So my one sentence definition is

我用一句話來定義

systems that don't yield to

某系統不會被迫於

compact forms of representation

集中的表達

or description, and I should explain that.

或描述形式，我應該解釋這個。

In the systems that physicists study,

通常物理學家們研究的系統，

you can often write down on one page

你可以在一頁紙上寫下

a few very beautiful, elegant equations, like Newton's

一些非常完美的公式，例如牛頓的

laws for the conservation of momentum, or the Maxwell field

動量守恆定律，或者是麥克斯韋場

equations for electromagnetism, and so forth.

電磁方程式，等等。

And you can explain a huge amount of empirical data

你可以去解釋很多的經驗資料。

when it comes to the genome, or the brain, or properties

但是當描述基因組，大腦或者是

of society or literary history, as far as we know,

社會特性，文明史這些問題，正如我們所知道的那樣

there are no such beautiful, elegant, compact descriptions.

並沒有完善的經驗法則和系統的表述

And that, for me, is evidence

對於我來說, 這就顯示

that we're dealing with a complex system.

我們正在處理一個複雜系統。

Now, why is that? So, the reason why I think it's difficult

為什麼呢？我認為之所以很難做到

to do is because those are systems that encode long histories.

是因為這些系統包含了很長的歷史。

One of the characteristics, for me,

我認為，複雜系統的某一項特徵，

of a complex system, is that it has found a means,

便在於它作為一種方式，

or a mechanism, for extracting from its environment

一個機制，來從其環境中

some information, in order to use it to behave

汲取資訊，一邊用來做適應性行為

adaptively. To predict and control.

為了預測和管控。

And consequently, it needs to be described using models

結果呢，這就需要用模型來描述

that have a slightly different flavor to the ones that

尤其是那些稍稍不同於

we have been traditionally familiar with in the mathematical natural sciences.

我們在數理自然科學傳統研究中所熟悉的那樣。

And typically, those models will be computation.

通常來說，這些模型需要通過計算。

So, I'm going to ask you

我想請問您

the same question that I'm asking everybody, which is

一個我用來問每一個人的同樣的問題，你對於

what is your definition of a complex system. Oh no!

複雜系統是怎樣定義的？哦，

That's what everybody says.

每個人都這樣說。

In theoretical computer science, we don't say that

在理論電腦科學中，我們通常不會說

systems are complex or simple, per se,

系統本身有複雜和簡單之分。

we more typically say that questions are

我們通常會說某些問題是

complex if those questions require a lot of computational

複雜的如果這些問需要很多計算

resources to solve. A lot of time, a lot of memory,

來解決，佔用很多時間，很多記憶體

a lot of communication between people.

並且需要很多的與人的交流。

Some limited resource.

而資源卻是有限的。

Different questions might have different levels of computational complexity. So for instance,

不同的問題會有不同程度的計算複雜度，例如

if what you want to know is what will the system

如果你想知道的是系統

look like t time steps from now,

在一段時間 t 之後會看起來如何

you can answer that question with about t time

那麼你可以在模擬 t 時間後來回答

by simulating it forward, but an interesting

但是一個有意思的問題在於，

question might be, well, maybe there is no algorithm that works much

也許並沒有某種計算方法可以

faster than that. Maybe there's no way to leapfrog over

算的如此快。也許我們並沒有辦法可以超越

the history. Maybe like a chaotic dynamical system that

歷史發展的過程。 例如一個混亂的動態系統

has no closed-form solution, maybe there is no shortcut to doing

其並沒有閉合形式的解，或許並沒有捷徑來

that laborious step-by-step simulation.

做冗長的每一步的模擬。

So, for me, I find it helpful to, rather than

所以，對我來說，我覺得是有幫助的，而不是

saying, is this system simple or complex? I mean, I don't deny

他說，這是系統簡單或複雜？我的意思是，我不否認

that we often have clear ideas about that, but I find it helpful

我們經常有關於明確的想法，但我發現它有用

to change the question a little bit to, give me

改變的問題一點點，給我

a yes or a no question you want to answer about this sytem,

回答這個系統是或否，

or a quantity you want to compute about this system, and then let's talk

或者你要計算這個系統，然後量讓我們來談談

about how hard it is computationally to answer that question

有關它用計算來回答這個問題是多困難，

or compute that quantity.

