Thoughts to minds is what songs to birds: a way to communicate a relationships between observable things. Such relationships get reduced to a set of things "inside" and everything else that's outside. The boundary must be a smooth shape, that could be arbitrarily precise if the physical medium allowed it. A mind receiving a thought sees it as a finite set of resonant frequencies, even if the thought is more complex than that. Furthermore, the ultimate receiver of the thought is brain with its finite number of neurons, and even though different frequencies get mapped to different neurons, each neuron reduces amplitudes even further by activating a chemical reaction only when its input exceeds a certain threshold. Thus a continuous amplitude gets reduced to a sequnce of 0s and 1s, or a rational number. Hence the thoughts thinkable by brain are "rational". In their own realm thoughts are more like birdsongs with infinitely many harmonics and precise amplitudes.

A very interesting, poetic interpretation - thank you for sharing.