Reminds me of this paper in Nature from some time back. Especially, the Euler's identity graph from the paper is pretty amazing.
https://www.nature.com/news/equations-are-art-inside-a-mathe...
Euler's identity is pretty obviously something elegant, and it's widely recognized. But Zeki seems to overlook the importance of acculturation in the appreciation of these things. The idea that a mind-blowing Ramanujan formula is ugly seems particularly problematic. Sure, it is surprising, complex, and apparently arbitrary, and most test subjects won't have any insight into how it works. But why should those people (let's say they are "ignorant" when it comes to Ramanujan's results) be expected to have any opinion on the formula? Any judgement they come up with will be superficial.
This problem runs through most of Zeki's work. His experiments take test subjects who are, as it were, preloaded with certain aesthetic experiences and norms, and attempt to derive universal cognitive principles of beauty from the result. What he doesn't do is try to discover just what those aesthetic prejudices are. He doesn't try to extract from the test subjects the key features of their aesthetic indoctrination. In the math situation, it's totally conceivable that a group of test subjects who were educated to find every Ramanujan formula transcendently fascinating would rate those formulas as beautiful.
The problem is more conspicuous when his research looks at art. Since he hasn't studied art himself, he really doesn't seem to appreciate the basic reality: that some people have learned to 'get' certain styles or genres of art, while others haven't had the good fortune to learn to appreciate those same styles. People walk around with extremely complex acquired aesthetic processing capabilities in their heads. Everyone's is different, and while Zeki may be able to find some universal regularities, (like Chomsky's hypothesized universal innate grammar) that wouldn't be a neural explanation of aesthetics any more than the success of Chomsky's programme would tell us about the nature of literature.
It's a frivolous exercise from the point of view of anyone seriously interested in art (or math).
(= (+ (exp (* i pi)) 1) 0)
The relationship is the same regardless of the notation.
Try to imagine complex interest rates. Now try to make them matrix-valued. It works. It all works.
I even more prefer the full form of Euler's Formula: [e^(ix) = cos(x) + isin(x)]. The real beauty of Euler's Formula I think is that it shows an equivalence between an algebraic function and a trigonometric function.
(Note that I'm only a mildly learned laymen when it comes to mathematics. Any experts in math should feel very free to tell me why I'm wrong.)
0 = 1 + * ○ 0j1