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The emerging science at the edge of order and chaos

Cat: ICT
#: 0501b

M. Mitchell Waldrop





The emerging science at the edge of order and chaos 秩序とカオスの縁に登場する科学
  1. Preface:
  2. Increasing Returns:
  3. The Santa Fe Institute:
  4. Secrets of the Old One:
  5. Economics vs. Physics:
  6. Master of the Game:
  7. At the edge of Chaos:
  1. 序:
  2. 収穫逓増:
  3. サンタフェ研究所:
  4. 悪魔の秘密:
  5. 経済学対物理学:
  6. ゲームの達人:
  7. カオスの縁に:
  • Everyone doesn't prefer complexity than simplicity; the term of complexity seems be misunderstood in its original meaning. I think he complexity used here has the following set of meaning:
    1. Nonlinearity
    2. Recursiveness
    3. Fractal
    4. Autonomy
    5. Self-replication
    6. Networktropism
    7. Distributed resources
    8. Edge of ordeer and chaos
    9. Initial value dependence
  • 誰もが複雑は単純ほど好きではない。「複雑系」の用語は、その本来の意味が誤解されると思う。ここで使われている複雑性とは以下の意味の組合せであると思う。
    1. 非線形性
    2. 循環性
    3. フラクタル
    4. 自律性
    5. 自己増殖性
    6. ネットワーク親和性
    7. 分散資源
    8. 秩序とカオスの縁
    9. 初期値依存性

>Top 0. Prologue

  • The science of complexity:
    A great many independent agents are interacting with each other in a great many ways. The very richness of these interaction allows the system as a whole to undergo spontaneous self-organization.
    • Thus, the human brain constantly organizes and reorganizes its billions of neural connections so as to learn from experience. Species evolve for better survival in a changing environment - and so do corporations and industries. And the marketplace respond to changing tastes, life-styles, immigration, technological developments, shifts in the price of raw materials, and a host of outer factors.
  • Chaos theory:
    In the past two decades, chaos theory has shaken science to its foundation with the realization that very simple dynamic rules can give rise to extraordinary intricate behavior.  And yet chaos by itself doesn't explain the structure, the coherence, the self-organizing cohesiveness of complex systems.
    • All these complex systems have somehow acquired the ability to bring order and chaos into a special kind of balance. This balance point - often called the edge of chaos - is the components of a system never quite lock into place, and yet never quite dissolve into turbulence, either. The edge of chaos is where life has enough stability to sustain itself and enough creativity to deserve the name of life.
  • Science of 21C:
    They believe that they are forging the first rigorous alternative to the kind of linear, redunctionist thinking that has dominated science since the time of Newton.


  • 複雑性の科学
    • 人間の脳は、経験を学習すべく、何十億ものニューロン結合を組織化、再組織化をいつも行っている。生物種は変化しつつある環境の中で、よりよい生存を求めて進化していくし、企業や産業も同じことである。また市場は変化する嗜好やライフスタイル、移民、技術革新、原料価格の変動など沢山の要素に反応する。
  • カオス理論
    • すべての複雑系は、秩序と混沌とをある特別な平衡に達する能力を有している。しばしばカオスの縁を呼ばれるこの平衡点は、システムの構成要素が秩序に固定されてもなく、まあ分解して混乱もしていないような状態である。カオスの縁とは生命が自らを支えるのに十分な安定性を有しており、かつ生命の名に値するような十分な創造性を有している場所である。
  • 21世紀の科学

>Top 1. Increasing Returns:

