But then she launches into this:
Now, I'm certainly not the first person to notice that patterns are part of how humans think. Mathematicians, of instance, have studied the patterns in music for thousands of years. They have found that geometry can describe chords, rhythms, scales, octave shifts, and other musical features. In recent studies, researchers have discovered that if they map out the relationships between these features, the resulting diagrams assume Möbius strip-like shapes.
The composers, of course, don't think of their compositions in these terms. They're not thinking about math. They're thinking about music. But somehow, they are working their way toward a pattern that is mathematically sound, which is another way of saying that it's universal. The math doesn't even have to exist yet. When scholars study classical music, they find that a composer such as Chopin wrote music that incorporated forms of higher-dimensional geometry that hadn't yet been discovered. The same is true in visual arts. Vincent van Gogh's later paintings had all sorts of swirling, churning patterns in the sky--clouds and stars that he painted as if they were whirlpools of air and light. And, it turns out, that's what they were! In 2006, physicists compared van Gogh's patterns of turbulence with the mathematical formula for turbulence in liquids. The paintings date to the 1880s. The mathematical formula dates to the 1930s. Yet van Gogh's turbulence in the sky provided an almost identical match for turbulence in liquid. "We expected some resemblance with real turbulence," one of the researchers said, "but we were amazed to find such a good relationship."
Even the seemingly random splashes of paint that Jackson Pollock dripped onto his canvases show that he had an intuitive sense of pattern in nature. In the 1990s, an Australian physicist, Richard Taylor, found that the paintings followed the mathematics of fractal geometry--a series of identical patterns at different scales, like nesting Russian dolls. The paintings date from the 1940s and 1950s. Fractal geometry dates from the 1970s. That same physicist discovered that he could even tell the difference between a genuine Pollock and a forgery by examining the work for fractal patterns. (pp.143-5)
I mean, what if a scientific proposition had to lead to new art in order to be accepted?
What I challenge here is the scientifically ungrounded assumption of the scientifically minded that science is the measure of all things. And I'm not picking on Grandin necessarily. A much more flagrant example is Hofstadter's Gödel, Escher, Bach, in which a superficial understanding of the latter two figures was deployed in service of the first, whose innovative approach to mathematical decidability was to have given Hofstadter the hammer to crack the mind-body problem.
Now, what were Escher and Bach really doing in there (heck, even Gödel for that matter)? My guess: Hofstadter had stapled them to the title to lend the allure of high culture to a very geeky exposition of a very geeky argument. Attract some bees, and maybe a butterfly. And it worked: the book went like wildfire. But did anyone get anything from it, aside from the belief that they, too, were now privy to the hidden nexus of math and art? And that this had something to do with 'FlooP' and 'GlooP'?
That I can't say--but someday GEB may just serve to inspire a great sculptor. Shall we call it worthwhile then?