论文标题
关于科学中数学模型的多样性和相似性
On the diversity and similarity of mathematical models in science
论文作者
论文摘要
在本文中，从多个角度开始尝试启发科学中数学模型的概念。特别是，这表明数学模型的引入方式不同，并且在不同的科学领域中使用不同。在本文中，在统计中使用模型作为基础，但与其他几个领域的链接相关。这里有两个特定的链接在这里进行了详细描述：首先，连接到化学分析最小二乘算法的链接，该链接现在已被推广到更复杂的信封模型。其次，众所周知，统计数据在很大程度上取决于做出决策，在某些情况下，它也可能与进行测量的过程有关。引入了这两个活动的数学模型，该模型与观察者的思想有关。该模型进一步采用，并在量子理论基础的新建议中证明很重要。从这个角度来看，量子力学在一些详细的范围内进行了描述。这里的讨论与作者最近发表的文章中的一本书和最近发表的文章相结合。
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different areas of science. In the present article the use of models in statistics is taken as a basis, but links are given to several other areas. Two particular such links are described in some detail here: First the link connected to the chemometrical Partial Least Squares algorithm, a link that now has been generalized to the more sophisticated envelope model. Secondly, statistics, as is well known, relies heavily on making decisions, and it may also in certain cases be connected to a process of taking measurements. A mathematical model for these two activities, connected to the mind of an observer, is introduced. This model is taken further, and shown to be important in a new proposal for a foundation of quantum theory. Quantum mechanics, as seen from this point of view, is described in some detail. The discussion here is close to the discussion in a recent book and in recently published articles by the author.
