Complexity versus Complex Systems: A New Approach to Scientific Discovery

Abstract

Extraction of quantitative features from observations via measuring devices M means that the words of science are coded as numbers, and the syntaxis is a set of mathematical rules, thus all consequences should be worked in a purely deductive way. This characteristic of science displays two orders of drawbacks, namely, undecidability of deductive procedures, and intractability of complex situations. The way out of such a crisis consists in a frequent readjustment of M suggested by the observed events. This adaptive strategy differs from the adaptivity of a learning machine, which — inputted by a data stream — readjusts itself over a class of theoretical explanations in order to select the optimal choice. On the contrary, the scientist not only modifies the explanations for a fixed data set, but also explores different data sets by modifying M, that is, by selecting a different point of view. This M-adjustment is a pre-linguistic operation, not expressible by a formal language. Hence, the scientific endeavor can not be reduced to a machine task.