University of Arizona, and Hockney's studio
 Charles M. Falco and David Graves
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Summary

Elsewhere within this site Christopher Tyler and David Stork stated various objections to our evidence that certain Renaissance painters as early as c.1430 used lenses as aids for some of the features in some of their works. However, as we have shown, all of Tyler's and Stork's objections arise from their errors in logic, lack of historical knowledge, or misunderstanding of perspective, resulting in none of them having any relevance whatever for the evidence reported in either Reference 1 or Reference 4. To summarize:

Christopher Tyler lists six objections, only two of which address in any way our optical evidence. However, as we have shown, these two objections are based on Tyler's simple misunderstanding of optical perspective, which in turn resulted in him arriving at incorrect conclusions. His other four points have no bearing on either the scientific or the visual evidence.

David Stork's arguments reduce to: 1) there is no historical documentation of the existence of appropriate mirrors and lenses during the early Renaissance; 2) artists had sufficient talent that they wouldn't have needed to use lenses anyway; and 3) it would have required an impossible number of candles to provide sufficient illumination to use such lenses. We have shown above that 1) documentation certainly does exist that demonstrates appropriate mirrors and lenses were being produced and used as imaging devices as early as the 13th century; 2) the question of whether or not artists had the talent to paint without the aid of lenses is a logical red herring, unrelated to evaluating the evidence we have presented that, irrespective of their skill level, certain of them indeed did use such lenses; and 3), as we clearly stated in New York, they didn't use candles, they used sunlight.

For anyone who has taken the time to read this far, it is perhaps worthwhile to briefly summarize our optical evidence that certain painters as early as c.1430 used "lenses"Ñrefractive lenses or concave mirrorsÑto aid them in creating portions of certain of their paintings. Within those paintings we have studied that show evidence of the use of lenses, every optical artifact we have identified is consistent with having resulted from the use of lenses to project portions of the images. Where sufficient details exist to allow us to extract quantitative information (e.g., of focal length or lens diameter), the values we determined are not only reasonable, they have allowed us to quantitatively reproduce the observed effects photographically. Further, we have found no features that are inconsistent with the use of optics (e.g., something that implied, say, an unrealistically short or long value for a focal length).

A lens isn't merely the simplest explanation for the discoveries reported in Reference 1, it is the explanation that accounts quantitatively and qualitatively for everything that we have discovered. Rather than invoking separate ad hoc reasons for each distinct optical artifact we have identified, or using the opaque shroud of "artistic genius" as a substitute for comprehension of any of this, we emphasize again that all the optical evidence we have discovered is explained by the properties of concave mirrors and lenses. Wide new areas of inquiry are now open to pursue the implications of these discoveries.


Charles M. Falco is a Professor of Optical Sciences at the University of Arizona where he holds the UA Chair of Condensed Matter Physics. He is a Fellow of both the American Physical Society and the Optical Society of America, has published more tham 250 scientific articles (including one in 'Optics and Photonics News' with David Hockney), coedited two books, and has seven U.S. Patents. In addition to his scientific research, in 1998 he shared an award from the AICA for his curatorial work on the Solomon R. Guggenheim Museum's 'The Art of the Motorcycle.'

David Graves works closely with David Hockney.


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