Speed of light: measured quantity or theoretical derivation?

Question

In a comment to this answer it was stated

Yes, the speed of light is not a measured value. In natural units, it equals one (e.g. one light second per second)... It is not a measured value, but a postulated whole number with no fractions. You cannot measure the speed of light, it is theoretically given as the unity that for every day convenience is multiplied by this whole number.

In my understanding the value of speed of light was found due to observations and it isn't possible to derive it theoretical.

How you can explain or discard the one or the other point of view?

Answer 1

The speed of light was found by observation, but then we discovered a remarkable property about the universe, which is that light is very unlike sound. If you move at a speed $v$ through the air then sounds move away from you at speed $v_\text{sound} - v$ in the direction that you're going and at speed $v_\text{sound} + v$ in the direction opposite. It turns out that nobody can experience the same thing with light -- no matter what speed you go, and no matter relative to who, light rays in vacuum always move at speed $c$.

Combined with the fact that around 1900 we developed a new way to measure distances based on the interference of light, our measurements of the velocity of light became dominated by uncertainty on what exactly "one meter" is, so we redefined the meter in terms of the distance light goes in a certain amount of time. Now the speed of light in vacuum is a mathematical constant for our unit system. But of course we chose the definition so that we did not need to change our meter-sticks.