Mathematical processes in the evaluation of the dangerous nature of chemicals

The present study was carried out on the basis of the question of "whether it is possible to use mathematical methods meaningfully for the evaluation of the environmental effects of chemicals." The analysis of the evaluation process showed that this may be considered as a relation between the set of test data and a target set, that of the danger classes. The very general structure of a relation considerably restricts the use of algorithms; in particular it can be shown that algorithms which would map the data directly onto the danger classes like a functional coordination are, in general, excluded. This is partly due to the highly nonhomogeneous parameter set which must be determined for evaluation purposes, and partly to the high degree of randomness or human participation in the selection of the parameters. Moreover, there was no indication whether or to what extent the parameters are interdependent, i.e., whether there are interdisciplinary regularities which could be expressed algebraically and interpreted scientifically. Questions of this kind remain components of interdisciplinary research, and they cannot be explained from a mathematical--i.e., theoretical--point of view. Considerably more empirical material needs to be available for use as the foundation for a reasonable theory.