If you look at all the constants that exist in nature, \(\pi, e, \phi, \hbar\), etc, they are all irrational. Makes me wonder: is Nature not perfect? Is irrationality built into the Universe?
Or is the flaw in our number system? Could an alien civilization have a number system in which all of the natural constants are nice rational numbers?
According to me, that cannot be the case. We can approximate \(\pi\) using a ratio. And a ratio will be the same in all conceivable number systems. So, maybe an irrational number will remain irrational. Am I wrong?