22 October 2008

The Archimedean property of reality

The Archimedean property of reality: if you put one foot in front of the other for long enough, you can travel an arbitrarily long distance.

This is, of course, the Archimedean property of the real numbers -- that is, for any two positive real numbers x and y, there exists an integer n such that nx > y -- if we can make the assumption that step length is constant.

It's also what got me through some hard times in the first year of grad school, when I doubted my mathematical abilities; at least I could successfully walk to and from school each day. The proverb "a journey of a thousand miles begins with a single step" comes to mind, but my walk is about a mile and a half.

1 comment:

Kea said...

Ah, but like a law of physics, the certainty of death gives the reals an unreal quality. The p adic numbers are much nicer.