CHAPTER 2

DEFINING SYSTEMS

With a foundation in systems thinking, you can now build a more formal and specific definition of what systems are. Here we explore how systems are organized and how new things and experiences arise from their disparate parts.
以系統思維為基礎，您現在可以建立一個更正式且具體的系統定義。在這裡，我們探討系統如何組織，以及新事物和經驗如何從其不同的部分中產生。

Doing so gives you the foundational concepts and vocabulary needed for analyzing and designing systemic games.
這樣做可以讓您獲得分析和設計系統性遊戲所需的基礎概念和詞彙。

What We Mean by Systems
我們所說的系統

As you have seen, systems are a familiar yet often only vaguely defined concept. By carefully examining what “things” actually are, this amorphous concept becomes clearer. As you saw in Chapter 1, “Foundations of Systems,” systems are things, and things are systems. Systems are literally all around us. They make up the physical world we live in and the social world we help create.
如您所見，系統是一個熟悉但通常僅模糊定義的概念。通過仔細檢視“事物”實際上是什麼，這個模糊的概念變得更加清晰。如您在第一章“系統的基礎”中所見，系統是事物，而事物是系統。系統實際上無處不在。它們構成了我們生活的物理世界以及我們幫助創造的社會世界。

It is important to remember, however, that systems (and things, deep down) are dynamic, not static: you cannot understand a system by freezing it in place; you must experience it operating in its context to truly understand it. Because systems embody Alexander’s “quality without a name,” (Alexander 1979, p.28) it is difficult to define them in a single bumper-sticker-like sentence.¹ Systems have the (perhaps maddening but also magical) quality that they must be understood in terms of their constituent pieces and how they all dynamically combine to form something greater—both at the same time. They must be understood in terms of their contextual operations, not as a static snapshot.
然而，重要的是要記住，系統（以及事物，深層次上）是動態的，而非靜態的：你無法通過將系統凍結在某個位置來理解它；你必須在其運行的背景中體驗它，才能真正理解它。因為系統體現了亞歷山大所說的「無名的品質」（Alexander 1979, p.28），所以很難用一句類似保險桿貼紙的簡短句子來定義它們。系統具有（或許令人抓狂但也神奇的）特質，即必須從其組成部分及其如何動態結合形成更大整體的角度來理解——這兩者是同時存在的。它們必須從其背景運行的角度來理解，而不是作為靜態的快照。

In other words, any definition of a system must itself be systemic.
換句話說，任何對系統的定義本身都必須是系統性的。

A Brief Definition

In the interest of providing a short definition that does not gloss over too much, a system can be described as follows:
為了提供一個不過於簡化的簡短定義，系統可以描述如下：

A set of parts that together form loops of interaction between them to create a persistent “whole.” The whole has its own properties and behaviors belonging to the group but not to any single part within it.
一組部件共同形成它們之間的互動迴圈，以創造一個持久的「整體」。這個整體具有屬於群體的自身特性和行為，而不是屬於其中任何單一部分。

That’s a lot. Throughout this chapter we will break this down (and assemble it back up!) to get closer to a formal definition and detailed explanation. As noted earlier, the linearity of language does become a problem here: you will see references to things that have not yet been explained, and it may take more than one reading (more than one loop!) to construct your own mental model of what a system is.
這是很多內容。在本章中，我們將逐步拆解這些內容（並重新組合起來！），以更接近正式的定義和詳細的解釋。如前所述，語言的線性在此處確實成為一個問題：你會看到對尚未解釋的事物的引用，可能需要多次閱讀（多次循環！）才能構建你自己的系統心智模型。

To start then, here is a list that expands a bit on the statement above. We will examine this in greater detail throughout this chapter:
那麼，首先，這裡有一個清單，稍微擴展了上面的陳述。我們將在本章中更詳細地檢視這些內容：

Systems are made out of parts. Parts have internal state and external boundaries. They interact with other parts via behaviors. Behaviors send information or, more often, resources to other parts to affect the internal state of the other parts.
系統由部分組成。部分具有內部狀態和外部邊界。它們通過行為與其他部分互動。行為將信息或更常見的資源傳送給其他部分，以影響其他部分的內部狀態。

Parts interact with other parts via behaviors to create loops. Behaviors create local interactions (A to B), while loops create transitive interactions (A to B to C to A).
部分通過行為與其他部分互動以創建循環。行為創造局部互動（A 到 B），而循環創造傳遞互動（A 到 B 到 C 到 A）。

Systems are organized into hierarchical integrative levels that arise from emergent properties based on their looped structures. At each level, the system displays organized state and behavior, synonymous with being a part in larger system at the next level up.
系統被組織成層級整合的層次，這些層次源自於其迴圈結構所產生的涌現特性。在每一個層次，系統展現出有序的狀態和行為，這與在更高層次的更大系統中作為一部分的特性相同。

At each level the system displays persistence and adaptability. It does not fall apart quickly, being self-reinforcing, and is able to tolerate and adapt to different conditions that exist outside its boundaries.
在每一個層次，系統展現出持久性和適應性。它不會迅速崩解，因為它具有自我強化的特性，並能夠容忍和適應其邊界之外存在的不同條件。

Systems exhibit organized, decentralized, but coordinated behaviors. A system creates a unified whole—which is in turn just a part of a larger system.
系統展現出有序的、去中心化但協調的行為。一個系統創造了一個統一的整體，而這個整體反過來又只是更大系統的一部分。

We will now examine each of those aspects of a system in greater detail.
我們現在將更詳細地檢視系統的每一個方面。

Defining Parts

Every system is made of and can be broken down into separate parts: the parts could be atoms in a molecule, birds in a flock, units in an army, and so on. Each part is independent of others in that each has its own identity and acts on its own. Specifically, each part is defined by its state, boundaries, and behaviors, as described in the following sections. (You will see these again in game-specific terms in Chapter 8, “Defining Game Parts.”)
每個系統都是由不同的部分組成，並且可以分解成獨立的部分：這些部分可能是分子中的原子、鳥群中的鳥、軍隊中的單位，等等。每個部分都是獨立於其他部分的，因為每個部分都有自己的身份並自行運作。具體來說，每個部分由其狀態、邊界和行為來定義，如以下章節所述。（在第八章“定義遊戲部分”中，您將再次看到這些內容以遊戲特定的術語呈現。）

State

Each part has its own internal state. This is made up of a combination of attributes, each of which has a specific value at any point in time. So each bird in a flock has its own speed, direction, mass, health, and so on. The bird’s speed and mass are attributes, and each have a value (for these, a number) that is the attribute’s current state. The part’s state overall is the aggregation of all of its current attribute values. This is static at any point in time but, if the part is affected by others, changes over time.
每個部分都有其內部狀態。這是由多個屬性組成的，每個屬性在任何時間點都有特定的值。因此，每隻鳥在群中都有自己的速度、方向、質量、健康狀況等等。鳥的速度和質量是屬性，每個屬性都有一個值（對於這些屬性來說，是一個數字），這就是屬性的當前狀態。整體來說，部分的狀態是其所有當前屬性值的集合。在任何時間點這都是靜態的，但如果部分受到其他因素的影響，則會隨時間改變。

In the real world, an object’s state is not defined by a simple attribute with a value. (People don’t really have a specific number of “hit points,” for example.) Instead, state emerges from the aggregate states of subsystems at one level of organization lower or finer in detail. (See the section “Hierarchy and Levels of Organization,” later in this chapter.) These subsystems are made of parts as well, all interacting together. As you have seen, in the real world we have to go down to quarks before we stop finding subsystems made of smaller parts.
在現實世界中，一個物件的狀態並不是由一個簡單的屬性和數值來定義的。（例如，人們並不真的有一個具體的「生命值」數字。）相反，狀態是從一個組織層次中較低或更細緻的子系統的總體狀態中浮現出來的。（詳情請參閱本章稍後的「層次與組織層級」部分。）這些子系統也由各個部分組成，彼此之間相互作用。如你所見，在現實世界中，我們必須深入到夸克層次，才能停止發現由更小部分組成的子系統。

In games, a part’s state is often determined by the states of parts within it at a finer level of detail: a forest might not have its own “health” attribute but instead may use the aggregate of the state of every tree defined within it. However, at some point you have to “hit bottom” and create simple parts with attribute/value pairs that are simple, nonsystemic types—integers, strings, and so on. For example, chess pieces have a type (pawn, rook, and so on) and a position on the board as their state. In a computer game, a monster might have 10 hit points and be named Steve.
在遊戲中，一個部分的狀態通常由其內部更細緻層次的部分狀態決定：例如，一片森林可能沒有自己的「健康」屬性，而是使用其內每棵樹的狀態總和。然而，最終你必須「觸底」並創建具有屬性/值對的簡單部分，這些是簡單的、非系統類型——整數、字串等等。例如，西洋棋的棋子有類型（兵、車等）和在棋盤上的位置作為其狀態。在電腦遊戲中，一個怪物可能有 10 點生命值，並被命名為 Steve。

This degree of specificity provides us with a feasible floor to our designs, enabling them to be implemented. Since the default or starting states of various parts in a game are typically kept in a spreadsheet, we sometimes refer to this level of definition as being “spreadsheet specific.” This is an important quality of game design, as you cannot actually build a game until you have hammered out all the vague parts of the design and brought them down to the level of being spreadsheet specific. You will see this again throughout the book, especially in Chapters 8 and 10, “Game Balance Practice.”
這種特定程度為我們的設計提供了一個可行的基礎，使其能夠被實施。由於遊戲中各個部分的預設或起始狀態通常保存在電子表格中，我們有時會將這一層次的定義稱為「電子表格特定」。這是遊戲設計的一個重要特質，因為在你將設計中所有模糊的部分具體化並達到電子表格特定的程度之前，你無法真正構建一個遊戲。你會在整本書中再次看到這一點，特別是在第 8 章和第 10 章「遊戲平衡實踐」中。

However, the spreadsheet level of specificity is not an upper limit to how systemic a game design can be. By building systems out of subsystems that contain parts, you can create a more engaging, dynamic “second-order design” (see Chapter 3, “Foundations of Games and Game Design”) that does not depend for success on extensive and costly content creation. You should look for opportunities in your designs to group simpler parts together to create greater systemic wholes.
然而，試算表的具體程度並不是遊戲設計系統化的上限。通過將子系統中的部分組合成系統，您可以創造出更具吸引力和動態的「二階設計」（參見第三章「遊戲與遊戲設計的基礎」），這種設計不依賴於大量且昂貴的內容創建來取得成功。您應該在設計中尋找機會，將較簡單的部分組合在一起，以創造更大的系統整體。

Boundaries

A part’s boundary is an emergent property (see below for a discussion of emergence) defined by the local neighborhood of interaction of subparts within it (see Figure 2.1). Parts that are closely networked together—those with more interactions with each other than with other parts—and in particular those with interactions that create loops, form a local subsystem that creates a new part at a higher level of organization (more on levels below).
一個部分的邊界是一種湧現的特性（關於湧現的討論見下文），由其內部子部分的局部互動鄰域所定義（見圖 2.1）。那些緊密聯繫在一起的部分——彼此之間的互動多於與其他部分的互動——尤其是那些形成迴圈的互動，構成了一個局部子系統，從而在更高的組織層次上創造出一個新的部分（關於層次的更多內容見下文）。

The boundary between parts isn’t absolute, as some local parts necessarily have interactions with other parts “outside” the boundary as well. As with our discussion of atoms and protons, it is important to remember that generally there is no overt skin or wrapper around a part²; its boundary is defined by clusters of closely interconnected subparts that make it up. In effect, the boundary may look well defined from a higher-level perspective, but on closer inspection, it becomes fuzzier and more difficult to say exactly where it lies.
部分之間的邊界並不是絕對的，因為一些局部部分必然也會與邊界“外部”的其他部分互動。正如我們對原子和質子的討論，重要的是要記住，通常情況下，部分周圍並沒有明顯的外皮或包裝；其邊界是由緊密互聯的子部分群組所定義的。實際上，從更高層次的角度來看，邊界可能看起來定義明確，但仔細觀察時，邊界會變得模糊，更難以確切地說出其所在位置。

The typical rule for defining something that is “outside” versus “inside” a part is whether it can change the higher-level system’s behavior. If so, then it’s inside the boundary and is part of the system. If something communicates with a part inside a system but cannot by its behavior change the system’s overall behavior, then it’s considered to be outside the part’s or system’s boundary.
判斷某物是屬於「外部」還是「內部」的一般規則是看它是否能改變高層系統的行為。如果能，那麼它就在邊界內，是系統的一部分。如果某物與系統內部的一部分進行交流，但其行為無法改變系統的整體行為，那麼它就被認為是在該部分或系統的邊界之外。

As a practical matter, the boundary and the organization it provides is a form of modularity that may be emergent or enforced when creating parts and systems, as in software. Using a boundary can make the parts of a system more comprehensible and reusable, and it also removes the temptation to rely on various forms of centralized control. This is the same idea behind the idea of “small pieces loosely joined” that Weinberger (2002) used to describe the decentralized World Wide Web: each web page is a part in the overall system. None controls the entire thing, and if one or another goes away, the rest continues to function.
從實際角度來看，邊界及其所提供的組織是一種模組化的形式，這種形式可能在創建零件和系統時自然出現或被強制執行，就像在軟體中一樣。使用邊界可以使系統的各個部分更易於理解和重用，並且也消除了依賴各種形式的集中控制的誘惑。這與 Weinberger（2002）用來描述去中心化的全球資訊網的「小塊鬆散結合」的理念相同：每個網頁都是整體系統中的一部分。沒有任何一個控制整個系統，即使其中一個或另一個消失，其他部分仍然可以繼續運作。

Behaviors

Parts affect each other via their behaviors. Each part has something that it does—most often some resource it creates, changes, or destroys in the system. These behaviors may be simple or complex, and they typically affect other parts by communicating some resource or value change to them. A given part may affect itself via its behaviors as well, such as by a monster in a game healing its own wounds over time or an account adding to its own balance via compound interest calculations.
各個部分透過其行為相互影響。每個部分都有其作用——通常是在系統中創造、改變或摧毀某種資源。這些行為可能簡單也可能複雜，通常是透過傳遞某種資源或價值的變化來影響其他部分。某個部分也可能透過其行為影響自身，例如遊戲中的怪物隨時間治癒自己的傷口，或是帳戶透過複利計算增加自身餘額。

An important concept related to behaviors is that a part may perturb or affect another part with its behavior, but each part determines its own changes to its internal state as well as any behavioral response. In object-oriented programming terms, each part encapsulates its state, meaning that no other part can “reach in” and change it. Each part determines on its own what behavioral messages it will pay attention to and be affected by. So one part may by its behavior send a message to another, but it is up to that second part to determine its own response: it may ignore the message or use it to change its internal state, based on its own internal rules.
與行為相關的一個重要概念是，一個部分可能會因其行為而擾動或影響另一個部分，但每個部分都會自行決定其內部狀態的變化以及任何行為反應。用物件導向程式設計的術語來說，每個部分都封裝了其狀態，這意味著沒有其他部分可以“進入”並改變它。每個部分自行決定會關注哪些行為訊息並受到影響。因此，一個部分可能會通過其行為向另一個部分發送訊息，但由第二個部分自行決定其回應：它可能會忽略該訊息，或者根據其內部規則使用該訊息來改變其內部狀態。

Sources, Stocks, and Sinks
來源、庫存與匯流

In discussing parts, the language of systems thinking often talks about different types of parts, such as sources, stocks, and sinks. The behaviors by which they interact are often shown as connectors, the most common type of which is a flow between two parts. What flows between parts may be messages or other forms of information but is often a resource of one type or another. (Note that while these names and the symbols for them have been used widely in systems thinking, science, and engineering, today there remains no canonical form for them. We will use common names and symbols here, but they are intended to be utilitarian, not prescriptive.)
在討論系統思維的組成部分時，經常會提到不同類型的部分，例如來源、庫存和匯流。它們之間的互動行為通常顯示為連接器，其中最常見的類型是兩個部分之間的流動。流動於部分之間的可能是訊息或其他形式的資訊，但通常是一種或另一種資源。（請注意，儘管這些名稱及其符號已廣泛用於系統思維、科學和工程中，但至今仍沒有一個標準的形式。我們在此使用常見的名稱和符號，但它們的目的是實用而非規範。）

A source is any part that increases another part’s state. One of the simplest examples of this is a faucet that fills a bathtub with water (see Figure 2.2). In the real world, the water comes from somewhere, but in games (and in systems thinking in general), we often assume that a source represents an inexhaustible supply of some resource, such as water.
來源是任何能增加另一部分狀態的部分。最簡單的例子之一就是水龍頭將水注入浴缸（見圖 2.2）。在現實世界中，水來自某個地方，但在遊戲中（以及一般的系統思維中），我們常假設來源代表某種資源的無窮供應，例如水。

