First, open kamona as they say. I was an Engineer for 30 years. Numbers and logic were the foundation of my existence. I have to struggle to let the other side of my brain win once in a while.
The Numbers, Rationale, etc. are good because it lets us understand what works and doesn't work - in a very broad sense. Once you know the 'rules' then its easier to make a conscious decision to break them and get good, pleasing results - or whatever it is you are striving for.
Example: Jazz improvisation - the 'teachable' method. You first learn the scales and modes that 'work' against a chord progression, then you learn the 'blue notes' that cause a little rub, then you learn ways to use all the other notes. Eventually, you arrive at the conclusion that every note in the chromatic scale are good notes. You just have to use them in the right way.