Kevin's Watch

Malik23 wrote:I'm a Platonist when it comes to mathematics. I believe that mathematical relations actually "exist" on a higher "plane" than tangible reality. But I believe abstraction is the way we discover them. Not invent.

In the interest in promoting mathematical Platonism, and perhaps in partial response to some of the foregoing posts, allow me to suggest that mathematics, like music, is a kind of anamnesis. That is, we un-forget what we ought to remember in a process of self elevation through mathematical and musical activity. Although I do not wish to engage in a technical debate regarding the concept of negation, I do recommend to the broad minded a work by Theon of Smyrna called Mathematics Useful for the Understanding of Plato, now available in the original Greek and decent French and English translations through many major research libraries. An incomplete and somewhat flawed translation was made available in 1973 by Wizard’s Bookshelf in San Francisco. This will give some idea of the necessary and anagogical relation of number to form.

Murrin wrote:The big conceptual leap was not the concept itself, but to go from the concept of none to the idea of none as a number. To numerate the absence of something is not as intuitive as it seems to us who have been raised with the idea there since brith.

I'm in complete agreement with Malik, but you're right too. If it was as simple as we now take it, it wouldn't have been invented so rarely in human history. But really, isn't it only the invention of the 0 as a place holder to allow easier calculation that we're talking about when it comes to mathematics? That doesn't mean a nothing exists; it just means there are no groups of 1's, 2's, 3's, 10's, or whatever.