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Christopher Tyler's objections
Christopher Tyler lists six objections, only two of which address in any way our optical evidence. As we show below, these two objections are based on an incorrect understanding of optical perspective, which in turn results in his conclusions being in error. His other four points are logical red herrings, having no bearing on either the scientific or the visual evidence. Tyler states:
I show several lines of contrary evidence, implying that Renaissance artists constructed their compositions purely through artistic intuition, without optical aids (or accurate geometric methods).
1. Most Renaissance artists show perspective discrepancies within local regions, refuting an accurate use of optics.
Irrespective of what "most" artists might have done, this point has no logical connection with evaluating our optical evidence on certain specific artists. Aside from this error in logic, Tyler's statement implies that our discoveries are inconsistent with the existence of perspective discrepancies. Quite the opposite. Discussed at length at various places in Reference 1 are the important clues multiple perspectives within local regions provide for our discoveries.
2. Construction lines reveal the use of geometric perspective.
There are many examples of Renaissance artists who used geometric perspective, intuitive perspective, diagonal perspective, and atmospheric perspective, to name some of the possibilities. However, the fact that many artists used geometric perspective, while obviously true, is logically unrelated to evaluating our optical evidence that demonstrates certain artists used lenses to project portions of images starting as early as c1430.
3. Even if the optics were moved, all vanishing points should still lie in the horizon, a requirement violated among the discrepant vanishing points observed.
Tyler's understanding of perspective is simply wrong, as therefore are his conclusions based on the above incorrect statement. A very simple example will illustrate why Tyler is incorrect. Aim a camera down and take a photograph of the sidewalk in front of your feet. Now aim your camera at the horizon and take a second photograph. If you make a collage by taking a portion of the first photograph and pasting it over the second, obviously one set of vanishing points will be at the horizon, but the other will be somewhere overhead. Renaissance artists had complete freedom to raise or tilt their lenses as well as slide them sideways, and various examples are shown in Reference 1 where artists moved their lenses vertically.
4. Optical aids such as mirrors and lenses are not photographs; they cannot explain the ability to capture elements in motion such as rearing horses.
This statement, while true, is another red herring. Actually, while incorrectly intended as an objection to our discoveries, in fact it actually supports our understanding of how the artists worked. A lens would have been used by an artist as an aid when it helped them accomplish his or her goals, but would not have been used when it did not. The complex shape and lighting of the chandelier in van Eyck's "Arnolfini Marriage" would have been much easier to produce with the aid of a lens, but the small dog would have been eyeballed. That is, both projected and eyeballed features are within a single painting.
5. The Hockney/Falco/Graves demonstrations reveal that optical projection has a very narrow depth of field. The 'optical look' therefore should include many regions being painted out of focus. No Renaissance paintings exhibit the literal optical look of such optics.
Here Tyler makes an incorrect inference that is at variance with what we would expect from understanding human vision. Since humans automatically refocus their eyes as they scan across a scene, an out-of-focus feature does not look at all natural, except to modern people who have been inundated with such images on TV, movies, magazines, and in the viewfinders of their own still and video cameras. In fact, out-of-focus features must have looked especially unnatural to people who had never before seen projected images. Only if patrons were interested in paying for paintings containing features that appeared to them unnatural would artists have deliberately left in such out-of-focus features. Like the actual Rosetta Stone, there is every reason to expect the Lotto example to be the exception, not the rule.
Lotto's representation of an out of focus image
6. Falco's "Rosetta Stone" of Lotto's 'Santa Lucia' does not have a unified geometry of its central pattern element, even though apparent blurring implies a single optical projection zone. The perspective is locally haphazard, and is compatible only with intuitive construction.
This incorrect statement by Tyler follows from his earlier statement No. 3 about perspective, which we already have shown is wrong. Lotto was free to raise, lower, rotate, and translate his lens as well as refocus it in his ultimately unsuccessful efforts to eliminate the unnatural out- of-focus feature. The resulting perspective in that region, while more complex than Tyler can understand by drawing a few simple lines on the painting, is far from "haphazard." In fact, it is quite "optical."
 David Hockney, Secret Knowledge: Rediscovering the Techniques of the Old Masters (Viking Studio, 2001).
 nb. In case there is any possible confusion about the work being referred to here, since this painting is in the Hermitage, we use the title "Husband and Wife" as used by Colin Eisler in his book "Paintings in the Hermitage" (Stewart, Tabori and Chang, 1990).