March 23, 2013

The concept of Infinity

One of the least appealing modern traits is to imagine that we've discovered everything new- in some ways that's true. The ancient world did not have television and were not plagued by endless reruns of Friends on E4. But equally they did have concepts that we might not have expected them to have: take this statement from Marcus Aurelius: 'the phrase infinity may pass, even if the world be in fact administered in finite cycles'. It seems to me what this throwaway comment is getting at is that there are different types of infinity: one might be an infinity which is truly infinite, one might be an infinity that is infinite because the finity that really exists is unccountable or unknowable and a last might be that infinity is a reasonable approximation of a set of a finite number of cycles. I'm happy with whichever infinity you want Marcus to define- but the fact seems to be here is an ancient author, not a mathematician, with at least two concepts of infinity.