In the contemporary world science can hardly be separated from society. Science is governed by a complex matrix of influence (Tauber, 1977) including the inner logic of science, social, economic and political pressures, aesthetic judgement and cultural values, reflecting society and societal needs. Society's relation to science is generally much more pragmatic. In addition to requesting and using the products of science, society asks such questions as: "Why conduct research? How much science can a country afford? To what extent should science be controlled?" A contemporary society tries to answer these questions in formalised, official documents called "White Papers" Often the primary focus in these documents, usually approved by Governments and Parliaments, is on research targeted to produce direct benefit to the particular country. Thus, the complex matrix of reciprocal influence between science and society is not always fully addressed. My view in this essay is to cover as much of the matrix as possible, offering examples from Estonia, as part of the larger framework. My tendency is to take a physicist's viewpoint rather than philosopher's. This naturally leads me to want to make everything as simple as possible but not simpler much in the sense of A. Einstein (although we may note that modern physics is not so simple!). Of course, it is clear that this principle will not always works, especially when discussing fuzzy concepts like understanding or ideology.