Using the bathtub example, an amount of water (the resource) flows from the source and into the stock. The state inside the part that represents the source specifies the rate at which it creates new units of its resource. So a source might have an internal variable with a value of 2, meaning that it creates 2 units of water per unit time (e.g., per second). The source’s behavior is what passes this water along; this is often called a flow. The source doesn’t keep any water itself; it just generates some amount and passes it along if it can.
以浴缸為例，水量（資源）從來源流入儲存。代表來源的部分內部狀態指定了它創造新資源單位的速率。因此，來源可能有一個內部變數，其值為 2，意味著它每單位時間（例如，每秒）創造 2 個單位的水。來源的行為就是將這些水傳遞出去；這通常被稱為流動。來源本身不保留任何水；它只是生成一定量的水並在可能的情況下傳遞出去。

The resource represents the numeric amount of something (in this example, water) that flows from one part to another, as from the source to the stock. Generally speaking, anything that is countable, storable, or exchangeable qualifies as a resource, even if it is not strictly physical. Health as represented by hit points in a role-playing game may be a resource, as may the provinces an empire controls. We will discuss resources again in Chapter 7, “Creating Game Loops,” and Chapter 8.
資源代表從一個部分流向另一個部分的數量（在此例中為水），如從來源到儲存。一般來說，任何可計數、可儲存或可交換的東西都可以算作資源，即使它不完全是物理的。在角色扮演遊戲中以生命值表示的健康可能是一種資源，帝國控制的省份也可能是資源。我們將在第 7 章“創建遊戲循環”和第 8 章中再次討論資源。

The stock is where the resource created by the source flows to. It is the bathtub in this example. You can also think of this in terms of a store having items “in stock” or how many fish are in a “stock pond.” Stocks accumulate things; for example, bathtubs accumulate water, and bank accounts accumulate money. For any stock, its state is described as an amount (of some resource) at a particular time. So a bathtub might contain 10 units of water, and a bank account might contain $100. Those amounts may change over time, but at any given time, you can check the stock’s state, and it will tell you how much of its resource it contains. Stocks may also have a limit past which they will accept no more. Your bank account probably doesn’t have an upper limit, but you can only put so much water into your bathtub before no more will go in!
庫存是資源從來源流向的地方。在這個例子中，它就是浴缸。你也可以把它想成商店裡有“庫存”的商品，或者池塘裡有多少魚的“魚池”。庫存會累積東西；例如，浴缸會累積水，銀行帳戶會累積金錢。對於任何庫存，其狀態被描述為在特定時間的某種資源的數量。因此，浴缸可能包含 10 單位的水，而銀行帳戶可能包含 100 美元。這些數量可能會隨著時間改變，但在任何給定時間，你都可以檢查庫存的狀態，它會告訴你它包含多少資源。庫存也可能有一個上限，超過這個上限就不會再接受更多。你的銀行帳戶可能沒有上限，但你的浴缸只能裝到一定的水量，超過這個量就無法再裝進去了！

The sink, then, is the drain: it is the outflow from the stock. Just as the stock’s state is “how much” of a resource it contains right now, its behavior is to send some amount of the resource onward per unit time. In this way, it functions very much like the source, with the key difference being that if the stock is empty, it cannot pass anything along, whereas the source is typically assumed to always be able to generate its resource.
水槽，然後，是排水口：它是庫存的流出。正如庫存的狀態是“當前”擁有多少資源，其行為是每單位時間將一定量的資源傳送出去。這樣，它的功能與源頭非常相似，關鍵的區別在於如果庫存是空的，它無法傳遞任何東西，而源頭通常被假設為總是能夠生成其資源。

While it might seem odd to talk about “faucets” and “drains” in systems, these are key elements, particularly for games. At some point, you have to draw the bounds around what you are designing and leave aside considerations from outside it. For example, if you are creating a system model for a factory, you might assume that water and electricity would flow in from an external (and unbounded) source rather than also taking on the modeling of the power plant and water distribution. In games in particular, as with making a part’s state “spreadsheet specific” by creating its details in nonsystemic terms, you typically need to specify a variety of sources and sinks, faucets and drains, in terms of how they affect the game.
雖然在系統中談論「水龍頭」和「排水口」可能顯得有些奇怪，但這些是關鍵元素，尤其是在遊戲中。在某個時刻，你必須劃定設計的界限，並將外部的考量排除在外。例如，如果你正在為一個工廠創建系統模型，你可能會假設水和電力是從外部（且無界限的）來源流入，而不是同時承擔發電廠和水分配的建模。在遊戲中特別是，通過以非系統性的方式創建其細節，使一個部分的狀態「特定於電子表格」，你通常需要指定各種來源和去處、水龍頭和排水口，來說明它們如何影響遊戲。

For example, in the early days of massively multiplayer online games (MMOs), the economic systems in these games were referred to as “faucet/drain” economies. Figure 2.3 is adapted from a diagram describing the economy in the game Ultima Online and shows how this was diagrammed in a way that highlights sources, stocks, flows, resources, and drains.
例如，在大型多人線上遊戲（MMOs）的早期，這些遊戲中的經濟系統被稱為「水龍頭/排水口」經濟。圖 2.3 改編自描述遊戲《Ultima Online》中的經濟的圖表，展示了如何以突出來源、庫存、流動、資源和排水口的方式進行圖示。

In this system model, there is an unbounded faucet (actually more than one) at the top left, representing an unbounded source of various “virtual resources,” including goods supplied by non-player characters (NPCs), monsters that pop out of nowhere, and gold that NPCs pay to players. These resources flow through various stocks and mostly drain out of the economy via the connecting flows leading to the lower right.
在這個系統模型中，左上角有一個無限制的水龍頭（實際上不止一個），代表著各種“虛擬資源”的無限來源，包括由非玩家角色（NPC）提供的商品、突然出現的怪物，以及 NPC 支付給玩家的金幣。這些資源通過各種儲存庫流動，並主要通過連接流向右下方的流動而從經濟中流出。

In this diagram, resources are shown being kept in various stocks (the gray dish-like boxes), but the grouping shown here is more diagrammatic than actual. For example, a player might “manufacture” goods and keep them in inventory (box 6), but their inventory is separate from that of any other player. These stocks are also typically not limited in how much they can store, and outflow through the drain is not guaranteed: Simpson (n.d.) relates a well-known story of a player who kept over 10,000 manufactured (virtual) shirts in his house in the game. This caused real problems for the game economy as it meant that each object (each shirt, for example) had to be tracked and accounted for at all times.
在這個圖表中，資源被顯示為保存在各種庫存中（灰色的碟狀盒子），但這裡所示的分組更具圖解性而非實際性。例如，一個玩家可能會「製造」商品並將其保存在庫存中（盒子 6），但他們的庫存與其他任何玩家的庫存是分開的。這些庫存通常在儲存量上沒有上限，並且通過排水口的流出也不是保證的：Simpson（n.d.）講述了一個著名的故事，某位玩家在遊戲中家裡存放了超過一萬件製造的（虛擬）襯衫。這對遊戲經濟造成了真正的問題，因為這意味著每一個物件（例如每一件襯衫）都必須隨時被追蹤和記錄。

A similar issue that arises from this sort of economic system is rampant inflation. Note that “gold” (one of the primary resources and the monetary currency in the game) is created ex nihilo from the unbounded faucet-source. Every time a player in the game kills a monster or sells an item to an NPC vendor, new gold is created and added to the economy. This gold might flow back out of the economy via the manufacture of goods or other means, but a great deal of it remains in the economy. As the amount of available gold grows, each individual unit of it becomes reduced in value to the players—the definition of economic inflation. While the solutions to this problem are typically complex, even the issue itself is difficult to understand without a sufficiently systemic view of the economy. You will see more about economies as game systems and their issues (including inflation) again in Chapter 7.
在這種經濟系統中出現的類似問題是猖獗的通貨膨脹。注意，遊戲中的“黃金”（作為主要資源和貨幣）是從無限制的水龍頭來源中無中生有創造出來的。每當玩家在遊戲中擊殺怪物或將物品賣給 NPC 商人時，新的黃金就會被創造並加入經濟體系。這些黃金可能會通過製造商品或其他方式流出經濟體系，但大量的黃金仍然留在經濟中。隨著可用黃金的數量增加，每個單位的價值對玩家來說都會降低——這就是經濟通貨膨脹的定義。雖然這個問題的解決方案通常很複雜，但即使是問題本身，如果沒有足夠系統的經濟觀點，也很難理解。在第七章中，您將再次看到作為遊戲系統的經濟及其問題（包括通貨膨脹）。

Converters and Deciders  轉換器與決策者

In addition to sources, stocks, and sinks, there are other specialized kinds of parts that we often encounter when diagramming systems. Two of them are converters and deciders. Figure 2.4 shows a system diagram that incorporates these, as well as a source and a sink.
除了來源、庫存和匯集之外，當我們繪製系統圖時，還經常會遇到其他專門類型的部分。其中兩個是轉換器和決策者。圖 2.4 展示了一個包含這些元素的系統圖，還有一個來源和一個匯集。

In this system, some resource flows from a source to a converter process and then to a sink. That in itself is not very remarkable (and it’s not really even a system), but it is an abstraction to help keep this diagram clear. As part of the process, there is also a measurement: is the process going too fast or two slow? This is where it becomes systemic, as these connections create a loop back to the source. By means of the measuring decider parts, the converter process is kept within the required bounds.
在這個系統中，一些資源從來源流向轉換器過程，然後到達匯集。這本身並不特別顯著（甚至不算是一個系統），但這是一種抽象化，以幫助保持這個圖的清晰。作為過程的一部分，還有一個測量：過程是否太快或太慢？這就是它變得系統化的地方，因為這些連接創造了一個回到來源的迴路。通過測量決策者部分，轉換器過程被保持在所需的範圍內。

Careful readers may note that this diagram is essentially the same as the more detailed drawing of a centrifugal governor in Figure 1.7: the engine is the source, and it provides power to some process (such as converting heat to rotational motion), and the sink is the exhaust. The engine goes faster or slower, making the weights move up or down with the centrifugal force. The weights act as a mechanical decider, keeping the engine within bounds.
細心的讀者可能會注意到，這個圖基本上與圖 1.7 中更詳細的離心調速器圖相同：引擎是來源，它為某些過程（如將熱能轉換為旋轉運動）提供動力，而匯則是排氣。引擎加速或減速，使配重隨著離心力上下移動。配重作為機械決策者，保持引擎在範圍內運行。

Complicated Versus Complex
複雜與繁複

Parts that connect to form systems always do so in ways that form loops. As you will see here, looping systems become complex. Nonlooping collections may create complicated processes, but ultimately they do not create complex systems. This has significant consequences for systems design overall and for game design in particular.
連接成系統的部分總是以形成迴圈的方式進行。如你在此所見，迴圈系統變得複雜。非迴圈的集合可能會創造繁複的過程，但最終它們不會創造出複雜的系統。這對於整體系統設計以及遊戲設計尤其具有重要影響。

Simple Collections and Complicated Processes
簡單集合與繁複過程

If you have a bunch of parts that don’t really have any connections in that they have no behaviors that affect each other’s state, then they form a simple collection and not a system: a heap of bricks (as Poincaré said) or a bowl of fruit is a collection.³ The items in these collections have no significant connections or interactions between them, and so they remain isolated. Parts have to have significant, state-changing connections based on their behaviors to create a system.
如果你有一堆部分，它們之間並沒有真正的連接，因為它們的行為不會影響彼此的狀態，那麼它們形成的是一個簡單的集合而不是一個系統：一堆磚塊（如龐加萊所說）或一碗水果就是一個集合。這些集合中的項目之間沒有顯著的連接或互動，因此它們保持孤立。部分必須基於其行為具有顯著的、改變狀態的連接才能創造出一個系統。

A complicated process is one with multiple parts and many interactions. However, these parts are connected sequentially and affect each other only linearly, one after another (see Figure 2.5). A process like this is often predictable and repeatable, and you know what happens after each step. However, because there are no loops to create feedback, the process does not form a system.
一個複雜的過程是由多個部分和許多互動組成的。然而，這些部分是按順序連接的，並且僅以線性方式相互影響，一個接著一個（見圖 2.5）。這樣的過程通常是可預測且可重複的，你知道每一步之後會發生什麼。然而，由於沒有迴圈來創造反饋，這個過程並不形成一個系統。

One example of a complicated assemblage is the simple pendulum we encountered earlier (refer to Figure 1.2). The weight of the pendulum and the length of the rod it hangs from interact to create a highly predictable (if sometimes complicated) path. But there are no significant feedback loops to make this into a complex system.
一個複雜組合的例子是我們之前遇到的簡單擺錘（參見圖 1.2）。擺錘的重量和懸掛的桿長相互作用，形成一個高度可預測（即使有時候複雜）的路徑。但沒有顯著的反饋迴路使其成為一個複雜系統。

Similarly, many assembly-line processes are complicated: there’s a lot involved in putting together a car on an assembly line, but it’s not going to vary a whole lot from car to car of the same type. Sending a rocket to the Moon is even more complicated: there’s a lot going on and no one would say it’s easy, but the different phases of the process don’t have disproportionate effects on each other. Once you get through launch and boost, those stages aren’t going to have unpredictable effects on later phases, such as lunar orbital insertion. More importantly, what happens in the lunar landing phase has no effect on the initial launch phase. And because the connections are linear, once you have sent a rocket to the Moon, there’s little variance in doing so a second time (at least until parts do interact and things go wrong, which is when the process veers into complex territory).
同樣地，許多裝配線的過程是複雜的：在裝配線上組裝一輛車涉及很多步驟，但同類型的車之間不會有太大的差異。將火箭送上月球則更加複雜：過程中有很多事情要處理，沒有人會說這是件容易的事，但過程中的不同階段不會對彼此產生不成比例的影響。一旦完成發射和推進，這些階段就不會對後續階段產生不可預測的影響，例如月球軌道插入。更重要的是，月球著陸階段發生的事情不會影響到最初的發射階段。而且，由於這些連結是線性的，一旦你成功將火箭送上月球，第二次再這樣做時變異性就很小（至少在零件相互作用並出現問題之前，這時過程就會進入複雜的領域）。

In game design terms, games that present the player with sequential levels are more complicated than complex: typically what happens on Level 10 has no effect on the state or gameplay on Level 2. Once a player has played through a level, they may never play it again (and if they do, it will not have changed even though they have been there before). This sequential rather than systemic game design requires the designer to create more content, as once the player has been through part of the game, its future gameplay value is sharply reduced.
在遊戲設計的術語中，向玩家呈現連續關卡的遊戲比起複雜更顯得繁瑣：通常第 10 關發生的事情不會影響第 2 關的狀態或遊戲玩法。一旦玩家通過了一個關卡，他們可能再也不會玩這個關卡（即使他們再次遊玩，關卡也不會改變，即便他們曾經到過這裡）。這種連續而非系統性的遊戲設計要求設計師創造更多內容，因為一旦玩家通過了遊戲的一部分，其未來的遊戲價值就會大幅降低。

The key concept here is that in a complicated process, there are interactions between parts, but these are essentially linear or random: there are no feedback loops in the process. One result of this is that when something unexpected happens in a complicated process, it’s either entirely random or, more often, it’s possible to trace the problem from the effect back to a single cause and fix or replace the specific part that caused it. Therefore, this kind of process is typically amenable to linear, reductionist thinking in looking back from one part to the previous one to find a root cause.
這裡的關鍵概念是，在一個複雜的過程中，各部分之間存在互動，但這些互動本質上是線性或隨機的：過程中沒有反饋迴路。這樣的結果是，當複雜過程中發生意外情況時，要麼完全是隨機的，要麼更常見的是，可以從效果追溯到單一原因，然後修復或更換導致問題的特定部分。因此，這種過程通常適合於線性、還原主義的思維方式，從一個部分回溯到前一個部分以找到根本原因。

Complex Systems

When parts affect each other in ways that connect together to form a loop, things become a lot more interesting. In a case like this, parts still interact with each other, but now they do so such that the actions of one part cycle around and come back again so that a part’s behavior inevitably comes back to alter its future state and behavior (see Figure 2.6). These loops are what create a complex system.
當各部分以某種方式相互影響並連結成一個迴圈時，事情就變得更加有趣。在這種情況下，各部分仍然相互作用，但現在它們的作用方式是，一個部分的行為會循環回來，最終改變其未來的狀態和行為（見圖 2.6）。這些迴圈正是創造複雜系統的原因。

