Chapter 44 Trajectories of howitzer shells

Trajectories of howitzer shells Kaufman sincerely hopes that the birth of a new theory doesn't take that long. "I heard Farmer say that it's a bit like the thermodynamic phase before Carnot came along, and I think he's right. What we're really looking forward to from complexity science is the pattern of non-equilibrium systems in the universe. The general law of formation. We need to have the right concepts to enable the birth of this general law. Although we now have all these clues, such as the clues such as the edge of chaos, I still feel that we are still on the verge of a breakthrough. We seem to It was a few years before Kano came along."

Indeed, Kaufman clearly hoped that the new Kano would bear Kaufman's name.Like Farmer, Kaufman's imagining of a new second law should explain how emergent entities generate their most interesting behaviors at the edge of chaos, and how adaptability endlessly complicates these entities.But Kaufman isn't bothered by the administrative headaches that Farmer has for chairing a research group.On the day he arrived at the Santa Fe Institute, he threw himself into the research of the problem.He talks like a man in desperate need of an answer, as if thirty years of trying to unravel the mysteries of order and self-organization have made the answer so near but elusive. Physical pain.

"For me, the notion of evolution on the edge of chaos was one step away from turning into a painstaking effort to understand the mix of self-organization and natural selection," Kaufman says. "I was annoyed because I almost I can already feel it, see it. I'm not a very cautious scientist. It's not over yet, I see only a hint of a lot of things. I feel more like a howitzer shell that shot through a hole. Wall after wall, leaving a mess. I feel like I'm breaking through one problem after another, trying to see the end of the howitzer's trajectory." Kaufman said the trajectory of this howitzer shell began in the sixties, from his work on autocatalytic group and gene network models.At the time he really wished he could believe that life had arisen entirely by self-organization, that natural selection was a side effect.Embryo development is the best proof.During embryonic development, interacting genes organize themselves into different shapes, corresponding to different cell types, and interacting cells organize themselves into various textures and structures. "I've never doubted the role of natural selection. It's just that, to me, the deepest truth has to do with self-organization."

"But one day in the early 1980s, I visited John Maynard Smith." Smith of the University of Sussex in England is his old friend and a famous biologist.At that time, Kaufman began to think seriously about self-organization after a ten-year pause due to the study of embryonic development in Drosophila. "When John, his wife Sheila, and I went out for a walk in the meadows, John said we weren't far from Darwin's house. Then he went on to say that those who seriously believed in natural selection were pretty much English country gentlemen, Like Darwin. Then he looked at me and smiled and said, 'The people who don't think natural selection has much to do with evolution are almost urban Jews!' That made me laugh. I sat in the bushes and laughed . But he said, 'Stewart, you really need to think about natural selection.' But I was very reluctant, and I wanted this to happen spontaneously."

Yet Kaufman had to admit that Maynard Smith was right.Mere self-organization alone cannot accomplish all this.After all, mutated genes self-assemble just as easily as normal genes.As a result, when self-organization produces deformed fruit flies whose legs grow to the place where they should grow whiskers, natural selection is still needed to complete the task of survival of the fittest. “So, in 1982 I sat down and drew up an outline for my book,” (titled The Origins of Order, Kaufman’s summation of three decades of thinking, revised and revised for publication in 1992. ) "This book is about self-organization and natural selection: how do you reconcile the two? At first I thought there must be competition between the two. Natural selection might want to do this, but the self-organization behavior of the system is The goal of natural selection cannot be achieved. So they will fight each other until they reach some equilibrium point where natural selection can promote the development of things. My imagination runs through the first two thirds of the book space.” More precisely, Kaufman’s imagination may have had a greater weight in his thinking.It wasn't until the mid-eighties, after he came to the Santa Fe Institute, that he began to hear the concept of the edge of chaos, and his view changed.

Kaufman says the idea of ​​the brink of chaos ultimately changed the place in his mind for the question of self-organization and natural selection.But at the same time, he has mixed feelings about the change.Because he began to study gene networks in the 1960s, and he had already observed behaviors similar to phase transitions in gene networks. By 1985, he himself was almost about to derive the concept of the edge of chaos from it. “This is one of the many papers I should have written that I didn’t write. I’ve always regretted it,” Kaufman said, still remorseful. In the summer of 1985, when he took his annual leave to do research in Paris, the idea of ​​the edge of chaos had already sprouted in his mind.He spent several months at the Haidasa Hospital in Jerusalem with Gerard Weisbuch and Francis Fogelman-Soule.Francis is a graduate student writing his doctoral dissertation on Kaufman's Genetic Algorithms.One morning, Kaufman began to consider what he called "frozen components" of genetic networks.He noticed this problem as early as 1971.In his lightbulb analogy, groups of interconnected nodes scattered throughout the network appear to be neither all on nor all off, and stay that way forever, while "lightbulbs" elsewhere in the network Continue to turn on and off.In the densely connected network, the lights flickering constantly, it is completely chaotic, and there is never a frozen component.But in sparsely connected networks, the frozen component dominates, which is why these systems are prone to freezing entirely.But he wondered, what happens in the middle?Such more or less interconnected networks seem to come closest to real genetic systems.They are in a state that is neither completely frozen nor completely chaotic...

