Chapter 10 Chapter 7 The Glass House Economy

We've gotten used to thinking of economic problems as butterflies, and when we examine a butterfly, we always pin it to a piece of cardboard so it's balanced and immobile, rather than letting it fly around you. At five o'clock in the morning on Tuesday, September 22, 1987, Horan and Arthur left the artificial life laboratory in Los Alamos and drove back to Santa Fe along the Mesa.In addition to stopping in the evening to admire the distant mountains in the twilight, they discussed the computer simulation experiment made by Craig Reynolds of Symbolics Corporation in Boid, Los Angeles.

This experiment fascinated Arthur.Reynolds attempted to understand the social behavior of birds, flocks or fish experimentally.As far as Arthur knew, Reynolds' experiment was very successful.His basic idea was to place a swarm of bird-like robotic agents in a computer environment full of walls and obstacles.Every Buzz follows three simple rules of behavior: (1) It tries to keep the shortest distance with other objects in the environment (including other Buzz). (ii) It tries to maintain the same speed as the neighboring Pads. (iii) It moves as far as possible to the center point of the adjacent large group of Bezes.

Most shockingly, the rules made no mention of herds at all, but only of what each individual bird was able to see and do within close proximity.Therefore, groups must be formed from the bottom up, just like emergent phenomena.In this manner, however, hordes of bez do form every time. At the beginning of the computer simulation experiment, Reynolds let the bots scatter on the computer screen completely randomly, and then the bots would naturally combine into groups and fly over obstacles.Occasionally, the group of Boz would split in two, go around the obstacle on both sides, and reunite at the other end, as if carefully planned in advance.In one experiment, a Pez bumped into a pillar by accident. It seemed dizzy, lost its direction, and flapped its wings and circled a few times.However, when the Paz group started to move, it immediately galloped away and rejoined the group.

Reynolds insists that the above example just proves that Betsy's behavior is completely emergent.There was absolutely nothing in the code of conduct or computer codes that taught that Pedz to behave in this way.So, as soon as Arthur and Horan got back in the car, they began to ponder the question: Which of Paz's behaviors were innate, and which were truly unexpected emergent behaviors? Berts' association Horan was still dubious. He had seen too many examples of emergent behaviors, but he found that they were pre-programmed skillfully by the experimenters.I told Arthur he must be very careful.Maybe everything that happened, including that pezzie that hit the post, was obvious from the original rules, and you didn't learn anything new.At the very least I would like to experiment with different objects, change the environment, and see if it still behaves reasonably?

Arthur could not refute Hornan's argument.But he said: To me, I don't know how you would define true emergent behaviour.In a way, everything that happens in the universe, including life itself, is preprogrammed in the rules of quark behavior.So, what exactly is emergence?How do you recognize emergent phenomena when you see them?This is the central question of artificial life. No one can answer this question, so the discussion between Horan and Arthur has no clear conclusion.But in retrospect, that discussion did plant a seed in Arthur's sleep-deprived mind.At the beginning of October 1987, Arthur finished his visiting scholar work in Santa Fe and returned to Stanford wearily and happily.After catching up on sleep, he continued to reflect on what he had learned in Santa Fe.Horan's Genetic Algorithm, Classifier System, and Burtz, etc., are all very memorable to me.I spend a lot of time thinking about these theories and the possibilities they open up.My hunch is that these theories provide answers, the question is, what is the problem in the field of economics?

My early interest was in how Third World economies change and develop, so around November 1987 I called Horan and told him I had thought about how new ideas could be applied economically.My idea is that you can build a glass house in the school office and develop a small farmer economy.Of course, what I really mean is simulated in the computer.But there have to be some little agents that are programmed to be smart and interact and react to each other. In my imagination, you come to the office one morning and say: Hey, look at these guys!Two or three weeks ago they were just bartering, now they have a joint stock company.And then you come in the next day and say: Oh, they invented central banks!After a few more days, you will call all your colleagues over to see it, and you say: Wow!They have a union now!What will they think of next?Or maybe half of the actors have become communists.

At the time, I couldn't express my thoughts clearly.Arthur said.But he knew that such a glass house economy would be very different from traditional economic simulations.In traditional economic models, the computer just puts together a bunch of differential equations.And his economic agents are not mathematical variables, but agents caught in a web of interactions and accidents that make mistakes, learn, and develop history.Like humans, they are not only governed by mathematical formulas, but they are still much simpler than humans.If Reynolds could generate life-like flocking behavior with three simple rules, it is not so unimaginable to generate life-like economic behavior with well-designed agents in a computer.

I have a vague feeling that we can use Horan's classifier system to design actors.I didn't know what to do, and Horan didn't immediately suggest what to do, but he was just as excited as I was.The two of them agreed that this research would be the first priority once Santa Fe's economic research project was on track next year. ready to go Meanwhile, Arthur was busy enough planning the economic research project before he began to understand what the position he was taking on meant. Horan soon discovered that he had no way to co-chair the project with Arthur. When he was invited to be a Los Alamos visiting scholar a year ago, he used up his professor's annual leave.In Michigan, he was involved in the dispute over the merger of the Department of Computer and Communications into the Department of Electrical Engineering, and his wife was also bound by the job of director of the Science Library, unable to separate herself.At most, Horan could only come to Santa Fe for a month or so at a time.

So the burden fell entirely on Arthur, who had never presided over a research project in his life, let alone reorganized a research project. He asked Xin Ge, who was in charge of coordinating, what exactly did Rhett want us to do?After asking Rhett, Xin Ge replied: He said that you can do any research you want, as long as it is not traditional research. He also asked Arrow and Anderson: What research would you like us to do?They said they wanted him to create a new and rigorous approach to economics based on the idea of ​​complex adaptive systems. He asked Ke Wen and various dignitaries in Santa Fe: What kind of research does the institute want us to do?They told him: The Scientific Committee wants you to open up entirely new research directions in the field of economics.The budget for the first year, by the way, is $560,000, partly from Citibank, partly from the MacArthur Foundation, and partly from the National Science Foundation and the Department of Energy.Of course, this is Santa Fe's first and largest major research project, so we'll be watching your progress closely.

Arthur said: I shook my head as I walked, $560,000 is only a medium-sized research project, but it is a big challenge for me.It's like someone told me: Here's an ice ax and a rope, go climb Mount Everest!Scared the hell out of me. Of course, the fact is that Arthur is not alone.Arrow and Anderson were both willing to offer moral support, encouragement and advice.Arthur said: They are the pillars and spiritual leaders of this project.Indeed, Arthur thought this was their research project, but they made it clear that Arthur must assume the responsibility of the top executive.Arthur said: They let me do it, let me decide the direction and push the plan.

