in very complex ways. The symbol sequence is correspondingly
complex. The next step is to realize
that any symbol sequence can be generated as the output of a finite automaton,
a more or less complex “neural” or “genetic” network of on off elements. Further, theorems assure us that for any such
symbol sequence, the smallest, or minimal automaton,
with the minimal number of elements and internal states, can be found. Thus, the number of elements, or states, of
such a system is a measure of the complexity of the symbol sequence. And now the wonderful surprise. The same three phases, ordered, chaotic, and
complex, are found again. That is, such
automata, like Kauffman nets and neural nets, har-
307 Index
bor
the same generic behaviors. And, as you
will now suspect, the complex regime again corresponds to the most complex
symbol sequences, which in turn arise in dynamical systems themselves on the
boundary between order and chaos.
If one had to formulate, still poorly articulated,
the general law of adaptation in complex systems, it might be this: Life adapts
to the edge of chaos.
2. The Origin of Life and its Progeny
This story, the story of the
boundary between order an chaos achieved by complex
coevolving systems, is but half the emerging tale. The second voice tells of the origin of life
itself, a story both testable and, I hope, true, a story implying vast stores
of novel drugs, vaccines, universal enzymatic tool boxes, a story latent with
the telling of technological and cultural evolution, of bounded rationality,
the coemergence of knower and known, hence at last,
of telling whether E. coli and IBM do, in fact, know their worlds, the worlds
they themselves created, in the same deep way.
Life is held a miracle, God’s breath
on the still world, yet cannot be. Too
much the miracle, then we were not here. There must be a viewpoint, a place to stand,
from which the emergence of life is explicable, not as a rare untoward
happening, but as expected, perhaps inevitable. In the common view, life originated as a self
reproducing polymer such as RNA, whose self complementary structure, since
Watson and Crick remarked with uncertain modesty, suggests its mode of
reproduction, has loomed the obvious candidate urbeast
to all but the stubborn. Yet stubbornly
resistant to test, to birthing in vitro is this supposed simplest molecule of
life. No worker has yet succeeded in
getting one single stranded RNA to line up the complementary free nucleotides,
link them together to form the second strand, melt them apart, then repeat the
cycle. The closest approach shows that a
polyC polyG strand, richer
in C than G, can in fact line up its complementary strand. Malevolently, the newly formed template is
richer in G than C, and fails, utterly, to act as a facile template on its own.
Alas.
Workers attached to the logic of
molecular complementarity are now focusing effort on
polymers other than RNA, polymers plausibly formed in the prebiotic
environment, which might dance the still sought dance. Others, properly entranced with the fact that
RNA can act as an enzyme, called a ribozyme, cleaving
and ligating RNA sequences apart and together, seek a
ribozyme which can glide along a second RNA, serving
as a template that has lined up its nucleotide complements, and zipper them
together. Such a ribozyme
would be a ribozyme polymerase, able to copy any RNA
molecule, including itself. Beautiful indeed. And
perhaps such a molecule occurred at curtain-rise or early in the first Act. But consider this: A free living organism,
even the simplest bacterium, links the synthesis and degradation of some
thousands of molecules in the complex molecular traffic of metabolism to the
reproduction of the cell itself. Were
one to begin with the RNA urbeast, a nude gene, how
might it evolve? How might it gather
about itself the clothing of metabolism?
There is an alternative approach
which states that life arises as a nearly inevitable phase transition in
complex chemical systems. Life formed by
the emergence of a collectively autocatalytic system of polymers and simple
chemical species.
Picture, strangely, ten thousand
buttons scattered on the floor. Begin to
connect these at random with red threads. Every now and then, hoist a button and count
how many buttons you can lift with it off the floor. Such a connected collection is call a “component” in a “random graph”. A random graph is just a bunch of buttons connected
at random by a bunch of threads. More
formally, it is a set of N nodes connect-
308
ed at random by B edge. Random graphs undergo surprising phase
transitions. Consider the ratio of E/N,
or threads divided by buttons. When E/N
is small, say .1, any button is connected directly or indirectly to only a few
other buttons. But when E/N passes 0.5, so there are half as many
threads as buttons, a phase transition has occurred. If a button is picked up, very many other
buttons are picked up with it. In short,
a “giant component” has formed in the random graph in which most buttons are
directly or indirectly connected with one another. In short, connect enough nodes and a connected
web “crystalizes”.