"I remember yelling at Francis and Gaillard that morning: 'Guys, look, as the frozen components melt and begin to gingerly connect to each other, and the unfrozen islands eagerly stretch out, we get the most complex calculations!" We had a lot of talk about this that morning, and everyone thought it was a very interesting phenomenon. I made a note of it and put it as a problem for further research. But then we were busy Something else. Also, at the time I was still like 'no one cares about this kind of stuff,' so I didn't put my full energy into it again." It turned out that Kaufman had a memory illusion when he heard all the talk about Edge of Chaos.He felt both regret and excitement.He couldn't help thinking of the concept as his own, but at the same time he had to admit that Langdon knew more about the connection between phase transitions, computer algorithms, and life than he had flashed that morning. Much deeper.Longton's painstaking efforts had brought the concept to rigor and precision.Moreover, Langton has recognized that Kaufman has not yet reached this point.The edge of chaos is much more than a simple boundary between a perfectly ordered system and a completely disordered system.It was indeed after several long talks between Langton and Kaufman that Kaufman finally realized this.The edge of chaos is the special boundary into which the self develops, and in this boundary, the system will produce life-like phenomena and complex behaviors.

Kaufman says Langton has undoubtedly produced important research of the first order.But although Langton's research has reached this point, although his research on economics and autocatalysis has made significant progress, although Santa Fe has also engaged in other research topics, although he is writing for self-organization and natural selection Much time and energy have been spent on the tension between the two, but we are still years away from revealing the full implications of Edge of Chaos.In fact, the full meaning of Edge of Chaos wasn't really revealed until the summer of 1988.At that time, Norman Packard passed by the Santa Fe Institute from Illinois. During his stay, he held an academic seminar and gave a report on his research on the edge of chaos.

Packard developed the concept of phase transitions alone, synchronized with Langton in time, and also thought deeply about adaptation.So he couldn't help asking: Are the systems that are most able to adjust themselves also the ones that compute best, that is, those that lie between order and disorder?It was a gripping thought, and Packard ran a simulation of it.He started with many cellular automata rules, requiring them all to individually do some kind of computation.Then he used a Dutch-German genetic algorithm to derive rules based on good and bad calculations based on cellular automata rules.He found that the final rules, those that can be computed efficiently, do end up clustering in the zone between order and disorder. In 1988, Packard included this observation in his paper "Adaptation at the Edge of Chaos," the first time anyone referenced the term "Edge of Chaos" in a published paper. (At the time Langton still informally called it "the beginning of chaos": onset of Chaos.)

Kaufman was dumbfounded when he heard this. "It dawned on me, and I blurted out: 'Yeah!' The idea of ​​complex calculations during phase transitions had crossed my mind, but I didn't realize that natural selection could lead to this, how stupid. I was Didn't expect that." But now that he thought about it, his old problem of self-organization versus natural selection became crystal clear: Living systems don't settle firmly in the realm of order.But for twenty-five years he has been emphasizing order when he proclaims self-organization to be the most powerful force in biology.Living systems are actually very close to phase transitions at the edge of chaos, where things appear looser and more fluid.And natural selection is not the enemy of self-organization. Natural selection is more like a law of motion, a force that constantly pushes the system with the characteristics of emergence and self-organization towards the edge of chaos.

