Kirjahaku

Culture, in fact, also plays an important role in science which is, per se, a multitude of different cultures. The book attempts to build a bridge across three cultures: mathematical statistics, quantum theory and chemometrical methods. Of course, these three domains should not be taken as equals in any sense. But the book holds the important claim that it is possible to develop a common language which, at least to a certain extent, can create direct links and build bridges. From this point of departure, the book will be of interest to the following three types of scientists — statisticians, quantum physicists and chemometricians — and in particular, statisticians and physicists who are interested in interdisciplinary research. Written at a level that is accessible to general readers, not only the academics, the book will appeal to graduate students and mathematically educated persons of all disciplines as well as philosophers, pure and applied mathematicians, and the general public.

In the literature, quantum mechanics is founded by a very abstract set of postulates. For several reasons I propose that this set should be replaced by straightforward postulates based on the notion of conceptual variables, a notion generalizing the statisticians' parameters: In his mind, any observer/ actor in each given situation may have several conceptual variables. Some of these are accessible, can in some future be given numerical values by measurements or experiments. The notion of a maximal accessible conceptual variable is crucial. This can be motivated by an assumption to the effect that all physical variables in the actor's context have parallels in his mind. Examples are given. Under weak technical conditions, basic postulates of quantum mechanics can be shown to be implied by a postulate assuming that the actor in his mind has two related maximally accessible variables. Some specific symmetry conditions are needed. The notion of being related has a precise definition. A parallel development can be based on conceptual variables shared by a group of communicating observers.