或計算的數量。

Well, it's a complicated

嗯，這是一個複雜的

concept. I didn't say complex, just kind of

概念。我並沒有說只是複雜的

complicated.

种类。

So, this actually ties in with a discussion I'm sure we'll

所以，這實際上關係在一個討論中，我敢肯定，我們會

have on information, so I have a rather precise notion

對資訊，所以我有一個相當準確的概念

of what I mean when I refer to a natural or artificial

我的意思是指自然或人工

system as complex, and what I mean in particular is that it has a very sophisticated

系統複雜，我的意思，特別是它有一個非常複雜的

internal causal architecture that stores and processes information.

內部架構来存儲和處理的資訊。

So, the technical things that we'll talk about shortly have to do

因此，在技術方面的東西，我們將討論在短期內要做的

with how we measure stored information and the amount of structure.

與我們如何測量所存儲的資訊和結構的量。

So, information in many ways stands in for trying to describe

所以，在很多方面的資訊代表了在試圖描述

how complex a complex system is, and various

多麼複雜的一個複雜的系統，以及各種

kinds of information processing and storage can be associated with how a system is organized.

種資訊處理和存儲能以怎樣的系統的組織相關聯。

So it's a key concept, certainly

所以這是一個關鍵的概念，當然

Shannon's original notion of information as degree of surprise,

香農的原始資料，驚喜度的概念，

degree of unpredictability in a system, or how random a system is

不可預測的系統的程度，或如何隨機系統是

needs to be augmented. So that's certainly the focus of a lot

需要被增強。所以這肯定是一個很大的关注

of my work is trying to delineate that there are many different kinds of information,

是我試圖描繪許多不同種類的資訊，

not just Shannonian information.

不只是香農信息。

So, my definition of complex systems

所以我定義複雜系統的

is a system that has

是一個系統，有

interactions. It has nonlinear elements in it.

互動。它有在它的非線性元素。

I tend to work on high dimensional systems not low dimensional systems.

我傾向于工作在高維系統不低維系統。

And I like to use the methods of statistical mechanics

我喜歡用統計力學的方法

from physics to understand problems in these systems.

從物理學理解在這些系統中的問題。

Most of the time, the interesting features in these systems have

大多數時候，在這些系統中，有趣的特性有

scaling properties, that is to say they have power laws

尺度屬性，也就是說，他們有幂率法则

or fractal objects in them, embedded in them someplace,

或者是分形物體，嵌在其中的某個地方，

either in the actual physical arrangement of them

無論是在他們的實際物理排列

or in terms of the statistics that you see.

或者，你看到的統計資料計算。

So my basic definition is that a complex system consists of a bunch of entities

所以我的基本定義是一組實體的複雜系統由

that may not start out diverse, but end up being diverse. They are connected

這可能開始不是多樣的，但最終會是多樣的。它們被連接

in some way, usually through some sort of network structure or some spatial

以某種方式，通常是通過某種網路結構或某些空間的

structure, and they get information and signals through that network

結構，他們通过網路或局部結構获得資訊和信號

or local structure, but they also sometimes get some global signals or global information,

但他們有時也得到一些全球性的信號或全球資訊，

which could be prices in a market, or temperature in a system, so that

這可能是價格在市場或溫度在一个系統中，從而使

in addition to be sort of diverse and interconnected, they are also interdependent, so the

除了是那種多樣化和相互關聯的，他們也是相互依存的，

actions of one agent in the system will sort of

所以 一個智能體動作在系統中的影響的排序

influence or have implications for another agent. So in the context

或有其它智能體的影響。因此在一個社會系統，

of a social system, like in economics, I'll say that if I go in and buy bread in the grocery store

如在經濟學方面，如果我進去雜貨店買麵包

whether I buy whole wheat bread or white bread, you really don't

我是否買全麥麵包或白麵包，你真的不關心。

care. It's not interdependent. There's no real strong interdependence, other than to

這不是相互依賴的。沒有比價格更強的

the prices. But if I decide to drive my car on the road

相互依存關係。但是，如果我決定要開我的車在路上

or drive my car really fast down the road, those sort of things, then that actually can affect you

