In the 2011 movie, Immortals, John Hurt's Zeus tells the Theseus to mind his rhythm when he fights. The concept of rhythm or periodicity—everything from cadence to static repeating patterns, mutating or regular—is fundamental aesthetics that is hard-wired to the human brain, and most of it is subconscious. It is truly the final arbiter in our acceptance of nature, and the "natural". It is, to me, manna from heaven dividing the insane from the mystical.
Pythagoras is famous for his willingness to kill to try and quell "irrational" numbers where non-repeating, endless expansion of numbers follow a decimal point is the definition, though it is not the psychological "irrationality" but the fact that a given number defies a whole numbers ratio representation. However simply because a number is irrational doesn't mean it has no inner beauty—the analytic and geometric proofs of the square root of 2, the number π, etc. have something of a divinely inspired beauty about them much akin to a landscape that only the mind's eye can perceive.
I personally have spent now literally years exploring the abstract structures of language and am ever on the look out for "new" ways of perceiving—I put quotation marks around the word new because sometimes the old (old English, or reconstructed proto-languages) provide insights not obvious in synchronic analysis alone.
For eg, taking cue from the Gematria (a numerological analysis of Hebrew letters in Jewish mysticism) I came up with a way of numeral coding of morpheme types allowable in Inuit language grammar and I saw beauty never before seen but was always there (a four number sequence, a genetic code of language if you will). -Sounds pretty "far out", doesn't it?
It is nothing less than a pons asinorum of linguistic analysis: impassive, inscrutable without a proper frame of mind, like the monolith in Arthur C Clarke's 2001: a space odyssey.
Having seen and tasted fruit not intended for the vulgar (and I say this in all humility) I join the author of psalm 19:
The heavens declare the glory of God;
the skies proclaim the work of his hands.
Day after day they pour forth speech;
night after night they reveal knowledge.
They have no speech, they use no words;
no sound is heard from them.
Yet their voice goes out into all the earth,
their words to the ends of the world.