He quickly made two crucial decisions.The first decision has to do with research topics, and Arthur is apparently not keen on using chaos theory and nonlinear dynamics in economics; Similar studies, and as far as he knows, the research results are lackluster.Second, Arthur had little interest in building a massive computer simulation of the global economy.He said: This may be the research that Reid wants to do, and engineers and physicists will also be very enthusiastic, but this is like me asking you, you are an astrophysicist, why don't you build a model of the universe?Such a model would be as complex and elusive as the real universe, which is why astrophysicists don't do it.Instead, they constructed a set of models of stellar objects, a set of spiral galaxy models, a set of star formation models, and so on, and then used sophisticated calculations to analyze specific phenomena. emphasis on old issues And that's exactly what Arthur wanted the Santa Fe Economic Research Project to do.Of course he doesn't want to cancel the plan to build a glass house economic model, but he wants everyone to learn to walk before running.In particular, he hopes that the project will revisit old questions in economics and see what changes when you look at them in terms of adaptation, evolution, learning, emergence, and complexity?For example, why do stock market bubbles and crashes occur?Why is there money? (That is, why are commodities like gold and seashells widely used as mediums of exchange?) Emphasizing old problems has since made economic research programs a target, with many science committees accusing them of not being innovative enough.But we think studying standard problems like this is good science and the right steps to take.These are all familiar questions for economists, and if we could show that simply changing what was supposed to be a theoretical assumption to a more realistic one, we could change your view of the problem, and maybe add some sense of reality to your view , then we can tell the economics community that we can indeed contribute. For the same reason, when Gellman urged him to draft a manifesto for the economic research project to attract audiences, he also resisted.He pitched his idea over and over again, hoping for something that said: Another form of economics is about to be born.and so on.After thinking about it, I decided to decline.We'd better proceed step by step and study the old problems of economics first, which will be more convincing. The second important decision was what kind of researchers Arthur would recruit.Of course, he needed someone who was open-minded and who shared Santa Fe's views.The ten-day economics seminar proved what a colorful group of people like this can whip up.He said: I learned very early on that neither I nor Arrow, Anderson, or anyone else could dictate the structure of the Santa Fe Economic Research Project from above.This framework must emerge from the research we do, the way we analyze problems, and the individual ideas that each of us has. After the bumpy road of publishing his increasing returns paper, Arthur now understands the importance of establishing credibility with mainstream economists.Therefore, he hoped that the talents recruited would include highly respected economists such as Arrow or Stanford's Sargent, who would not only convince everyone that the immature Santa Fe views fully met the existing rigorous academic standards, And when they go out and give Santa Fe economics, everyone listens. Crusaders to Transform Economics Unfortunately, pulling together such a team is easier said than done.Arthur drew up a list after consulting Arrow, Anderson, Paines, and Hornan.In the part of non-economists, he successfully recruited the talents he needed.Anderson and his former student, Duke University's Richard Palmer, both agreed to come and stay for a while.Hornan, of course, will be there, as will David Lane, a brilliant and articulate probability theorist at the University of Minnesota.Arthur even got the nod from his co-authors, Russian probability experts Omerev and Ganyowski.Kaufman, Farmer, and others from Los Alamos and Santa Fe were also willing to join in the festivities. But when Arthur started calling economists, he quickly discovered that his doubts about credibility were well-founded. Just about everyone had heard something about Santa Fe.But what exactly is the Santa Fe Institute, or who are it?Many people still don't understand.Arthur said: So when I called, a lot of economists said: Well, I'm afraid it's too late now, I have other plans.Several said they wanted to see how the project went.Basically, it's going to be really hard to get people interested in the project who haven't been to the last meeting. The good news is that the economists who attended last time were all flimsy picks; after all, Arrow picked them himself.Moreover, the reaction of people outside this circle is not completely