Geometry, like combinatorics, is absolute –
The problem is human error.
If you were able to draw a perfect triangle, and measure it perfectly, you would find the Pythagorean theorem holds, perfectly, if you assume the universe is at least countably infinite, which would produce no real number error, if the triangle is drawn with countable precision.
Empiricism suggests the same –
The more precisely we draw, and the more precisely we measure, the more consistent observation is with mathematics. It also suggests the possibility that physics is absolute, and simply unknown to us.
There is combinatorics, which is plainly absolute, with no possible deviations, since it requires only finite discernment, and a finite number of observations –
In contrast, Geometry requires an infinite number of points, and is therefore not observably absolute, like combinatorics, but because it requires only finite length proofs, it is absolute as an idea, in that you can prove in a finite number of steps, any knowable claim about a geometric object.
Physics requires infinite observation to know with certainty, and therefore, it is not possible to know without infinite time, whether a given model of physics is truly absolute.
This creates a hierarchy of knowledge:
- Combinatorics, known to be absolute.
- Geometry, known to be absolute as an idea.
- Physics, cannot be known as absolute in finite time.
However, if the Universe is for example countably infinite, and if your perspective were infinitesimal, able to make infinitesimal measurements, then you would see the imperfections in what appear to be perfect curves, since you would see the local linearity of a curve that is perfect from our perspective, which is limited to computable measurement.