[ithkuil]

We're clearly talking about different things.

You're talking about measuring something in the real world. Measuring is basically counting how many thing a given reference thing fits into the thing you're measuring. I have no problems with the assumption that for all intents and purposes we live in a finite (space and time) physical universe and there is a maximum precision that will ever be necessary.

What I am talking about is that in order for the math we use to describe that universe to work out we need irrational numbers; otherwise you couldn't be able to prove theorems and whatnot. I think this makes the irrational numbers (e and pi in particular) quite fundamental tools and I don't care if the real world doesn't allow objects (or positions) to be measured with irrational numbers.

> there is no (known?) way to compute the ratio between the length of an ellipse and the properties of its foci.

There is no closed-form expression for the circumference of an ellipse. There is an infinite series though. Same for a circle; there is no closed-form for computing pi either!