  • Conventional economics:
    Theoretical economics endless talked about the stability of the marketplace, and the balance of supply and demand. They transcribed the concept into mathematical equations and proved theorems about it.
  • Increasing Returns:
    But the marketplace isn't stable, The world isn't stable. It's full of evolution, upheaval, and surprise. Economics had to take that ferment into account; a principle known as "Increasing Returns",or in the King James translation, "To them that hath shall be given."
  • Ilya Prigogine, Belgian economist:
    "The economy is a self-organizing system." Self-organizing  depends upon self-reinforcement; a tendency for small effects to become magnified when conditions are right, instead of dying away.
    • Positive feedback:
      Tiny  molecular motions grow into convention cells. Mild tropical winds grow into a hurricane. Seeds and embryos grow into fully developed living creatures. Positive feedback seemed to be the sine qua non of change, of surprise, of life itself.
  • QWERTY keyboard layout:
    Christopher Scholes designed the QWERTY layout in 1873 specifically to slow typists down; the typewriting machines of the day tended to jam if the typist went too fast. Then the Reminton Sewing Machine Company mass-produced a typewriter using the QWERTY keyboard, which meant that lots of typists began to learn the system.
Old Economics
New Economics
Decreasing returns Much use of increasing returns
Based on 19C physics (equilibrium, stability, deterministic dynamics) Based on biology (structure, pattern, self-organization, life cycle)
People identical Focus on individual life; people separate and different
If only there were no externalities and all had equal abilities, we'd reach Nirvana Externalities & differences become driving force. No Nirvana. System constantly unfolding.
Elements are quantities & prices. Elements are patterns & possibilities.
No real dynamics in the sense that everything is at equilibrium. Economy is constantly on the edge of time. It rushes forward, structures constantly coalescing, decaying, changing.
Sees subject as structurally simple Sees subject as inherently complex.
Economics as soft physics. Economics as high-complex science.
  • Clock with hands that went backward:
    Florence Cathedral clock, which had been designed by Paolo Uccello in 1443 - and which ran backward. (It also display all 24 hours.)
  • Gasoline engines:
    They were also inherently less fuel-efficient. If things had been different and if steam engines had benefited from the same 90 years of development lavished on gasoline engines, we might now be living  with considerably less air pollution and less dependence on foreign oil.
  • Nuclear power:
    When US embarked on its civilian nuclear power program in 1956, a number of designs were proposed: reactors cooled by gas, by ordinary light water, by  heavy water, and even by liquid sodium. Each design had its technical advantages and disadvantages; indeed, with a perspective of 30 years, many engineers believe that a high-temperature, gas-cooled design would have been inherently safer and more efficient than the others.


  • 伝統的な経済学
  • 収穫逓増
  • ベルギー経済学者イリヤ・プリゴジン
    • ポジティブ・フィードバック:
  • QWERTY配列
    Christopher Scholesは1873年にタイピストの入力を遅くするためにQWERTY配列を考案した。当時のタイプライターはタイピストがあまり速く打つと挟まって動かなくなったからである。その後レミントン・ソーイング・マシン社がこのQWERTY配列のキーボードを大量生産し、それで多くのタイピストがこのシステムを学んだ。
収穫逓減 収穫逓増
19C物理学 (均衡、安定、決定論的力学) 生物学的 (構造、パターン、自己組織化、生命サイクル)
人々は同一 個人の性格重視 (人々は分離し、異質)
外的事情がなく、かつすべては同じ能力があれば、我々は極楽状況に至る 外的事情や差異が原動力になる。極楽は存在しない。システムは常に展開する。
要素は数量と価格 要素はパターンと可能性
すべては平衡状態なので、真のダイナミックスは存在しない。 経済は常に時間と共にある。経済は前進し、構造は合体、崩壊、変化している。
対象は構造的に単純なものとみなす。 対象は本質的に複雑なものと見なす
ソフト物理学としての経済学 高度に複雑な科学としての経済学
  • 反対方向に針が動く時計
  • ガソリン・エンジン
  • 原子力

>Top 2. The Santa Fe Institute:

  • George A. Cowan:
    What make it even more remarkable is that the entrepreneur in the picture - George A. Cowan - was about as un-New Age as anyone could imagine.
    • The royal road to a Nobel Prize has generally been through the reductionist approach," he says - dissecting the world into the smallest and simplest pieces you can. "You look for the solution of some more or less idealized set of problems, somewhat divorced from the real world, and constrained sufficiently so that you can find a solution. And that lead to more and more fragmentation of science. Whereas the real world demands a more holistic approach. Everything affects everything else, and you have to understand the whole web of connections."
  • Molecular biology:
    One of their inspiration, ironically enough, seemed to be molecular biology. A slime volume entitled "What Is Life?", a series of provocation speculation about the physical and chemical basis of life published in 1944 by the Austrian physicist Erwin Schrodinger.
    • One of the those who was influenced by the book was Francis Crick, who deducted the molecular structure of DNA along with James Watson in 1953.
    • George Gamow, a Hungarian theoretical physicist who was one the original proponents of the Big Bang theory of the origin of the universe, became intensely interested in the structure of the genetic code in the early 1950s.
    • After the discovery of recombinant DNA technology in the early 1970s gave biologist the power to analyze and manipulate life-forms almost molecule by molecule.
    • "Once you're in a partnership with biology, you give up that elegance, you give up that simplicity. And from there it's so much easier to start diffusing into economics and social issues.", says Cowan.
  • Computer simulation:
    When you're stuck with solving mathematical equations by paper and pencil, how many variables can you handle without bogging down? Three? Four? By the early 1980-s, computers were everywhere. PC were booming. And the big corporate and national labs were sprouting supercomputers like mushrooms.
    • Properly programmed, computers could become entire, self-contained worlds, which scientists could explore in ways that vastly enriched their understanding of the real world. In fact, computer simulation had become so powerful by the 1980s that some people were beginning to talk about it as a "third form of science."
  • Nonlinear dynamics:
    In part because of their computer simulations, and in part because of new mathematical insights, physicists had begun to realize by the early 1980s that a lot of messy, complicated systems could be described by a powerful theory known as "nonlinear dynamics." And in the process, they had been forced to face up to a disconcerting fact; the whole really can be greater than the sum of its parts.
    • They had spent the past 300 years having a love affair with linear systems - in which the whole is precisely equal to the sum of its parts.
    • Sound is a linear system The sounds waves intermingle and yet retain their separate identities.
    • Light is also a linear system. The various light rays operate independently, passing right through each other as if nothing were there.
    • In some ways the economy is a linear system, in the sense that small economic agents can act independently.
    • Our brains certainly aren't linear; the emotional impact of both sounds together may be very much greater than either one alone. This is what keeps symphony orchestras in business.
    • Nor is the economy really linear. Millions of individual decisions to buy or not to buy can reinforce each other, creating a boom or a recession.
    • The whole is almost always equal to a good deal more than the sum of its pats. The mathematical expression of that property is a nonlinear equation; one whose graph is curvy.


