||'THE IVORY GHETTO" 15 out what he took to be an analogy with the number tc. it is the ratio of the circumference of a circle to its diameter. One way to establish this number is by measuring circumferences and diameters of circles. But there is, of course, a mathematical approach which gives tt as the limit of an infinite sum 7T 111 - =1- -+ -- -+___ 4 3 5 7 Eddington tried to construct a theory that would give some such mathematical construction for numbers occurring in physics. It is now generally agreed that this attempt of Eddington's failed. Nonetheless, the success of the mathematical formulation of physical laws has been continuously astonishing. When Euclidean geometry turns out to be of use in surveying, we are not surprised. This is due to the direct way in which that sort of geometry got its start in abstractions from such problems. After all, the word "geometry" means earth measurement. When complex numbers, which I mentioned as a simple example of a rather abstract mathematical idea, turn out to be an essential feature of quantum theory, we are justified in being surprised. Quantum theory in its applications is very mundane. It describes solid, tangible matter, visible light and audible sounds. The mathematical structure of the theory is highly abstract and seems far from these direct physical sensations. No one really understands why this peculiar relationship between mathematics and our efforts to understand natural phenomena exists.6 Mathematics turns out to be not just a game but an extension of language allowing us to express things that ordinary language is incapable of expressing. This is surely one of the great discoveries of all history. How many have been equipped to use or even appreciate it? Mathematical illiteracy is the barrier which separates the majority of educated people from this appreciation. Suppose that mathematical illiteracy could be stamped out. What could we do in this Utopia? Foremost, it would be possible to give a meaningful scientific education to far more people than ever get a chance at it now. The most direct advantage of this would be in expanded human delight. Education is supposed to cultivate a delight in knowledge for its own sake. This seems to me to be a completely uncontroversial goal. So much has been said about the power of physics that we've tended to ignore the glory. Physics is surely one of the most beautiful things created by man, 6 For some interesting speculations on this problem see: E. P. Wigner, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," in Symmetry and Reflections, (Indiana University Press, 1967); A. Einstein, "Geometry and Experience," in Readings in the Philosophy of Science. H. Feigl and M. Brodbeck, eds. (New York: Appleton-Century-Crofts) and S. L. Jaki, The Relevance of Physics (University of Chicago Press), Ch. 3.