Mathematics
Mathematics, rather unexpectedly, is the object of the first chapter of Spengler's book, which suggest its importance there. Conceptions of space, as expressed by an "Ursymbol" are central for each culture and, along with time and number, they form a specific "mathemetical style". Against the universal validity of mathematical results, Spengler asserts that mathemathics is not a single science but a plurality of sciences.
He notes that in Greek classical mathematics that there are only integers and no real concepts of limits or infinity. Therefore, without a concept of the infinite, all events of the distant past were viewed as equally distant, thus Alexander the Great had no problem declaring himself a descendant of a god. On the other hand, the western world—which has concepts of the zero, the infinite, and the limit—has a historical world-view which places a high amount of importance on exact dates.
Read more about this topic: The Decline Of The West
Famous quotes containing the word mathematics:
“I must study politics and war that my sons may have liberty to study mathematics and philosophy.”
—John Adams (1735–1826)
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (1909–1943)