  • George A. Cowan:
    サンタフェ研究所を際だたせているのは、この図式の中の創業者George A. Cowanがどう見てもニューエイジ的でないことである。
    • ノーベル賞への王道はこれまではほとんどが還元主義的方法だった」とCowanはいう。「還元主義的方法とは、この世界を可能な限り小さく単純な断片に刻んでいくことである。何か理想化した問題設定に対して解を求めるのであるが、それは現実離れしており、かなり制約されているゆえに解答も見つかる。そのことがさらに科学の断片化をもたらす。現実世界が求めているのは、もっと全体論的な (ホリスティックな)アプローチである。すべてがすべてに影響し合っている。だから全体のネットワークを理解する必要がある。」
  • 分子生物学
    皮肉なことに、彼らを刺激したものの一つは分子生物学であった。「生命とは何か」という薄い本がオーストリアの物理学者Erwin Schrodingerが1944年に書いた一連の刺激的な物理・化学的生命論だった。
    • その本に影響を受けた一人がFrancis Crickで、1953人にJames Watsonと共にDNAの分子構造を明らかにした。
    • ビッグバン宇宙創成論の提唱者の一人であるハンガリーの理論物理学者George Gamowは、1950年代初めに遺伝子コードの構造に強い関心を持つようになっていた。
    • 1970年代初めのDNAの組み替え技術が発見され、生物学者にほぼ分子レベルでの生命形態を分析・操作する能力を与えた。
    • Cowan曰く、「一旦、生物学と手を組んでしまったら、優雅さとか単純さとか言っていられない。そこから経済学や社会の問題に入っていく方がずっとわかりやすい」
  • コンピュータ・シミュレーション
    数学の方程式を紙と鉛筆で解く場合、どれだけの変数を扱えるだろうか。3つ、あるいは4つ? 1980年代初めにはコンピュータはどこにでもあった。また大企業や国の研究所はキノコのようにスーパーコンピュータを増やしていった。
    • うまくプログラムすると、コンピュータは一個の自立的な世界となる。科学者その世界を探検することで、現実の世界の理解を大いに深めることができる。実際コンピュータ・シミュレーションは1980年代までにはかなり強力なものになっていたので、それを理論と実験の中間にある第三の形態の科学として語られ始めていた。
  • 非線形力学
    • 彼らは300年間専ら線形システムに夢中になっていた。そこでは全体は正確にその部分の総和に等しい。
    • は線形システムである。音波は混じり合うがそれぞれの同一性は保たれている。
    • も線形システムである。様々な光は独自に振る舞いあたかもそこに何もないかのように他の光線の中を直進する。
    • 小さな経済単位は独自に機能できるという意味では、経済も線形システムである。
    • 人間の脳は確かに線形システムではない。両方の音の感情的な衝撃は個々の単独の場合よりもずっと大きい。だからオーケストラが成り立つ。
    • 経済も本当は線形ではない。何百万という個人の買う買わないの意志決定が相互に強め合って、好況や不況を引き起こす。
    • 全体はほとんどいつも、部分の総和よりかなり大きい。そのような数学的表現が非線形方程式である、グラフは曲線になる。
  • >Top Cognitive science:
    Rota, in particular, thought of it as extending all the way to the study of the mind - based on the idea that thinking and information processing were fundamentally  the same thing. Also known as cognitive science, this was a hot area and getting hotter.
  • Murray Gell-Mann:
    55-year-old enfant terrible of particle physics.(Gell-Mann named 'quark' after a made-up word in James Joyce's Finneguns Wake.)   He wanted to tackle problems like the rise and fall of ancient civilizations and the long-term sustainability of our civilization - problems that would transcend the disciplinary boundaries in a big way.
  • Phil Anderson:
    However, says Anderson, this belief does not imply that the fundamental laws and the fundamental particles are the only things worth studying - and that everything else could be predicted if you only had a big enough computer. Back in 1932, the physicist who discovered the positron declared, "The rest is chemistry!"
    • E.g.: There's nothing very complicated about a water molecule. Those zillions of molecules have collectively acquired a property, liquidity, that none of them possesses alone. The liquidity is "emergent."
    • Weather, life or the mind is an emergent property. At each level of complexity, entirely new properties appear. And at each stage, entirely new law, concepts, and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one. Psychology is not applied biology, nor is biology applied chemistry."
  • Workshop at the Santa Fe-based archeology:
    Researchers in the field were confronted with three fundamental mysteries:
    • First, when did nonhuman primates first begin to acquire the essence of humanity, including complex language and culture?
      • Did it happen nearly a million years ago, with the rise of Homo erectus?
      • Or only a few tens of thousands of yeas ago, as the Neanderthals gave way to fully Homo sapiens sapiens?
      • And either way, what caused the change? Millions of species have gotten along just fine without brains as large as ours. Why was our spices different?
    • Second, why did agriculture and fixed settlement  replace nomadic hunting and gathering?
    • Third, what forced triggered the development of cultural complexity, including specialization of crafts, the rise of elites, and the emergence of power based on factors such as economics and religion?
  • How should you organize the institute?
    A institute without departmental walls; where people could talk and interact creatively. "It's important to have people who steal ideas!"
    • They basically had the same world view, in the sense that they all seemed to feel that 'emerging syntheses' really meant a restructuring of science - that the overlapping themes of different parts of science would put together in a new way.
    • Every topic of interest had at its heart a system composed of many, many "agents."  These agents might be molecules or neurons or species or consumes or even corporation. But whatever their nature, the agents were constantly organizing and reorganizing themselves into larger structures through the clash of mutual accommodation and mental rivalry.
    • Complexity, in other words, was rally a science of emergence.
  • 認知科学
  • Murray Gell-Mann:
    55歳の粒子物理学のきかん坊。(Gell-MannはJames joyceの"Finneguns Wake'の小説から名付けた。) 彼は、古代文明の消長や、我々の文明の長期的な持続可能性という学問分野を大きく超越するような問題にぜひ取り組みたいと思っていた。
  • Phil Anderson:
    • 例:水の分子それ自体には特に複雑なことはない。何兆という分子全体が、個々の分子にはない液体という特性を獲得した。液体という特性は創発的なのである。
    • 気象、生命、あるいは心は創発的な特性である。複雑性のそれぞれのレベルで、全く新しい特性が出現している。それゆえ、各段階で全く新しい法則や概念や一般化が必要なのであり、したがって前段階におけると同じように、インスピレーションと創造力が要求される。心理学は応用生物学ではなく、生物学は応用化学ではない。
  • サンタフェ考古学センタでのワークショップ
    • 第一に、人以前の霊長目はいつ複雑な言語や文化など人間性を獲得したのか
      • それは100万年ほど前のホモ・エレクトゥスの出現した時か
      • あるいは2-3万年前に、ネアンデルタールがホモ・サピエンスに道を譲った時か
      • いずれにせよどのような変化が生じたのか。何百万種もが我々のような大脳をもたずにやってこれたが、なぜ我々の種は異なったのか。
    • 第二に、なぜ農業や定住生活が遊牧的な狩猟と採集生活に取って代わられたのか。
    • 第三に、どのような力が、技術の分化、エリートの誕生、経済や流今日のような要素に基づく権力の出現という文化の複雑性が生じたのか。
  • 研究所をどう組織化すべきか
    • 彼らは基本的には世界観を共有していた。「新たな統合」とは科学の再構築すること。つまり、異なる科学分野の重なるテーマを新たなやり方で統合することだと感じていた。
    • どの話題にもその中心に多くのエージェントからなる一つのシステムがあることが明白になった。そのエージェントは、分子や、ニューロン、あるいは種かも知れないし、消費者や企業かも知れない。しかしそれが何であれ、それらな相互の調整や精神的な拮抗を通じて、絶えず大きな構造へと自己組織化していく。
    • 複雑性とは別の表現では創発の科学だったのである。

