To Infinity and Beyond (Our Obsession with Infinite Progress)

Oswald Spengler, the author of The Decline of the West, says that our Culture is defined by its belief in the infinite — a concept he believes is completely foreign to the Classical way of thinking. This belief, he argues, affects almost every aspect of our Culture, particularly its relationship with time. Unlike almost every other Culture to have existed, we don’t believe that history is cyclical. We believe that history is linear and that progress is inevitable — a belief that may be blinding us to our imminent demise.

In Volume 1 of his book, The Decline of the West, Spengler states that there is not one mathematics, beginning in antiquity and culminating in the present, but many mathematics, each as irreconcilable with one another as Newtonian physics is today with quantum mechanics:

There is not, and cannot be, number as such. There are several number-worlds as there are several Cultures. We find an Indian, an Arabian, a Classical, a Western type of mathematical thought and, corresponding with each, a type of number — each type fundamentally peculiar and unique, an expression of a specific world-feeling, a symbol having a specific validity which is even capable of scientific definition, a principle of ordering the Become which reflects the central essence of one and only one soul, viz., the soul of that…