Just as the simple pendulum is an example of a complicated assemblage, the double pendulum (refer to Figure 1.2) is a relatively simple example of a complex system. The parts of the double pendulum—the mass of the weight, the location of the joint, and the position in space of the weight, the joint, and the pivot from which it all hangs, all interact and feedback on each other. This is why the path the double pendulum takes is so sensitive to its initial conditions: as it moves, the position and force on each part change, each part feeding back on the others (and thus itself), creating wildly divergent paths from similar starting locations.
就如同單擺是複雜組合的例子，雙擺（參見圖 1.2）則是複雜系統中相對簡單的例子。雙擺的各個部分——重物的質量、關節的位置，以及重物、關節和支點在空間中的位置——彼此互動並相互反饋。這就是為什麼雙擺的運動路徑對初始條件如此敏感的原因：隨著它的運動，每個部分的位置和受力都在改變，每個部分都對其他部分（以及自身）進行反饋，從而從相似的起始位置創造出截然不同的路徑。

There are many examples of complex systems across every part of our existence, including the human body, the global economy, a romance, hurricanes, termite mounds, and, of course, many games. Even Figure I.1 at the start of this book shows an abstract view of the complex system that this book is about.
在我們生活的每一個角落，都有許多複雜系統的例子，包括人體、全球經濟、一段戀情、颶風、白蟻丘，當然還有許多遊戲。甚至本書開頭的圖 I.1 也展示了本書所探討的複雜系統的抽象視圖。

Each of these systems has the qualities of having multiple, independent parts that have their own internal state and affect each other via their behavior in ways that form feedback loops. They also, as you will see here, remain adaptive and robust to external changes over time and create organized behavior and emergent properties.
這些系統各自擁有多個獨立的部分，每個部分都有其內部狀態，並通過其行為相互影響，形成反饋迴路。正如你將在此看到的，它們隨著時間的推移，對外部變化保持適應性和穩健性，並創造出有組織的行為和湧現的特性。

The way in which parts form loops means that each part affects its own future state and behavior. Part A affects B, which affects C, which then affects A again. These behavioral effects take some amount of time, so “future A” will be in a different state from “current A” after one cycle through the loop and having been affected by C. This looping connection has dramatic consequences. It means that, despite the reductionist view of the universe (as championed by Descartes and Newton), complex systems cannot easily be broken down to be turned into merely complicated ones: “unwinding the loop” destroys its essential nature by breaking the final connection (for example, from C back to A).
部分形成迴圈的方式意味著每個部分都會影響其自身的未來狀態和行為。部分 A 影響 B，B 影響 C，然後 C 又影響 A。這些行為影響需要一些時間，因此“未來的 A”在經過一個迴圈並受到 C 的影響後，將與“當前的 A”處於不同的狀態。這種迴圈連接具有顯著的後果。這意味著，儘管笛卡兒和牛頓倡導的宇宙還原主義觀點，複雜系統不能輕易被分解成僅僅是複雜的系統：“解開迴圈”會破壞其本質特性，因為這會打破最終的連接（例如，從 C 回到 A）。

We will return to this point as it relates to nonlinearity and the whole being other, or greater, than the sum of its parts—as understood by those from Aristotle to the psychologist Koffka and the ecologist Smuts, and as referred to by Lawrence as the “third thing” in his poem about water and Alexander as the “quality without a name.” This connection between complicated and complex, between reductive parts and how they can create emergent wholes, is vital for understanding and creating systems.
我們將回到這一點，因為它涉及到非線性以及整體不同於或大於其部分之和的概念——這一點從亞里士多德到心理學家科夫卡和生態學家斯穆茨都理解過，並且在勞倫斯的詩中被稱為「第三件事」，在亞歷山大的描述中則是「無名的品質」。這種複雜與簡單之間的聯繫，還有還原的部分如何能夠創造出新興的整體，對於理解和創建系統至關重要。

Loops

Complex systems contain parts that have behaviors, and these behaviors connect the parts in ways that form loops. These loops are in many ways the most important structures in systems and in games. Recognizing them and building them effectively is key to working in systems.
複雜系統包含具有行為的部分，而這些行為以形成迴圈的方式將各部分連接起來。這些迴圈在許多方面是系統和遊戲中最重要的結構。識別並有效地構建它們是處理系統的關鍵。

At their most basic, loops may either be constructive or destructive. In systems thinking, they are typically called reinforcing or balancing loops (sometimes positive feedback or negative feedback loops). Reinforcing loops increase the effects of each part’s behavior in the loop, while balancing loops decrease them. Both are important, but in almost all cases, if a system does not have at least one primary reinforcing loop, it will soon diminish and cease to exist: if the loop extinguishes the behaviors of the parts within it, they will soon cease their function and have no connection to each other at all. (The exceptions are when stable loops are made by each part preventing another from acting, as in a wall held up by opposing buttresses, either of which would topple the wall if not for the other.)
在最基本的層面上，迴圈可以是建設性的或破壞性的。在系統思維中，它們通常被稱為增強迴圈或平衡迴圈（有時稱為正反饋或負反饋迴圈）。增強迴圈會增加迴圈中每個部分行為的效果，而平衡迴圈則會減少它們。兩者都很重要，但在幾乎所有情況下，如果一個系統沒有至少一個主要的增強迴圈，它將很快減弱並停止存在：如果迴圈消除了其中部分的行為，它們將很快停止其功能，並且彼此之間完全沒有聯繫。（例外情況是當穩定的迴圈由每個部分阻止另一個部分行動時，如同由對立的扶壁支撐的牆，如果沒有另一個扶壁，任何一個都會使牆倒塌。）

Loops exist as the interactions between parts. Each part has a behavior that affects another and that is shown by the arrows in the loop, as in Figure 2.7. In the examples shown here, the text portions (for example, “Account balance” and “Properties owned”) are examples of stocks, as described earlier: this is where some amount or value is held. The arrows indicate an effect on the amount in stock, as enacted by a part’s behavior: if an arrow has a + beside it, then the more there is of the first stock, the more is added to the second. If there is a − beside an arrow, then an increased amount in the first stock reduces the amount in the second.
迴圈存在於各部分之間的互動。每個部分都有一種行為會影響另一個部分，這在圖 2.7 中的箭頭所示。在這裡顯示的例子中，文字部分（例如，「帳戶餘額」和「擁有的財產」）是先前描述的庫存的例子：這是某些數量或價值被持有的地方。箭頭表示由部分的行為所引起的對庫存數量的影響：如果箭頭旁有一個+，那麼第一個庫存越多，第二個庫存增加的也越多。如果箭頭旁有一個−，那麼第一個庫存增加的數量會減少第二個庫存的數量。

Reinforcing and Balancing Loops
強化迴圈與平衡迴圈

Reinforcing loops involve two or more parts where each enhances or increases the amount of some resource in stock of the next, which increases its behavioral output. These loops can be found in a lot of situations in life and in a lot of games. Two common examples are shown in Figure 2.7. In a bank account, the account balance increases the interest earned—and the interest earn then increases the account balance. That is, the more money-resource you have in stock (the account balance), the more this amount is increased due to interest. Similarly, in the game Monopoly, the more cash you have (your stock of cash as a resource), the more properties you can buy. Properties are also resources, and the more of this resource you have, the more cash-resource you gain.
增強迴圈涉及兩個或更多部分，其中每個部分都增強或增加下一個部分的某種資源庫存，從而增加其行為輸出。這些迴圈在生活中和許多遊戲中都可以找到。圖 2.7 中顯示了兩個常見的例子。在銀行帳戶中，帳戶餘額會增加所賺取的利息，而所賺取的利息又會增加帳戶餘額。也就是說，你擁有的金錢資源越多（帳戶餘額），由於利息的關係，這個數量就會增加。同樣地，在大富翁遊戲中，你擁有的現金越多（作為資源的現金庫存），你就能購買更多的地產。地產也是資源，而你擁有的這種資源越多，你獲得的現金資源就越多。

In general, reinforcing loops increase the value or activity of the parts involved. In a game, they tend to reward winners, magnify early success in a game, and destabilize the gameplay. They can lead to runaway win conditions if one player is able to capitalize even a little bit better on a reinforcing loop in the game. Because of this property, these loops are sometimes called “snowball” loops (like a snowball that grows larger and larger as it rolls downhill) or “the rich get richer” loops. You will see these conditions again in Chapter 7, with a more detailed discussion of how reinforcing loops in games can go awry.
一般來說，增強迴圈會增加所涉及部分的價值或活動。在遊戲中，它們往往會獎勵贏家，放大遊戲中的早期成功，並使遊戲玩法不穩定。如果一名玩家能夠稍微更好地利用遊戲中的增強迴圈，這可能會導致勝利條件失控。因此，這些迴圈有時被稱為「雪球」迴圈（就像一個雪球在下坡滾動時越滾越大）或「富者愈富」迴圈。您將在第七章再次看到這些情況，並更詳細地討論遊戲中的增強迴圈如何出錯。

Balancing loops are the opposite of reinforcing loops: each part reduces the value and thus the activity of the next part in the loop. Two simple examples of balancing loops are shown in Figure 2.8. The first is an abstract depiction of an oven thermostat. Based on the temperature set for the oven, there is a gap between its current temperature and this setting. The larger that gap, the more heat is applied. The gap acts as a resource in stock that is slowly draining down. As more heat is applied, the gap becomes smaller (the resource is reduced), causing the amount of heat being applied to become smaller as well.
平衡迴圈與增強迴圈相反：每個部分都會減少下一部分的值，從而降低迴圈中下一部分的活動。圖 2.8 中顯示了兩個簡單的平衡迴圈例子。第一個是烤箱恆溫器的抽象描述。根據烤箱設定的溫度，會存在一個當前溫度與設定溫度之間的差距。差距越大，施加的熱量就越多。這個差距就像是一個正在慢慢耗盡的資源庫存。隨著施加的熱量增加，差距變小（資源減少），導致施加的熱量也隨之減少。

The diagram on the right in Figure 2.8 shows a common scheme for how experience points (XP) are handled in a role-playing game (RPG). On gaining a new level, the XP needed for the next level increases (often dramatically) over the number needed to attain the current one. This has the effect of reducing the speed with which the character will gain another level.
圖 2.8 右側的圖示展示了一個常見的角色扮演遊戲（RPG）中經驗值（XP）處理方式。當角色升級時，下一級所需的經驗值會比當前級別所需的經驗值大幅增加。這樣的設計會減緩角色升級的速度。

Balancing loops are used to maintain or restore equilibrium, or parity, between parts in a loop. In games, they tend to be more forgiving to players who are behind, stabilizing and thus prolonging the game, preventing early winners from permanently pulling ahead. A classic example of this is the “blue shell” (officially called a “spiny shell”) in the game Mario Kart. This item is a power-up randomly made available in the game to anyone except the person in first place. Once fired, it moves forward and can hit anyone who does not get out of the way, but it only specifically targets the racer in first place. Upon hitting, it flips the player’s cart over, slowing them down. In this way, it acts as a powerful balancing factor, providing those behind the opportunity to catch up.
平衡迴圈用於維持或恢復迴圈中各部分之間的平衡或對等。在遊戲中，它們往往對落後的玩家更為寬容，穩定並延長遊戲時間，防止早期的勝利者永久領先。這方面的一個經典例子是遊戲《Mario Kart》中的「藍色龜殼」（官方名稱為「刺刺龜殼」）。這個道具是遊戲中隨機提供給除第一名以外的任何玩家的強化道具。一旦發射，它會向前移動並可能擊中任何未能避開的玩家，但它的主要目標是第一名的賽車手。擊中後，它會將玩家的車翻倒，減緩其速度。如此一來，它成為一個強大的平衡因素，給予落後者追趕的機會。

Combined, Linear, and Nonlinear Effects
綜合、線性與非線性效應

Every system has both reinforcing and balancing loops. To return to the centrifugal governor (refer to Figures 1.7 and 2.4), you can see that it uses both kinds of loops: if the engine is going too slow, the reduced spin causes the weights to drop and the valve to open, increasing the engine’s speed (a reinforcing loop). But if the engine is going too fast, the weights rise, the valve closes, and the engine’s activity is reduced (a balancing loop).
每個系統都有增強迴路和平衡迴路。回到離心調速器（參見圖 1.7 和 2.4），你可以看到它使用了這兩種迴路：如果引擎運轉過慢，減少的旋轉會使配重下降，閥門打開，增加引擎的速度（增強迴路）。但如果引擎運轉過快，配重上升，閥門關閉，引擎的活動減少（平衡迴路）。

In the case of the centrifugal governor, the output results may be linear: that is, the weights rise and fall in direct proportion to the engine’s speed. Relationships like this are easy to understand. Most systems, however, have outputs with a nonlinear relationship to the inputs or underlying changes, and this makes their behavior far more interesting.
以離心調速器為例，其輸出結果可能是線性的：也就是說，配重的升降與引擎速度成正比。這樣的關係容易理解。然而，大多數系統的輸出與輸入或潛在變化之間具有非線性關係，這使得它們的行為更加有趣。

For example, suppose you have two populations of animals, one predator and one prey: lynxes and hares. Both will try to reproduce and increase their own population, and of course lynxes will hunt and eat the hares. (The lynxes probably also have their own predators, but we will represent them only abstractly in this model.)
例如，假設你有兩個動物族群，一個是掠食者，一個是獵物：山貓和野兔。兩者都會試圖繁殖並增加自己的族群數量，當然，山貓會獵捕並吃掉野兔。（山貓可能也有自己的掠食者，但在這個模型中，我們只會抽象地表示它們。）

You might imagine that the lynxes and hares form a balancing loop, as shown in the big loop in Figure 2.9. For now don’t worry about the Greek letters shown there; just focus on the loops. The hares reproduce, increasing (reinforcing) their number, as shown in the little loop on the right. However, the lynxes eat the hares, which reduces (balances) their population. As a result, when the hare population goes down, the lynxes have a harder time surviving because there’s less to eat. What emerges from this complex relationship is not just a linear balancing act but a nonlinear oscillating graph, as shown in Figure 2.10. This graph shows time moving to the right, with the number of predators and prey rising and falling over time. The lines show how the numbers of predators and prey (lynxes and hares) change as a result of their mutual and overall balancing relationship to each other. The predators are never as numerous as their prey, and their rise and fall is consistently offset in time from that of the prey: once the hares start to disappear, the lynxes have a more difficult time reproducing (or surviving), and so their numbers start to dwindle. As that happens, the hares have an easier time surviving, and so their numbers begin to grow again. This makes it easier for the lynxes to survive and have offspring, who then eat more of the hares, starting the cycle all over again.
你可以想像猞猁和野兔形成了一個平衡迴圈，如圖 2.9 中的大迴圈所示。現在先不用擔心那裡顯示的希臘字母，只需專注於迴圈。野兔繁殖，增加（強化）了它們的數量，如右側的小迴圈所示。然而，猞猁捕食野兔，這減少（平衡）了它們的數量。因此，當野兔的數量下降時，猞猁因為食物減少而更難生存。從這種複雜的關係中產生的不是一個線性的平衡行為，而是一個非線性的振盪圖，如圖 2.10 所示。這個圖顯示時間向右移動，捕食者和獵物的數量隨著時間的推移而上升和下降。線條顯示捕食者和獵物（猞猁和野兔）的數量如何因為它們彼此之間的相互和整體平衡關係而改變。捕食者的數量從未超過獵物，並且它們的增長和下降始終與獵物的時間錯開：一旦野兔開始消失，猞猁就更難繁殖（或生存），因此它們的數量開始減少。 隨著這種情況的發生，野兔的生存變得更加容易，因此它們的數量開始再次增長。這使得猞猁更容易生存並繁衍後代，然後這些後代又吃掉更多的野兔，從而再次開始這個循環。

The nonlinearity that emerges from this system is important to understand. We often (naively) expect that a quantity that is rising now will continue to rise indefinitely: if things are going well today, they will continue to go well tomorrow. This ignores any underlying nonlinear effects, as any mathematical or systemic modeling will show. If you think about the relationships between the parts of the system, the reason for the nonlinear and oscillating relationship becomes clear: whenever a predator kills a prey animal, it is removing from the prey population not just the animal it has killed but all of the potential offspring it might have had. This has a magnifying effect over time. Thus, the relationship between the two is not merely additive but multiplicative. Stepping through this may help make that last point clear:
從這個系統中出現的非線性是重要的理解。我們常常（天真地）期望一個現在正在上升的數量會無限期地繼續上升：如果今天一切順利，明天也會繼續順利。這忽略了任何潛在的非線性效應，正如任何數學或系統建模所顯示的那樣。如果你考慮系統各部分之間的關係，非線性和振盪關係的原因就變得清晰：每當捕食者殺死一隻獵物時，它不僅從獵物群體中移除了它所殺死的動物，還移除了該動物可能擁有的所有潛在後代。這隨著時間的推移產生了放大效應。因此，兩者之間的關係不僅僅是加法的，而是乘法的。逐步分析這一點可能有助於使最後一點變得清晰：