Now life. Proteins and RNA molecules are linear polymers
build by assembling a subset of monomers, twenty types in proteins, four in
RNA. Consider the set of polymers up to
some length, M, say 10. As M increases
the number of types of polymers increases exponentially, for example there are
20 M proteins of length M. This is a familiar
thought. The rest are not. The simplest reaction among two polymers
consists in gluing them together. Such
reactions are reversible, so the converse reaction is simply cleaving a polymer
into two shorter polymers. Now count the
number of such reactions among the many polymers up to length M. A simple consequence of the combinatorial
character of polymers is that there are many more reactions linking the
polymers than there are polymers. For
example, a polymer length M can be formed in M 1 ways by gluing shorter
fragments comprising that polymer. Indeed, as M increases, the ratio of reactions
among the polymers to polymers is about M, hence increases as M increases. Picture such reactions as black, not red,
threads running from the two smaller fragments to a small square box, then to
the larger polymer made of them. Any
such triad of black threads denotes a possible reaction among the polymers; the
box, assigned a unique number, labels the reaction itself. The collection of all such triads is the
chemical reaction graph among them. As
the length of the longest polymer under consideration, M, increases, the web of
black triads among these grows richer and richer. The system is rich with crosslinked
reactions.
Life is an autocatalytic process
where the system synthesizes itself from simple building blocks. Thus, in order to investigate the conditions
under which such a auto-catalytic system might
spontaneously form, assume that no reaction actually occurs unless that
reaction is catalyzed by some molecule. The next step notes that protein and RNA
polymers can in fact catalyse reactions cleaving and ligating proteins and RNA polymers: trypsin
in your gut after dinner digesting steak, or ribozyme
ligating RNA sequences. Build a theory showing the probability that
any given polymer catalyzes any given reaction. A simple hypothesis is that each polymer has a
fixed chance, say one in a billion, to catalyze each
reaction. No such theory can now be accurate,
but this hardly matters. The conclusion
is at hand, and insensitive to the details. Ask each polymer in the system, according to
your theory, whether it catalyzes each possible reaction. If “yes”, color the corresponding reaction
triad “red”, and note down which polymer catalyzed that reaction. Ask this question of all polymers for each
reaction. Then some fraction
of the black triads have become red. The red triads are the catalyzed reactions in
the chemical reaction graph. But such a
catalyzed reaction graph undergoes the button thread phase transition. When enough reactions are catalyzed, a vast web of polymers are linked by catalyzed reactions. Since the ratio of reactions to polymers
increases with M, at some point as M increases at least one reaction per
polymer is catalyzed by some polymer. The
giant component crystalizes. An autocatalytic set which collectively
catalyzes its own formation lies hovering in the now pregnant chemical soup. A self reproducing chemical system, daughter
of chance and number, swarms into existence, a connected collectively
autocatalytic metabolism. No nude gene,
life emerged whole at the outset.
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I found this theory in 1971. Even less than order for
free in model genomic systems did this theory find favor. Stuart Rice, colleague, senior chemist, member
of the National Academy of Science asked, “What for?” Alas again. When famous older scientists say
something warrants the effort, rejoice. When
famous older scientists are dismissive, beware. I turned to developmental genetics and pattern
formation, the beauty of Alan Turing’s theory of pattern formation by the
establishment of chemical waves, the quixotic character of homeotic
mutants in the fruit fly, Drosophila melanogaster,
where eyes convert to wings, antennas to legs, and heads to genitalia. Fascinating disorders, these, called metaplasias, whose battered sparse logic hinted the logic
of developmental circuits. But
experimental developmental genetics, even twelve years and surgery on ten
thousand embryos, is not the central thread of the story.