indifferent.Both Arrow and Sargent agreed to visit for a few months, as did John Rust and William Brock of the University of Wisconsin, and Ramon Marimon of Minnesota.Miller (John Miller), who has just received his doctorate from the University of Michigan, will also participate. His doctoral thesis made extensive use of Hornan's classifier system.Arthur was particularly relieved that Frank Hahn, England's leading economic theorist, would be flying in from Cambridge. Therefore, in the first year, about 20 scholars will more or less participate in this research project, and at most seven or eight scholars will be stationed in Santa Fe at the same time.That's roughly the size of a small college's economics department, and they're going to work together to transform economics. Santa Fe Viewpoint The Economic Research Program is scheduled to start in September 1988 and will begin with a week-long economics seminar.Therefore, Arthur has moved to Santa Fe since June, and spent the whole summer preparing, not a single second was wasted.As the attendees arrived in Santa Fe in the fall, Arthur found time even tighter. He said: "People come to me every day.Like a guy who doesn't know how to change a light bulb and asks if I can help him?The space here is so small that sometimes I have to solve things like: Which office should the smoker be assigned?Would this guy share an office with a dude with a pair of scuds who always wears shorts?This kind of question.To plan the seminar, I travel and invite academics to attend, talk to them, ask their opinion, and hopefully spread the word. Arthur discovered that when you're the boss, you can't go outside and play with other kids, you have to act like an adult all the time.Despite the help of the Institute staff, Arthur found that 80 percent of his time was still spent on non-scientific tasks, and none of them were very interesting.On one occasion, he returned to the house the couple rented in Santa Fe and complained to his wife that he had little time for research.She said: Don't be silly, you have never been so happy in your life.She was right. She was right!Because despite the tedious administrative work, the remaining 20 percent is more than enough to make up for everything.By the fall of 1988, Santa Fe was alive and well, but not entirely because of the economic research program.The previous fall, they had finally received long-awaited funding from the National Science Foundation and the Department of Energy.Cowen was not able to persuade the two agencies to grant him the amount he had requested. They still did not have enough money to hire tenured fellows, but starting in January 1988, the two agencies committed to subsidizing a total of three years. $1.7 million.Therefore, until the beginning of 1991, the financial security of the Santa Fe Research Institute was guaranteed, and finally there was funding to seriously study the target complex science founded by Santa Fe. Under the leadership of Gellman and Paines, the scientific committee reviewed and approved fifteen new workshops.Some seminars approach problems of complexity science from the perspective of core physics, the best example being Information, Entropy and Complexity Physics, organized by the young Polish physicist Wojciech Zurek in Los Alamos. seminar.Zurek's idea is to start with the complex concepts of information and computation as defined by computer science, and explore the deep connections between these concepts and quantum physics, thermodynamics, quantum radiation from black holes, and the (hypothetical) quantum origin of the universe. Other workshops intend to explore complex issues from a biological perspective.Los Alamos biologist Alan Perelson, for example, organized two seminars on the immune system.Pirison had chaired a major seminar on immunology in Santa Fe in June 1987, and is now leading a small research project in Santa Fe. The immune system in our body is composed of billions of very active cells. Immune cells with antibodies are flooded in the blood. Once viruses and bacteria invade, they will be eliminated as soon as possible.Pirison's idea is that the immune system, like the ecosystem or the brain, is a complex adaptive system.So new ideas and technologies from the Santa Fe Institute should help address immune system-related problems like AIDS, or treat autoimmune diseases like multiple sclerosis or arthritis.And, because researchers know so much about the molecular details of the immune system, the immune system research program should help implement some of Santa Fe's high-altitude concepts. At the same time, the Scientific Committee also strongly supports the invitation of scholars or postdoctoral fellows who have not participated in any research projects and seminars. See what sparks can be stirred up.The running joke among the science committee is that the Santa Fe Institute itself is an emergent phenomenon!In fact, they took the joke