還是開我的車在路上非常快，那些之類的東西，那麼這實際會很大程度上

in a big way. So they're interdependent. And the last thing

影響到你 。所以，他們是相互依存的。和過去的事情

is in addition to having these

是除了具有這些

interdependent behaviors and networks and diverse agents, that the agents adapt

相互独立行為和多樣網路，agent適應

and respond to the environment which that they're in. So it's not just a case of them following

並回應環境，所以這不只是下面的情況

simple rules, but that they sort of adapt. Now this last part

簡單的規則，但那種適應。現在，這最後一部分

gets a little bit tricky philosophically, because adaptation is really just a higher-order

變得有點棘手的哲學，因為適應性是真的只是一個高階

rule, so you can have a first-level rule and then a meta rule

規則，所以你可以有第一級規則，然後一個元規則

and so, you could say that they are rule based, but they are sort of meta rule based,

所以，你可以說他們是基於規則的，但他們是那種基於元規則，

that they allow for behavior that

他們允許的行為

can respond to the signals that they are getting both globally and locally. Now the last thing

可以回應他們獲得在全球和地方的信號。現在過去的事情

will mention is another sort of paradox in the definition of complex adaptive systems

會提到是複雜適應系統的定義另一種悖論

is that a system like that can be complex, but it need not be.

就是這樣的系統可以是複雜的，但它不一定是。

So a system can have those components to it, but it can end up producing

這樣的系統可以具有這些部件构成，但它可以最終產

an equilibrium. Especially if I look at an economic system

一個平衡。尤其是當我看到一個經濟體系

some parts of economic systems really equilibriate quite well, but then others

經濟體系的某些部分確實平衡的很好，但隨後其

end up being really complex. So if you look at oil consumption

最終非常複雜。所以，如果你看一下隨著

over time at the global level, that's pretty predictable, it's a pretty stable pattern

時間的推移在全球範圍內的油耗量，這是相當可預測的，這是一個非常穩定的模式

but if I look at oil prices over time, that's complex, because

但如果我看到油價隨著時間的推移，這是複雜的，因為

there's much more interdependencies and all those things come into play.

還有更多的相互依存關係，所有這些東西在起作用。

So John Holland and I sometimes joke that we should call them systems capable of producing

因此約翰荷蘭和我有時候開玩笑說，我們應該稱他們為能生產系統 複雜性。

complexity. That doesn't sound as remarkable.

這聽起來並不為顯著。

Okay, well, that is a question that people have debated a lot.

好了，好了，這是一個問題，人們已經討論了很多。

I guess

我猜

most people would agree that a complex system is a system of many interacting parts

大多數人都會同意，一個複雜的系統是許多局部系統的相互作用，

where the

相互作用的系統

system is more than just the sum of its parts.

不仅仅是其各個部分簡單相加。

It shows emergent behaviors which are not just the sum of the individual behaviors

它显示了突發行為而不是個人行為的簡單相加

of the parts. Other people add

的部分。其他人加入

extra elements to that, but that's probably what my definition is

額外的元素，這可能就是我的定義是

pretty much. It's a system of interacting parts which shows emergent behaviors.

相当好。系統相互作用的部分顯示出了涌现的的行為。

Okay, that's pretty simple. Sort of unpacking that

這很簡單的。排序

takes a little more time.

需要多一點的時間。

So I'm going to give you a definition of complex systems, but

因此我給你複雜系統的定義，但

I will remind you that many important concepts

我要提醒你很多重要概念

like virtue and life are very hard to define

例如美德和人生是很難下定義的

and I think complex systems are somewhat in that category.

我認為複雜系統也是這一類。

Nonetheless, the kinds of systems that I call complex

儘管如此，該種系統稱之為複雜

have many interacting active components

有許多相互作用的部分

and the interactions between the components have

和部件之間的相互作用有

nontrivial or nonlinear interactions

平凡的或非線性的相互作用

and that leads to the system having unpredictable behavior. You may have

並導致系統其不可預知的行為。你可能有

heard those things before. But importantly,

之前聽說過這些事情。但重要的是，

all of the components are either learning or

所有的元件都要麼學習或

modifying their behavior in some way while the system

以某種方式修改在

is behaving.