>Top 3. Secrets of the Old One:

  • Chaos:
    Human beings and all other living things are undoubtedly the heirs of four billion years of random mutation, random catastrophes, and random struggles for survival; we are not here as the result of divine intervention, or even space aliens. Darwin didn't know about self-organization - matter's incessant attempts to organize itself into ever more complex structures, even in the face of the incessant forces of dissolution described by the second law of thermodynamics.
    • So the story of life is, indeed, the story of accident and happenstance. But it is also the story of order.
  • Order:
    All cell contains a number of "regulatory" genes that act as switches and can turn one another on and off. If genes can turn one another on and off, then you can have genetic circuits. Somehow, the genome has to be some kind of biochemical computer. It is the computing behavior - the orderly behavior - of this entire system that somehow governs how one cell can become different from another."                                            
    • Instead of executing its instructions step by step by step, the way human-built computers do, the genomic computer must be executing most or all of its genetic instructions simultaneously, in parallel. What mattered was whether the genome as a whole could settle down into a stable, self-consistent pattern of active genes.
  • Natural laws of complex system:
    Whence cometh the order? Stuart Kauffman started to concentrate on networks in between, where the connections were sparse, but not too sparse. To keep things simple, he looked at networks with precisely two inputs per gene. He already knew that densely connected networks were hypersensitive in the extreme. Densely connected networks tended to be chaotic. They could never settle down. But in his two-input networks, Kauffman discovered that flipping one gene would typically not produce an ever-expanding wave of change; they would tend to converge.
    • Instead of wandering through a space of one million trillion trillion states, his two-input network had quickly moved to an infinitesimal corner of that space and stayed there. It settled down and oscillated through a cycle of five or six or seven or, more typically it turned out about ten states.
  • Death and Life:
    The irony of it was that when Kauffman used the word "order," he was obviously referring to the same thing that Arthur meant by the word "messiness" - namely emergence, the incessant urge of complex systems to organize themselves into patterns.
    • Until about 15 or 20 years ago, technology wasn't part of economics at all. It was "exogenous" - delivered magically by noneconomic process. More recently there had been a number of efforts to model technology as being "endogenous."
    • Technology isn't like a commodity at all. It is much more like an evolving ecosystem. They are usually made possible by other innovations being already in place. In short, technologies form a highly interconnected web, a network. Furthermore, these technological webs are highly dynamic and unstable. Technology A, B, and C might make possible technology D, and so on.
    • Moreover, these technological webs can undergo bursts of evolutionary creativity and massive extinction events, just like biological ecosystems. Say a new technology like the automobile comes in and replaces an older technology, the horse. The whole subnetwork of technologies that depended upon the horse suddenly collapses in what the Joseph Schumpeter once called "a gale of destruction."
    • The dynamics of genetic regulatory networks turned out to be a special case of "nonlinear dynamics."
  • How did life get stared?:
    According to the standard theory, the origin of life was rather straightforward. DNA, RNA, proteins, polysaccharides, and all the other molecules of life must have arisen billions of years ago in some warm little pond.
    • But most biological molecules are enormous objects. If the formation were truly random, you would have to wait far longer than the lifetime of the universe to produce even one useful protein molecule, mush less all the myriads of proteins and sugars and lipids and nucleic acids that you need to make a fully functioning cell.
    • Kauffman imagined that a primordial soup containing some molecule A that was busily catalyzing the formation of another molecule B. Suppose that molecule B itself had a weak catalytic effect, so that it boosted the production of some molecule C. And suppose that C also acted as a catalyst, and so on. Then somewhere down the line a molecule Z that closed the loop and catalyzed the creation of A.
    • Maybe an autocatalytic set would have been alive. Moreover, the set would have possessed a kind of metabolism; The web molecules would take in a steady supply of "food" molecules in the form of amino acids and others.
    • If there was any fixed probability that a polymer catalyzed a reaction, there'd be some complexity a which this thing would have to become mutually autocatalytic. In other words, it was just like his genetic networks: if the primordial soup passed a certain threshold of complexity, then it would undergo that funny phase transition.
  • Economic takeoff:
    Moreover, an autocatalytic set can bootstrap its own evolution in precisely the same way that an economy can, by growing more and more complex over time. If a country ever managed to diversify and increase its complexity above the critical point, then you would expect it to undergo an explosive increase in growth and innovation, called an "economic takeoff."
    • Cambrian explosion:
      the period some 570 million years ago when a world full of algae and pond scum suddenly burst forth with complex, multicellular creatures in immense profusion. Maybe there was an explosion of processes acting on process to make new processes. It's the same thing as in an economy.


  • カオス
    • 即ち、生命の物語は、実際には、偶然の出来事の物語であると同時に、それは秩序の物語でもある。
  • 秩序
    • ゲノム・コンピュータは人間が作ったコンピュータのような逐次処理ではなく、遺伝子の命令のほとんどもしくはすべてを並行処理で同時に実行しているに違いない。重要なのは、ゲノムが全体として、活性遺伝子の安定した自律的なパターンに落ち着くかどうかである。
  • 複雑なシステムに関する自然法則
    • 彼の2入力型ネットワークは、2の100条という状態空間をさまよう代わりに、すぐにその空間の非常に小さな片隅に移動し、そこに落ち着いた。それはそこで安定し、5,6,7,いや典型的にはおよそ10の状態を1サイクルとして振動していることがわかった。
  • 生と死
    • 約15-20年前までは、技術は経済の一部では全くなかった。それはあくまで経済とは関係ないプロセスによって「外生的」に魔法のように生み出されるものだった。その後、技術を「内生的」と見なそうとする多くの試みが出てきた。
    • 技術は、コモディティとは全く異なる。むしろ進化するエコシステムにずっと似ている。イノベーションを可能にするのは、すでに存在している他のイノベーションである。つまり、技術は互いに複雑に結びついたウェブでありネットワークを形成している。さらに、これらの技術ウェブはダイナミックで不安定である。技術A、B、Cがあるから技術Dが可能になる。
    • さらに、これらの技術Webは、生物的なエコシステムと同様に、進化的な創造と大量絶命事件を引き起こす。例えば、自動車という新技術の登場で、馬という古い技術に取って代わる。馬に依存していた技術のサブネットワーク全体が突然崩壊する。シュンペーターが言った「破壊の嵐」である。
  • 生命はどうして始まったか?
    • しかし多くの生物的分子は巨大な物質である。もしその物質形成が完全でランダムであるとすれば、たった一個の有用なタンパク質が生み出されるまでには、宇宙の年齢より長い時間を待たねばならない。まして完全に機能する一個の細胞を作るのに無数のタンパク質、糖、脂質、核酸などが必要となる。
    • Kauffmanは、もし原始スープの中に触媒作用をもつA分子が含まれていて、その分子が、触媒作用によってB分子をせっせと生成すると考えた。B分子自体には弱い触媒効果があって、それがC分子の生成を促したとする、そのCもまた...おそらくずっと先にZ分子が生まれ、ループを閉じるようにそれが触媒作用でA分子を生成したのではないかと推論した。
    • おそらく自動触媒セットは生きてたのではないだろうか。自動触媒セットには、一種の代謝作用があり、網の中の分子はアミノ酸などのような食糧となる分子の安定供給を手にしている。
    • もしある一定の確率で一つの重合体が一つの反応を触媒誘導するとすれば、そこでは必然的に互いに自動触媒作用を起こすある種の複雑さが存在する。それはあたかも遺伝子ネットワークのようなものである。もし原始スープの複雑さがある閾値を超えると、奇妙な相転移が起こるであろう。
  • 経済的離陸
    • カンブリア紀の爆発的事件:

>Top 4. Economics vs Physics:

  • Economists vs. Physicists at the Santa Fe Institute:
    Arthur's first formal presentation: When he used the words "self-reinforcing mechanisms," he was basically talking about nonlinearity in economics.
    • "Stop!" said Arrow. "In precisely what sense do you mean nonlinear? Aren't all economic phenomena nonlinear?"
    • To be mathematically precise, said Arthur, the ordinary assumption of decreasing returns corresponds to economic equations with a "second-order" nonlinearity, which drives the economy toward equilibrium and stability. What he was looking at were "third-order" nonlinearities - factors that would drive some sector of the economy away from equilibrium. This is what an engineer would call positive feedback.
  • Isn't economy a lot like a spin glass?:
    Just as in more familiar magnetic materials, the components of a spin glass are metal atoms whose electrons possess a net whirling motion, or "spin." And just as in iron, these spins cause each atom to produce a tiny magnetic field.
    • Unlike in iron, the interatomic forces in a spin glass do not cause all the spins to fall into line with one another. Instead, the forces in a spin glass are completely random. This atomic-scale disorder means that a spin glass is a complex mixture of positive and negative feedbacks, as each atom tries to align its spin in parallel with certain of its neighbors and opposite to all the rest. There are a vast number of ways to arrange the spins so that the frustration is reasonably tolerable for everyone - a situation of "local equilibrium."
    • In this sense a spin glass is quite a good metaphor for the economy. It naturally has a mixture of positive and negative feedbacks, which gives it an extremely high number of natural ground states, or equilibria.
  • Physics vs. Mathematics:
    Physics is far and away the most thoroughly mathematized science in existence. But what most of the economists didn't know was that physicists are comparatively casual about their math.
    • "They use a little rigorous thinking, a little intuition, a little back-of-the-envelope calculation - so their style is really quite different," says Arrow. "Physical scientists are obsessive about founding their assumptions and their theories on empirical fact. But the general tendency is that you make a calculation, and then find some experimental data to test it. So the lack of rigor isn't so serious. The errors will be detected anyway. Well, we don't have data of that quality in economics. We can't generate date the way the physicists can."
  • Isn't economics simpler than physics?:
    Arthur replied. "In one sense it is. We call our particles 'agents' - banks , firms, consumers, governments. And those agents react to other agents, just as particles react to other particles. Only we don't usually consider the spatial dimension in economics much, so that makes economics a lot simpler.
    • However, there is one big difference. Our particles in economics are smart, whereas yours in physics are dumb. In physics, an elementary particle has no past , no experience, no goals, no hopes or fears about the future. It just is. That's why physicists can talk so freely about "universal laws"; their particles respond to forces blindly, with absolute obedience.
    • But our particles have to think ahead, and try to figure out how other particles might react if they were to undertake certain actions. Our particles have to act on the basis of expectations and strategies. That's what makes economics truly difficult."
  • In nonlinear systems - and the economy is most certainly nonlinear - chaos theory tells you that the slightest uncertainty in your knowledge of the initial conditions will often grow inexorably.


