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Over the past three centuries, the application of mathematics to physics has produced some of the deepest insights into the nature of the universe and into the limitations of human knowledge. Recent indications are that similar insights may come of the application of mathematics to engineering. This article is an account of the field in which this seems to be happening. It surveys the main results of information theory, and of related theories, from the point of view which is likely to become useful in this connection. This article was written originally for the audience of Science, a publication chiefly for persons of nonengineering background. It is reprinted here at the suggestion of the Editor of these TRANSACTIONS, in the hope that it will be diverting, and perhaps also instructive, to an audience of engineers.