Abstract

It is clear that there is a mathematical dimension to technology; modern science is predicated upon the ability to measure nature. Technological society, the society where the application of techniques is so pervasive, has a mathematical dimension as well, but its existence is more subtle. Unlike the formal mathematical language of science, the mathematical nature of the technological world shows itself in its calculations of efficiency and its indifference to the poetic. What significance should be given to the widespread complaint that people are now just numbers being processed in a system that no one can understand, much less control? ;To pursue the question of the mathematical nature of technological society, it is necessary then to think about the mathematical beyond the boundaries of formal mathematics. One way to confront this question is to look at mathematical thinking in its origins and through its histories. To that end, part of this inquiry is a reflection on the philological origins of the term mathematics. Mathematics comes from a Greek word meaning "that which can be learned," which raises the question of how mathematics might be related to learning in general. ;In the Platonic Dialogues, one finds the position that mathematical thinking, while being an important part of an education, is not adequate for attaining to an understanding of the most important of matters, the Good itself. In the story of the divided line, mathematical thinking is the model for dianoia, understood here to be an ability for problem-solving characteristic of the arts in general. Philosophy, however, requires a circumspection that mathematical rigor finds unfamiliar. Problem-solving proceeds, like a Euclidean demonstration, straight from its beginning to its end. ;The problem-solving mind is drawn to the clarity of mathematical form. It is reasonable, therefore, that changes in the conceptions of formal mathematics might influence those ways of thinking which find inspiration in such clarity. Modern mathematics, which imagines itself as progress over its ancient predecessors, introduces the idea of symbolic structure, wherein a thing's intelligibility is connected not with pretheoretical experience but with an axiomatic foundation that sets forth the nature of how everything functions in its realm. Such a mentality is common to the modern world, wherein ideas are taken as models of reality to be tested by experience. In some fashion or another, moderns are preoccupied with how ideas are brought to reality, as well as the consequences of that bringing. ;An awareness of the nature of problem-solving, in both its ancient and modern forms, makes clearer why it is not fully adequate to the demands of wisdom. The pervasiveness in modernity of this way of thinking points to the spiritual deficiency of the times