On Hockney, mathematicians, and the cross-cultural fallacy

Via Udell, a link to a paper that attempts to refute David Hockney’s theory that the sudden shift to photographic styles in the Renaissance was due to the use of optical projection.

It’s an interesting paper because it introduces what seems to be a new method of objectively measuring geometric deviations of paintings from “reality”, and applies that geometry to a chandelier that figures prominently in Hockney’s book :

In Sect. I we introduce the basic mathematics of homographies and plane-induced image registration. In Sect. II, we apply digital image registration to detect and measure geometric imperfections in the painted chandelier. The analysis of photographs of a representative sample of surviving 15th-century dinanderie is conducted in Sect. III. Finally, in Sect. IV we judge the abilities of contemporary realist painters in the absence of optical aids by testing the perspective of paintings of elaborate chandeliers done “by eye”. We find the accuracy comparable to that in the Arnolfini painting.

I haven’t sorted through the method yet, and in all likelihood I doubt I’ll be able to add anything to that side of the debate. But the fascinating part of the article is toward the end.

Underlying the arguments of Hockney and Falco is the assumption that good perspective cannot be easily achieved “by eye,” that is, without the help of optical devices.

To test their assumption, as part of our research, British realist painter Nicholas Williams painted two chandeliers entirely “by eye.” Figure 6 shows one of the two chandelier paintings he realized for us. Our perspective analysis applied to this painting resulted in a good but, as expected, imperfect alignment of arms. The average measured deviation was about 8.55% the image width, of the same order of magnitude as that of van Eyck’s chandelier. This experiment confirms that realistic-looking structures can be painted merely by eye, without the help of optical tools of any sort.

This part of the experiment shows more than a little historical naïveté. They took a 21st century painter, who has seen photographs and realistic paintings every day of his life, and found that he can paint photo-realistically.

What they of course miss is that to a person in a pre-photorealist society the process of mapping a three-dimensional reality onto a flat plane is considerably more difficult — that is, if such a notion even occurs to them.

Technology changes us. It changes what is possible to think. Take a top-notch mathematician trained before the computer and ask them to model the growth of lemming populations in a limited resource environment and watch as they drive themselves slowly insane in pursuit of the solution. Take an average Excel user or the most novice programmer of today, and watch how effortlessly they stumble into the algorithmic thinking that is crucial to the solution.

Does this prove it was possible for the mathematician to have come up with the solution on his own? Quite the opposite. The computational thinking that is now taken for granted in our society evolves not from native cognitive abilities, but from a cultural store that finds it’s birth in giving machines iterative instructions where output states become inputs.

Such historical thinking is crucial to Hockney’s premise. In the history of computing, one notes that Turing and Post came up individually with their theories of computing in 1936 — and from there the logical progression is to ask what was happening, technologically, that led two people to individually come up with the same model at the same time.

Hockney has before him a similar conundrum — the sudden explosion of photorealistic technique in Rennaissance art. And he searches for the technology that may have made such photographic thinking possible. He concludes, based on various effects of darkness and light, restricted focus, and orientation that optical projection technology may have been largely responsible for this sea-change in technique, and more importantly, this sea-change in thinking.

The research paper may be right about the irregularities in the painting for all I know. But in structuring their final test they show that they have very little understanding of cultural history. The briefest look at Derrida, the history of fractals, or the development of the slow-motion action shot in film would have demonstrated to them the fallacy taking a modern painter to prove a historical point. Technology, and the cultural store that evolves from it, changes us. My eight year old paints cups from life in a way that was simply not available to the Ancient Egyptians. My four year old concieves of quick events happening in slow motion. Both of them have a conception of language impossible before writing — and my four year old can’t even spell yet.

The ultimate thing to take away from Hockney is not whether the Masters “cheated”. It is to better understand the fluid boundaries between technology, culture, and our own cognition. Hockney may or may not be right about methods or particular paintings. But his impulse is right on target.

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