I almost got myself mixed up I a philosophical discussion again.
Somebody was talking about the Planck time and length which are, according to him, the minimal possible time and distance, and how that means that ordinary (Euclidean) geometry can not be the geometry of the real world, and that from this alone all kind of non-mathemnatical subjects follows.
Luckily (this time) I did manage not get very involved in this discussion, but still.
I think in one thing he is right normal Euclidean geometry expects that you can infinitly divide a segment into smaller parts and that if the Planck length is the physical shortest distance possible then there is a (not very big??) problem.
But still euclidean geometry is not the only geometry around so are there geometries where that is not the case?
Are there geometries where there is a limit to the minimum size of a point, so with a limit to how far you can split up a segment?
What would the axioms and theorems of such a geometry be?
I was first thinking that would be some kind of taxicab geometry (alternative link) But even this geometry uses infinitly dividable segments.
At another end there are geometries that just have a fixed (low) number of points (like the Fano plane or affine geometry but I think even these are not particulary suitable for this discussion.
But is there a geometry that would be describing the real world as this person percieves it?