When a lynx kills a hare, it reduces the hare population by one.
當猞猁捕殺一隻野兔時，野兔的數量便減少了一隻。

But the future hare population also loses the offspring that this hare would have had.
但未來的野兔族群也失去了這隻野兔本來會有的後代。

And the next generation of hares isn’t down by one but by one multiplied by the number of offspring that one would have had.
而下一代的野兔不僅少了一隻，而是少了一隻乘以這隻本來會有的後代數量。

The following generation is down by the number of offspring each of those hares would have had…and on and on.
接下來的世代因為每隻野兔本應擁有的後代數量而減少……如此循環不已。

The overall result is that killing one hare has a magnified, multiplicative relationship with the future hare population.
總體結果是，捕殺一隻野兔對未來野兔族群有著放大且倍增的影響。

Finally, since the lynx population needs the hares to survive, when there are few hares, the lynxes have a hard time surviving, which allows the hares to bounce back a bit.
最後，由於猞猁族群需要野兔來生存，當野兔數量稀少時，猞猁也難以生存，這讓野兔有機會稍微恢復。

By looking at the system of the lynxes and the hares, you can see that their relationship isn’t merely linear or additive. There’s more than the sum of each at work. Another way of saying this, from a systemic level is, as Smuts (1927) said, the result of interactions like this at an individual level creates a nonlinear whole that is “more than the sum of its parts.”
透過觀察猞猁和野兔的系統，可以看出他們的關係不僅僅是線性或加法的。這其中有超越各自總和的運作。從系統層面來說，正如 Smuts（1927）所言，這種在個體層面的互動結果創造了一個非線性的整體，這個整體「超越其部分的總和」。

However, nonlinear output from a system is not necessarily periodic and oscillating like this population data; all sorts of results are possible. You have already seen one example of this in the unpredictable behavior of the path traced by a double pendulum (refer to Figure 1.3). The behavior of a few stable parts (the weight and two rods connected by joints) is completely nonlinear and chaotic.
然而，系統的非線性輸出不一定像這些人口數據那樣具有週期性和振盪性；各種結果都是可能的。你已經看到過一個例子，即雙擺所描繪的路徑中不可預測的行為（參見圖 1.3）。幾個穩定部件（重物和由關節連接的兩根桿）的行為完全是非線性和混沌的。

Mathematical Modeling of Nonlinear Effects
非線性效應的數學建模

To be more precise about the multiplicative relationship between predator and prey, we can look to what have long been known as predator–prey, or Lotka–Volterra, equations (Lotka 1910, Volterra 1926), as shown in Figure 2.11. These equations look a lot more daunting than they are—and we don’t typically use them in game design or even in general systemic representations of relationships like those between predator and prey. Nevertheless, it’s useful to understand how these equations work and how to approach the same kind of problem from a systems point of view.
要更精確地描述捕食者與獵物之間的乘法關係，我們可以參考長久以來被稱為捕食者-獵物方程式，或洛特卡-沃爾泰拉方程式（Lotka 1910, Volterra 1926），如圖 2.11 所示。這些方程式看起來比實際上要複雜得多——而且我們通常不會在遊戲設計中使用它們，甚至在一般系統性地表示像捕食者與獵物之間的關係時也不會使用。然而，了解這些方程式的運作方式以及如何從系統的角度來處理同類問題是有益的。

What both the equation in Figure 2.11 and the causal loop diagram in Figure 2.9 show is that prey increase at a rate of αx—that is, the number of prey, x, multiplied by how fast they have offspring, designated by α (alpha, used here as a variable). Another way of saying this is that every living prey animal x is assumed in this model to give rise to α offspring in the next generation. These prey animals die at a rate given by βxy, where y is how many predators there are, and β (beta) is a parameter that states how often a meeting of x and y, prey and predator, results in a prey animal dying. This equals the left side of the first equation, which expresses the “change over time” in x, the number of prey animals (dx/dt is used in calculus to mean “a very small change in x over a very small period of time,” with d indicating an amount of change or time that is as close to zero as possible and t representing time).
圖 2.11 中的方程式和圖 2.9 中的因果循環圖所顯示的是，獵物以 αx 的速率增加——也就是說，獵物的數量 x 乘以它們繁殖的速度，這裡用 α（阿爾法，作為變數使用）表示。換句話說，在這個模型中，每一隻活著的獵物 x 被假設在下一代會產生 α 的後代。這些獵物以 βxy 的速率死亡，其中 y 是捕食者的數量，而 β（貝塔）是一個參數，表示 x 和 y，獵物和捕食者相遇時，獵物死亡的頻率。這等於第一個方程式的左側，表達了 x 的“隨時間變化”，即獵物數量（在微積分中，dx/dt 用來表示“x 在一個非常短的時間內的非常小的變化”，其中 d 表示變化或時間的量盡可能接近零，t 代表時間）。

So, to state that whole first equation again, the change in the number of hares (prey animals) at any given time is based on the number of hares times their birth rate, minus the number of hares eaten by lynxes, which is given by the number of lynxes, the number of hares, and the rate at which a lynx gets a hare.
因此，重新陳述整個第一個方程式，任何給定時間內兔子（獵物動物）數量的變化，取決於兔子數量乘以其出生率，減去被猞猁吃掉的兔子數量，這由猞猁的數量、兔子的數量以及猞猁捕獲兔子的速率所決定。

The equation for the predators is similar, but here we abstract out their reasons for dying. So the number of lynxes (predators, y) at any given time is based on how much food they have and their birth rate (δxy) and the rate at which they die off (γy), where δ (the lowercase Greek letter delta) is the modifier for how efficiently they can essentially turn food into little lynxes, and γ (gamma) is the modifier for how quickly each one dies off.
捕食者的方程式類似，但在這裡我們抽象化了它們死亡的原因。因此，任何給定時間的猞猁（捕食者，y）的數量取決於它們擁有的食物量及其出生率（δxy）和它們的死亡率（γy），其中 δ（小寫希臘字母 delta）是它們將食物有效轉化為小猞猁的效率修正值，而 γ（gamma）則是每隻猞猁死亡速度的修正值。

To show that this kind of nonlinear model is reflected in the real world, Figure 2.12 shows a depiction of data of actual lynx–hare population oscillations collected in the late 19th and early 20th centuries (MacLulich 1937). This data is messier than the model above, of course, because there are other dependencies not used in our abstract system: food sources for the prey animals, other animals preying on either predator or prey, weather effects, and so on. The nonlinear oscillations in the populations are nevertheless apparent.
為了顯示這種非線性模型在現實世界中的反映，圖 2.12 展示了 19 世紀末和 20 世紀初收集的實際猞猁與野兔族群波動數據（MacLulich 1937）。當然，這些數據比上述模型更為混亂，因為在我們的抽象系統中未使用的其他依賴因素：獵物動物的食物來源、其他動物對捕食者或獵物的捕食、天氣影響等等。然而，族群中的非線性波動仍然顯而易見。

Mathematical Versus Systemic Modeling
數學模型與系統模型

The Lotka–Volterra equations used in the preceding section create a concise mathematical model for a set of systemic effects. They demonstrate well the nonlinearities that emerge from the predator–prey relationship, and they do so in a way that those who are familiar with such mathematical modeling can find not only succinct but even beautiful. Such a set of mathematical statements does not, however, inform our understanding of the inner workings of the system itself. It treats the parts of the system, the individual hares and lynxes, as abstracted aggregate symbols rather than as entities interacting with each other via their behaviors.
在前一節中使用的 Lotka–Volterra 方程式為一組系統效應創建了一個簡潔的數學模型。它們很好地展示了捕食者與獵物關係中出現的非線性特性，並且以一種熟悉此類數學建模的人可以認為不僅簡潔而且甚至美麗的方式呈現。然而，這樣一組數學陳述並不能告知我們對系統內部運作的理解。它將系統的部分，即個別的野兔和猞猁，視為抽象的聚合符號，而非通過其行為相互作用的實體。

It may be worth taking a moment to discuss what is meant by a model in this context. Both the systemic and mathematical representations above provide abstract approximations of real-world processes. As shown in Figure 2.12, the real-world relationship between lynxes and hares is messier than the inexact illustrations provided by either the systems diagram and its graph or the mathematical equations. In games, as in most other systems you create, you are making a model of some part of the world. No model is ever really completely accurate, just as a model ship is never quite like an actual full-size ship. The models we make are nevertheless useful, as they allow us to improve our understanding of a larger-scale, more detailed process—and, in our case, to make games. We’ll talk more about the internal model of games in Chapters 3 and 7.
在這個背景下，值得花點時間來討論模型的意義。上述的系統和數學表示法都提供了現實世界過程的抽象近似。如圖 2.12 所示，猞猁和野兔之間的現實世界關係比系統圖和其圖表或數學方程式所提供的不精確插圖要複雜得多。在遊戲中，就像在您創建的大多數其他系統中一樣，您正在對世界的一部分進行建模。沒有任何模型是完全準確的，就像模型船永遠不會完全像實際的全尺寸船一樣。然而，我們所製作的模型仍然是有用的，因為它們使我們能夠更好地理解更大規模、更詳細的過程——在我們的情況下，則是製作遊戲。我們將在第三章和第七章中更深入地討論遊戲的內部模型。

In the mathematical model shown in the equations in Figure 2.11, the parameters like the birth, predation, and death rates—α, δ, β, and γ above—are controls you can tweak to change the overall behavior. In games, these parameters are often informally called “knobs,” with the designer’s action being that of turning a knob up or down to change a particular response. In a mathematical model, these knobs are essentially on the outside of a black box: they affect the internal workings via the equations given, but their actions may not be at all obvious to the observer.
在圖 2.11 所示的數學模型中，像是出生率、捕食率和死亡率這些參數——α、δ、β和γ——是可以調整的控制項，用來改變整體行為。在遊戲中，這些參數通常被非正式地稱為「旋鈕」，設計師的行為就像是調高或調低旋鈕以改變特定的反應。在數學模型中，這些旋鈕基本上位於黑箱的外部：它們通過給定的方程式影響內部運作，但對觀察者來說，它們的作用可能完全不明顯。

In systemic design, these parameters are more typically implemented via lower-level interactions of the internal state of the predator and prey rather than as high-level parametric knobs. For example, in a systemic model, the lynxes and hares likely have their own internal states and behaviors that determine their effective birth rate (α and δ in the equations above), and the attack strength of the lynxes versus the defense value of the hares will together determine what is shown in the above equations as the aggregated predation (β) parameter. Such a systemic view can make for more comprehensible and nuanced models that are less opaque from the designer’s point of view. It is important to construct your systems such that nonlinear results like these emerge from them at higher levels. Nevertheless, at some point, as a designer, you will need to decide the lowest level of detail for your system and implement appropriate parameters there (including random values) to represent even lower-level behavior.
在系統設計中，這些參數通常是透過捕食者與獵物內部狀態的低層次互動來實現，而不是作為高層次的參數旋鈕。例如，在一個系統模型中，猞猁和野兔可能有其自身的內部狀態和行為，這些狀態和行為決定了它們的有效出生率（在上述方程式中為α和δ），而猞猁的攻擊強度與野兔的防禦值將共同決定在上述方程式中顯示的聚合捕食（β）參數。這樣的系統觀點可以使模型更易於理解且更具細微差別，從設計者的角度來看也不那麼不透明。構建系統時，重要的是要讓這些非線性結果在更高層次上自然浮現。然而，作為設計者，在某個時刻你需要決定系統的最低細節層次，並在那裡實施適當的參數（包括隨機值）以代表更低層次的行為。

Chaos and Randomness  混沌與隨機

In discussing mathematical and systemic models in the context of looping systems, we should also touch on the differences between chaos and randomness. You will see another detailed discussion of probability and randomness in Chapter 9, “Game Balance Methods.”
在討論迴圈系統中的數學和系統模型時，我們也應該觸及混沌與隨機性之間的差異。您將在第九章“遊戲平衡方法”中看到關於概率和隨機性的詳細討論。

Random Effects

A system that is random is unpredictable, at least within a range; for example, a system with a random state between 1 and 10 may be at any value within that range. That is, whenever a value for an attribute on a part is called for, rather than simply assigning it a single number, say 5, you randomly determine what the number is within its range. In the simplest case, if the range is 1 to 10, then each number in that range has the same chance—1/10, or 10%—of appearing any time the next value is determined. Since the attribute’s state is random, you can’t tell what its value will be in the future based on what it is now.
一個隨機的系統是不可預測的，至少在某個範圍內；例如，一個隨機狀態在 1 到 10 之間的系統可能在該範圍內的任何值。也就是說，當需要為某個部分的屬性指定一個值時，與其簡單地賦予一個單一數字，例如 5，不如在其範圍內隨機確定該數字。在最簡單的情況下，如果範圍是 1 到 10，那麼該範圍內的每個數字都有相同的機會——1/10，或 10%——在下一次確定值時出現。由於屬性的狀態是隨機的，您無法根據其當前的值來預測未來的值。

In games, systems like this are useful as a way to simulate the action of low-level systems we are not actually modeling: rather than have the output of a system always be the same, we can enable it to vary randomly across its prescribed range. This provides variability to the higher-level system of which this is just one part so that the result here is not predictable and boring. A common example of this in games is how much damage is dealt by an attack. While a multitude of factors may be taken into account (the weapon used, the user’s skill, the type of attack, any armor or other defenses, and so on), at some point a variable amount of damage, random within a specified range, takes the place of simulating 1,000 more factors that in themselves are too difficult, time-consuming, or negligible to simulate on their own.
在遊戲中，這樣的系統有助於模擬我們實際上並未建模的低階系統的動作：與其讓系統的輸出總是相同，我們可以讓它在規定的範圍內隨機變化。這為更高階的系統提供了變化性，而這只是其中的一部分，從而使結果不再可預測和乏味。在遊戲中，這方面的一個常見例子是攻擊造成的傷害量。雖然可能會考慮多種因素（使用的武器、使用者的技能、攻擊類型、任何護甲或其他防禦等），但在某個時刻，隨機在指定範圍內的可變傷害量取代了模擬 1,000 個更多因素，這些因素本身太難、耗時或微不足道，無法單獨模擬。

Chaotic Effects

In the real world, we encounter chaotic systems far more often than we experience random ones: like the double pendulum discussed earlier, these are systems that are deterministic, meaning that in principle, if you know the complete state of the system at some point in time, you can predict its future behavior. However, these systems are also highly susceptible to minute changes in conditions. So starting a double pendulum or another chaotic system from two positions that are different by a tiny amount will result in two paths that are not just a little different but completely different from each other.
在現實世界中，我們遇到混沌系統的頻率遠高於隨機系統：就像之前討論的雙擺一樣，這些系統是確定性的，這意味著理論上，如果你知道某個時間點系統的完整狀態，你就可以預測其未來的行為。然而，這些系統對於條件的微小變化也極為敏感。因此，從兩個僅有微小差異的位置啟動雙擺或其他混沌系統，將導致兩條路徑不僅僅是有些不同，而是完全不同。

But of course things are not always this simple. A system that is chaotic but deterministic and not random is not amenable to reductionist, “clockwork” analysis, as discussed earlier. Systemic, nonlinear effects often make it impossible to analyze a system by taking it apart; such a system must be analyzed as a whole system, either by representing its subparts, their relationships, and the effects that come from these interactions, or by use of mathematical modeling like the Lotka–Volterra equations discussed earlier.
但事情當然並不總是如此簡單。一個混沌但具決定性而非隨機的系統，無法用還原論的「鐘錶」分析來處理，如前所述。系統性的非線性效應常常使得無法通過拆解來分析一個系統；這樣的系統必須作為一個整體系統來分析，無論是通過表示其子部分、它們的關係以及這些交互作用所產生的效應，還是通過使用如前所述的洛特卡-沃爾泰拉方程等數學建模。