quite seriously. This is how the characteristics are born And the talent Ke Wen is eager to find is the kind of person with an indescribable fire burning in his soul.Ke Wen does not only value superficial talents; in fact, the Institute may be filled with a group of outstanding talents, but none of them understand the purpose of the Institute.It can't be like this. What Ke Wen is looking for is talents who can inspire and resonate with each other. It was never easy to find such people, but they did exist, and more and more of them came to Santa Fe, so many that the little monastery was often overcrowded.Throughout the year, various seminars are held non-stop in the church. The research room that originally only accommodated one person has been crammed into three or four people. The roommates in the research room are endlessly explaining and arguing on the blackboard. Under the big tree, impromptu free discussions can be seen everywhere.These scenes are unimaginable, and the surging vitality and warm comradely love are even more exciting.As Kaufman puts it: About twice a day I have the opportunity to learn to see the world from a new perspective. The people of Santa Fe feel the same way.Arthur said: "Let me describe a typical day here.Most of you will be locked in your research room in the morning, all you hear is the sound of computer terminals and keyboards, and then someone starts poking around your door.Have you ever done this problem?What are your thoughts on that question?Could you spare half an hour to talk to the visitor?Then, we went to have lunch, usually in groups to the canyon restaurant, which we jokingly called Santa Fe’s faculty restaurant, and the waiters in the restaurant knew us so well that they no longer took menus to take our order , We don’t even need to bother them to ask, we will automatically report: Give me a No. 5 meal. Discussions among scholars are never-ending and interesting.What impressed Arthur most was the impromptu discussions that popped up at any time in the evening or near noon.Three or five times a week, someone's going down the corridor yelling, "Hey, let's talk about this!"So, five or six people would meet in the chapel, or probably in a small meeting room by the kitchen.It's dimly lit, but close to vending machines and coffee ovens, and the room has a Cajun feel to it, with a photo of Einstein smiling at us with an Indian headdress. So we sat around the table, Kaufman reclining on the mantel.Maybe someone would write a question on the board, and we'd start debating piles of questions.These debates are very good debates, and people never speak ill of each other, but they are sharp, because these recurring issues are very fundamental issues.These problems are not technical problems in economics research, such as how to solve the fixed-point theorem, or like in physics, why does this material produce superconductivity at minus 253 degrees?These are all questions about where science is going.How do you deal with limited rationality?When the problems of economics become more and more complicated like a chess game, what should the next step of economics be?How do you parse an ever-evolving economy that never settles in equilibrium?How do you use computer experiments in economics? And I think that's where the Santa Fe identity came from, because the answers we started to come up with and the research techniques we developed started to shape the Santa Fe economic perspective. How to set rational rules? One series of discussions in particular stands out for Arthur because they helped him clarify some of his ideas.Both Arrow and Hann of Cambridge were there, so it must have been around October or November 1988.Arthur said: We decided we were going to have a meeting of Hornan, Arrow, Hann and myself, and maybe Kaufman and others, and we could figure out which economists to look for to study bounded rationality.That is, what would economic theory look like if economists no longer assumed that any economic problem could be solved instantly by a computer, even if the problem was as difficult as a chess game? They meet every day in small conference rooms to discuss the issue.Arthur recalls Hahn once pointing out that economists like to cite the principle of perfect rationality because: perfect rationality is a benchmark, and if people are perfectly rational, then theorists can perfectly predict their reactions.But what would total irrationality look like?Hann was curious. He said: Arthur, you are Irish, perhaps you will know. When Arthur was about to laugh, Hann went on to say that there is only one way to be completely rational, but there are countless ways to be partially rational.So, which one is human rationality?He asked: How do you set the rules of rationality? How do you set rational rules?Arthur said: Hann's metaphor lingered in my mind, I thought about it for a long time, and bit off an unknown number of pencils.We discussed