Kreinovich Vladik, Kosheleva Olga
Departments of Computer Science (V.K.) and Teacher Education (O.K.), University of Texas at El Paso, El Paso, TX 79968, USA.
Entropy (Basel). 2021 Apr 22;23(5):501. doi: 10.3390/e23050501.
As a system becomes more complex, at first, its description and analysis becomes more complicated. However, a further increase in the system's complexity often makes this analysis simpler. A classical example is Central Limit Theorem: when we have a few independent sources of uncertainty, the resulting uncertainty is very difficult to describe, but as the number of such sources increases, the resulting distribution gets close to an easy-to-analyze normal one-and indeed, normal distributions are ubiquitous. We show that such limit theorems often make analysis of complex systems easier-i.e., lead to blessing of dimensionality phenomenon-for all the aspects of these systems: the corresponding transformation, the system's uncertainty, and the desired result of the system's analysis.
随着一个系统变得越来越复杂，起初，对它的描述和分析会变得更加复杂。然而，系统复杂性的进一步增加往往会使这种分析变得更简单。一个经典的例子是中心极限定理：当我们有几个独立的不确定性来源时，由此产生的不确定性很难描述，但随着这些来源数量的增加，所产生的分布会接近一个易于分析的正态分布——实际上，正态分布无处不在。我们表明，对于这些系统的所有方面，即相应的变换、系统的不确定性以及系统分析的期望结果，这样的极限定理通常会使对复杂系统的分析更容易——也就是说，会导致维度诅咒现象。