In 1983 interest in serious
theories of the origin of life was rekindled. In 1971 and the ensuing decade, Nobelist Manfred Eigen, together
with theoretical chemist Peter Schuster, developed a well formulated, careful
model of the origin of life, called the “hypercycle”.
In this theory, the authors begin by assuming
that short nude RNA sequences can replicate themselves. The hooker is this: During such replication,
errors are made. The wrong nucleotide
may be incorporated at any site. Eigen and Schuster showed that an error catastrophe occurs
when RNA sequences become too long for any fixed error rate. The RNA population “melts” over RNA sequence space, hence all information accumulated within the “best”
RNA sequence, culled by natural selection, is lost. The “hypercycle” is
a clever answer to this devastation: Assume a set of different short RNA
molecules, each able to replicate itself. Now assume that these different RNA molecules
are arranged in a control cycle, such that RNA 1 helps RNA 2 to replicate, RNA
2 helps RNA 3, and so on until RNA N closes the loop by helping RNA 1. Such a loop is a hypercycle,
“hyper” because each RNA itself is a tiny cycle of two
complementary strands which copy one another. The hypercycle is,
in fact, a coevolving molecular society. Each RNA species coevolves in company with its
peers. This model has been studied in
detail, and has strengths and weakness. Not
the least of the latter is that no RNA sequence can yet replicate itself.
But other voices were lifted, from
the most intelligent minds. Freeman Dyson, of the Institute of Advanced
Studies, an elegant scientist and author of lyric books such as Disturbing the Universe, suggested, in Origins of Life, that life arose as a
phase transition in complex systems of proteins. Philip Anderson, with Daniel Stein, and Rothkar, borrowed from spin-glass theory to suggest that a
collection of template replicating RNA molecules with overlapping ends and
complex fitness functions governing their survival might give rise to many
possible self reproducing sequences.
Lives in science have their peculiar
romance. I heard of these approaches at
a conference in India. Central India, Madya Pradesh,
sweats with the sweet smell of the poor cooking over fires of dried buffalo
dung. The spiritual character of India
allows one to speak of the origin of life with colleagues such as Humberto Maturana, riding in
disrepair except for his glasses and clear thoughts, in a bus of even greater
disrepair among the buffalo herds to Sanchi, early Buddest shrine. The Budda at the west portal, thirteen hundred years old, ineffably
young, invited only a gentle kiss from the foreigners in time, space, culture. Dyson’s and Anderson’s approaches appeared
flawed. Dyson had assumed his conclusion,
hidden in assumption. Life as an
autocatalytic crystalization was trivially present in
his model, slipped in by hand, not accounted for as a
deeply emergent property of chemistry. And
Anderson, overwhelmingly insightful, proposed nothing truly deep not already
resting on RNA self complementarity. The romance continues with a flurry of
theorems and lemmas, simple to a real mathematician.
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This hiccup of creativity, I hoped,
warranted investigation. Doyne Farmer, young physicist at Los Alamos, and his
childhood friend Norman Packard, and I began collaborating to build detailed
computer simulations of such autocatalytic polymer systems. Six years later, a Ph.D. thesis by Richard
Bagley later, it is clear that the initial intuitions were fundamentally
correct: In principle complex systems of polymers can become collectively self
reproducing. The routes to life are not
twisted backalleys of thermodynamic improbability,
but broad boulevards of combinatorial inevitability.
If this new view of the crystalization of life as a phase transition is correct,
then it should soon be possible to create actual self reproducing polymer
systems, presumably of RNA or proteins, in the laboratory. Experiments, even now, utilizing very complex
libraries of RNA molecules to search for autocatalytic sets are underway in a
few laboratories.