"Let's talk about gene networks as gene regulatory systems," Kaufman said, with transformed enthusiasm. "I'm talking about sparsely connected networks in the ordered kingdom, but not too far from the edges. Such networks can produce many features that are consistent with the real situation of embryonic development, cell type and cell differentiation. If this is true. , then we have reason to speculate that billions of years of evolution are actually tuning cell types to the brink of chaos." "So we can say that phase transitions are where complex calculations are made. The second assertion is a bit like 'transition and natural selection will take you to the edge of chaos.'" Of course, Packard has long used simple molecular automata models shows the assertion.But this is just a model.Kaufman hopes to see this happen in his genetic network.So soon after he heard Packard's report, he teamed up with a young programmer named Sonke Johnsen, a recent Penn graduate, to develop a computer simulation.Kaufman and Johansen modeled a pair-pair network based on Packard's fundamentals: a challenging "mismatch" game.That is: connect each network so that six simulated light bulbs flash each other to form various light patterns, and the "most adaptable" networks are those that can flash a series of light patterns that are completely different from the other's light pattern.The "mismatch" game can make networks more complex or simpler, Kaufman said.The question is whether the combined pressures of natural selection and genetic algorithms are powerful enough to steer the network toward the phase transition zone, that is, toward the brink of chaos.And the answer is, in all cases it is.In fact, the answer was the same whether he and Johansen started the network from the realm of order or from the realm of disorder.Evolution always seems to lead to the edge of chaos. So does this confirm Kaufman's conjecture?not at all.Kaufman said.A few simulations prove nothing. "If games of all kinds of complexity turn out to prove that the edge of chaos is the best region for these games, that it's mutation and natural selection that steers you to the edge of chaos, that might confirm this loose and speculative conjecture. That's right." But Kaufman admits it was just one piece of rubble he didn't have time to clean up.He felt that too many wonderful conjectures were beckoning to him. Danish-born physicist Per Bak is an out-of-the-box card in a game of Edge of Chaos.He and his colleagues at Brookhaven National Laboratory on Long Island first published the theory of "criticality of self-organization" in 1987.Phil Anderson has been obsessed with the line of thought ever since. In the fall of 1988, when Buck finally came to Los Alamos and Santa Fe to participate in the discussion, it was discovered that he was a young man in his thirties with a round face and a plump figure. , speaking and bearing the recklessness and provocation of the Germanic nation.When Langton asked him a question at a seminar, he replied, "I know what I'm talking about. Do you know what you're talking about?" But he was undeniably very smart.His formulation of the concept of phase transitions was at least as concise and as beautiful as Langton's, yet their concepts were so different that they sometimes seemed irrelevant. Barker explained that when he and his collaborators Chao Tang and Kurt Wiesenfeld in 1986 were studying the esoteric phenomenon of condensed matter known as "charge density waves" Discovered the criticality of self-organization.They quickly recognized its wider and far-reaching implications.For the best and most vivid analogy, he says, let us imagine a heap of sand on a table, from which trickles of fine sand flow evenly. (By the way, someone has actually done this experiment with both computer simulations and real sand.) The pile of sand piled up until it couldn't get any higher.As the new sand continues to flow down, the original sand flows down the slope like a waterfall, constantly falling from the table to the ground.In reverse, you can also start with a large pile of sand and achieve the same situation: the pile will slump down until all the excess sand has flowed down the pile. Regardless of the method used, the resulting sand pile is self-organizing, that is, the sand has reached a stable state by itself, without any human intervention.The sand pile is in a critical state, that is, the sand grains on the surface are only just enough to stay.In fact, a sand pile in a critical state is very similar to a plutonium pile in a critical state. The chain reaction of a plutonium pile in a critical state is just on the verge of a nuclear explosion, but has not yet caused a nuclear explosion.The fine layers and the corners of the grains of sand are locked together in every imaginable way, and they are on the verge of collapsing.So as soon as one grain of sand rolls down, it's impossible to predict what will happen, maybe nothing will happen, maybe only a few grains of sand will slide down, or maybe a small area of ​​sand will just roll down and start a chain reaction .In fact, all of