Moreover, chaotic systems sometimes display what looks like nonchaotic behavior. This is particularly evident when a chaotic system can behave nonlinearly with itself; such events are often known as “resonance events.” Resonance events happen when a large number of small, chaotic events combine in a reinforcing loop to create a nonlinear result with an enormous effect on the system itself. This can be seen in the ways that wind or even people walking across a bridge cause it to sway, sometimes disastrously.
此外，混沌系統有時會展現出看似非混沌的行為。這在混沌系統能夠與自身非線性互動時尤為明顯；這類事件通常被稱為「共振事件」。共振事件發生在大量小型混沌事件結合成一個增強迴圈，從而產生對系統本身有巨大影響的非線性結果。這可以從風或甚至人們走過橋面時引起橋面搖晃，有時甚至造成災難性後果中看出。

Collapsing Bridges

The Tacoma Narrows Bridge in Washington State famously self-destructed in 1940 after being buffeted by wind. While the wind alone couldn’t have caused the bridge to collapse, it did push on the bridge, causing it to sway—just a little at first. As the wind pushed on the bridge, the length of the main span caused it to sway with a particular frequency. This swaying then increased how much the bridge caught the wind, further increasing the intensity of its motion. The bridge and the wind quickly became joined in a chaotic system with a dominant reinforcing loop that had violent and disastrous results (Eldridge 1940). See Figure 2.13.
華盛頓州的塔科馬海峽大橋在 1940 年因風力的衝擊而著名地自毀。雖然僅靠風力不足以使大橋倒塌，但風的確推動了大橋，最初只是輕微地搖晃。隨著風力的推動，大橋的主跨長度使其以特定的頻率搖擺。這種搖擺進一步增加了大橋迎風的面積，進一步加劇了其運動的強度。大橋和風很快形成了一個混亂的系統，這個系統中有一個主導的增強迴圈，導致了劇烈而災難性的結果（Eldridge 1940）。見圖 2.13。

In a similar case, authorities in London in the late 1800s posted signs on the Albert Bridge that read, “Officers in command of troops are requested to break step when passing over this bridge” after other similar bridges collapsed due to the resonance created by many stamping feet. Each footfall in itself was small compared to the strength of a bridge, but together they created enough of a reinforcing loop that the soldiers’ steps could lead to a tragic, nonlinear resonant result (Cookson 2006).
在類似的情況下，十九世紀末的倫敦當局在阿爾伯特橋上張貼告示，寫著：「部隊指揮官請在通過此橋時打破步伐」，因為其他類似的橋樑因為眾多腳步的共振而倒塌。每一步的力量相較於橋樑的強度而言微不足道，但它們共同創造了一個足以加強的迴圈，使得士兵的步伐可能導致悲劇性的非線性共振結果（Cookson 2006）。

Fireflies

A far less destructive example of a chaotic system that achieves a kind of nonlinear resonance can be found in some fireflies. These little bugs provide a wonderful light show in the evenings in many parts of the world, as each one emits a flash of light to try to attract a mate. However, in some parts of Southeast Asia and the Smoky Mountains of the southern United States, entire populations of fireflies will blink at the same time, all synchronized together (NPS.gov 2017).
在一些螢火蟲身上，可以找到一種達到非線性共振的混沌系統的例子，這種例子破壞性要小得多。這些小昆蟲在世界許多地方的夜晚提供了美妙的燈光秀，因為每隻螢火蟲都會發出閃光來吸引配偶。然而，在東南亞的某些地區和美國南部的煙霧山脈，整個螢火蟲群體會同時閃爍，全部同步在一起（NPS.gov 2017）。

They do this on their own, without any firefly conductor telling them when to flash, by means of a simple mechanism: whenever one firefly sees another nearby light up, it hurries up to flash a little sooner than it would have otherwise. With this simple mechanism, the whole system moves from chaos to resonance.
牠們自行這樣做，沒有任何螢火蟲指揮家告訴牠們何時閃爍，這是透過一個簡單的機制：每當一隻螢火蟲看到附近的另一隻亮起時，牠就會加快速度，比原本預計的時間更早閃爍。透過這個簡單的機制，整個系統從混亂走向共鳴。

Each firefly here is a part in a system, with a behavior of flashing its abdomen light. When another firefly (another part in the system) sees this behavior, it alters its own internal state to flash sooner than it might otherwise—which of course is seen by other fireflies. The result is that in a short period of time, more and more fireflies are flashing at the same time, until they are all flashing in unison. The system is chaotic in that it is highly sensitive to its starting conditions, and there’s no way to tell exactly when any firefly will light up. However, because of their one form of local interaction, the entire population of fireflies soon begins to resonate: first in small patches, then in big waves, then all together, as each bug slightly adjusts its next flash time based on what it’s seeing.
這裡的每一隻螢火蟲都是系統中的一部分，具有閃爍腹部燈光的行為。當另一隻螢火蟲（系統中的另一部分）看到這種行為時，它會改變自己的內部狀態，比原本預期的更早閃爍——這當然也會被其他螢火蟲看到。結果是，在短時間內，越來越多的螢火蟲同時閃爍，直到它們全部同步閃爍。這個系統是混沌的，因為它對初始條件極為敏感，無法確切預測任何一隻螢火蟲何時會亮起。然而，由於它們的一種局部互動形式，整個螢火蟲群體很快開始共振：先是小範圍的，然後是大波浪，最後全部一起，因為每隻螢火蟲根據所見稍微調整下一次閃爍的時間。

Similar resonance effects can be found in nerve cells in the mammalian heart, in the brain, and in many other parts of nature. They are excellent examples of nonlinear effects that create resonant, synchronized order out of distributed actions of parts in a system.
在哺乳動物的心臟神經細胞、大腦以及自然界的許多其他部分中，都可以發現類似的共振效應。這些都是非線性效應的絕佳例子，能夠從系統中各部分的分散行動中創造出共振的同步秩序。

Examples of Loop Structures
迴圈結構的範例

There are many examples of systemic loops that illustrate how these structures create various (often nonlinear) effects. We discuss a few of them here.
有許多系統循環的例子，說明這些結構如何產生各種（通常是非線性）效果。我們在此討論其中幾個。

One general class is often called “fixes that fail” and is exemplified by the “cobra effect” (Siebert 2001) discussed in Chapter 1. In that situation, the problem was “too many cobras!” and the solution was “reward for cobras,” as shown in Figure 2.14. This forms a nice balancing loop: as people take the reward for turning in cobra heads, there are fewer cobras around (and fewer to breed the next generation), so the severity of the problem diminishes.
一種常見的類型通常被稱為「失敗的修正」，以第一章中討論的「眼鏡蛇效應」（Siebert 2001）為例。在那種情況下，問題是「眼鏡蛇太多了！」而解決方案是「獎勵眼鏡蛇」，如圖 2.14 所示。這形成了一個良好的平衡循環：隨著人們因上交眼鏡蛇頭而獲得獎勵，周圍的眼鏡蛇變少了（繁殖下一代的眼鏡蛇也減少了），因此問題的嚴重性減輕了。

However, there is another outer loop here, as shown in Figure 2.15. This is often called an unintended consequences loop, as it creates a reinforcing loop that is hidden for a little while and brings back the original problem (or another, related condition) with a vengeance. Notably, in this loop there is a delay, signified by the two hash marks (\\) on one arc, meaning that this outer loop happens more slowly than the inner loop. The result in the end is typically that the problem is worse than when it started—plus a great deal of time and energy have been spent on an illusory “solution.”
然而，這裡還有另一個外環，如圖 2.15 所示。這通常被稱為意外後果環，因為它創造了一個隱藏了一段時間的增強環，並以猛烈的方式帶回了原始問題（或其他相關情況）。值得注意的是，在這個環中存在一個延遲，由一個弧上的兩個井號（\\）表示，這意味著這個外環的發生速度比內環慢。最終的結果通常是問題比開始時更糟糕——而且大量的時間和精力已經花在了一個虛幻的“解決方案”上。

There are many examples of this structure in real life: you need to save money, so you don’t maintain your car regularly. This works for a little while, until that delayed outer loop catches up with you, and now you need to spend more money to fix a major failure that could have been prevented at a lower cost. Or, a division at a company is in trouble, so a new manager institutes a bunch of quick fixes. Revenue starts to rise, things look great, and the manager who “saved the day” is promoted. However, soon the long-term unintended consequences (the metaphorical “farmed cobras”) begin to become apparent. The person who replaced the promoted manager begins to scramble, but the situation is now far worse than it was before, and they end up being blamed not only for the poor performance but for messing up the terrific situation provided by the previous manager (who may now be their boss). A short-term view that ignores the underlying systemic causes and effects often leads to this kind of fix-that-fails.⁴
在現實生活中有許多這種結構的例子：你需要存錢，所以不定期維修你的車。這樣做在短期內有效，直到那延遲的外部循環追上你，現在你需要花更多的錢來修理本可以以較低成本預防的重大故障。或者，公司的一個部門陷入困境，因此一位新經理實施了一系列快速修正措施。收入開始上升，情況看起來很不錯，而那位“拯救了局面”的經理被晉升。然而，很快地，長期的意外後果（比喻中的“養殖眼鏡蛇”）開始顯現。接替被晉升經理的人開始手忙腳亂，但情況現在比以前更糟，他們不僅被指責表現不佳，還被指責搞砸了前任經理（可能現在是他們的上司）留下的良好局面。忽視潛在系統性原因和影響的短期觀點往往導致這種失敗的修正。

In a game context, a player in a strategy game who builds a huge army quickly may actually find themselves at a disadvantage to another player who instead invested some of their resources in researching how to make better troops. The first player took the fast route but ignored the deficit built up by not thinking longer term; their “fix” failed to take into account the value of troops that were more effective individually but that took longer to make. The second player avoided the quick fix (having a large army) by investing their resources with a longer-term view. This choice between “build fast now” and “invest for the future” is an example of a looping structure called an engine that you will see again in Chapter 7.
在遊戲情境中，一名策略遊戲的玩家若快速建立起龐大的軍隊，可能會發現自己反而處於劣勢，因為另一名玩家將部分資源投入於研究如何製造更優良的部隊。第一名玩家選擇了快速的路徑，但忽略了因未考慮長期而累積的劣勢；他們的「解決方案」未能考慮到那些雖然製造時間較長但單兵作戰能力更強的部隊的價值。第二名玩家則避免了快速解決方案（擁有龐大軍隊），而是以長遠的眼光投資資源。這種「現在快速建造」與「為未來投資」的選擇，是一種稱為引擎的循環結構的例子，您將在第七章再次看到。

Limits to Growth—And the Crashes That Can Follow
成長的極限——以及隨之而來的崩潰

Another example of a loop structure, and one that shows nonlinear results well, is the class that shows limits to growth (see Figure 2.16). This name comes originally from a book of the same title (Meadows et al. 1972) that was intended as a forward-looking commentary on the overall world system and whether its growth could be maintained through the 21st century. (The authors were not optimistic.) Beyond this particular usage, the pattern overall is worth examining and understanding.
另一個迴圈結構的例子，並且能很好地展示非線性結果的，是顯示增長極限的類別（見圖 2.16）。這個名稱最初來自一本同名書籍（Meadows 等，1972），該書旨在對整體世界系統進行前瞻性的評論，探討其增長是否能持續到 21 世紀。（作者並不樂觀。）除了這個特定的用法之外，整體模式值得進一步檢視和理解。

We often assume that given some result, doing more of what led to it will give us a result that continues to increase linearly. We often hear statements like “if our business continues to grow at this rate…” or “if the population continues to grow at this rate” that contain the implicit assumption that things will continue in the future as they have been in the past. This is almost never the case. The reason is that for every accelerating condition fed by a reinforcing loop—increased sales, crop yield, or number of units built—there is a separate balancing loop fed by a limiting condition. This condition is typically some resource that is necessary for and diminished by increasing growth (new customers available as a market becomes saturated, a mineral in the soil taken up and not replenished, ability to pay for units, and so on).
我們常常假設，既然已經得到某種結果，那麼多做一些導致該結果的事情就會讓我們得到一個持續線性增長的結果。我們經常聽到類似「如果我們的業務以這個速度持續增長……」或「如果人口以這個速度持續增長……」的說法，這些說法隱含著一種假設，即未來的情況會像過去一樣持續下去。然而，情況幾乎從來不是這樣。原因在於，對於每一個由增強循環驅動的加速條件——如銷售增加、作物產量提高或建造單位數量增加——都存在一個由限制條件驅動的平衡循環。這個條件通常是某種資源，這種資源對於增長是必要的，但隨著增長而減少（例如，隨著市場飽和而可用的新客戶、土壤中被吸收而未補充的礦物、支付單位的能力等等）。

The overall nonlinear result is a curve that rises slowly, then quickly, and then more slowly until it levels off again. A typical example of this is depicted in Figure 2.17, which shows how yields of wheat production have leveled off since the late 1990s (Bruins 2009). The factors contributing to this slowdown in growth are no doubt complex in a global situation like this one, involving physical, economic, and political resources, but the overall effect is the same: if someone predicted the future based on a linear extrapolation from data in the 1970s or 1980s, they would have been sorely disappointed a decade later.
整體的非線性結果是一條曲線，先緩慢上升，然後迅速上升，接著再緩慢上升，直到再次趨於平緩。這種典型的例子如圖 2.17 所示，顯示自 1990 年代末以來，小麥產量的增長已經趨於平緩（Bruins 2009）。在這樣的全球情況下，導致增長放緩的因素無疑是複雜的，涉及物理、經濟和政治資源，但整體效果是一樣的：如果有人根據 1970 年代或 1980 年代的數據進行線性外推來預測未來，那麼十年後他們將會大失所望。

Even some seemingly simple and potentially unending reinforcing loops have limits to their growth—and, as with the unintended consequences of fixes that fail, these limits sometimes appear abruptly. A classic version of this is evident in the stock market crash of 1929. In the years prior to the crash, the economy was booming, and stock prices seemed to only go one way: up. For an investor, buying something today that you could turn around and sell tomorrow for a profit seemed like an easy bet. As a result, many investors bought stocks on credit. As long as the cost of the credit was less than the profit they would make when they sold, it was, as the saying goes, “easy money.” A form of stock purchasing called “buying on the margin” made this even easier for investors. In buying this way, an investor only had to keep a cash reserve of 10% to 20% of the total stock they were buying, with the assumption that they could always sell some stock (at a profit) to cover any costs from buying a different stock. This meant, in effect, that if you deposited $100 into a stock brokerage account, you could buy as much as $1,000 worth of stock. Since stock prices were continually rising, the belief was that you could always sell and still make a profit. Lots of people became wealthy this way, which enticed even more people to flood into the market.
即使是一些看似簡單且可能無止境的增強循環，其增長也有其限制——而且，正如那些失敗的修正措施所帶來的意外後果一樣，這些限制有時會突然出現。這一經典例子在 1929 年的股市崩盤中顯而易見。在崩盤前的幾年，經濟蓬勃發展，股價似乎只有一個方向：上漲。對於投資者來說，今天買入某物，明天就能轉手賺錢，似乎是一個簡單的賭注。因此，許多投資者以信用購買股票。只要信用成本低於他們賣出時的利潤，這就如俗話所說，是“輕鬆賺錢”。一種稱為“保證金購買”的股票購買方式讓投資者更容易進行這種操作。以這種方式購買時，投資者只需保留所購股票總額的 10%到 20%的現金儲備，假設他們總能賣出一些股票（並獲利）來支付購買其他股票的任何成本。這意味著，實際上，如果你在股票經紀賬戶中存入 100 美元，你就可以購買價值高達 1,000 美元的股票。 由於股價不斷上漲，人們相信無論何時賣出都能獲利。許多人因此致富，這吸引了更多人湧入市場。

