Counterpoint

Two phenomena, vaguely related. The one, a superb demonstration of the power of really clear thinking; the other, a demonstration of … well, I’m still not sure what.
 
A visit to the Abstract Expressionist exhibition at the RA was not a terribly stimulating half-hour for me. Two things stood out: I discovered, as I had suspected I might, that I rather liked the Jackson Pollock paintings. The large Guggenheim mural was not to my taste but many of the others were ‘pleasing to the eye’. Applying my test for ‘good’ art - would I like to see it again? - I found that with many of Pollock’s canvases, ‘Yes I would’.

​Mark Rothko was a different matter. I remember the fuss some years ago, when it was discovered that a Rothko had been hung upside down in some gallery or another. ‘How could they tell?’ was the refrain. Rothkos are not displeasing to the eye, but whether one really wants to see a room full of smudgy rectangles of different colours and call it ‘art’ is a moot point. The curators at the RA had added the following words by way of explanation:

…Rothko’s iconic paintings of the 1950s and ‘60s epitomize his perennial quest to formulate abstract embodiments of powerful human emotions: as he once memorably put it, "tragedy, ecstasy, doom'. Instantly recognizable…"

Instantly recognizable? Hmm.
 
But contrast Rothko and his smudgy rectangles with the most beautiful, clear and un-mathematical demonstration of one of the foundations of mathematics, the theorem of Pythagoras. This was contained in Roger Penrose’s massive door-stop of a book Road to Reality (a Christmas present). The book’s subtitle is ‘A complete guide to the laws of the universe’. The right-angled triangle rule that the square of the side opposite the right angle is equal to the sum of the squares of the other two sides was drummed into us at school – rightly so. We even learned how to prove it using Euclidean geometry although I could never remember how to reproduce that proof. Penrose, using repeated squares of three different sizes, was able to show, just by eye, that the law is true for any shape of right-angled triangle. This was so beautifully clear that no mathematics was needed to understand it.