If not since Darwin, then since
Weisman’s doctrine of the germ plasm was reduced to
molecular detail by discovery of the genetic role of chromosomes, biologist
have believed that evolution via mutation and selection virtually requires a
stable genetic material as the store of heritable information. But mathematical analysis of autocatalytic
polymer systems belies this conviction. Such
systems can evolve to form new systems. Thus,
contrary to Richard Dawkin’s thesis in “The Selfish
Gene”, biological evolution does not, in principle, demand self-replicating
genes at the base (Dawkins 1976). Life
can emerge and evolve without a genome. Heresy, perhaps? Perhaps.
Many and unexpected are the
children of invention. Autocatalytic
polymer sets have begotten an entire new approach to complexity.
The starting point is obvious. An autocatalytic polymer set is a functional
integrated whole. Given such a set, it
is clear that one can naturally define the function of any given polymer in the
set with respect to the capacity of the set to reproduce itself. Lethal mutants exist, for if a given polymer
is removed, or a given foodstuff deleted, the set may fail to reproduce itself.
Ecological interactions among coevolving
autocatalytic sets lie to hand. A
polymer from one such set injected into a second such set may block a specific
reaction step and “kill” the second autocatalytic set. Coevolution of such
sets, perhaps bounded by membranes, must inevitably reveal how such systems
“know” one another, build internal models of one another, and cope with one another.
Models of the
evolution of knower and known lay over the conceptual horizon.
Walter Fontana, graduate student of
Peter Schuster, came to the Santa Fe Institute, and Los Alamos. Fontana had worked with John McCaskill, himself an able young physicist collaborating
with Eigen at the Max Planck Institute in Gottingen. McCaskill dreamt of
polymers, not as chemicals, but as Turing machine computer programs and tapes. One polymer, the computer, would act on
another polymer, the tape, and “compute” the result, yielding a new polymer. Fontana was entranced. But he also found the autocatalytic story
appealing. Necessarily, he invented
“Algorithmic Chemistry”. Necessarily, he
named his creation “Alchemy”, (Fontana 1991).
Alchemy is based on a language for universal computation called the
lambda calculus. Here almost any binary
symbol string is a legitimate “program” which can act on almost any binary
symbol string as an input to compute an output binary symbol string. Fontana created a “Turing gas” in which an
initial stock of symbol strings randomly encounter one another in a “chemostat” and may or may not interact to yield symbol strings.
To maintain the analogue of selection,
Fontana requires that a fixed total number of symbol string polymers be
maintained in the chemostat. At each mo-
311
ment,
if the number of symbol strings grows above the maximum allowed, some strings
are randomly lost from the system.
Autocatalytic sets emerge again! Fontana finds two types. In one, a symbol string which copies itself
emerges. This “polymerase” takes over
the whole system. In the second,
collectively autocatalytic sets emerge in which each symbol string is made by
some other string or strings, but none copies itself. Such systems can then evolve in symbol string
space evolution without a genome.
Fontana had broken the bottleneck. Another formulation of much the same ideas,
which I am now using, sees interactions among symbol strings creating symbol
strings and carrying out a “grammar”. Work
on disordered networks, work which exhibited the three broad phases, ordered,
chaotic and complex, drove forward based on the intuition that order and
comprehensibility would emerge by finding the generic behavior in broad regions
of the space of possible systems. The
current hope is that analysis of broad reaches of grammar space, by sampling
“random grammars”, will yield deep insight into this astonishingly rich class
of systems.
The promise of these random grammar
systems extend from analysis of evolving proto-living systems, to
characterizing mental processes such as multiple personalities, the study of
technological coevolution, bounded rationality and
non-equilibrium price formation at the foundations of economic theory, to
cultural evolution. And the origin of
life model itself, based on the probability that an arbitrary protein catalyzes
an arbitrary reaction, spawned the idea of applied molecular evolution the
radical concept that we might generate trillions of random genes, RNA sequences,
and proteins, and learn to evolve useful polymers able to serve as drugs,
vaccines, enzymes, and biosensors. The
practical implications now appear large.