Of course, there is always some limit to growth. In 1929, the first sign of trouble came with some companies reporting disappointing performance in March, which caused the market to dip and gave investors pause about their behavior. However, the market rebounded by the summer, which had the ironic effect of making people even more certain that the values of their shares would continue to rise without limit. Then, in October 1929, with stock prices at incredibly high values, several companies reported poor performance. This made some investors think that, while things were still going well economically, perhaps the time had come to cash in and get out of the market. Since so many had invested on the margin, they had to cover their prior purchases, which meant they had to sell more stock to do so. As stock prices began to fall late in October, investors had to sell more and more shares to cover their previous purchases, and a new reinforcing, snowballing loop came into effect (see Figure 2.18). The previous “irrational exuberance”⁵ exhibited by investors now turned to panic, and they all tried to salvage what they could by selling as fast as they could. With everyone trying to sell and few buying, prices fell even further, and the reinforcing loop—in this case, one driving prices downward—accelerated quickly. By the end of the year, over 90% of the value and accumulated wealth from the stock market rise had been wiped out, ushering in the global Great Depression.
當然，成長總是有其限制。1929 年，第一個麻煩的跡象出現在三月，一些公司報告業績不佳，這導致市場下跌，讓投資者對自己的行為有所顧慮。然而，市場在夏季反彈，具有諷刺意味的是，這讓人們更加確信他們的股票價值會無限上升。然後，在 1929 年 10 月，當股票價格達到極高的價值時，幾家公司報告業績不佳。這讓一些投資者認為，儘管經濟狀況仍然良好，但或許是時候套現並退出市場了。由於許多人是以保證金投資，他們必須彌補之前的購買，這意味著他們必須賣出更多的股票來做到這一點。隨著十月底股票價格開始下跌，投資者不得不賣出越來越多的股票來彌補之前的購買，於是出現了一個新的增強性滾雪球效應（見圖 2.18）。投資者之前表現出的「非理性繁榮」 ⁵ 現在轉為恐慌，他們都試圖以最快的速度賣出來挽救他們所能挽救的。 由於人人都在拋售而少有人購買，價格進一步下跌，這種強化循環——在此情況下，是推動價格下跌的循環——迅速加速。到年底，股市上升所帶來的價值和累積財富超過 90%已被抹去，全球大蕭條隨之而來。

Unfortunately, a similar example can be seen in the financial situation in 2017. According to Turner (2016), subprime lending is on the rise, as it was prior to the financial crash of 2008. This time, however, the lending is in credit cards and things like cars rather than mortgages. “Subprime” means that the loans are risky, an acknowledgement that many will not be paid back just because those borrowing won’t have the money to do so. To cover this risk, borrowers pay more in interest for the loans. The more risky loans that are made, the more defaults—borrowers not being able to pay back the loans—there are (see Figure 2.19). In addition, this is happening against an economic backdrop in which there has for several decades (unalleviated by the crash of 2008) been an increase in concentration of money among the very wealthiest in U.S. and global society. This means that there are a few who want to make a further profit on their (already increasing) wealth, and there are many more who need to borrow that money even at a high cost. Basing his analysis of figures from UBS Bank, Turner characterizes the situation this way:
不幸的是，2017 年的金融狀況中可以看到類似的例子。根據特納（2016）的說法，次級貸款正在上升，就像 2008 年金融危機前一樣。然而，這次的貸款主要集中在信用卡和汽車等方面，而非房屋貸款。「次級」意味著這些貸款具有風險，這是因為借款人可能無法償還貸款。為了彌補這種風險，借款人需要支付更高的貸款利息。貸款風險越高，違約——即借款人無法償還貸款的情況——就越多（見圖 2.19）。此外，這一切發生在一個經濟背景下，數十年來（即使 2008 年的危機也未能緩解）美國和全球社會中最富有的人群中資金集中度不斷增加。這意味著有少數人希望在其（已經增加的）財富上獲得更多利潤，而有更多的人即使在高成本下也需要借款。特納基於瑞銀銀行的數據分析，將這種情況描述如下：

As the pool of wealth becomes more concentrated, the greater the asymmetry between the haves, who typically want to invest and get a return on their money, and the have nots, who are typically borrowers. That pushes down the creditworthiness of the average borrower. Add in a low-interest-rate environment, where investors are searching for yield, and you have a problem. (Turner 2016)
隨著財富的集中程度越來越高，擁有財富的人通常希望投資並獲得回報，而沒有財富的人通常是借款者，這之間的不對稱性也越來越大。這降低了平均借款者的信用度。再加上低利率環境，投資者在尋找收益，這就形成了一個問題。（Turner 2016）

That is, the more concentrated the wealth is, the more difficult it is for those holding that money to find ways to increase it via investment because so many others have less money and are increasingly risky as investments. This difficulty pushes investors to look further and further afield for ways to make a profit and to become increasingly willing to take on higher-risk investments. Those higher-risk investments will increase the rate of loan defaults, which reinforces the investor’s need to show a profit, thus driving their search into riskier and riskier territory (refer to Figure 2.19). What’s worse is that there is another component to this loop, as shown in Figure 2.20: for those on the borrowing side (the “have nots”), their need to make purchases (including necessities like food and rent) drives them to take out more loans and increase their debt. Sometimes people feel forced to take out very high-cost loans to cover other loans they already have, but this just leaves them further in debt. Between additional interest, fees, and in some cases not being able to repay these debts, the loop becomes reinforcing, with those same people needing more loans for further purchases.
也就是說，財富越集中，持有這些財富的人就越難通過投資來增加財富，因為其他人擁有的資金較少，作為投資對象的風險也越來越高。這種困難促使投資者不斷尋找更遠的投資機會，並越來越願意承擔更高風險的投資。這些高風險投資將增加貸款違約率，進一步強化投資者需要獲利的需求，從而驅使他們進入更高風險的領域（參見圖 2.19）。更糟糕的是，這個循環還有另一個組成部分，如圖 2.20 所示：對於借款方（“沒有的人”）來說，他們的購買需求（包括食物和租金等必需品）驅使他們借更多的貸款，增加債務。有時，人們感到被迫借取高成本貸款來償還已有的貸款，但這只會讓他們陷入更深的債務。在額外的利息、費用以及有時無法償還這些債務的情況下，這個循環變得更加強化，這些人需要更多的貸款來進行進一步的購買。

Neither of these reinforcing loops is sustainable; both have strong limits to their growth as the cost of borrowing increases and the ability to pay decreases. Unlike in 1929, as of this writing, we do not yet know the end of this financial story. Hopefully, if we can recognize and analyze systemic effects like this around us, we can prevent the worst of the crashes that may follow.
這兩個增強循環都無法持續；隨著借貸成本的增加和償還能力的下降，它們的增長都有強大的限制。與 1929 年不同，截至本文撰寫時，我們尚未知道這個金融故事的結局。希望如果我們能夠認識並分析我們周圍這樣的系統性影響，我們可以防止可能隨之而來的最嚴重崩潰。

Apart from these grim examples of limits to growth, we will see the effects of this same principle along with others in uneven competition in games when we discuss the use of loops in game design in Chapter 7.
除了這些成長限制的嚴峻例子之外，我們還會在第七章討論遊戲設計中迴圈的使用時，看到這一原則與其他原則在遊戲中不均衡競爭的影響。

The Tragedy of the Commons
公地的悲劇

Another well-known issue best understood from a systemic point of view is known as the tragedy of the commons. This ancient problem, described originally in modern times by Lloyd (1833), still occurs in many forms today. Lloyd described the situation in which individuals acting on their own, and with no ill intent, nevertheless manage to destroy a shared resource—and thus their own future gains. As shown in Figure 2.21, each actor has their own reinforcing loop: they takes some action and gains some positive result. This could be anything, but the original description was of grazing animals in an area open to all in a village—known as the “commons.” By grazing cattle or sheep there, an individual increased the value of their herd. As the commons was available to anyone, any farmer who grazed more cattle there would benefit more and so had an incentive to do so. However, the grass eaten by the cattle was a shared resource. Therefore, if too many people tried to graze too many cattle there, soon the grass would be depleted, and no one would be able to use it.
另一個從系統觀點來看最容易理解的知名問題是「公地悲劇」。這個古老的問題最早在現代由 Lloyd（1833）描述，至今仍以多種形式存在。Lloyd 描述了一種情況，即個人各自行動，並無惡意，卻仍然設法摧毀了一個共享資源，從而毀掉了他們未來的收益。如圖 2.21 所示，每個行動者都有自己的增強循環：他們採取某些行動並獲得一些正面結果。這可以是任何事情，但最初的描述是村莊中一個對所有人開放的區域內放牧動物，稱為「公地」。通過在那裡放牧牛或羊，個人增加了他們畜群的價值。由於公地對任何人都開放，任何在那裡放牧更多牛的農民都會獲得更多利益，因此有動機這樣做。然而，牛吃的草是一種共享資源。因此，如果太多人試圖在那裡放牧過多的牛，草很快就會被耗盡，沒有人能夠再使用它。

In systemic terms, the use of the shared resource forms an outer balancing loop not unlike that seen in the unintentional consequences in fixes that fail. Certainly in the tragedy of the commons no single individual intends to make the resource fail for everyone, and it is often the case that no one has used so much of it that they feel at all responsible. As another example, dropping a single piece of litter on the street doesn’t seem to add much to the unsightliness of the community, and puffing out a bit of smoke doesn’t seem to add much to overall pollution. But when taken together with everyone else’s actions, the loss of environmental beauty or air quality can be significant and obvious—even if no one feels responsible. This is another example of how looking for reductionist root causes can lead you astray: just because too much grass has been eaten from the commons, or there is too much trash on the ground or pollution in the air does not mean there is a single villain responsible. Systemic responsibility often equates to distributed, decentralized responsibility. Recognizing that and how individual actions can create unintended consequences is an important aspect of systems thinking.
從系統的角度來看，共享資源的使用形成了一個外部的平衡迴圈，這與那些失敗的修正中所見的無意後果相似。在公地悲劇中，確實沒有任何個人意圖讓資源對所有人都失效，通常情況下，沒有人使用了太多以至於感到有責任。另一個例子是，隨手丟一片垃圾在街上似乎不會對社區的美觀造成太大影響，吐出一點煙霧似乎也不會對整體污染造成太大影響。但當這些行為與其他人的行為結合在一起時，環境美觀或空氣品質的損失可能會變得顯著且明顯——即使沒有人感到負責。這是另一個例子，說明尋找還原論的根本原因可能會讓你誤入歧途：僅僅因為公地上的草被吃得太多，或地上有太多垃圾，或空氣中有太多污染，並不意味著有一個單一的罪魁禍首。系統性的責任往往等同於分散的、去中心化的責任。 認識到個人行為如何能夠產生意想不到的後果，是系統思維的一個重要方面。

In games, systemic conditions like the tragedy of the commons can be seen whenever there is a limited resource that multiple people want to use, especially if they want to maximize their use of it. The resource may be physical in the game, like a gold mine or animals that can be used for food, or it can be anything with a limited availability and dwindling value with use. In a game with a working ecology, for example, if the players each kill a few rabbits for food, but in so doing cause the rabbit population to crash, this puts them into a tragedy of the commons situation. (Moreover, if the rabbits are food for lynxes, and the lynxes also keep some other kind of pest at bay, losing the rabbits means losing the lynxes, which can lead to other consequences for the players.)
在遊戲中，像公地悲劇這樣的系統性條件可以在任何有限資源被多個人想要使用時看到，尤其是當他們想要最大化使用該資源時。資源可能是遊戲中的實體，例如金礦或可用作食物的動物，或者是任何有限可用性且隨著使用而價值減少的東西。在一個具有生態系統運作的遊戲中，例如，如果玩家各自獵殺幾隻兔子作為食物，但這樣做卻導致兔子數量崩潰，這就使他們陷入了公地悲劇的情境。（此外，如果兔子是猞猁的食物，而猞猁也能抑制某種害蟲，失去兔子就意味著失去猞猁，這可能會給玩家帶來其他後果。）

Trophic Cascades

For a more positive example, we can also look back to the example of the trophic cascade created by reintroducing wolves into Yellowstone National Park (see Figure 2.22). This is a complex series of reinforcing and balancing loops: the wolves reduced (balanced) the number of elk and deer, and their reduced numbers reduced the balancing effect they were having on trees. Thus, in effect, the wolves were in a reinforcing relationship with the trees, and thus (transitively) with the bears, fish, birds, and so on.
舉一個更正面的例子，我們可以回顧將狼重新引入黃石國家公園所創造的營養級聯效應（見圖 2.22）。這是一個由多個增強和平衡迴圈組成的複雜系列：狼減少了（平衡了）麋鹿和鹿的數量，而牠們數量的減少也減少了牠們對樹木的平衡影響。因此，實際上，狼與樹木之間形成了一種增強關係，進而（傳遞性地）與熊、魚、鳥等形成了關聯。

Many systemic loops you will find and create will be even more complex and potentially confusing than this one. As long as you can remember to look for the stocks and resources (number of wolves, number of elk, and so on) and figure out the behavioral relationships between them (the arrows that make the loop), you will be able to disentangle even highly systemic, highly complex situations.
你會發現並創造的許多系統循環將比這個更為複雜，甚至可能更令人困惑。只要你記得尋找庫存和資源（如狼的數量、麋鹿的數量等），並弄清它們之間的行為關係（形成循環的箭頭），你就能夠解開即使是高度系統化、高度複雜的情況。

Emergence

When reinforcing and balancing loops in a complex system are themselves in a dynamic balance, they create a metastable, organized systemic behavior. That is, every part in the system is changing, influencing and being influenced in their behavior, and yet the overall structure remains stable (at least for a time). This metastability creates a set of organized behaviors not found in any of the individual parts. For example, the action of each bird traveling together creates a metastable flock, just as the action of each atom bound together creates a metastable molecule. Similarly, the populations of fireflies discussed above create an emergent effect when they all flash at the same time. The effect is metastable and persistent, creating a surprising, often breathtaking visual property not found in (or directed by) any single firefly.
當複雜系統中的增強迴圈和平衡迴圈本身處於動態平衡時，它們會創造出一種亞穩定的、有組織的系統行為。也就是說，系統中的每個部分都在改變，影響並被影響著它們的行為，但整體結構仍然保持穩定（至少在一段時間內）。這種亞穩定性創造出一組在任何單一部分中都找不到的有組織行為。例如，每隻鳥一起飛行的行動創造出一個亞穩定的鳥群，就像每個原子結合在一起的行動創造出一個亞穩定的分子。類似地，上述螢火蟲的群體在同時閃爍時創造出一種突現效應。這種效應是亞穩定且持久的，創造出一種驚人且常常令人屏息的視覺特性，這在任何單一隻螢火蟲中都找不到（或由其指導）。

This overall metastability is an emergent effect, one that arises from the action of multiple parts. Emergent effects create new properties that are qualitatively different from any of the individual parts and do not result from a simple sum of the parts themselves. Such metastability also enables other emergent effects to arise from the actions of all the parts in the system.
這種整體的亞穩態是一種湧現效應，由多個部分的作用所產生。湧現效應創造出新的特性，這些特性在質上與任何單一部分都不同，並非僅僅是各部分簡單相加的結果。這種亞穩態也使得系統中所有部分的作用能夠產生其他湧現效應。

As another example, in a school of fish, each part (each individual fish) has internal state such as mass, velocity, and direction. The overall weight of a school of such fish is not an emergent property, as it is just the sum of the weights of all the fish in the school. However, the shape of the school may well be emergent, as when they form a closely packed school called a baitball to get away from predators (see Figure 2.23) (Waters 2010). While each fish has its own shape, that shape does not itself determine the shape of the group of fish. Instead, each fish’s position, velocity, and direction contributes to (but does not itself determine) the shape of the school.
另一個例子是，在魚群中，每個部分（每條魚）都有內部狀態，如質量、速度和方向。魚群的總重量並不是一種突現性質，因為它只是魚群中所有魚的重量總和。然而，魚群的形狀可能是突現的，當它們形成一個緊密的魚群，稱為誘餌球，以躲避掠食者時（見圖 2.23）（Waters 2010）。雖然每條魚都有自己的形狀，但這個形狀並不決定魚群的形狀。相反，每條魚的位置、速度和方向都對魚群的形狀有所貢獻（但並不決定）。

The shape of the school cannot be found in any one fish, nor is any fish responsible for determining the shape of the school; there is no central controlling fish calling out shapes the fish should create together, like a marching band. Recognizing that there is no “fish in charge,” no “central control system” (as Wiener said in his 1948 book Cybernetics) is an important aspect of truly grasping emergence and systemic functioning. It may be an artifact of our centralized culture (an aspect that has many positive effects), but in some cases even scientists have a difficult time seeing past it. As one example, Wilensky and Resnick (1999) pointed out that at least as late as the 1980s, scientists assumed that certain kinds of molds that aggregate themselves together must have had “founder” or “pacemaker” cells to start and guide the process. These molds start as single-cell organisms and end as large groups that even differentiate into organ-like structures. Is it possible this could happen without some kind of central control? For many years, this wasn’t even a question that scientists asked. They had to first learn to see the distributed system and the organized behavior arising out of it without any central controller whatsoever.
學校的形狀無法在任何一條魚中找到，也沒有任何一條魚負責決定學校的形狀；沒有一條中央控制的魚像行進樂隊一樣呼喊著魚群應該共同創造的形狀。認識到沒有“負責的魚”，沒有“中央控制系統”（正如維納在他 1948 年的著作《控制論》中所說）是真正理解湧現和系統運作的一個重要方面。這可能是我們中央集權文化的一個產物（這一方面有許多積極的影響），但在某些情況下，即使是科學家也很難看透它。舉個例子，Wilensky 和 Resnick（1999）指出，至少在 1980 年代，科學家們假設某些類型的黴菌聚集在一起，必須有“創始”或“起搏”細胞來啟動和引導這一過程。這些黴菌從單細胞生物開始，最終形成大型群體，甚至分化成類似器官的結構。這種情況可能在沒有某種中央控制的情況下發生嗎？多年間，這甚至不是科學家們會問的問題。 他們必須首先學會觀察分散式系統，以及在沒有任何中央控制器的情況下由此產生的有序行為。