these scenarios are possible, Barker said.Large-scale sand avalanches are rare, but small sand avalanches are common.Evenly flowing fine sand leads to sand avalanches of different sizes, which is the "power law" behavior of sand avalanches that can be expressed by mathematical formulas: the frequency of sand avalanches of a certain scale is inversely proportional to certain powers of its size. Crucial to all of these questions, Buck says, is the fact that power-law behavior is a common occurrence in nature.This phenomenon can be seen in the activity of the sun, in the light of the Milky Way, or in the flow of electric current through electrical resistance and the flow of river water.Great impulses are extremely rare, but small impulses are everywhere.But the frequency of impulses at all scales follows a power law.The behavior is so common that explanations for its ubiquity have become vexing physics mysteries: why? The sandpile metaphor, he says, leaks an answer.Just like the evenly flowing sand can make the sand pile reach the critical state through self-organization, the uniform input of energy, or flowing water, or electricity can make many systems in nature reach the same critical state through self-organization, making them become A collection of subtly interlocked subsystems that stay just on the verge of criticality—avalanches of all sizes keep popping up, and things reorganize just so often that they balance critically. An important example, Buck said, is the spread of earthquakes.As anyone who lives in California knows, small earthquakes that shake dish pans are far more frequent than large earthquakes that generate international headlines. In 1956, geologists Beno Gutenberg and Charles Richter showed that these tremors actually have a power law: In any given region, the annual rate of earthquakes that release a certain amount of energy The number of times is inversely proportional to a specific energy power. (According to the evidence, the power is about 3 to 2.) This sounds like self-organized criticality to Barker, so he and Tang Chao did a computer simulation of the fault area.In the San Andreas region, for example, the sides of the fault are pushed in opposite directions by steady, inexhaustible crustal movements.Conventional seismic models tell us that the boulders on either side of the fault are locked in by enormous pressure and friction, resisting crustal movement until a sudden and catastrophic slip occurs.In Barker and Tang Chao's simulation, the boulders on either side of the fault would twist, deform, and separate from each other.During this process, the fault slips in varying amounts, just enough to keep its tension at a critical point.So they argue that the power law of earthquakes is exactly what we need, which just proves that the earth's faults have been twisting and deforming for a long time to push themselves to the critical state of self-organization.Indeed, the earthquakes that Barker and his team modeled follow a power law very similar to what Goodenberg and Lichter found. Not long after this paper was published, evidence for self-organized criticality was found in various fields.For example, fluctuations in stock prices, or unpredictable urban traffic conditions. (The phenomenon of stop-and-go traffic jams is the equivalent of avalanche tipping points.) Buck concedes that there is no general theory that pinpoints which systems will go critical and which will not.But it's clear that many systems tend to be critical. Unfortunately, self-organized criticality can only tell you the overall statistics of avalanches, but not any one particular avalanche, he added.This also shows that understanding and prediction are not the same thing.Scientists trying to make predictions about earthquakes may eventually be able to make accurate predictions, but not because they understand the criticality of self-organization.Their situation is like that of a small group of scientists living on a borderline sandpile.Of course, these microscopic researchers can measure the surrounding sand grains in detail, and try their best to predict when those specific sand grains will avalanche.But having a global power law does nothing to help them make such microscopic predictions, because global behavior does not depend on local details.In fact, if sandpile scientists are going to do their best to prevent the sand avalanches they've already predicted, they won't be able to, even if they understand global laws.Of course they can use the method of setting up brackets and supporting structures to prevent sand avalanches, but in the end they just transfer the sand avalanches