it many times.Slowly, as if seeing the image of a photograph slowly emerging in the developing solution, they began to see the answer: the best way to set a rational ruler is to leave it alone and let the agent set itself. Arthur said: You take Hornan's approach and think of these agents as classifier systems, or neural networks, or other adaptive learning systems, where the rulers change as the agents learn from experience .Therefore, all actors are dull at the beginning, making random and blind decisions.But when they start interacting with each other, they get smarter and smarter.Maybe they become extremely intelligent because of it, maybe they don't, it all depends on what kind of experience they have.But in any case, these adaptive, artificially intelligent actors are exactly what you want in a real theory of economic dynamics.If you put these agents in a stable, predictable economy, you might find that they make highly rational decisions, as the neoclassicals predicted, but not because they have perfect information and infinite speed reasoning ability, but because the stable situation will give them time to learn. However, if you put the same agents in a simulated economic transition, they can still function, maybe not as smoothly, and they will make mistakes or fail, just like humans.However, under the influence of the learning algorithm rooted in the agent body, these agents will gradually master the reasonable way of action.Likewise, if you put agents in a competitive environment like chess, where they have to make moves against their opponents, you can watch how they choose.If you place actors in situations that are experiencing economic prosperity, you will observe how they mine treasures in vast possibilities.No matter where you put them, in fact, these actors will try to take some action.So, unlike the neoclassical school, which hardly mentions economic change, in a model full of adaptive actors, change is already deeply embedded in it. evolutionary economics This obviously coincides with Arthur's glass house economy. Indeed, this is exactly the insight he had after reading the eighth day of creation ten years ago, but now he can see this concept crystal clear.The elusive Santa Fe point is this: Unlike the neoclassicals who emphasized diminishing returns, static equilibrium, and perfect rationality, Santa Fe economists emphasized increasing returns, bounded rationality, and the dynamics of evolution and learning.Instead of resting on easily mathematical assumptions, the Santa Fe school devises realistic models; instead of viewing economic systems as Newtonian machines, they view economic systems as adaptable, surprising , living things that can learn how to see the world as an ever-changing system on the brink of chaos. Arthur said: Of course, this is not a new economic view.The great economist Schumpeter, although he did not know the word edge of chaos, was promoting the evolutionary view of economics as early as the 1930s.Richard Nelson and Sidney Winter of Yale University have also been promoting the evolutionary movement in economics since the mid-1970s, and they have achieved some results.Others have even tried to model learning effects in economics.In the early learning models, it is assumed that the agent has formed a correct model of the external situation, and learning is just a partial adjustment to modify the model more correctly.What we want to do is a more realistic model, and we want these internal models to emerge, as the agent learns, from within its mind.We have many ways to analyze this process. There are Hornan's genetic algorithms and classifier systems. Palmer has just finished a book on neural networks. Lane and I both know how to analyze probability-based algorithms mathematically. Learning, Omerev and Ganiowski are the authorities on speculative learning, and we've collected all the relevant material on psychology.These methods allow me to accurately simulate the conditions of adaptation. Arthur said: In fact, the most influential to us in the first year, in terms of scope, is the theory of machine learning; in terms of meaning, it is Horan's theory. Its level of influence is not in condensed matter physics, compensation Incremental or computer science while studying and adapting.When we discussed this idea with Airl, Hahn, and others, it was clear that what everyone was most excited about was that we could approach economics in such a different way. From Deduction to Induction While excited by the promise of a new economic outlook, Santa Fe's economists are a little troubled.The reason is that economics usually operates according to the deductive method. Economists first translate every economic situation into a mathematical equation, and then use rigorous analytical reasoning to solve economic problems.But now there are Hornans, neural netists, and other machine learning theorists who say that agents operate on the principle