Understanding Imaginaries Through Hidden Numbers

This essay describes a way of finding hypercomplex numbers—ones that extend complex numbers to more dimensions—with only basic algebra plus Ayn Rand’s philosophy, Objectivism. The result has implications for mathematics and the philosophy of science. The “RADN numbers” (known by science under another name) have a property of rotation like complex numbers, and are also commutative/distributive. (Division is deemed less crucial.) The author of UITHN asked himself what exactly numbers are, how they arise in our mind, and what their relation to reality is. But these questions were so fruitful only because he used a correct philosophy. Another philosophy, such as Karl Popper’s, would not have worked. This has two implications: Rand’s philosophy has epistemological truth; and the RADN numbers may have unique significance. May spur thought on mathematics, addition, multiplication, dimensions, imaginary units, and dimensioned numbers, and lead to more appreciation of Rand’s ideas.