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How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality?
There exists an intrinsic similarity between the human imagination (mind) and mathematical reality (body). Spinoza recognized that “measure, time and number are nothing but modes of thought or rather imagination.” (Cf. Einstein's statement: “Time and space are modes by which we think and not conditions in which we live.”) Jung asserted that mathematical reality, while certainly adhering to outer objects, is indisputably a reflection of our own mental structure.
In this brief communication, I should like to discuss the correspondence between mind and body by comparing the structures of inner space and the mathematical constant pi ((). In two previous papers, I conceptualized the mind as a sphere simultaneously possessing and expressing opposite and complementary qualities: inner space could be seen at once as finite (left hemisphere) and unbounded (right hemisphere). This structure permitted shifts, for example, from figure (finite) to background (unbounded), object to subject, particle to field, and thinker (I) to object (Self).
Along similar lines, an analysis of the mathematical construct pi reveals that it is both a constant (finite) – reflecting the unchanging relation between two elements (the circumference and diameter of a circle) – and an incommensurable (unbounded) – an expression of an endless succession of digits for which there is no law predicting sequence. According to Kasner and Newman, in Mathematics and the Imagination, pi can never be completely expressed in a finite number of digits. It can only be expressed as the limit of a convergent infinite series or of a continued fraction, such as Wallis's (1616-1703) series: