Department of Chemical Engineering, Center for the Management of Systemic Risk, Columbia University , New York, New York 10027, United States.
Langmuir. 2017 Oct 24;33(42):11703-11718. doi: 10.1021/acs.langmuir.7b02166. Epub 2017 Aug 28.
The central scientific challenge of the 21st century is developing a mathematical theory of emergence that can explain and predict phenomena such as consciousness and self-awareness. The most successful research program of the 20th century, reductionism, which goes from the whole to parts, seems unable to address this challenge. This is because addressing this challenge inherently requires an opposite approach, going from parts to the whole. In addition, reductionism, by the very nature of its inquiry, typically does not concern itself with teleology or purposeful behavior. Modeling emergence, in contrast, requires the addressing of teleology. Together, these two requirements present a formidable challenge in developing a successful mathematical theory of emergence. In this article, I describe a new theory of emergence, called statistical teleodynamics, that addresses certain aspects of the general problem. Statistical teleodynamics is a mathematical framework that unifies three seemingly disparate domains-purpose-free entities in statistical mechanics, human engineered teleological systems in systems engineering, and nature-evolved teleological systems in biology and sociology-within the same conceptual formalism. This theory rests on several key conceptual insights, the most important one being the recognition that entropy mathematically models the concept of fairness in economics and philosophy and, equivalently, the concept of robustness in systems engineering. These insights help prove that the fairest inequality of income is a log-normal distribution, which will emerge naturally at equilibrium in an ideal free market society. Similarly, the theory predicts the emergence of the three classes of network organization-exponential, scale-free, and Poisson-seen widely in a variety of domains. Statistical teleodynamics is the natural generalization of statistical thermodynamics, the most successful parts-to-whole systems theory to date, but this generalization is only a modest step toward a more comprehensive mathematical theory of emergence.
21 世纪的核心科学挑战是发展一种能够解释和预测意识和自我意识等现象的涌现的数学理论。20 世纪最成功的研究纲领还原论，从整体到部分，似乎无法应对这一挑战。这是因为解决这个挑战本质上需要一种相反的方法，从部分到整体。此外，还原论，由于其探究的本质，通常不关心目的论或有目的的行为。相比之下，涌现模型需要解决目的论。这两个要求共同给发展成功的涌现数学理论带来了巨大的挑战。在本文中，我描述了一种新的涌现理论，称为统计动力学生物学，它解决了一般问题的某些方面。统计动力学生物学是一个数学框架，它将统计力学中无目的的实体、系统工程中的人为目的论系统以及生物学和社会学中的自然进化的目的论系统统一在同一个概念形式中。该理论基于几个关键的概念见解，最重要的是认识到熵在经济学和哲学中数学模型化了公平的概念，并且在系统工程中等价于稳健性的概念。这些见解有助于证明收入的最公平的不平等是对数正态分布，它将在理想的自由市场社会的平衡中自然出现。同样，该理论预测了广泛存在于各种领域的三种网络组织类别的出现——指数、无标度和泊松。统计动力学生物学是统计热力学的自然推广，这是迄今为止最成功的部分到整体系统理论，但这种推广只是朝着更全面的涌现数学理论迈出的一小步。
