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It is easy to argue that real signals must be bandlimited. It is also easy to argue that they cannot be so. This paper presents one possible resolution of this seeming paradox. A philosophical discussion of the role of mathematical models in the exact sciences is given and a new formulation of the 2 WT theorem is presented. The paper is a written version of the second Shannon Lecture given at the 1974 International Symposium on Information Theory. An appendix giving proof of the 2 WT theorem has been added.