(October 18, 2016 at 6:03 pm)Jörmungandr Wrote:(October 18, 2016 at 2:37 pm)Arkilogue Wrote: A perfect circle can be physically made. And nature makes perfect spheres all the time as bubbles.
No it can't. A perfect circle consists of a line composed of an infinite set of dimensionless points. There is no such thing in the real world. Do you realize how big soap molecules are? It approximates a sphere, nothing more. You are constructing the sphere by imagining that the molecules in a particular layer are connected, forming the sphere. They aren't. They are just molecules arranged on a circular pattern. That you can't understand how there are no actual circles or spheres in the world does not bode well for the credibility of your 'theories'.
Is this a circle and a square?
Listen to Jorm.... she knows stuff.
Think about space as divided into 3D pixels.... voxels... each with a dimension of a Planck length, cubed.
The fact that we have a finite minimum length tells you that any circle made up by real particles, even really tiny ones, like neutrinos, would never ever ever ever be a perfect sphere.
For all our purposes, it would be as perfect as can be... but never perfect enough to yield the infinity of terms in PI.