Strings of symbols which act upon
one other to generate strings of symbols can, in general, be computationally
universal. That is, such systems can
carry out any specified algorithmic computation. The immense powers and yet surprising limits,
trumpeted since Gödel, Turing, Church, Kleene, lie
before us, but in a new and suggestive form. Strings acting on strings to generate strings
create an utterly novel conceptual framework in which to cast the world. The puzzle of mathematics, of course, is that
it should so often be so outrageously useful in categorizing the world. New conceptual schemes allow starkly new
questions to be posed.
A grammar model is simply
specified. It suffices to consider a set
of M pairs of symbol strings, each about N symbols in length. The meaning of the grammar, a
catch-as-catch-can set of “laws of chemistry” is this: Wherever the left member
of such a pair is found in some symbol string in a “soup” of strings,
substitute the right member of the pair. Thus, given an initial soup of strings, one
application of the grammar might be carried out by us, acting Godlike. We regard each string in the soup in turn, try
all grammar rules in some precedence order, and carry out the transformations
mandated by the grammar. Strings become
strings become strings. But we can let
the strings themselves act on one another. Conceive of a string as an “enzyme” which acts
on a second string as a “substrate” to produce a “product”. A simple specification shows the idea. If a symbol sequence on a string in the soup,
say 111, is identical to a symbol sequence on the “input” side of one grammar
pair, then that 111 site in the string in the soup can act as an enzymatic
site. If the enzymatic site finds a substrate
string bearing the same site, 111, then the enzyme acts on the substrate and
transforms its 111 to the symbol sequence mandated by the grammar, say 0101. Here, which symbol string in the soup acts as
enzyme and which is substrate is decided at random at each encounter. With minor effort, the grammar rules can be
extended to
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allow one enzyme string to
glue two substrate strings together, or to cleave one substrate string into two
product strings.
Grammar string models exhibit
entirely novel classes of behavior, and all the phase transitions shown in the
origin of life model. Fix a grammar. Start the soup with an initial set of strings.
As these act on one another, it might be
the case that all product strings are longer than all substrate strings. In this case, the system never generates a
string previously generated. Call such a
system a jet. Jets might be finite, the
generation of strings petering out after a while, or infinite. The set of
strings generated from a sustained founder set might loop back to form strings
formed earlier in the process, by new pathways. Such “mushrooms” are just the autocatalytic
sets proposed for the origin of life. Mushrooms
might be finite or infinite, and might, if finite, squirt infinite jets into
string space. A set of strings might
generate only itself, floating free like an egg in string space. Such an egg is a collective identity operator
in the complex parallel processing algebra of string transformations. The set of transformations collectively specifies
only itself. The egg, however, might
wander in string space, or squirt an infinite jet. Perturbations to an egg, by injecting a new
string, might be repulsed, leaving the egg unchanged,
or might unleash a transformation to another egg, a mushroom, a jet. Similarly, injection of an exogenous string
into a finite mushroom might trigger a transformation to a different finite
mushroom, or even an infinite mushroom. A
founder set of strings might galvanize the formation of an infinite set of
strings spread all over string space, yet leave local “holes” in string space
because some strings might not be able to be formed from the founder set. Call such a set a filigreed fog. It may be formally undecidable
whether a given string can be produced from a founder set. Finally, all possible strings might ultimately
be formed, creating a pea soup in string space.
Wondrous
dreamlike stuff, this. But more
lies to hand. Jets, eggs, filigreed fogs
and the like are merely the specification of the string contents of such an
evolving system, not its dynamics. Thus,
an egg might regenerate itself in a steady state, in a periodic oscillation
during which the formation of each string waxes and wanes cyclically, or
chaotically. The entire “edge of chaos”
story concerned dynamics only, not composition. String theory opens new conceptual territory.
Models of mind, models of
evolution, models of technological transformation, of cultural succession, these grammar models open new provinces for precise thought.
In “Origins of Order” I was able only to
begin to discuss the implications of Fontana’s invention. I turn next in this essay to mention their
possible relation to artificial intelligence and connectionism, sketch their
possible use in the philosophy of science, then discuss their use in economics,
where they may provide an account, not only of technological evolution, but of
bounded rationality, non-equilibrium price formation, future shock, and perhaps
most deeply, a start of a theory of “individuation” of coordinated clusters of
processes as entities, firms, organizations, so as to optimize wealth
production. In turn, these lead to the
hint of some rude analogue of the second law of thermodynamics, but here for
open systems which increase order and individuation to maximize something like
wealth production.