of induction, in which they try to infer useful internal models from pieces of information.Induction allows us to deduce that a cat is nearby from a tail that flickers around a corner, and it also allows us to classify some magnificently plumed creatures in zoos as birds, even though we have never seen the red-crowned parrot It doesn't matter.Because of induction, we can survive in this chaotic, unpredictable, and incomprehensible world. Arthur said: It is as if you have parachuted into Japan to participate in the negotiations, and you have never been to Japan before, and you have no understanding of the Japanese way of thinking and behavior or the way of working.You are ignorant of what's going on around you, so you often behave in ways that are completely out of touch with Japanese customs.However, you will gradually find that some things have been done by you, so you gradually learn to adapt, and advance and retreat are appropriate. (Of course, whether the Japanese will buy your product is another matter.) Think of this situation as a game of chess, where the players have only fragments of information about their opponent's intentions and capabilities, so they use Logical reasoning is used to make up for the lack of information, but with this method, they can at most foresee a few moves ahead.Therefore, chess players more often resort to induction, relying on assumptions, analogies, rules of thumb, etc. on the fly.Even if they don't understand the rationale behind these methods, the methods that work naturally still work.Therefore, induction cannot rely solely on precise, inferential logic. Arthur admits that even he was baffled at the time.Before I came to Santa Fe, I always thought that before talking about economic issues, we must first define the problems clearly.How do you study a problem if you haven't clearly defined it?Of course there is no way to apply logic to solve the problem. But Horan tells us that's not the case.After talking to Horan and reading his paper, it became clear that he was talking about problems that were not well defined, and environments that were not fixed.We asked him: How is it possible for you to learn in that environment? Hornan's answer is basically that you learn in that environment because you have to: evolution doesn't care if the problem is well-defined.He pointed out that adaptive agents only respond to rewards, they don't need to make assumptions about where the rewards will come from.In fact, this is the whole point of the classifier system.These systems are well defined from the point of view of calculus logic, yet they can still operate in poorly defined environments.Because the classifier's rules are all just assumptions about the outside world, not the truth, they may contradict each other.More importantly, because the system is always testing these assumptions to discover which ones are most useful, it can get paid: so even when faced with no value or insufficient information, or the external environment keeps changing in unexpected ways , the system still continues to learn. Accidents will happen However, such behavior is not in line with maximum benefit!Economists complain that they have always believed in the role of rationality in seeking its own maximum benefit. Horan replied: Compared with what is the biggest?In the real world, the space of possibilities is vast, and there is no way for the agent to find the ideal state, not to mention the possibility that the environment may change unexpectedly. Arthur said: I am fascinated by the law of induction. You can still do economics research even when the economic agent is not clearly defined, the environment is not clearly defined, the environment may change continuously, and the change is completely unknown.Of course, you don't need to think too much to understand that life is not like this!We often have to work and make decisions in an ambiguous situation. You confuse the past, adjust your thinking, copy others, try the methods that have worked in the past, and try various possibilities.Indeed, economists have discussed this behavior in the past, but we now find ways to analyze it precisely and root it at the heart of the theory. Arthur recalls an important debate during this period directly addressing the difficulty of such research.It was a lengthy discussion in October-November 1988 with Arrow, Hann, Horan, myself, and five or six other scholars.We're just beginning to understand that if we're going to do economic research like this and if that's really the Santa Fe view, the economy might not be in equilibrium at all.Like our living environment, the economy will continue to evolve, change, and explore new areas. Our concern is that it would then seem impossible to study economics, since the point of economics is to study equilibrium.We've grown accustomed to thinking of problems as butterflies, and when we examine a butterfly, we pin it to a piece of cardboard to keep it balanced and immobile, rather than letting it fly around you.