Everything that is considered a "mystery" or "sheer opinion" is, in-fact, PERFECTLY LOGICAL.
The "mystery" is simply a consequence of Private Axioms.
Before Democritus, people believed the weather was (fundamentally) unpredictable and reasoned it was subject to the (mysterious and inscrutable) personal whims of the gods (which were also presumed to be fundamentally unpredictable).
Democritus figured out that, with proper data, weather can be predicted.
Democritus identified the Axioms of weather patterns.
Pythagoras observed the natural world, very carefully, and noticed (among other things) that musical notes that "sound right" are comprised of strings that have particular proportions relative to each other.
Pythagoras did not invent music of course, he did not even invent the idea of instruments, but he devised an occult (secret) system that he only shared with his most trusted acolytes (and even murdered those who might share this occult system with the uninitiated or his rivals, the followers of Cylon), this occult (secret) system applied, not only to music, but to nearly all observable natural phenomena. Those lucky few who knew the code were better able to predict outcomes than everyone else.
The code dispelled the precious "mystery".
The physical world always functioned according to logic, but the axioms were unknown and therefore the physical world appeared to be "unpredictable".
Pythagoras identified the Axioms of nature.
It seems insane that so many seem to love and protect the "mystery" (appeal to ignorance) so much.