Not the least of these new
territories might be a new model of mind. Two great views divide current theories of
mind. In one, championed by traditional
artificial intelligence, the mind carries out algorithms in which condition
rules act on action rules to trigger appropriate sequences of actions. In contrast, connectionism posits neural
networks whose attractors are classes, categories, or memories. The former are good at sequential logic and
action, the latter are good at pattern recognition. Neither class
313
has the strengths of the
other. But parallel processing symbol
strings have the strength of both. More
broadly, parallel processing string systems in an open coevolving set of
strings, wherein individuation of coordinated clusters of
these production processes arise, may be near universal models of minds,
knower and known, mutually creating the world they inhabit.
Next, some comments about the
philosophy of science by an ardent amateur. Since Quine we have
lived with holism in science, the realization that some claims are so central
to our conceptual web that we hold them well neigh unfalsifiable,
hence treat them as well neigh true by definition. Since Kuhn we have lived with paradigm
revolutions and the problems of radical translation, comparability of terms
before and after the revolution, reducability. Since Popper we have lived ever more uneasily
with falsifiability and the injunction that there is
no logic of questions. And for decades
now we have lived with the thesis that conceptual evolution is like biological
evolution: Better variants are cast up, never mind how conceived, and passed
through the filter of scientific selection. But we have no theory of centrality versus peripherality in our web of concepts, hence no theory of pregnant versus trivial questions, nor of
conceptual recastings which afford revolutions or
wrinkles. But if we can begin to achieve
a body of theory which accounts for both knower and known as entities which
have coevolved with one another, E. coli and its world, I.B.M. and its world,
and understand what it is for such a system to have a “model” of its world via
meaningful materials, toxins, foods, shadow of a hawk cast on newborn chick, we
must be well on our way to understanding science too as a web creating and
grasping a world.
Holism should be interpretable in
statistical detail. The centrality of
Newton’s laws of motion compared to details of geomorphology in science find
their counterpart in the centrality of the automobile and peripherality
of pet rocks in economic life. Conceptual
revolutions are like avalanches of change in ecosystems, economic systems, and
political systems. We need a theory of
the structure of conceptual webs and their transformation. Pregnant questions are those which promise
potential changes propagating far into the web. We know a profound question when we see one. We need a theory, or framework, to say what we
know. Like Necker
cubes, alternative conceptual webs are alternative grasped worlds. We need a way to categorize “alternative
worlds” as if they were alternative stable collective string production
systems, eggs or jets. Are mutually
exclusive conceptual alternatives, like multiple personalities, literally
alternative ways of being in the world. What pathways of conceptual change flow from a
given conceptual web to what “neighboring” webs, and why? This is buried in the actual structure of the
web at any point. Again, we know this,
but need a framework to say what we know. I suspect grammar models and string theory may
help. And conceptual evolution is like
cultural evolution. I cannot help the
image of an isolated society with a self consistent set of roles and beliefs as
an egg shattered by contact with our supracritical
Western civilization.
Now to economic webs, where string
theory may provide tools to approach technological evolution, bounded
rationality, non-equilibrium price formation, and perhaps individuation of
“firms”. I should stress that this work
is just beginning. The suspected
conclusions reach beyond that which has been demonstrated mathematically or by
simulations.
A first issue is that string theory
provides tools to approach the fundamental problem of technological evolution. Theoretical economists can earn a living
scratching equations on blackboards. This
is a strange way to catch dinner. One
hundred thousand years ago, their grandfathers and grandmothers scratched a
living in a more direct way. Economists
survive only because the variety of goods and services in an economy has
314
expanded since Neanderthal to
include the services mathematical economists. Why? And what role does the structure of an
economic web play in its own growth?