When a metastable structure resulting from multiple interactions of the parts within it is
當一個由其內部多重交互作用所產生的亞穩定結構

not determined by any one part within it,
並非由其中的任何一部分決定，

not based on the linear sum of the attributes of its parts,
並非基於其部分屬性的線性總和，

more easily described in terms of the aggregation (“a spherical school of fish”) than in terms of the individual parts and relationships (a tedious recounting of each fish’s position, velocity, and direction),
更容易以聚合的方式來描述（“一群球形的魚群”），而不是以個別部分和關係來描述（繁瑣地重述每條魚的位置、速度和方向），

then a new thing with its own properties has emerged. As discussed in Chapter 1, a water molecule has electrical polarity that is simpler to describe in terms of the “lumpy sphere” as a unified metastable structure (that is, as a thing on its own) than in terms of the contributing atoms—just as each atom has an electrical character that is easier to describe on its own than by referring to the protons and electrons or by diving still further down to the quarks with their fractional electrical charges inside the atom’s nucleus.
那麼一個具有自身特性的全新事物便已經出現。如同在第一章中所討論的，水分子具有電極性，這比起貢獻的原子來說，更容易以“團狀球體”作為一個統一的亞穩定結構來描述（即作為一個獨立的事物），正如每個原子具有的電性特徵，比起參考質子和電子或進一步深入到原子核內部具有分數電荷的夸克來說，更容易單獨描述。

There is no clear demarcation for emergence, just as there is no wrapper around a proton or an atom, but the unification of the constituent parts and relationships into new properties held by the whole thing is the telltale sign of emergence, of identity and integrity—and systems.
沒有明確的界限來劃分「湧現」，就像質子或原子沒有包裹一樣，但組成部分和關係的統一，形成了整體所擁有的新特性，這正是湧現、身份和完整性——以及系統的明顯標誌。

Upward and Downward Causality
向上和向下的因果關係

In a system with emergent properties, the interactions of individual parts within the system cause the emergence. This is what is known as upward causality: a new behavior or property emerges from the distributed actions of lower-level structures. An example of this is in a stock market, where each individual person is making decisions to buy and sell. The aggregate behavior of these individuals can cause new effects to occur: for example, many decisions to buy by individuals can cause a rise in the overall market (as measured by its indexes of activity, volume of trades, and so on) that changes the character and behavior of the market, just as fish all trying to escape a predator change the shape of their school.
在具有湧現特性的系統中，系統內部各個部分的相互作用導致了湧現。這就是所謂的向上因果關係：一種新的行為或特性從低層結構的分佈行動中湧現出來。這方面的一個例子是股市，每個人都在做出買賣的決策。這些個體的總體行為可以引發新的效果：例如，許多人做出購買決策可能會導致整體市場上升（通過其活動指數、交易量等來衡量），從而改變市場的特性和行為，就像魚群為了逃避掠食者而改變其群體形狀一樣。

Similarly, the aggregate—the stock market as a thing, or the school of fish—can exhibit downward causality on the parts within it. When individuals in a stock market all begin to sell rapidly, the market itself goes into a crash—and this crashing affects the decisions of those in the market to sell more, thus creating a downward spiral. This is why stock market bubbles and crashes and similar phenomena seem to be so extreme and so irrational: the individuals within them are causing (upward) the behavior of the market, and the market is reciprocally causing (downward) the future behavior of the individuals. When many individuals buy, a bubble forms (out of their “irrational exuberance”); when a few begin to sell, they can quickly form a reinforcing loop that affects the behavior of others who also start to sell, and the market quickly crashes.
同樣地，整體——如股票市場或魚群——可以對其內部的部分產生向下的因果影響。當股票市場中的個人都開始迅速拋售時，市場本身就會崩盤，而這種崩盤又影響市場中其他人的決策，使他們進一步拋售，從而形成一個向下的螺旋。這就是為什麼股票市場的泡沫和崩盤以及類似現象看起來如此極端和不理性：市場中的個人正在（向上）影響市場的行為，而市場又反過來（向下）影響個人的未來行為。當許多人買入時，泡沫形成（源於他們的“非理性繁榮”）；當少數人開始拋售時，他們可以迅速形成一個增強的循環，影響其他人也開始拋售，市場迅速崩盤。

This downward causality helps explain otherwise baffling realities of how systems behave. It also highlights why reductionist thinking is insufficient to explain how complex systems work. By taking apart a complex system, you can reveal the upward causality—how the parts come together to create the whole. But such a reductionist approach will not yield the contextual downward causality that occurs only when the entire system is in operation and as a result affects its lower-level parts.
這種向下因果關係有助於解釋系統行為中那些令人困惑的現象。它也突顯了為何還原主義思維不足以解釋複雜系統的運作。通過拆解一個複雜系統，你可以揭示向上因果關係——即各部分如何組合成整體。但這種還原主義的方法無法產生只有在整個系統運行時才會發生的上下文向下因果關係，這種關係會影響其較低層次的部分。

Hierarchy and Levels of Organization
層次與組織階層

Several times thus far, phrases like “levels of organization” have appeared here without definition. We have talked about these levels and upward and downward causation without really defining what these terms mean. As with emergence, levels of organization can be a difficult concept to articulate, though you may already have an intuitive idea about what this is.
到目前為止，像「組織階層」這樣的詞語已經多次出現，但尚未給出明確的定義。我們討論了這些層次以及向上和向下的因果關係，但並未真正定義這些術語的含義。與「涌現」一樣，組織階層是一個難以表達的概念，儘管你可能已經對此有直觀的理解。

The fundamental idea is, again, that a functioning metastable system creates a new thing. This thing’s properties (its state, boundaries, and behaviors) are typically emergent from the mutual, looping interactions of the parts within it. Once such a new thing has emerged as the conglomeration of underlying parts, we describe it as being at a “higher level” of organization. This is easily recognized in the precedence from quark to proton to atom to molecule and on upward to planet and solar system, galaxy, and further on still. At each level of metastability, new recognizable, persistent things emerge. Likewise, as we dive down from our everyday world to the level of the molecule, atom, proton, and quark, we are able to recognize “lower level” systems. Each contains and emerges from the systems within it, and each (with those at the same level) creates the system at the next higher level.
基本的概念是，一個運作中的亞穩定系統會創造出一個新事物。這個事物的特性（其狀態、邊界和行為）通常是從其內部各部分的相互循環互動中湧現出來的。一旦這樣的新事物作為底層部分的聚合體出現，我們就將其描述為處於一個「更高層次」的組織中。這在從夸克到質子、原子、分子，然後向上到行星和太陽系、星系，甚至更遠的過程中很容易被識別。在每一個亞穩定的層次上，都會出現新的可識別的、持久的事物。同樣地，當我們從日常世界深入到分子、原子、質子和夸克的層次時，我們能夠識別出「較低層次」的系統。每一個系統都包含並從其內部的系統中湧現出來，而每一個系統（與同層次的系統一起）創造出下一個更高層次的系統。

As Alexander et al. (1977) were quoted earlier as saying, “Each pattern [or system] can exist in the world, only to the extent that it is supported by other patterns: the larger patterns in which it is embedded, the patterns of the same size that surround it, and the smaller patterns which are embedded in it.” Every system is a part of another higher-level system, interacts with those around it, and contains lower-level systems within it. (See Figure 2.24 for an abstracted version of this.) As mentioned earlier, in the real world, these levels go down at least to the level of quarks—and we have no idea where the highest integrative level of organization is. In games, fortunately, we are able to choose our levels of organization and abstraction, though as you will see, there are rewards for taking the difficult road to making them deeper rather than shallower.
正如 Alexander 等人（1977）先前所言：「每一個模式 [或系統] 只能在世界上存在，前提是它受到其他模式的支持：嵌入其中的較大模式、圍繞它的同等大小的模式，以及嵌入其中的較小模式。」每個系統都是另一個更高層次系統的一部分，與周圍的系統互動，並包含其中的較低層次系統。（參見圖 2.24 以獲得抽象版本。）如前所述，在現實世界中，這些層次至少可以下降到夸克的層次，而我們對於最高整合層次的組織位置毫無頭緒。在遊戲中，幸運的是，我們可以選擇我們的組織和抽象層次，然而如你所見，選擇艱難的道路以使其更深而非更淺是有回報的。

Like boundaries, these levels are not absolute or externally defined. They are an emergent property, whereby the state, behaviors, and loops of one set of parts work together to create new discernible properties. In this way, the system at one level becomes a part of a system at a higher level of organization.
如同邊界，這些層次並非絕對或外部定義的。它們是一種湧現的特性，其中一組部分的狀態、行為和循環共同作用以創造出新的可辨識特性。如此一來，一個層次的系統成為更高層次組織系統的一部分。

At each level, the system also displays persistence and adaptability. The property of persistence can be thought of as a boundary through time. That is, systems that persist are self-reinforcing within their own boundaries across time. A key part of this persistence is that the system is able to adapt, at least to some degree, to new signals or inputs from a changing environment. In living systems, this persistence and adaptability is called homeostasis—the ability to maintain internal conditions (within the organism’s boundary) within a narrow range despite significant changes outside.
在每一個層級，系統也展現了持續性和適應性。持續性的特性可以被視為時間上的邊界。也就是說，持續存在的系統在其自身的邊界內隨著時間自我強化。這種持續性的關鍵部分在於系統能夠在某種程度上適應來自變化環境的新信號或輸入。在生命系統中，這種持續性和適應性被稱為恆定性——即使外界發生重大變化，仍能在狹窄範圍內維持內部條件（在生物體的邊界內）的能力。

Structural Coupling

This hierarchical organization—parts within parts—is another hallmark of organized systems. It also leads to what Maturana (1975) called structural coupling. This is what occurs when “recurrent interactions [lead] to the structural congruence between two (or more) systems” (Maturana and Varela 1987). These systems are parts within a higher-level system that interact closely together. Each benefits from molding itself to the other in one way or another. In so doing, they alter each other and create a new, tightly integrated higher-level system. Examples of this include a horse and rider, car and driver, and many co-evolutionary relationships, as when an insect and flower over time affect each other as part of their mutual relationship.
這種層級組織——部分中的部分——是有組織系統的另一個特徵。這也導致了 Maturana（1975）所稱的結構耦合。這是指當「反覆的互動導致兩個（或多個）系統之間的結構一致性」（Maturana 和 Varela 1987）。這些系統是更高層次系統中的部分，彼此緊密互動。每個系統都從某種方式上塑造自己以適應另一個系統，從而受益。在這樣做的過程中，它們彼此改變，並創造出一個新的、緊密整合的高層次系統。這方面的例子包括馬與騎士、汽車與駕駛員，以及許多共同進化的關係，例如昆蟲與花朵隨著時間的推移在相互關係中影響彼此。

A game and player also form a structurally coupled relationship. If the game is systemically designed, it will have defined a sufficiently broad and diverse state-space (a consequence of its “second-order” design, as described in Chapter 3) that it can adapt to the player as the player adapts to it. As you will read in Chapter 4, “Interactivity and Fun,” this structural coupling is important for building engagement and fun in a game: the close mutual interactions between a game and player can make it difficult to break out of the interconnecting loops.
遊戲與玩家也形成了一種結構耦合的關係。如果遊戲是系統性設計的，它將定義一個足夠廣泛且多樣的狀態空間（這是其「二階」設計的結果，如第三章所述），使其能夠隨著玩家的適應而進行調整。正如你將在第四章「互動性與樂趣」中讀到的，這種結構耦合對於建立遊戲的投入感和樂趣至關重要：遊戲與玩家之間緊密的相互作用可能使人難以脫離這些相互連結的循環。

Systemic Depth and Elegance
系統的深度與優雅

Having discussed emergence, hierarchy, and levels of organization, we can now turn to what are otherwise difficult areas to define and discuss: the concepts of depth and elegance in systems and in games in particular.
在討論了湧現、層級和組織層次之後，我們現在可以轉向那些通常難以定義和討論的領域：系統，特別是遊戲中的深度與優雅概念。

A system can be said to have depth when its parts exist at multiple levels of organization—when they are themselves subsystems composed of lower-level parts interacting together. When considering such systems, you can think of them as unified things at each level and then change your perspective to go up or down a level, just as you did in our journey down to quarks and up to drops of water. These changes in perspective may at times become dizzying, but there is something so universally compelling about this experience that we often see it as harmonious and beautiful. This is why the quality of self-similarity seen in fractals, where each part resembles the whole but in miniature (see Figure 2.25), is so captivating: it is the visual manifestation of systemic depth.
一個系統可以被認為具有深度，當其部分存在於多層次的組織中時——當它們本身是由較低層次的部分組成的子系統，並相互作用時。在考慮這樣的系統時，你可以在每個層次上將它們視為統一的整體，然後改變你的視角，向上或向下移動一個層次，就像我們在探索夸克到水滴的旅程中所做的那樣。這些視角的變化有時可能會讓人感到眩暈，但這種經驗中有某種普遍吸引人的特質，使我們常常將其視為和諧而美麗。這就是為什麼在分形中看到的自相似性質如此引人入勝的原因：每個部分都像整體的縮影（見圖 2.25），這是系統深度的視覺表現。

Whether in real-world systems or in games, it can be difficult to build a mental model of systems-within-systems. Once you are able to construct a model that parallels this hierarchy, it is fascinating to comprehend the system from different perspectives at different levels, looking up and down the organizational hierarchy in your mind. The same is true in various forms of art, literature, and so on, where a thoughtful compliment is to say that something “works on so many levels.” This is both an acknowledgement and a reflection of our own internal model-building process, as well as our fascination in seeing a system from different perspectives.
無論是在現實世界的系統中還是在遊戲中，構建系統中系統的心智模型都可能是困難的。一旦你能夠構建一個與這種層級結構平行的模型，從不同層次以不同視角理解系統就變得引人入勝，在心中上下觀察組織層級。在各種形式的藝術、文學等中也是如此，當我們說某件事物「在多個層面上運作良好」時，這是一種深思熟慮的讚美。這既是對我們自身內部模型構建過程的承認，也是對從不同視角觀察系統的著迷。

Games with Depth

Designing game systems that each contain subsystems with their own subspaces that can be explored by the player provides multiple benefits. The depth is itself attractive, if for no other reason than it enables players to build multilevel systemic mental models: the player is rewarded for learning each new subsystem over time, much like opening a present to find another present inside. In addition, a game with depth in its systems creates enormous variability for the player to explore as gameplay, since the designer has set up a wide space for the game using systemic design rather than creating a narrow path of custom content that never changes.
設計遊戲系統時，每個系統包含各自的子系統，並擁有可供玩家探索的子空間，這樣的設計帶來多重好處。其深度本身就具有吸引力，因為它讓玩家能夠建立多層次的系統性心智模型：玩家在學習每個新子系統的過程中獲得獎勵，就像打開一個禮物，裡面還有另一個禮物。此外，擁有深度系統的遊戲為玩家創造了巨大的變化性，讓玩家在遊戲過程中可以探索，因為設計師利用系統性設計創造了一個廣闊的遊戲空間，而不是設計一條永遠不變的狹窄自訂內容路徑。

In some cases, deep games may have few rules. The spare but systemic design enables players to more quickly grasp the structure and see it from multiple levels of perspective—though this is still cognitively taxing for most of us!
在某些情況下，深度遊戲可能只有少數規則。這種簡約但系統化的設計使玩家能更快地掌握結構，並從多個層次的視角來看待它——儘管對大多數人來說，這仍然是認知上的挑戰！