here to other places.The global law remains unchanged. "The concept is simply brilliant," Kaufman said. “As soon as Buck came to the Institute, I fell in love with his concept of self-organized criticality.” Despite Buck’s vitriol, all the members of Langton, Farmer, and Santa Fe shared his concept with equal affection.Obviously, in solving the mystery of the edge of chaos, they have another key clue to answer.The question now is how to properly use this problem-solving clue to find the answer. Self-organized criticality is clearly on the edge of something.In many ways, this "something" is very similar to the phase transition that Langton tried to explain in his doctoral dissertation.For example, in second-order phase transitions, which he believes are central to the edge of chaos, Barker's concept reveals the true nature of microscopic density fluctuations at all scales.In fact, this kind of microscopic density fluctuation that happens to happen in the transition period follows a certain power law. Take the relatively abstract second-order phase transition discovered by Langton in the von Neumann universe. Four-level molecular automata show structures, fluctuations, and "extended transients" at various scales. In fact, you can even draw an analogy to Buck and Langton's concepts in precise mathematical language.In Langton's ordered state, the system can always gather into a stable state, just like a bosom below the critical point, the chain reaction always disappears without a trace, or like a small sand that can never lead to avalanche heap.In Langton's chaotic state, the system always turns into unpredictable riots, like a supercritical pile that will trigger a chain reaction, or like a huge sand pile that cannot support itself and causes a sand avalanche.The edge of chaos is like the critical state of self-organization, which is exactly in between the above two situations. But there are still confusing differences between the two concepts.The whole point of Langton's edge of chaos is that systems at the edge of chaos have the potential to perform complex computations and exhibit life-like behavior.Barker's notion of a critical state seems irrelevant to life and computation. (Can earthquakes be counted?) Moreover, Langton's theory does not mention that systems must be at the edge of chaos, which, as Packard points out, can only be reached by natural selection.Buck's system spontaneously goes critical, pushed by grains of sand, energy, or any kind of input.How these two concepts of phase transition fit into each other has been an open question. But Kaufman isn't terribly worried about that.The two concepts clearly fit together.Regardless of the details, the two concepts are clearly synonymous in the criticality of self-organization.Even better, Buck's perspective helped clarify some of the issues that had been troubling him.A single actor on the brink of chaos is one of those things that puzzles him.The edge of chaos is precisely the region where the economy allows individual actors to think and survive.But how to look at these actors as a whole?Take the economy, for example. People talk about the economy as if it's something that has emotions, that responds, that catches enthusiasm.Are economies on the verge of chaos?Is the ecological balance system on the verge of chaos?What about the immune system?What about global international relations? In order for mutations to make sense, you instinctively believe these are systems on the brink of chaos, Kaufman said.Molecules collectively form a living cell, which can be assumed to be on the brink of chaos because it is alive.Molecules collectively form organisms, organisms collectively form ecologically balanced systems, and so on.These analogies suggest that it seems plausible that each new layer is alive in the same sense, existing at or near the edge of chaos. But that's exactly the problem: whether or not the assumption is plausible, how do you test it?Langton learned about phase transitions by observing the complex behavior of molecular automata on a computer screen.But he had no clue how to observe real-life economies or ecosystems.When you look at the behavior of Wall Street, how do you distinguish between complex behavior and simple behavior?Precisely, what do we mean when we say that global politics or the Brazilian rainforest are on the brink of chaos? Buck's concept of self-organized criticality offers an answer, Kaufman said.A system is critical if it exhibits changes and disturbances of various scales, if the magnitude of the changes follows a power law.Or on the brink of chaos.Of course, this is a more accurate