Maybe the problem is not a math problem and that is the difficulty.
Great post! thanks...
Especially that part:
Every time you make a decision on even/odd, you are throwing away information. That knowledge does not carry to the next step, therefore you can never go backwards, only forwards.
You are right....Then we need a new theory of information which basis are explained in the Indian scientist book...And a new way to do non Turing mathematic....
Hearing is not explained by being the solution of a mathematical problem in the usual sense of the word..,
It is not even the result of a decision based algorithm, there is no linear Turing computing here in the brain/ear, but more an integrated chain of non excluding choices converging without rejecting anything, but more integrating everything , like a "resonating" tree of which we consciously perceive only some leafs... Sound/silence is already meaning not mere sound...
All the book of Anirban Bandyopadhyay is a reflection about that and an explanation i cannot resume save with a few metaphors...
I cannot resume that here...
Read this page:
https://nanobraintech.com/about/
My goal are not to explain sound or hearing, only to point to something which cannot be understood with the objective/subjective external usual border ... Meaning is neither objective nor subjective and sound is already meaning...
Music is the meaning of this meaning....