I understand your point, but your analogy is off. You can't make a ruler with that small of length increments because the Planck length is the smallest possible length and it is larger than your hypothetical ruler increments. Reality is in fact quantifiable with distinct units. Pi is not a length, nor is a square root, so how based in reality is math? Perhaps math is merely the realm of the imaginary but following rules of noncontradiction. It is a tool for prediction.
Discussion
A line is not a physical thing, so the imaginary ruler is not either, so the Planck length limit isn’t really relevant.
Pi is absolutely a number on the line, and the imaginary ruler can’t mark it, no matter how fine its units of measurement.
The analogy is between one degree of infinity, the kind you can get by dividing by ever smaller rational numbers and a higher order kind (real numbers) which represent every point on a line.
The ratio of rationals to reals is zero. The ratio of map to territory is zero. AI to Tao is zero.
Pi is absolutely NOT a number on the line. Please don't create new philosophies while defendjng old ones. Someone needs a math review.
Okay, so it's an imaginary line, a geometrical line. Those aren't real things, but you are using one as an example of what reality is. Sure, you can't make an imaginary ruler good enough to measure an imaginary line, but you could make a real ruler good enough to measure a real line.
Yes, it’s an analogy. The line is analogous to reality, the ruler is analogous to a map of reality. The ruler is not the line, it can only map certain points on it.
And I'm suggesting the analogy is bad. A line is continuous. Reality may not be, and in fact there is evidence that it is not.