expression of what Langton has been saying in the language of mathematics: a system can only produce complex, life-like behavior if it can maintain the right balance between stability and fluidity.But power laws can be measured. To see how this could happen, Kaufman says, we can imagine a stable ecosystem, or a mature industrial system, where the actors are all well-tuned to each other, creating evolutionary pressures for change. very small.But the actor cannot stand still forever, because if no improvement is made, there will always be an actor who will eventually be eliminated in a drastic change.It may be that the elderly company founder finally dies, and a new generation succeeds him, bringing with him a new business idea; or it may be a random genetic exchange that makes a species more The ability to run faster than ever before."One actor starts to change, which then causes changes in its neighbors, which sets off an avalanche of change until all the changes stop," Kaufman said. Then the other actors start changing again. .Indeed, the whole population is bathed in a randomly varying drizzle, as Buck's pile is bathed in evenly falling grains of sand.This means that you can expect any group of tightly connected actors to bring itself into a state of self-organized criticality, where the avalanche of change follows a power law. According to Kaufman, according to the fossil record, a long period of stagnation is always followed by a stormy upheaval.This is consistent with what many paleontologists, especially Stephen J. Gould and Niles Eldridge, have declared to be a "punctuated equilibrium" that is indeed documented in fossils.And, if you take this concept to a logical conclusion, you could say that these avalanches are what caused the mass extinctions in Earth's history.During a mass extinction, an entire species disappears from the fossil record and is completely replaced by a new species.Perhaps the fall of asteroids and comets wiped out the dinosaurs 65 million years ago, and all the evidence supports that.But the extinctions of most, or all other species may be entirely internal.Larger-than-normal avalanches of ecosystems at the edge of chaos can lead to species extinction. "With regard to the extinction of species, we have not found enough fossil records and lack convincing explanations. But you can look for power laws through simulations, and you can do some kind of approximate simulation." Indeed, after hearing Buck's talk, he Such a simulation experiment was done soon.The resulting diagram does not perfectly represent the law of the act.The graph is curved so that there are no illustratively large avalanches compared to smaller avalanches.The results may not be so convincing, but the instability of its data can also explain some problems. This temporary success led Kaufman to wonder whether power-law waterfalls of change are a common feature of "living" systems on the brink of chaos, such as stock markets, technologically interactive networks, and rainforests.While the evidence for this is scant, in the long run he feels the prediction still stands.But now, thinking about ecosystems at the edge of chaos has drawn his attention to another question: How did these living systems get to the edge of chaos? Packard's original answer, and Kaufman's own, was that these systems arrived at the brink of chaos through adaptation to their environment.Kaufman still believes that this answer is basically correct.The problem was that when he and Packard actually got their hands on the simulations, they both required the systems to accommodate some arbitrary definition of robustness introduced from the outside.But in the real ecosystem, what constitutes robustness is not given externally at all, but emerges from the dance of co-evolution through mutual adaptation among individual actors.It was this question that drove Holland to work on ecosystem models: importing definitions of robustness from the outside is self-deception.Kaufman recognized that the real question is not whether adaptation by itself can lead you to the edge of chaos, but whether coevolution can lead you to the edge of chaos. To figure that out, or at least clear up the questions in his head, Kaufman would have to do another computer simulation, again in collaboration with Johansen.He concedes that computer simulations make a nice connectionist network as ecosystem models progress. (At the heart of the program is a variable model of "NK landscapes," which he's been developing over the years to better understand natural selection. He also wants to use the simulation to understand that a species' robustness depends