系統中的表现。

And so that leads to all kinds of interesting dynamics.

導致各種有趣的動態。

So that's roughly what I think of when I think

所以這大概是我覺得當我想到

of a complex system. So do you think that adaptation is

一個複雜的系統。你認為適應

essential for complex behavior?

對於複雜的行為所必需的吗？

Well, it's essential for the kind of complex behavior that I'm most interested in

嗯這是我最感興趣的是对各種複雜行為是必需的

Okay, fair enough.

好，很公平。

I think my definition is probably like a lot of other people's

我認為我的定義可能是像很多其他人的

definition in that a complex system is something

在定義複雜系統是什麼，

with a lot of interacting parts where something

有很多相互作用的部分的東西

about the way those parts behave when they interact is qualitatively different

它們相互作用的部分行為方式是質的不同

than the way they behave if you look at them individually. So

相比于你看他們的個體行為。

it's something with emergent phenomena. And I think we can then quibble

這件一些涌现現象。我認為，那麼我們就可以狡辯

about what exactly all those words really mean

關於究竟那些話的真正含義

so for example I might mean something a little bit different than some other people, but I

所以我可能意味著与其他人有點不同，

don't think I have anything particularly unique in my definition.

但我不覺得我有什麼在我的定義中特別獨特。

Complex systems tend to be things that

複雜系統往往從簡單

are different from simpler, usually

趋向于不同，通常

physical, systems in that they tend to be heterogenous, they tend to

物理的該系統中，它們往往是趋向異質的

be made up of parts that are the not the same kind of parts. For example,

可以由不同種部分构成的。

people and firms in a city are all different. They are not all the same.

在一個城市的人與企業都是不同的。它們不是都一樣的。

They tend to be, many of them are open ended, although not all of them.

很多往往是開放式的，雖然不是所有的人。

So a city or an ecosystem can keep on evolving

因此一個城市或一個生態系統可以繼續進化

Often the thing that makes them hardest to study in terms of making predictions

通常对最難的事情進行預測方面，研究

about them is that they also typically have chains of causation

對他們來說，他們通常也有因果關係鏈

mechanisms that make things happen that are circular, so there are feedbacks

讓事情發生有回路機制，因此是有回饋的

both positive and negative that make their evolution

正反馈与负反馈都会使他們進化

at least more difficult to study than in simpler physical

至少比研究更簡單的物理系統或工程系統 難比更困難

systems or engineered systems, where we can deal with them in regimes where they're simpler

在這裏他們处理的很簡單

and linear, and they can respond in ways that we can at least hope to characterize.

和線性的，且可以在一些方法來表徵回應。

So those things are still an operating definition of what a complex system

所以這些東西仍然是定義什麼是複雜系統

might be. But they go a long way to say what a complex system typically

通常典型的複雜系統

is, from ecosystems to organisms to cities to brains.

就是從生態系統到組織到城市到腦。

A complex system is one

一個複雜的系統是

that contains enormous numbers of actors or agents

一個包含大量的智能體之間的

that are interacting in usually in a nonlinear kind of fashion

交互， 通常有非線性各種類型

form which all kinds of

的多層次

multi-level behavior evolves from

行為的演變，

So there are these emergent phenomena, but also

因此有這些突發現象，但是

I think a critical part of a complex system that distinguishes it

我覺得複雜的系統關鍵部分

from what we might call a simple system, like the motion of the planets around the sun,

是識別它來自什麼，也许我們可以稱之為一個簡單的系統，如圍行星繞太陽的的運動，

is that on the one hand, you can't

是在一方面，你不能封裝

encapsulate the dynamics in just a few

動力學幾個簡單

simple equations and that is intimately related

的公式，這是密切相關的，

to the fact that these systems are evolving

這些事實表示系統是進化的

and are adaptable. And I think that this is one of the most

且適應性強。我認為，這是在與傳統系統間的

crucial differences between that and traditional systems that I

最重要的區別之一，我職業生涯大部分

have dealt with in most of my career under the guise of physics.

是在物理學的指導下。

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