A prime example of this is the ancient game Go, shown in Figure 2.26. The game has fascinated people for thousands of years with its simplicity, depth, and subtlety. Go consists only of a square board, typically marked by 19x19 intersecting lines, and a collection of black and white pieces, each color played by one player. Players take turns placing a stone of their color on an empty spot on the board. Each player attempts to surround and capture the other player’s pieces. The game ends when the board is filled or both players have passed in succession, and the player with the most territory on the board wins. With that very brief description, you have all the state, boundaries, and behavior of the system: you know enough to play the game and see its many levels of emergence. There is of course a great deal more to the game—lives have been spent and books written on comprehending the game’s decision-space more fully—but that is how deep, emergent games work.
這方面的一個典型例子就是古老的圍棋，如圖 2.26 所示。這款遊戲以其簡單、深度和微妙吸引了數千年來的人們。圍棋僅由一個方形棋盤組成，通常標有 19x19 的交叉線，以及一組黑白棋子，每種顏色由一名玩家使用。玩家輪流將自己顏色的棋子放置在棋盤上的空位上。每位玩家試圖包圍並吃掉對方的棋子。當棋盤被填滿或雙方玩家連續棄子時，遊戲結束，擁有最多地盤的玩家獲勝。通過這個非常簡短的描述，你已經了解了系統的所有狀態、邊界和行為：你知道足夠的資訊來玩這個遊戲，並看到其多層次的湧現。當然，遊戲還有更多的內容——有人花費一生時間並撰寫書籍來更全面地理解遊戲的決策空間——但這就是深度湧現遊戲的運作方式。

Such games are often described as “easy to learn, difficult to master” (known as Bushnell’s Law, after Atari founder Nolan Bushnell [Bogost 2009]). Such games present the player with only a few states and rules to start, each of which opens up into hierarchical subsystems to reveal more detailed inner workings as the player learns the game. The depth of the internal systems and their multiple perspective requires great skill to comprehend.
這類遊戲常被形容為「易學難精」（被稱為布希內爾法則，以 Atari 創辦人 Nolan Bushnell 命名 [Bogost 2009]）。這類遊戲在開始時只向玩家呈現少數的狀態和規則，每一個都會開啟層次分明的子系統，隨著玩家學習遊戲，揭示出更詳細的內部運作。內部系統的深度及其多重視角需要極高的技巧才能理解。

Finally, elegance is the quality we see in games where several characteristics of the game and the gameplay experience are brought together:
最後，優雅是我們在遊戲中看到的一種品質，這種品質將遊戲的多個特徵和遊戲體驗結合在一起：

There is a metastable rather than static uniformity to the entire system that is cognitively and emotionally satisfying. The game changes each time it is played but retains an overarching familiarity in the experience it provides. The player is able to continue to find satisfaction in exploring the ever-changing gameplay space through repeat plays without feeling that the theme or the overall experience itself changes.
整個系統呈現出一種亞穩態而非靜態的均勻性，這在認知和情感上令人滿意。每次遊戲時都會有所變化，但仍保留其提供的整體熟悉感。玩家能夠在反覆遊玩中探索不斷變化的遊戲空間，並持續獲得滿足感，而不會覺得主題或整體體驗本身發生了變化。

The high-level systems are simply defined but have great hierarchical depth. As a result, the player is able to gradually discover this depth, building a mental model of the game along the way. This multilevel organization gives rise to complex behaviors and gameplay that further inform the player and reveal the game’s systems and theme.
高層次的系統定義簡單，但具有很大的層次深度。因此，玩家能夠逐漸發現這種深度，並在此過程中建立遊戲的心理模型。這種多層次的組織結構引發了複雜的行為和遊戲玩法，進一步啟發玩家並揭示遊戲的系統和主題。

The deep systems exhibit a degree of symmetry or self-similarity: each lower-level system reflects the overall structure of the system of which it is a part (as shown in loop form in Figure 2.24 and in plant form in the broccoli in Figure 2.25). The subsystems need not be exactly the same as those above them, as long as they are similar enough that higher-level systems provide scaffolding for learning more detailed ones. This creates an unobtrusive, highly contextual aide to the player’s ability to easily increase comprehension and build a mental model of the game. As players explore the game more deeply, they have the positive feeling that they almost already know what they are seeing for the first time.
深層系統展現出某種程度的對稱性或自相似性：每個較低層次的系統反映出其所屬系統的整體結構（如圖 2.24 中的迴圈形式和圖 2.25 中的花椰菜形式所示）。子系統不必與其上層系統完全相同，只要它們足夠相似，使得高層系統能夠為學習更詳細的系統提供支架。這為玩家提供了一種不顯眼且高度情境化的輔助，讓他們能夠輕鬆地增加理解並建立遊戲的心智模型。當玩家更深入地探索遊戲時，他們會有一種積極的感覺，彷彿他們幾乎已經知道自己第一次看到的事物。

There are few “loose ends” in the form of rules exceptions or special cases. Such exceptions ruin the mental symmetry of the self-similar hierarchical systems and increase the player’s mental load—requiring the player to focus on remembering rules and how to play the game rather than just playing it.
在規則例外或特殊情況的形式上，幾乎沒有「鬆散的結尾」。這些例外會破壞自相似層次系統的心理對稱性，並增加玩家的心理負擔——要求玩家專注於記住規則和如何玩遊戲，而不是僅僅享受遊戲本身。

Finally, as players have thoroughly learned the hierarchical systems of the game to the point that they can reflect on them (an instance of metacognition), they are able to perceive and appreciate the qualities of depth and symmetry in the game’s dynamic structures. At this point, the game is enjoyable and satisfying not only while it’s being played but even when the players are musing on its rules and systems.
最終，當玩家已經徹底掌握遊戲的層級系統，甚至能夠反思這些系統（這是一種元認知的表現）時，他們便能夠感知並欣賞遊戲動態結構中的深度和對稱性。在這個階段，遊戲不僅在進行時令人愉悅和滿足，即使玩家在思索其規則和系統時，也同樣能夠享受其中的樂趣。

Elegance of this degree is rarely attained. It requires a masterful comprehension of the game systems by the designer, who must apprehend them all at once, as if they were laid out, while at the same time seeing them in linear form as the players experience them.
如此程度的優雅實屬罕見。這需要設計師對遊戲系統有著精湛的理解，必須能夠同時掌握所有系統，彷彿它們已經展現在眼前，同時又能以玩家的體驗方式線性地看待它們。

While this level of game design mastery is a difficult apex to attain, we will revisit emergence, depth, and elegance as desirable targets of systemic design throughout this book.
雖然達到這種遊戲設計的精通境界是困難的巔峰，但在本書中，我們將不斷重溫作為系統設計理想目標的湧現、深度和優雅。

Wholes

Systems form greater wholes out of constituent, interacting parts. The whole is itself a part in the next-highest level of systemic organization.
系統由相互作用的組成部分構成更大的整體。整體本身又是下一層系統組織中的一部分。

When designing a game, the ultimate whole that emerges is not just the game itself. Instead, it is the system that is composed of the game and the player. This game+player system is the game designer’s true goal; the game itself is just the means to get there. The game as experienced by the player and the player acting within the game create the overall system. When we discuss the systemic architecture in terms of designing a game in Chapter 3 and Chapter 6, “Designing the Whole Experience,” we will return to this thought. You will look then at the importance of interactivity, depth, and systemic elegance in enabling the player to create a truly meaningful experience.
在設計遊戲時，最終呈現的整體不僅僅是遊戲本身。相反地，它是由遊戲和玩家組成的系統。這個遊戲+玩家系統才是遊戲設計師的真正目標；遊戲本身只是達成目標的手段。玩家所體驗的遊戲以及玩家在遊戲中的行為共同創造了整體系統。在第三章和第六章中討論遊戲設計的系統架構時，我們將回到這個想法，這兩章的標題是「設計整體體驗」。屆時，你將會看到互動性、深度和系統優雅在使玩家創造真正有意義的體驗中所扮演的重要角色。

Summary

In keeping with the hierarchical nature of systems, having gone through all the parts and interactions within a system, we can now return to the initial description given at the start of the chapter.
遵循系統的層次性特質，經過系統內所有部分和互動的探討後，我們現在可以回到本章開頭所給出的初步描述。

A system is the integrated whole that arises out of independent, interacting parts. Those parts have their own internal state, boundaries, and behaviors by which they mutually affect each other. This whole persists over time, adapts to external conditions, and has its own coordinated behaviors that emerge from the interactions of its parts. The system both contains lower-level systems within it and is itself part of a higher-level system.
一個系統是由獨立且相互作用的部分組成的整體。這些部分有其自身的內部狀態、邊界和行為，並通過這些特性相互影響。這個整體在時間中持續存在，適應外部條件，並從其部分的互動中產生自身協調的行為。系統既包含其內部的低階系統，也本身是高階系統的一部分。

Note that while the definition given at the start of the chapter is similar to this one, the first was more bottom-up, starting with parts and going to systems, while this one is more top-down, starting with the systems first. These two views are equivalent. It is important to be able to switch perspectives on systems in this way—both as part of comprehending and “thinking in systems” and as part of the process of game design. Game designers have a particular need to be able to see their games bottom-up, top-down, or anything in between. This is a particular challenge that is best met by understanding games as systems and game design as system design.
注意，雖然本章開頭給出的定義與這個相似，但前者是自下而上的，從部分開始到系統，而這個則是自上而下的，從系統開始。這兩種觀點是等價的。能夠在系統上切換視角是很重要的——這既是理解和“系統思考”的一部分，也是遊戲設計過程的一部分。遊戲設計師特別需要能夠自下而上、自上而下或介於兩者之間地看待他們的遊戲。這是一個特別的挑戰，最好通過將遊戲理解為系統，將遊戲設計理解為系統設計來應對。

Postscript: Thinking About Things
附錄：思考事物

To return briefly to the philosophical discussion of things, identity, and “thingness,” you can now consider the earlier discussion in light of the extended definition of systems and see where this takes you. You should now be able to see atoms and molecules as both systems with internal structure and as unified things. This also means that you can understand more fully systems as things that we might not otherwise see in that light.
回到對事物、身份和「物性」的哲學討論，現在你可以根據系統的擴展定義來重新考慮之前的討論，看看這會帶你到哪裡。你現在應該能夠將原子和分子視為既有內部結構的系統，又是統一的事物。這也意味著你可以更全面地理解那些我們可能不會以這種方式看待的系統作為事物。

For example, our brains are systems, and it appears that our minds emerge as unified things from their functioning. It may be that our understanding of how new things arise from relationships provides the answer to the contemplation of the deceptively simple ancient Buddhist “Diamond Sutra” koan: “Out of nowhere the mind comes forth” (Seong 2000). As with D. H. Lawrence’s poetic musing about water, it turns out there is no “third thing,” no identifiable single place from which water becomes wet, or from which the mind comes—but these are also not from “nowhere.” Like flocks of birds, the fractal patterns in plants, hurricanes, or enormous structures built by unguided termites, complex systems like the mind emerge from the innumerable relationships between the constituent parts to become something more than—and entirely different from—these underlying components.
例如，我們的大腦是系統，而我們的心智似乎是從其運作中統一地浮現出來的。或許，我們對於新事物如何從關係中產生的理解，提供了對古老而看似簡單的佛教《金剛經》公案的思考答案：「心從何處來？」（Seong 2000）。正如 D. H. Lawrence 對水的詩意沉思，事實證明並不存在「第三者」，沒有一個可識別的單一地方是水變得濕潤的來源，或是心智的來源——但這些也不是「無中生有」。如同鳥群、植物中的分形圖案、颶風，或是由無指導的白蟻建造的巨大結構，像心智這樣的複雜系統是從組成部分之間無數的關係中浮現出來，成為某種超越且完全不同於這些基礎組成部分的東西。

So too do corporations and cultures arise from their component parts. No one at my university was there 100 years ago, and no one who is there today is likely to be there in another 100 years: and yet the university itself, as a thing, has persisted and adapted; it was there and continues on beyond any of us as individuals. It is a metastable system with its own very real identity. The same is true of a family, a conversation, or an economy. Some may persist longer than others, but each is the result of a process of emergence, of the complex interactions and relationships between lower-level parts creating new properties not found in them.
企業和文化也是由其組成部分產生的。我的大學裡沒有人在 100 年前就存在，而今天在那裡的人也不太可能在 100 年後還在那裡：然而，大學本身作為一個實體，已經持續並適應了；它存在於那裡，並超越我們每一個個體繼續存在。這是一個具有自身真實身份的亞穩定系統。家庭、對話或經濟也是如此。有些可能比其他的持續更久，但每一個都是一個湧現過程的結果，是低層次部分之間的複雜互動和關係創造出它們所沒有的新特性。

This leads to a conclusion that we have touched on already. It’s one that initially sounds at best metaphorical yet which is now supported by the examination of systems that we have made: atoms, ships, flocks, cultures, universities, and even marriages, friendships, conversations, minds, and tornadoes.… These are all not only systems; they are, in every sense that matters, things. To look at just two examples, there are metastable structures that emerge over time from the relationship I have with my spouse and that many thousands of us have with our universities that are in every way identical to properties of persistence, identity, and integrity—the thingness—we observed from the interactions of virtual quarks in forming protons, protons and electrons in forming atoms, hydrogen and oxygen in forming water. Recall that at its root, even what we think of as solid matter is itself elusive in its nature. A marriage may not have mass or shape, but it is nonetheless a real, non-metaphorical thing every bit as much as a desk, a computer, or a drop of water.
這引出了我們已經觸及的結論。這個結論乍聽之下似乎只是比喻，但經過我們對系統的檢驗後，卻得到了支持：原子、船隻、鳥群、文化、大學，甚至婚姻、友誼、對話、心靈和龍捲風……這些不僅僅是系統；在每一個重要的意義上，它們都是事物。舉兩個例子來看，我與配偶的關係中，以及我們許多人與大學的關係中，隨著時間的推移而出現的亞穩定結構，在各方面都與我們從虛擬夸克形成質子、質子和電子形成原子、氫和氧形成水的交互作用中觀察到的持久性、身份和完整性——事物性——的特性完全相同。請記住，從根本上說，即使是我們認為的固體物質，其本質也是難以捉摸的。婚姻可能沒有質量或形狀，但它仍然是一個真實的、非比喻的事物，與桌子、電腦或一滴水一樣真實。

The truly curious aspect of this is that, stuck as we are being where we are in the systemic organizational hierarchy in which we are all parts, we often have such difficulty perceiving the emergent properties of the systems, the things, of which we are part: our culture, economy, company, or family—much less the emergence in a biome, in our planet’s biosphere, or in the unimaginably vast cosmological structures we now know exist. We seem, at least for now, to be poor at recognizing and accounting for systemic effects, even though these are for us like water for fish. Hopefully, this is not a limitation of our species but a skill we can learn. A systemic view of games and game design can help us create more engaging, effective games; hopefully in so doing we also come to a deeper, fuller understanding of the systems that are all around us as well.
真正令人好奇的是，身處於我們所屬的系統性組織層級中，我們常常難以察覺我們所屬系統的湧現特性：無論是文化、經濟、公司或家庭，更遑論生物群系、地球的生物圈，或是我們現在知道存在的無比龐大的宇宙結構。我們似乎，至少目前為止，對於辨識和考量系統效應的能力相當不足，儘管這些對我們而言就如同水之於魚。希望這不是我們物種的限制，而是一種我們可以學習的技能。對遊戲和遊戲設計的系統性觀點可以幫助我們創造出更具吸引力和效果的遊戲；希望在此過程中，我們也能對周圍的系統有更深刻、更全面的理解。

 

1. The closest I have seen is “This sentence is a system.” The interactions between letters and words creates emergent organized meaning in a brief statement. Thanks to Michael Chabin for this concise definition.
我所見過最接近的例子是「這句話是一個系統。」字母與單詞之間的互動在簡短的陳述中創造出新興的有序意義。感謝 Michael Chabin 提供這個簡潔的定義。

2. In some cases, like that of a cell membrane, there literally is a skin that forms the boundary between inside and outside. Even here, though, there are specialized channels that allow the densely interconnected inside to bring things in or send things out through the boundary.
在某些情況下，例如細胞膜，確實存在一層皮膚般的結構，形成內外之間的界限。然而，即便如此，仍然有專門的通道，允許內部緊密相連的部分通過邊界進行物質的進出。

3. This is mostly true. Fruits in a bowl actually do interact on a long enough time scale as they ripen and spoil, but for most purposes, we can look at each piece of fruit as a separate thing that doesn’t interact with the other fruits around it.
這大致上是正確的。碗中的水果在足夠長的時間尺度上確實會相互影響，因為它們會成熟和腐壞，但在大多數情況下，我們可以將每一顆水果視為一個獨立的個體，不會與周圍的其他水果互動。

4. I am sorry to say that this is a pattern I have observed many times in the software industry.
我很遺憾地說，這是我在軟體行業中多次觀察到的模式。

5. A phrase used by Federal Reserve Chair Alan Greenspan (1996) to describe a similar situation in the markets of his day.
5. 美國聯邦儲備理事會主席艾倫·葛林斯潘（1996 年）用來描述當時市場類似情況的一句話。