on many different genes What does it mean. The two letters NK mean that each species has N genes, and the robustness of each gene depends on K other genes.) Holland's ecosystem model is quite pure, and Kauf Mann's model is more abstract than Holland's model of ecosystems.But as far as its concept is concerned, it is quite concise.You start by imagining an ecosystem in which species are free to change and evolve through natural selection, and they can only interact in certain specific ways.Frogs are always trying to catch flies with their sticky tongues, foxes are always hunting hares, and so on.Or, you can think of this model as an economic system, where each company internally organizes and adjusts according to its own free will, but the relationship between companies is defined by various contracts and regulations. Kaufman says there is still a lot of room for co-evolution within constraints, both in ecosystems and in economies.For example, if frogs evolved to have longer tongues, flies would learn how to escape more quickly.And if flies evolve a taste that's hard to swallow, frogs have to learn to live with it.So, how to present all this concretely?One way, Kaufman says, is to look at the species one by one.For example, first observe the frog.At any point the frog will find that some strategies work better than others.So at any given time, for the frog, the set of available strategies forms some imaginary "fitness" landscape, with the most useful strategies at the top and the least useful at the bottom.Moreover, the frog roamed the landscape as it evolved, and each change it experienced was a step from its current strategy to a new one.Natural selection, of course, ensures that the average movement of its evolution is always towards higher fitness, and that the variants that cause the frog to go downhill always tend towards extinction. The same thing happened in the evolution of species such as flies, foxes and hares, Kaufman said.Every species wanders in its own landscape.But the whole point of coevolution is that none of these landscapes exists independently, but rather condition each other.A good strategy for the frog depends on the behavior of the fly, and vice versa. "So an adjustment in one agent causes a change in the fitness landscape of all the other agents. You have to imagine frogs climbing to the peak of their strategy space, and flies climbing to the peak of their strategy space, but the landscape changes as their Climb and deform." It's as if every species walks on rubber. Kaufman said, now we come to think about the dynamics of such a system?What about global behavior?How are these behaviors related to each other?That's the simulation we're going to do.When he and Johansen built and launched their NK ecosystem model, their three major discoveries happened to be exactly like Langton's: a phase of order, a phase of chaos, and a phase transition resembling the edge of chaos. This result is very satisfactory."It didn't have to be that, but it was," Kaufman says, but it's easy to see why in retrospect. “想象一个巨大的生态系统，其中的景观都成双配对。那就只能发生两种事情。要么所有物种都向上攀登，身后的景观随着它们的攀援而变形，这样它们就一直不停顿地往前走。或者，有一群彼此近邻的物种真就停顿下来，因为它们达到了史密斯所谓的进化的稳定策略。”那就是，这群物种彼此合作得十分默契，失去了需要改变的直接动力。 “这两种情形能够在同一时间发生在同一个生态系统中，有赖于其景观的具体结构和它们相互之间是如何配对成双的。”考夫曼说。“让我们来观察一组选手，它们因为已经达到了局部最优化而不再向上攀援了。把这些选手涂成红色，把其它作用者涂成绿色。”考夫曼和约翰森确实用这种方法在计算机屏幕上显示了这个模拟。当这个系统深陷于混沌之中，几乎没有作用者能够静止不动时，计算机屏幕显示出一片绿色之海，只有少数红色孤岛闪烁其间，代表少数力图找到暂瞬均衡的物种。相反，当这个系统凝固在有序之中时，几乎所有作用者都锁定在均衡状态中，计算机屏幕就会呈现出一片红色之壤，只有少数绿色迂回其间，代表无法安顿下来的单个物种。 当然，当这个系统处于相变阶段时，秩序和混沌正好持平，一切都恰如其分，计算机屏幕似乎出现生命的脉冲。红色岛屿和绿色岛屿相互交织，喷射出的卷须就像随机的碎片。这个生态系统的一部分永远都能达到均衡状态，转为红色，而另一部分永远闪烁不定，随着不断发现新的进化途径而转为绿色。大小不一的变化之波扫过计算机屏幕，包括偶尔出现的巨大波涛自发地席卷屏幕，使整个生态系统变得面目全非。 考夫曼说，这看上去像是间断式平衡行为。但有意思的是，我们所能看到的三种动力形式都是以这种方式在屏幕上显示出来的。令人满意的是，我们可以看到，共同进化的模型确实存在混沌边缘的相变，但这只是故事的一半，仍然缺乏对生态系统是怎样到达这个边缘地区的解释。另一方面，迄今为止，考夫曼在整个的橡胶故事和变形的适应度景观中只告诉了我们单个基因的变种过程这一件事，却没有涉及每个物种的基因组结构的变化，即，能够显示一个基因如何与其他基因相互作用的内部组织图。考夫曼说，也许基因组织结构和基因本身都是进化的产物。“因此你可以想象进化的总趋势，一个能够调整每个作用者的内部组织，使这些作用者一直驻足于混沌的边缘的过程。” 为了检测这个概念，考夫曼和约翰森允许他们模拟的作用者改变其内部组织。这相当于荷兰德所谓的“探索性学习”，也很像法默在关于关联论模型的罗塞塔巨石论文中所提及的从根本上重组关联的概念。结果是，当物种具备了进化自我内部组织的能力之后，整个生态系统确实向着混沌的边缘发展。 现在回想起来，同样很容易看清楚为什么会是这样的情形。考夫曼说。“如果我们深陷于有序状态，那么所有的人都在适应度的制高点上，并保持相互一致。但这是很糟糕的制高点。”也就是说，所有人都步入了下坡的道路，无法挣脱羁绊，向顶峰迈进。在人类的组织中，这就像把工作细化到让所有人都失去自由，只能在受雇的岗位上学会如何干好这个工作。但不管这个比喻是否恰当，很显然，如果各种组织中的每个人被允许有一点踩着不同鼓点前进的小小的自由，那么所有的人都会有所受益，严酷凝冻的系统就会有一点儿松动，整体的适应度就会上升，其作用者就会集体向更接近混沌边缘的方向移动。 反过来说，“如果我们深陷混沌状态，我的每次变化都会把你也搅得乱七八糟，你的每次变化也会把我搅得乱七八糟，我们就永远达不到高峰。因为你不断踢我，我也不断踢你，就像西西弗斯（古希腊大力士）使劲要把石头推上坡一样。我的整体适应度就会因此变得相对较弱，你的整体适应度也同样会变得相对较弱。”从组织上来说，这就好像一个公司的指挥系统陷入一片混乱之中，弄得所有的人都完全不知道该做什么。或者说，每个作用者都显然应该稍稍加强一些与对手的相互配合，这样就能很好地根据其它作用者的行动来调整自己。