  • サンタフェ研究所での経済学者対物理学者
    • 「待ってくれ!」Arrowが言った。「あなたはどういう意味で非線形性といっているのか? すべての経済現象は非線形的ではないのか?」
    • Arthurは次のように言った。数学的に厳密に言えば、収穫逓減という通常の仮定は二次の非線形で、それが経済活動を均衡と安定性に向かわせる。これに対し注目しているのは、三次の非線形で、それは経済活動のある部分を均衡から遠ざけようとする。これはエンジニアが正のフィードバックと呼ぶものである。
  • 経済学はスピン・グラスに似ている?:
    • 鉄の場合は原子間で相互に作用する力によってすべてのスピンが一方向に並ぶが、スピン・グラスの場合はそうはならない。スピン・グラスの中の力は完全にランダムである。この原子レベルでの無秩序は、スピン・グラスが、正のフィードバックと負のフィードバックとが複雑に混じったものであることを意味する。各原子ともそのスピンを近傍の一部の原子のスピンに会わせ、それ以外とは逆向きになるようにしている。どの原子も合わせたくないものと合わせねばならないものという、ある種のフラストレーション状態に耐えている。つまり局所的平衡の状態である。
    • この意味で、スピン・グラスは経済に対するうまい隠喩である。そこには、正のフィードバックと負のフィードバックの混合があり、それが極端に多い自然の基底状態、即ち均衡を作り出す。
  • 物理学と数学
    • Arrow (経済学者) 曰く、「彼らは少し厳格な思考と少し直感を使い、封筒の裏で少し計算をする。つまり彼らのやり方はまったく経済学者と違うんだ。物理学者は、仮定と理論とを実験的事実の上に打ち立てることに執着している。一般的な傾向としては、まず計算して、次にそれを検証する実験データを見つけることである。だから厳密でないことはそれほど重大ではない。誤りはいずれ発見されるだろう。我々経済学の方は、そういう質のデータを持っていない。物理学者がやるような方法でデータを生み出すことはできない。」
  • 経済学は物理学より易しい?
    Arthur (経済学者)は答えた。「ある意味ではそうだ。我々は、銀行、会社、顧客、政府などをエージェントと呼んでいる。本物の粒子が他の粒子に反応するように、これらのエージェントも他のエージェントに反応する。但し、経済学では、通常、空間的な次元を考えないから、経済学の方がずっと単純である。
    • しかし、一つ大きな違いがある。経済学の粒子はスマートだが、物理学の粒子はバカだということである。素粒子には、過去も経験も目標も未来に関しての希望も恐れもない。ただ存在しているだけだ。だから物理学者は宇宙の法則について自由に語ることができる。物理学の粒子は、力に対して絶対服従で反応する。
    • しかし我々経済学の粒子は先を考える。こっちがこのような行動をとったら、他の粒子がどう反応するのかを考慮する。我々の粒子は予測と戦略を基に行動しなければならない。そのことが経済学を本当に困難なものにしている。」
  • 経済現象は明らかに非線形的だが、カオス理論によれば、非線形のシステムでは、初期条件についての知識のわずかな不確実性が、しばしばどうしようもなく大きくなる。

>Top 5. Master of the Game:

