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Bringing equations into humans sciences: a simple and robust method

机译：将方程式纳入人文科学：一种简单而强大的方法

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摘要

A system of n nonlinear coupled differential equations is constructed out of a set of n time series. The method is based on a nonlinear fit of n time derivatives, each function of n variables, which can be enhanced by the Newton-Gauss method, Verification of the validity of the method is done with data constructed using the Lotka-Volterra and Lorenz systems. The method is also applied to psychology (addictions), giving clues for therapy, an explanation of the phenomenon and classification of various types of addictions. A set of two differential equations is constructed out of data for competition between two bacteria types, and obtains a good similarity with data. Additionally, this method is applied to macroeconomics (growth prediction) and finance (exchange rates). The method also applies to n times series and n series over m regions, for at least two different moments: two differential equations are constructed, Using data for birth rate and alphabetisation, for four different years and 137 countries. Two solutions are obtained, the first giving a low birth rate and high alphabetisation, corresponding to post-industrialised countries, the second (unstable) giving a high birth rate and low alphabetisation, corresponding to peoples in a pre-industrialised status.
机译：由一组n个时间序列构成一个n个非线性耦合微分方程组。该方法基于n个时间导数的非线性拟合，其中n个变量的每个函数都可以通过牛顿-高斯方法进行增强。使用Lotka-Volterra和Lorenz系统构建的数据对方法的有效性进行验证。该方法还适用于心理学（成瘾），提供治疗线索，现象解释和各种类型的成瘾分类。从数据中构造出一组两个微分方程，用于两种细菌之间的竞争，并获得与数据的良好相似性。此外，此方法还应用于宏观经济学（增长预测）和金融（汇率）。该方法还适用于m个区域的n个时间序列和n个序列，至少持续两个不同的时刻：构造了两个微分方程，使用出生率和字母化数据，用于四个不同年份和137个国家。获得了两种解决方案，第一种解决方案对应于工业化后的国家，其出生率低且字母化程度高，第二种（不稳定）对应于工业化之前的民族，其出生率高且字母化率低。

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