混乱的系统就会变得稍稍稳定一些，其整体适应度就会上升。这样，整个生态系统就又会移近混沌的边缘。 当然，在介于有序的状态和混沌的状态之间，整体适应度无疑会达到顶峰。考夫曼说：“从我们做过的无数模拟的结果来看，最大的适应度恰恰出现在相变阶段。所以关键在于，所有作用者都改变自己的景观，就好像受到一只无形的手的控制。每一个作用者这样做都是为了有利于自己，从而使整个系统在共同进化中向着混沌的边缘发展。” 考夫曼说，所以情况就是这样：根据隐含在化石记载中的一种幂律，全球的生物圈接近混沌的边缘。一些计算机模拟也表明，各种系统可以通过自然选择法来调整自己，不断走向混沌的边缘。目前已经有一个计算机模型表明，生态系统也许能够通过共同进化达到混沌的边缘。“迄今为止，这还是唯一的证据，证明混沌的边缘其实就是复杂的系统为解决复杂的问题而走向的区域。这一证明还相当粗略。所以，尽管我非常欣赏这个假设，认为它绝对具有说服力和信服力，也非常有诱惑力，但我却不知道它是否具有普遍的意义。” 最后，这个新的第二定律起码应该还有一方面的解释：“它必须包括这样一个基本事实，即生物体自诞生开始就趋于越变越复杂。我们需要知道，为什么生物体会越变越复杂？越变越复杂对生物体有什么益处？”考夫曼说。 当然，唯一诚实的回答是：迄今为止无人知晓其答案。“然而这却是我对这整个问题思考的关键。我从对生命起源——自动催化——聚合物组模型的研究开始，到对也许跟随其后的复杂和组织的理论的研究，都是在对这一问题进行思考。”他承认，这个理论仍然含糊不清、非常不明确。他无法宣称他对这个理论的研究已经令自己满意了。“但这正是我对卡诺式的暗示所寄予的最深的希望。” 不无讽刺的是，就他自己而言，自动催化组的概念被遗忘已久。考夫曼说，1986年他和法默、派卡德共同出版生命起源模拟时，法默已经转向预测理论的研究了，派卡德正在帮助史蒂芬·伍弗雷姆在伊利诺斯大学创办一个复杂系统研究所。考夫曼觉得他一个人无法继续这个模型的开发，这不仅仅是因为桑塔费研究所每天都有许多吸引他的注意力的热门课题，也因为他也缺乏耐心和计算机编程技术，无法每天坐在计算机面前，从复杂的软件程序中纠正编程错误来。（确实，对生命起源的研究1987年才重新恢复。当时法默找到了一个名叫里查德·巴格雷的研究生，他有兴趣以此项研究作为他博士论文的题目，巴格雷极大地完善了这个模拟，对热动力学做了更为逼真的度量，还做了一些其它修改，而且还大大提高了计算机编码速度。他于1991年获得了博士学位。） 结果，考夫曼在后来的四年中在自动催化方面没有做多少研究。一直到1990年，他听了德意混血的年轻博士后沃尔特·方塔纳（Walter Fontana）的一次讲演。方塔纳最近已经加入了罗沙拉莫斯法默的复杂性系统小组。 方塔纳的研究是从听起来简单得让人难以置信的宇宙观察开始的。他指出，当我们观察从夸克到银河的宇宙万物万象时，只有在分子层才能发现与生命有关的复杂性现象，这是为什么呢？ 方塔纳说，一种回答仅仅只涉及“化学”。生命很显然是一个化学现象，而只有分子与分子之间才能自发地产生复杂的化学反应。但还是这个问题，这是为什么呢？是什么让分子产生化学反应，而夸克和类星体却不能？ 他说，是两件事。化学力量的第一个来源就是多样性：原子能组合、重组成各种不同的分子结构，不像夸克只能三个一组地组成中子和质子。分子的可能性空间受到了很大的限制。化学力量的第二个来源是反应性：结构A可以通过操纵结构B，组合成某种新的结构：结构C。 当然，这个定义遗漏了许多事情，比如像速率常数和温度变化，而这些恰恰是理解真正的化学的关键。方塔纳说，他是故意遗漏这些的。他的观点是，“化学”实际上是一个可以应用于各种复杂系统的概念，包括经济、技术、甚至思维系统。（各种货物和服务之间相互进行交易，产生新的货物和服务。各种思想之间也能撞击出火花，产生新的思想，等等。）因此，一个把化学提炼到最纯粹的本质的计算机模型，即，能够提炼出多样性和反应性本质的计算模型，应该能够给你提供一个研究世界上复杂性增进问题的全新的视角。 为了达到这个目的，方塔纳回到计算机编程的实质上，对他称为算法的化学、或“炼金术”做出界定。他说，正如冯·诺意曼很久以前所指出的那样，一条计算机编码有一个双重生命。一方面，它是一个程序，一系列告诉计算机怎么做的指令，但另一方面，它又只是数据，是存储在计算机内部某处的一序列符号。所以让我们利用这一事实来界定两个程序之间的化学反应：程序A把程序B当输入数据来读，然后通过“执行”来产生一系列输出数据，这样，计算机就等于译出了一个新的程序，程序C。（因为用FORTRAN或PASCAL这样的计算机语言显然不能做好这个实验，所以方塔纳实际上是用LISP语言编写了反应程序。在这个程序中，几乎所有程序序列都能代表一个有用的程序。） 方塔纳说，下一步就是将无数符号序列程序置入一口模拟大锅，让它们可以随机地相互反应，然后观察会发生什么，事实上，其结果与考夫曼、法默、派卡德他们的自动催化模型的结果相差无几，只是，方塔纳的系统还产生了些离奇而美妙的变化。能够自我维持的自动催化组当然出现了，但还产生了许多可以无限制发展的组合。有些组合在它们的某些化学成分消除之后还能够自我修复，有一些组合在被注入了新的成分之后能够进行自我调整和改变。还有一些组合的成分完全不同，但却能相互催生。总之，炼金术程序意味着，纯过程的集合，也就是方塔纳的符号串程序，确实足以自发地涌现出某种非常具有生命力的结构来。 考夫曼说：“我确实对方塔纳的研究感到激动万分。我已经对自动催化聚合物问题思考了很久，为此做了经济和技术网络模型，却不能对聚合物研究出个结果来。但我一听说方塔纳的研究就知道答案就是它了。他想出了个结果。” 考夫曼立即决定跟进方塔纳的思路，以极大的精力重返自动催化游戏，但要在方塔纳的研究基础上做出他自己的修正。他认识到，方塔纳已经认识到抽象化学，将此作为思考涌现和复杂的一个全新的视角。但他的研究结果是抽象化学的一般性特征吗？或这只是他实施他的炼金术程序的方法？ 考夫曼在1963年刚开始设计网络模型，研究基因调节系统时也问过同样的问题。他说：“就像我当时想找出基因网络的一般性特征一样，我也想观察抽象化学的基因特征。这就要调试化学的复杂性和其它一些因素，诸如分子的原始组合有多大的多样性、所展现的行为的一般性结果是什么？”考夫曼没有直接采取方塔纳的炼金术，而是把这个概念更加抽象化了。他仍然利用符号序列来代表系统内的“分子”，但他甚至并不要求它们一定是程序。它们可以只是符号序列： 110100111、10、111111，等等。他模型中的“化学”则只是一组告知某些符号序列怎样转换另外一些符号序列的规则。既然符号序列就像语言中的字符，那他就把这组规则称为“语法”。（事实上，这种符号序列转换的语法已经从计算机语言的角度被广泛地研究，考夫曼也是从中得到了启示。）结果，他可以通过制定任意一组语法规则，来对各种化学反应行为进行抽样研究。 他说：“我是在凭直觉做这个实验。我从一锅符号序列开始，让这些符号序列根据语法规则相互作用。也许新的符号序列总是比旧的符号序列长，这样就永远不会重复以前的符号序列。”我们把所有可能的符号序列中的那些向外发射得越来越远，并从不回顾的符号序列称之为“发射器”。“当出现一朵符号序列云时，也许会是以前的符号序列的重复，但其组合方式却与以往不同，我就把它称为'蘑菇'，那都是些自动催化组，是依靠自身的力量而诞生的模型。然后也许会出现一组依靠集体的力量诞生、倘徉于符号序列空间的符号序列，我就把它称为'卵'。卵会自我繁衍，但其中任何一个单一的实体都无法实现自我繁衍。或者也可能会出现被我称为'金丝雾'，即散布于各处的各种符号序列。但有些符号序列你是无法得到的，比如像110110110。因此还会有些新的东西可以玩玩。” 所有这些与神秘而永不衰竭的复杂性增长有什么关系呢？考夫曼说，也许大有关系。“复杂性的增长确实与远远超越均衡、阶式地连接成越来越高层次组织的系统的自我繁衍有一定的关系。这些系统从原子、分子，发展到自动催化组，依次渐进。但关键的问题是，一旦更高层次的实体出现以后，它们之间就能够进行相互作用。” 一个分子可以和另一个分子相连接，形成一个新的分子。于符号序列群中突现出来的那些物体所发生的也是这种情形。创造了那些物体的化学同样能够让它们通过相互交换符号序列来产生丰富多样的相互反应。“比如说，现在有一个卵，你从外面扔进一串符号序列，它也许会变成一个喷射器、或变成另外一个卵，或变成一团金丝雾。这对其它物体也一样。” 考夫曼说，不论在哪种情况下，一旦产生了相互作用，一般来说，只要条件允许就会出现自动催化，无论你讨论的是分子还是对经济，都一样。“一旦在更高层次上积累了一定数量的多样性，就会进入某种自动催化相变阶段，就会在这个层次上引发新的实体的激增。”然后这些激增的实体继续相互作用，产生更高层次的自动催化组。“所以就出现了由低层次到高层次阶梯式上推的发展，每一个层次的上推都要经过某种类似自动催化的相变阶段。” 考夫曼说，如果事情确实如此，你就能够看到，为什么复杂性增长显得如此无止无休，复杂性增长只不过反映了生命起源的自动催化法则。这一点当然必须包括在假设的新的第二定律之中。但尽管如此，考夫曼认为这也并非故事的全部，因为他最终认识到，自组织并不是生物学的全部。事实上，当你思考这个问题时，这个层层上推的阶梯式发展只不过是另一种自组织的形式。所以，自然选择和适应性是怎样影响和左右这种层层上推的发展的呢？ 考夫曼说，他确实还无法确定地回答这个问题，但他还是有些想法的。“我的想法既不是深刻的洞见，也不是什么愚见。但最近有一天我突然被这个想法吞噬了。如果你从某些原始符号序列组开始，这些原始符号序列组也许会产生符号序列的自动催化组、也许产生喷射器自动催化组、也许产生蘑菇，或卵，或不管什么吧。但它们同样也会产生死符号序列。'死'符号序列意味着这个符号序列是无效的，不能作为触媒，也不能和任何符号序列产生相互反应的符号序列。” 很显然，如果一个系统产生许多死符号序列，则这个系统就不会迅速扩展，这就像一种经济，将其大多数产品都转产成既无人问津、又不能再用来制成其它东西的小玩艺。“但如果'有生命力的'、有繁殖能力的符号序列能够进行自组织，不至于产生这么多的死符号序列，那么就会出现更多的有生命力的符号序列。”这样净生产力就会上升，这组有生命力的符号序列对那些不能很好进行自组织的符号序列组来说就有了一种可选择的优势。事实上，当你观察计算机模型，就会发现，趋于死亡的符号序列确实随着模拟的进行而减少。 “同时我想，这个概念尚有可改进之处。假设从原始组合中发展而来的两个喷射器为了争抢符号序列而发生竞争。如果第一个喷射器能够帮助第二个喷射器避免产生死序列，而第二个喷射器也能反过来帮助第一个喷射器避免产生死序列，就能产生多喷射器。”这对互动喷射器也许就能形成一个新的、多喷射器结构，即一个更高层次上的新型的、更为复杂的个体。考夫曼说：“我有一个预感，更为有序的物质之所以出现，是因为它们能够更快地吞入更多的资源。所以我想把所有这些整合成一个互生共进的过程理论，事物在这个过程中通过相互竞争获取资源，从而自我发展。与此同时又使自己走向混沌的边缘。”