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I. INTRODUCTION With the introduction of computers, automata have been playing a continuously increasing role in the natural sciences. In this paper I focus on special automata called learning systems. A learning system has a learning procedure by which it can develop methods that cannot be deduced trivially from its learning procedure. The learning system tries out hypotheses (methods) and selects the better ones. It has a priori a well defined universe of hypotheses from which it must choose those to be tried. If this universe is small, then the" inventiveness" of the machine is severely limited, and the value of the methods that it develops depends more on the astuteness of the programmer in choosing a universe containing good hypotheses than an ability of the learning system to pick the best hypothesis from among those in the universe. In order to give the learning system a" free hand", it should have a universe which, although well-defined, is so large and varied that the user of the system is not even acquainted with the forms of all the methods it contains. Artificial learning systems need huge processing capabilities. New physical concepts of information processing have to be developed to meet these requirements. A promising research direction is molecular electronics. But I would like to mention a second reason why molecular electronics might be interesting for the design of artificial learning systems. Learning systems, natural or artificial, face the problem of finding good hypotheses that explain the past data and that