所以漢恩說：如果沒有重複的狀況，沒有均衡的狀態，那麼我們經濟學家能談些什麼呢？我們怎麼作預測？又如何產生一門科學？ 賀南很嚴肅的看待這個問題，他對這個問題思索了很多。賀南告訴他們，看看氣象學吧！天有不測風雲，天氣從來不會完全重複，你無法預測一週以後的氣象。然而我們還是可以明白和解釋天空中的各種現象，我們可以辨認重要的氣象特徵，例如鋒面、氣流、高氣壓等，我們可以了解氣象的變動，這些特徵如何彼此影響，而形成本地或區域的天氣狀況。 簡而言之，儘管我們沒有辦法預測所有的氣象，氣象學仍然是一門真正的科學。科學的本質不是預測，而是理解與詮釋，而這正是聖塔菲希望對經濟學及其他社會科學能有所貢獻之處。賀南說，社會學家應該理解並且詮釋變動的社會現象，正如氣象學家解析鋒面一樣。 亞瑟說：賀南的話使我茅塞頓開，激動得無法自持。經濟並非處於均衡狀態，這是我已經思考了將近十年的問題，但是我一直想不通如果沒有均衡，我們如何研究經濟？賀南的論點為我打開死結，從此我就豁然開朗。 從一九八八年秋天的各種討論中，亞瑟才真正開始體會到聖塔菲觀點將如何深遠的影響未來經濟學的研究。包括我自己在內，許多人都天真的以為，我們從物理學家及像賀南這樣的機械學習專家學到的，會是新的演算法、新的問題解決技巧或新的技術性架構。結果我們學到的是新的態度、新的觀點，以及全新的世界觀。 達爾文的相對論原理 同時，賀南正在聖塔菲享受他生命中的黃金時光。他最喜歡和一群絕頂聰明的人一起討論各種想法，更重要的是，這些討論促使他改變了研究方向。也在這個時候，他為了不知如何對葛爾曼說不而煩惱。 賀南笑著說：葛爾曼是施壓高手。那年夏末，葛爾曼打電話到密西根找賀南：既然你做了這麼多關於遺傳演算法的研究，能不能給我們一個例子來駁斥創世主義者？ 對抗創世科學是葛爾曼熱中的許多事情之一。幾年前，路易斯安那州高等法院曾經舉行聽證會，辯論是否應立法要求學校平等傳授創世科學與達爾文進化論。葛爾曼幾乎說服了美國所有的諾貝爾獎得主簽署了一份文件，呼籲撤銷這條法律，法院也的確以七票對二票否決了這條法律。但是，在法院判決之後，葛爾曼卻在看報的時候發現這個問題絕不只是幾名宗教狂熱分子的活動那麼簡單。很多人投書到報館，說些像：我不是基督教基本教義教徒，我也不相信創世科學的一派胡言，但是他們在學校教的叫進化論的東西，好像有點問題，所有這一切不可能全靠盲目的機率而發生。這類的話。所以這些人不是創世主義的信徒，但是他們也不相信機率和天擇就能產生我們所見到的這一切。 所以，他想要設計出一系列的電腦程式、甚至電腦遊戲，讓人們看看這一切是怎麼發生的，看看機率和天擇的壓力在綿延許多代的運作之後，能產生多大的演化變遷。你可以先設定最初的狀況，基本上是一個星球，然後就讓一切自行發展。葛爾曼說，他在考慮是不是要在聖塔菲辦個研討會，來討論像這樣的電腦遊戲，賀南有沒有興趣貢獻一下？ 事實上，賀南興趣缺缺。他當然很贊成葛爾曼想做的事情，但是他的研究計畫已經排得滿滿的了，其中還包括要為亞瑟設計一個能應用於經濟模型的分類者系統。就他的角度來看，葛爾曼的演化模擬只會使他分心。除此之外，他已經完成遺傳演算法了，他不認為換個形式從頭再做一次，能讓他學到什麼新東西。所以，賀南斬釘截鐵的拒絕了。 葛爾曼說，好吧，那麼你再想想看。過了不久，他又打電話來：賀南，這件事真的很重要，你可不可能改變主意？ 賀南努力的再說了一次不行，但是他已經預見，要抵抗到底將不是件容易的事。所以，最後在長談之後，他束手就縛。好吧，我試試看。他告訴葛爾曼。 自發的突現 賀南承認，事實上，他的抗拒心愈來愈微弱。在與葛爾曼通話之間，為了讓葛爾曼死了這條心，賀南開始思考如果他答應了之後，會做什麼事。他開始領悟到這裏面可能蘊藏了大好機會。演化當然不只是隨機的突變和物競天擇，演化同時也是突現及自我組織的過程，然而儘管經過了考夫曼、蘭頓、以及其他許多人傑出的研究，大眾仍然對此一知半解。也許這正是一個教育大眾的契機。賀南說：我開始正視這個問題，我發現我可以設計出一個模型，一方面可以向葛爾曼交差，另一方面也可以做一點有趣的研究。 這個模型事實上重現了他一九七○年代所建立的模型。當時，他仍然在辛苦的研究遺傳演算法，並同時在撰寫他的書適應（Adaptation），而那時他也應邀到荷蘭演講。純粹為了好玩，他決定談一個截然不同的題目：生命的起源。 他把講題訂為自發的突現。現在看來，他當時的觀點和考夫曼、艾根及羅斯勒研究的自動催化模型有異曲同工之妙。賀南說：我的論文不是電腦模型，而是包含很多數學運算的正式模型。我想要證明的是，你可以設計一個自動催化系統，其中會產生簡單的、能自我複製的實體，而且產生的速度比平常的計算快很多。 創世主義信徒最喜歡引用的計算方法，是由科學家在一九五○年代提出的。當時的爭論是：能自我複製的生命形式不可能起源於太初渾湯中隨機的化學作用，因為如此一來所需要的時間會遠超過宇宙的歷史。這就好像要期待英國博物館地下室的猴子靠著胡亂敲打鍵盤，而終於有一天寫出莎士比亞全集一樣，不是不可能，而是要花很長、很長的時間。 然而，賀南就像過去的考夫曼等人，並沒有因而卻步。他認為隨機反應當然很不錯，但是化學催化作用就完全不是隨機的。所以在他的數學模型中，賀南模擬了分子湯一堆由長短不同的弦所連接的任意符號，這些弦會受自由流動的催化酵素（運算素，operator）刺激而起反應。賀南說：例如像拷貝（copy）這樣非常原始的運算素會附著在任何弦上，複製這條弦。事實上，我能證明一條定理：如果系統中有一些這類的運算素四處流動，而且如果你容許長短不一的弦任意重組，那麼系統就能夠快速產生一種能自我複製的實體，速度比靠隨機運作快得多。 賀南其實一直都還在思考突現及自我組織的問題。一年前，他在羅沙拉摩斯花了很多時間和法默、蘭頓、考夫曼等人討論這些問題。所以，當葛爾曼緊迫釘人的時候，我想也許多做一些這方面研究的時機已經成熟，也許這次我會建立一個有關自發突現的真正的電腦模型。 共同演化之舞 研究了幾年分類者系統後，架構電腦模型的方式對他來說再明白不過了。既然他原先論文中提及的自由流動的運算素，已經具備規則的效應，例如若碰到這種和這種弦，則做以下動作。賀南需要做的只是把規則寫成程式，讓整個系統愈像分類者系統愈好。然而，當他開始思考這些問題時，賀南也了解他必須面對分類者系統最大的哲學瑕疵。在自發的突現論文中，自發性是真實的，而突現也完全存乎系統內部。但是在分類者系統中，儘管作用體有學習能力，能夠自己發現突現的規則群，但是系統仍然要依賴程式設計師的幕後黑手來運作。分類者系統能得到報酬，只不過是因為我指定了輸贏的狀況。Horan said. 這個問題在他腦中一直揮之不去。他說，如果不談宗教，真實的世界似乎沒有一個宇宙裁判，也能運作得很好。生態系、經濟、社會全都在達爾文的相對原理之下運作，每個人都在適應彼此，因此，你不可能看著一個作用體，說：它的適應度（fitness）是一．三七五。無論你如何定義適應度（生物學家自從達爾文時代就一直為此爭辯不休），適應度絕不可能是一個固定的數字。就好像你問體操選手和相撲選手誰比較厲害，這個問題毫無意義，因為兩者無法以同一個尺度來衡量。任何有機體的生存和繁殖能力，都要視它生存的利基、附近還有哪些有機體、它能採集的資源有哪些，甚至過去的發展歷史為何而定。 賀南說：轉換這個觀點很重要。的確，演化生物學家認為這個觀念太重要了，他們甚至創造了一個新名詞：生態系中的有機體不是單純的演化，而是共同演化（coevolve）。有機體並不是藉著攀登適應度的高峰來改變自己，這是費雪這一代生物學家的信念。在無限複雜的共同演化之舞中，真正的有機體不斷的轉圈圈，彼此追逐。（古典人口遺傳學中最高適應度的有機體，就好像新古典學派經濟學中最大效益的作用體。） 賀南說，表面上，共同演化聽起來像是一片混沌。考夫曼在聖塔菲把共同演化比喻為攀登由橡膠製成的適應度高峰你每推進一步，整幅景觀就會變形。然而，賀南說，共同演化之舞產生的結果並非混沌一片。在大自然中，共同演化產生的結果是，花要靠蜜蜂來協助受精，而蜜蜂則要靠花蜜維生；印度豹追逐瞪羚，瞪羚則躲避印度豹。共同演化產生了數不清的生物，不但彼此高度適應，同時也適應周遭的環境。 此外，在人類世界中，共同演化之舞也產生了政治和經濟上相互依賴的錯綜複雜網路盟友、敵人、顧客與供應商等等關係。這是亞瑟的玻璃屋經濟發展的原動力，你可以在其中看到人造的經濟作用體彼此適應；這也是亞瑟和考夫曼的自動催化技術變遷中隱含的原動力；這更是在一個缺乏中央集權的世界中，各國事務發展的原動力。 fighting game 賀南說，的確在任何複雜適應性系統中，共同演化都是推動突現和自我組織的強大力量。因此，如果他想要從最深的層次了解這種現象，就必須先在系統中去除外界所回饋的報酬。不幸的是，他也知道，外界報酬的假設與分類者系統的市場隱喻息息相關。在系統中，每一個分類者規則都是經濟體系中一個很小、很簡單的作用體，在這個經濟體系中，通貨代表力量，財富的唯一來源就是最終消費者（程式設計師）給予的報酬。除非完全改變分類者系統的架構，否則無法改變這個狀況。 所以，賀南採取了以下的做法。他需要的是一個截然不同、更根本的互動比喻：戰鬥。於是他設計出艾可系統（Echo），艾可是生態系（ecosystem）的簡寫。在艾可這個高度簡化的生物社區中，數位有機體在數位環境中漫遊，尋找它們可以賴以生存及繁殖的資源（水、草、核果等的數位相似物）。當生物相遇的時候，它們當然也試圖把彼此當成資源。賀南說：我把這個系統比喻為我女兒玩的一種叫郵購怪獸的遊戲。你有一堆攻擊和防衛的可能作法，你如何組合這些戰略，就會決定了你和這些怪獸對抗的戰績。 賀南再進一步解釋，艾可把環境塑造為一個隨處可見噴泉的大平原，噴泉中會湧出以a、b、c、d等符號代表的各種資源。個別的有機體像羊群般在環境中自由移動，平靜的吃著草及它們所見到的資源，並且把資源存放在內部的儲藏庫。然而，當兩個有機體彼此相遇的時候，它們立刻從羊群心態搖身一變為狼群心態，相互攻擊。 賀南說，在後續的戰鬥中，結果完全取決於每一個有機體的染色體配對，也就是由一組資源符號串成像aabc及bbcd的兩個序列。他說：如果你是其中一個有機體，你會把你的第一串序列攻擊和對手的第二串序列防禦相配，如果能匹敵，那麼你就拿高分。所以這種互動關係再簡單不過了，主要就看你的攻擊和防禦能力能不能壓制對方。 如果答案是肯定的，那麼你就得到了一餐：對手儲藏的所有資源符號以及染色體都進了你的儲藏庫。此外，如果吃掉你從前的對手表示你現在有了充足的資源符號，可以複製你自己的染色體；那麼你就藉著創造一個新的有機體，而達到了繁殖的目的（或許其中發生一、兩個突變）。 如果答案是否定的，那麼就回到羊群吃草，從頭開始。 演化的軍備競賽 艾可並不完全符合葛爾曼的想法，因為其中沒有新奇的圖像，使用者也不容易上手。賀南對此置之不理。要讓這個系統運作，他得先輸入一長串密碼和符號，然後看到許多夾雜了字母數字的亂碼流瀉而出，顯現在電腦螢幕上。（這時候，他已經升級到麥金塔Ⅱ電腦的程度了。）艾可是賀南式的電腦遊戲，在這個系統中，他終於成功的去除了明顯的外在報酬。他說：你得回到最初的觀點如果我不能找到足夠的資源來進行自我複製，我就無法生存。賀南抓住了他心目中生物競爭的本質，現在，他可以把艾可當作知識的遊樂場，利用這個遊戲來探索並了解共同演化。他說：生態系中的很多現象，我都有興趣研究。 他最感興趣的是英國生物學家道金斯稱為演化的軍備競賽現象。例如，植物會演化出愈來愈堅硬的表面，以及毒性愈來愈強的化學驅蟲劑，來防止饑餓的昆蟲襲擊；然而，昆蟲也會演化出愈來愈堅強的顎及愈來愈複雜的抗化學機制來攻擊植物。所謂的紅皇后假設也是一例。