📚 The Process of Globalisation: A Mathematical Perspective | 全球化进程：数学视角
Globalisation is often described qualitatively by economists and geographers, but its measurable features - trade growth, technology diffusion, supply chain connectivity - are inherently quantitative. This article explores how A-level mathematical tools, including exponential functions, differential equations, network theory, and statistical inference, can model the process of globalisation.
全球化通常由经济学家和地理学家进行定性描述，但其可量化特征——贸易增长、技术扩散、供应链连通性——本质上是定量的。本文探讨A-level数学工具，包括指数函数、微分方程、网络理论和统计推断，如何为全球化进程建模。
1. Defining Globalisation Indicators | 定义全球化指标
growth rate is r = [x(t+1) - x(t)] / x(t). This simple ratio underpins all dynamic models.
全球化不是单一变量，而是一组可测量指标：贸易开放度、外国直接投资（FDI）、移民存量以及互联网普及率。设 x(t) 为指标在时间 t 的值。年增长率为 r = [x(t+1) - x(t)] / x(t)。这个简单比率是所有动态模型的基础。
r = (x(t+1) - x(t)) / x(t)
2. Exponential Growth in Trade and Capital Flows | 贸易与资本流动的指数增长
If an indicator grows at a constant rate r, the discrete model is y = a(1+r)t. The continuous version is y = a ekt ere k is the continuous growth rate. Doubling time is ln2/k. World exports grew from about $2.0 trillion in 1980 to $19.0 trillion in 2019, giving k = (1/39)ln(19/2) ≈ 0.058, i.e. 5.8% continuous annual growth.
如果指标以恒定速率 r 增长，离散模型为 y = a(1+r)t。连续版本为 y = a ekt，其中 k 是连续增长率。翻倍时间为 ln2/k。世界出口从1980年约2.0万亿美元增长到2019年19.0万亿美元，得 k = (1/39)ln(19/2) ≈ 0.058，即5.8%的连续年增长率。
y = a ekt, tdouble = ln2 / k
3. The Logistic Model of Market Integration | 市场一体化的逻辑斯蒂模型
ogistic differential equation dP/dt = rP(1 - P/K) has solution P = K / (1 + ((K - P₀)/P₀)e-rt). Here K is the carrying capacity, for example the maximum proportion of firms using container shipping.
全球标准（如集装箱航运、英语商务语言）的采用呈S形曲线，因为早期采用缓慢，随后加速，最后饱和。逻辑斯蒂微分方程 dP/dt = rP(1 - P/K) 的解为 P = K / (1 + ((K - P₀)/P₀)e-rt)。其中 K 是承载能力，例如使用集装箱航运的最大企业比例。
dP/dt = rP(1 - P/K), P = K / (1 + ((K - P₀)/P₀)e-rt)
4. Differential Equations for Diffusion of Technology | 技术扩散的微分方程
potential adopters. This is a logistic equation with solution N = M / (1 + ((M - N₀)/N₀)e-βt). The parameter β measures the intensity of global interaction.
技术传播的一个简单扩散模型为 dN/dt = β N (M - N)/M，其中 N 是已采用技术的国家数，M 是潜在采用者总数。这也是一个逻辑斯蒂方程，解为 N = M / (1 + ((M - N₀)/N₀)e-βt)。参数 β 衡量全球互动强度。
dN/dt = β N (M - N)/M
5. Network Models of Global Connections | 全球连接的网络模型
Global trade and airline routes form a graph. Nodes are countries, edges are direct routes. The degree of a node counts direct partners. The shortest path length between two nodes measures how "globalised" a connection is. In a random graph, average path length is about ln n / ln k, where n is number of nodes and k is average degree.
全球贸易和航空路线构成一个图。节点是国家，边是直接路线。节点的度计算直接伙伴数量。两个节点之间的最短路径长度衡量连接的“全球化”程度。在随机图中，平均路径长度约为 ln n / ln k，其中 n 是节点数，k 是平均度。
- Graph = set of nodes and edges | 图 = 节点和边的集合
- Degree = number of direct connections | 度 = 直接连接数
- Shortest path = minimum number of edges between two nodes | 最短路径 = 两节点之间的最少边数
6. Measuring Inequality: Gini Coefficient and Lorenz Curve | 衡量不平等：基尼系数与洛伦兹曲线
nd curve, and B is area under curve, Gini = A/(A+B). A Gini of 0 means perfect equality; 1 means all income held by one person.
全球化改变收入分配。洛伦兹曲线绘制累计收入份额对累计人口份额。基尼系数是平等线与洛伦兹曲线之间的面积除以平等线下的总面积。若 A 是线与曲线之间的面积，B 是曲线下的面积，则 Gini = A/(A+B)。基尼系数为0表示完全平等；1表示所有收入归一人所有。
Gini = A / (A + B)
7. Correlation and Causation in Globalisation Data | 全球化数据中的相关与因果
easures linear association between two indicators such as FDI and GDP growth. r = Σ(xᵢ - x̄)(yᵢ - ȳ) / √[Σ(xᵢ - x̄)² Σ(yᵢ - ȳ)²]. A high |r| rnet penetration and trade growth may both rise with time, producing spurious correlation.
皮尔逊相关系数衡量两个指标（如FDI与GDP增长）之间的线性关联。r = Σ(xᵢ - x̄)(yᵢ -
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