  • Complex adaptive systems:
    • Multiple agents:
      First, each of these systems is a network of many "agents" acting in parallel. In a brain the agents are nerve cells, in an ecology species, in a cell organelles such as nucleus and mitochondria, in an embryo cells, and so on. In an economy, they might be individuals or households. At business cycles, might be firms. At international trade, might be whole nations. Each agent finds itself in an environment produced by its interactions with the other agents in the system.
    • Building blocks:
      Second, a complex adaptive system has many levels of organization, with agents at any one level serving as the building block for agents at a higher level. In the brain, one group of neurons will form the speech centers, another the motor cortex, and still another the visual cortex.
    • Internal models:
      Third, all complex adaptive systems anticipate the future. In situation ABC, action XYZ is likely to pay off. every complex adaptive system is constantly making predictions based on its various internal models of the world - its implicit or explicit assumptions about the way things are out there. These models are much more than passive blueprints. They are active. Like subroutines in a computer program, they can come to life in a given situation.
    • Perpetual novelty:
      Finally, complex adaptive systems typically have many niches, each one of which can be exploited by an agent adapted to fill that niche. The space of possibilities is too vast, they have no practical way of finding the optimum. Complex adaptive systems are characterized by perpetual novelty.
  • What is the real problem with eocnomics?:
    "Chess!" replied Arthur. There is a theorem that any finite, two-person, zero-sum game such as cehss has an optimal solution.
    • Claude Shannon of Bell Labs had extimated the toal number of possible moves in chess. His answer, 10^120, was a numer so vast as to defy all metaphor. There havn't been that many microseconds since the Big Bang. There aren't that many elementary particles in the observable unives. There is no conceivable compuer that could examine all of those moves. We human players have to make do with rules of thumb - hard-learned heuristic guides that tell us what kind of strategies will work best in a given situation.


  • 複雑適応系:
    • 多様なエージェント
    • ビルディング・ブロック
    • 内部モデル
    • 永続的な斬新さ
  • 何が経済学の本当の問題なのか?
      • ベル研のClaude Shannonは、チェスの駒の可能な動きの総数を算定した。その答えは、10の120乗であり、それは例えようもないほど莫大だった。ビッグバン以来今日までのマイクロ秒時間はそれほどにはならない。観測可能な宇宙の中の素粒子の数も同様である。このような駒の動きをすべて確かめることができるコンピュータはあり得ない。我々人間は経験則、つまりある状況下でどのような戦略をとるのが最善かを教えてくれる熱心に学習した経験則で済ませるしかない。

>Top 6. At the edge of Chaos:

  • Artificial life:
    Chris Lanton at Los Alamos invented the name of "Artificial life."
    • John Conway, English mathematician developed the Game of Life: a two-dimensional grid full of black squares that were "alive" and white squared that were "dead." Once you set the game going, the squares would live or die from then on according to a few simple rules. Each square in each generation would first look around at its immediate neighbors.
      • If too many (4 or more) of those were already alive, then in the next generation the square would die of overcrowding.
      • If too few (0-1) neighbors were alive, then the square would the loneliness.
      • If the number of neighbors was just right (2-3), then in the next generation that central square would be alive - either by surviving if it were already alive or by being "born" if it weren't.


  • 人工生命:
    ロスアラモスのChris Lantonが人工生命の名称を発明した。
    • 英国の数学者であるJohon Conwayは、ゲーム・オブ・ライフを制作した。これは二次元の格子状で、生きている黒い四角形セルと死んでいる白い四角形セルが詰まっている。ゲームを始めると、セルはいくつかの簡単な規則に従って生きたり死んだりする。どの世代のそれぞれのセルは、自分に隣接するセルを見回す。そして、
      • もし、生きているセルが多すぎると (4以上) 次世代のセルは過密のために死ぬ。
      • もし、セルがあまり少な過ぎると (0-1)、そのセルは孤独のためにしんでしまう。
      • もし、ちょうど良い数 (2-3) の数のセルが回りに生きていれば、それらに囲まれたセルは次世代まで生き延びる、つまり、すでに生きているセルは生き残り、死んでいた場合は新たに誕生する。
  • Complexity is really complex, but it might be simpler to understand the nature by a complex way. If we try to understand the nature in a simple way, which would be more complex and more complicated.
  • The nature may be simple and beautiful, or complex and beautiful, or even complex but may not be beautiful.
  • 複雑系は正に複雑である。しかし自然は複雑な方法で理解する方が、単純な方法なのだろう。もし我々が自然を単純な方法で理解しようとすると、それこそもっと複雑で混乱してくる。
  • 自然は、単純で美しいのか、複雑で美しいのか、あるいは複雑で美しくないのかも知れない。

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