這個假設是脫胎於愛麗絲夢遊仙境，故事中紅皇后告訴愛麗絲，她必須跑得愈快，才愈可能停留在原地。演化的軍備競賽似乎推動了大自然朝向愈趨複雜與專精的方向發展，就好像真正的軍備競賽在冷戰期間，推動了軍備朝向日益繁複與精密的方向發展。 一九八八年秋天，賀南當然還沒有辦法作演化的軍備競賽研究，當時艾可還停留在紙上談兵的階段。但是，再過一年左右，艾可就表現得很出色了。賀南說：如果我一開始設定的只是非常簡單的有機體，分別只以一個字母代表攻擊染色體及防禦染色體，然後我開始看到擁有幾個字母的有機體出現。（有機體能經由突變來加長染色體。）這些有機體開始演化，其中一個有機體加強了一點攻擊能力，另外一個有機體就會加強防禦能力，所以，它們變得愈來愈複雜。有時候，它們還會分裂，所以我會得到新的品種。 也就在這個時候，我看到即使藉著這麼簡單的設計，我都能看到演化的軍備競賽，以及由演化而產生新品種的現象，我愈來愈感興趣。 賀南說，他特別想了解一個演化的弔詭：導致演化軍備競賽的殘酷競爭，同樣也導致了共生及其他形態的合作。賀南對各種形式的合作興趣濃厚其來有自，這是演化生物學中的基本問題，更是經濟學、政治學及所有人類事務的基本問題。在一個競爭的世界裏，為什麼有機體還要合作？為什麼它們對盟友門戶洞開？ 背叛？還是合作？ 由數學的博弈理論中發展出來的囚犯的兩難困境，正充分抓住了這個問題的本質。 故事是這樣的：兩個囚犯分別關在不同的囚室，而警察正在偵訊他們共同犯下的一個案子。每一個囚犯都有一個選擇：他可以告密（背叛）或是保持沉默（合作和他的夥伴合作，而不是和警方合作。）現在，囚犯知道如果兩個人都保持沉默，兩個人都將可以獲釋，沒有他們的自白，警方無法拿到證據指控他們。然而，警方對這個狀況自然瞭若指掌，所以他們提供這兩個囚犯小小的誘因：誰告密，誰就可以無罪開釋，還可以得到獎賞！同時，不合作的囚犯除了會被處以重刑外，還要被科罰金，罰金的數目正好用來支付告密者的獎金。當然，如果兩個囚犯都互相告密，那麼兩個人都將被處以重刑，沒有人會得到獎賞。 所以，這兩個囚犯該怎麼辦，合作還是背叛？ 表面上，他們應該相互合作，閉緊嘴巴，因為這樣一來，兩個人都能得到最大的好處：自由。但是，他們慢慢會開始三心二意。囚犯甲不是傻瓜，他很快就知道，他根本不相信同夥不會向警方提供不利於他的證據，然後帶著豐厚的獎金揚長而去，留下他一人在囚室中受苦，還要負擔這個背叛者的獎金。這個誘惑太大了，他也知道夥伴也不傻，一定在心裏轉著和他一模一樣的念頭。所以囚犯甲的結論是，背叛朋友，對警察吐實，是唯一明智的決定；因為如果他的夥伴發起瘋來，堅不吐實，那麼囚犯甲就可以帶著獎金，走出牢門。如果他的夥伴也作了最合乎邏輯的選擇，向警方告密，反正都得坐牢，那麼至少他還不需要付罰金。 結果，因為這個無情的邏輯，兩個囚犯都走上他們最不樂見的結局：坐牢。 當然在真實世界中，信任和合作的兩難困境很少這麼黑白分明，談判、人情及許多其他的因素都會影響當事者的決定。儘管如此，囚犯的困境確實呈現了關於不信任以及需要保護自己不被出賣等心態的一部分事實。想想冷戰吧，兩大超級強權把自己鎖定在對彼此都沒有好處的軍備競賽中，長達四十年；或是以阿之間的僵持；或是國與國之間總禁不住樹立起貿易障礙；或是在大自然中，過度信任其他生物很可能就遭到被吞食的厄運。 那麼，為什麼有機體還敢相互合作呢？ 以牙還牙，以眼還眼 一九七○年代末期，部分的答案在一次電腦競賽中揭曉。這個比賽是由賀南巴哈小組中的同事、政治學家愛梭羅德所籌畫，他一直對合作問題興趣濃厚。愛梭羅德的想法很簡單：任何人都能寫一個電腦程式，扮演其中一名囚犯角色，來參加比賽。他們會把這些程式以不同的組合配對，然後玩囚犯的兩難困境遊戲，看是選擇合作還是背叛。但是，每一種配對不是只玩一次遊戲，而是重複玩兩百次，因此能更逼真的代表一般的長期人際關係。此外，重複也能讓程式依據其他程式的表現來決定合作或背叛。如果不同的程式只配對玩一次，那麼顯然結果一定是唯一理性的選擇。 但是，當同一組配對重複玩許多次以後，每一個程式都有了歷史和聲譽，配對的程式究竟應該如何因應，就不像原本那麼清楚了。這正是愛梭羅德想從這個比賽中學到的最重要的幾件事之一：長遠來看，什麼策略會獲致最高的報酬？不管對手做什麼，一個程式都應該乖乖合作嗎？它應該永遠扮演出賣朋友的小人嗎？它是不是應該以更複雜的方式來回應對手的動作？它的因應之道應該是什麼？ 事實上，在比賽的第一回合，交來的十四個程式呈現了各式各樣的複雜策略，但是叫大家跌破眼鏡的是，冠軍寶座卻落在其中最簡單的策略你踢我踏（TIT FOR TAT）手中。 你踢我踏的設計者是多倫多大學心理學家拉普波特（Anatol Rapoport）。你踢我踏的策略是第一次先合作，接著就亦步亦趨的採取與對手上一次相同的舉動，換句話說，你踢我踏策略融入了以牙還牙，以眼還眼的基本精神。這個策略基本上是善意的，因為它絕不先出賣對方；它也是寬容的，因為它會藉著下次的合作來獎勵對方；然而，你踢我踏也是強悍的，因為它會藉著下次的背叛來懲罰不合作的行為；此外，它也是坦白的，因為這個策略太簡單了，對抗的程式很快就會弄清楚這個策略。 當然，因為只有十幾個程式參加比賽，有可能你踢我踏只是僥倖得勝；但是也不盡然。在十四個參賽的程式中，有八個程式是善意的程式，絕不先背叛，而這些程式都很輕易就擊敗非善意的程式。所以，為了解決這個問題，愛梭羅德舉行了第二回合的比賽，特別邀請人們想辦法挑戰你踢我踏的冠軍寶座。六十二個參賽的程式都一一向你踢我踏叫陣，結果你踢我踏又贏了。結論毋庸置疑，好人（或更明確的說，是善意、寬容、強悍而坦白的人）的確能出頭。 你踢我踏策略萬歲 賀南和巴哈小組其他成員當然對這一切如痴如醉。賀南說：囚犯的兩難困境一直都讓我很頭痛，我很不喜歡這個故事，所以看到這樣的結果我很高興，這真是大快人心，太棒了！ 每個人都心知肚明，你踢我踏的成功無論在生物演化或人類事務上，都有深遠的含義。愛梭羅德在一九八四年出版的著作合作的演化（The Evolution of Cooperation）中指出，你踢我踏遊戲中的互動關係可以引申到許多社會上的合作關係，包括許多最沒有希望的情況。他最喜歡引用的例子，就是第一次世界大戰時自然發展出來的自己活，也讓別人活的體系。當時前線戰壕中的部隊會自動約束自己不射殺敵人，只要對方也不開槍。分居無人地帶兩端的敵對軍隊，根本沒有機會彼此溝通，而且他們當然不是朋友。這個系統所以行得通，是因為兩邊都是由相同的部隊對峙了數個月，因此讓他們有機會適應彼此。 在另外一本和巴哈小組同事漢彌頓合著的書中，愛梭羅德也指出，你踢我踏的互動模式能在大自然促成合作，即使是缺乏智慧的生物也一樣。青苔就是其中一個例子。青苔中的黴菌從岩石中吸取養分，同時也為藻類提供了棲息之地，而藻類則相對的以光合作用供養黴菌。蟻金合歡樹供養一種螞蟻吃住，而螞蟻則相對的保護這種樹；無花果樹開的花是黃蜂的佳肴，而黃蜂則為無花果樹傳授花粉，散播種子。 更廣而言之，愛梭羅德說，即使在叛徒充斥的世界裏，這種共同演化的過程都會讓你踢我踏式的合作行為蓬勃發展。假定有一些你踢我踏個體由於突變而出現，只要這些個體彼此碰面的次數頻繁，形成利害關係，它們就會開始合作。一旦合作關係建立，它們就會比周遭背後放冷箭型的個體表現得好很多，數目也會增加。愛梭羅德說，很快的，你踢我踏式的合作會接管一切，這時候，合作的個體就有了立足之地，如果比較不合作的形態想要侵犯或利用它們的善意，那麼你踢我踏凶悍的一面就會嚴厲的懲罰它們。愛梭羅德寫道：所以，社會演化就受到掣肘。 這本書出版後不久，愛梭羅德和賀南的學生芙芮斯特（Stephanie Forrest）合作用電腦模擬這些情況。他們的問題是：經由遺傳演算法共同演化的群體，會不會發現你踢我踏？結果答案是肯定的，在電腦實驗中，無論是你踢我踏或其他類似的策略都會出現，而且很快散布到整個群體中。賀南說：當我們眼見它發生時，都不由得高舉雙手，大呼萬歲！ 不必把全國人拖下水 當賀南告訴聖塔菲人，應該要在社會科學中尋找類似鋒面的題目，他指的正是像你踢我踏合作起源的機制這類的東西。而當他發展艾可系統時，他腦中正盤旋合作的問題。程式的第一個版本假定個別作用體永遠都會戰鬥，因此當然沒有出現合作的情況，但是在後來的版本中，他擴大有機體的儲藏庫，以包含合作的可能性。他試圖把艾可變成共同演化的統一模型。 賀南說：除了艾可之外，聖塔菲現在正進行的模型有三種：股市模型、免疫系統模型，以及沙金特所建立的包含交易的模型。這三種模型都有非常類似的特性。模型中都出現交易的情況以不同的方式交換商品；都有經由酵素或生產過程而產生的資源轉換；也都包含了配對的過程，並因此激發了技術創新。所以，我開始設計這個統一的模型。還記得我和芙芮斯特、米勒坐下來討論：如何在艾可中作最小的變動來模擬這些狀況？結果，我們認為，只要在攻擊和防禦的染色體上加一些東西就可以了，並不需要更改基本模型。我於是在染色體上提供了額外的識別物，以增加交易的可能性，這些識別物就好像商標或細胞表面的分子記號一樣。同時，我必須第一次在艾可系統中加上一條類似規則的東西：若對方出現像這樣的識別標籤，則我就試圖交易，而非戰鬥。因此，這就可能發生合作的演化以及像說謊和模仿等越軌行為。我由此勾勒出沙金特模型的修正版本，我也開始勾畫如何使艾可變得像免疫系統等等。目前的艾可模型就是由此而來。 統一的艾可模型很成功，在同一個生態系中，他同時展現了合作的演化和掠奪者與獵物的關係。這次成功激勵他繼續研究更複雜的修正版，我現在正在設計的最新版本能演化出多細胞有機體。所以現在除了交易之類的事情外，我希望能討論個體及組織的突現。每一個作用體雖然都試圖達到最大的繁殖率，卻不能不顧及整體組織的延續，甚至為它所限制，這其中有很多的學問。癌症就是一個抑制繁殖失敗的好例子。 賀南說，這種模型的實際應用還早，但是他相信這類的電腦模擬對世界的貢獻將遠大於聖塔菲的其他計畫。他說：如果我們研究成功，那麼非科學界的人，例如華盛頓的官員，就能創造一些模型，使他們對於不同政策的含義能夠多一些感覺，即使他們不完全了解模型運作的細節也無妨。他說，事實上，這樣的模型就好像公共政策的飛行模擬器，政治家不需要把美國的二億五千萬人口全拖下水，就可以練習經濟出軌的狀況。模型不需要非常複雜，只要能讓人們真實的感覺到情勢發展的方向，以及最重要的變數之間如何互動即可。 賀南承認，當他在華盛頓提到飛行模擬器的想法時，真是言者諄諄，聽者藐藐。大部分的官員都忙著閃避眼前的攻擊，而無暇顧及下一場戰役的策略。另一方面，他顯然並不孤單。一九八九年，加州歐林達（Orinda）的麥克西斯公司（Maxis Company）推出一種叫模擬城市的電腦遊戲，可讓遊戲者扮演市長，在面臨犯罪、污染、交通阻塞及抗稅等問題時，努力把城市帶向繁榮。這個遊戲很快就登上暢銷排行榜，賀南當然也立即買了一份，而且立刻愛上了這個遊戲。模擬城市是把飛行模擬器的概念運用得最好的例子之一。He said.聖塔菲研究院認真的和麥克西斯公司討論把模擬城市的一個介面，用在他們的許多電腦模擬上。而賀南現在正在和麥克西斯公司合作，發展更容易上手的艾可版本，要讓任何人都可以用它來作電腦實驗。 心智的實驗室 在聖塔菲經濟研究計畫的草創期，亞瑟也同時對電腦實驗保持濃厚的興趣。在研究過程中，我們像傳統經濟學一樣作數學分析以及證明定理。但是因為我們研究報酬遞增、學習，以及適應和歸納的混沌未明世界，因此問題常常複雜得超出一般數學分析的範圍。所以，我們必須求助於電腦。電腦就像我們的實驗室一樣。 然而，亞瑟的問題是，即使在聖塔菲，很多經濟學家一想到電腦模型就忐忑不安。有一天吃中飯的時候，艾羅怏怏不樂的對亞瑟說：我猜我們得用電腦模擬來研究經濟學，但是我想我太老了，要在這個時候改變實在太困難了。 在另外一個場合中，六十幾歲的漢恩說：我的天哪，小夥子，我都快退休了。如果定理的時代已經過去，那麼我也退出