In a certain sense, uncertainty andignorance have been recognized in science andphilosophy from the time of the Greeks.However, the mathematical sciences have beendominated by the pursuit of certainty.Therefore, experiments under simplified andidealized conditions have been regarded as themost reliable source of knowledge. Normally,uncertainty could be ignored or controlled byapplying probability theory and statistics.Today, however, the situation is different.Uncertainty and ignorance have moved intofocus. In particular, the global character ofsome environmental problems has shown that theproblems cannot be disregarded. Therefore,scientists and technologists (...) have in many wayscome into a new situation. The Chernobylaccident is a dramatic example, however,problems such as a possible greenhouse effect,a possible reduction of the ozone layer, and soon are all of the same type. These encompasstotally different problems than scientists andtechnologists are traditionally trained to dealwith. In these cases, the standard use ofstatistics has to change, the burden of proofshould be reversed, one should draw ondifferent kinds of expertise, and, in general,science should be ``democratized.''. (shrink)