If you take the chromatic scale and then swap every other pair of notes on opposite sides of the circle, it yields the circle of fifths. You'll notice that on the circle of fifths notes that skip a step are a whole tone apart in the chromatic scale.
Although there have been some claims in these comments to the contrary, harmony is particularly mathematical. Symmetry and the breaking of within the integers mod 12 form the foundational principles of harmony.
Abstract Algebra, Combinatorics, and Discrete Mathematics are all definitely worth the squeeze; and incidentally something that could easily be taught to middle- and high-schoolers with the right examples.
Many artists in fact do exactly this -- they do not make the art themselves, but instead imagine and manage the 'art project' and delegate tasks to other artists that work for them. Leonardo (Da Vinci) in fact himself did this with much of the work required for his paintings, although the most crucial parts he left for himself.
They are slant rhymes of one another. B and M are phonetically nearby, as are ia and ih and ao and ou. In no way like hacker news and cake her knees -- but more like hacker news and hagger moos ;)
I have also found that programming is the gateway drug to Math B. Thanks to Functional Programming and Type Theory I eventually found may way into Abstract Algebra, Topology, and Category Theory... Wish I had time to go back and study these with a mentor, though!
>>> The Pythagorean theorem becomes intuitively true not when you have some deep insight about Euclidean space, but when, on seeing a right triangle, three proofs of it spring instantly to mind.
To be honest, this sounds like orienting one's self in the 'space of mathematics'. Is it not possible that, just like one can navigate by landmarks (proofs) or by the space itself (deep understanding), that there are in fact two roads to intuition in mathematics, of which ones is practice and fluency, and the other is deep insight and understanding?
perhaps he's suggesting that they seize the software, weights, and training data from every company who's engaged in this? Or maybe he's just trying to protect profits and doesn't mean a word of it...
Although there have been some claims in these comments to the contrary, harmony is particularly mathematical. Symmetry and the breaking of within the integers mod 12 form the foundational principles of harmony.