by Larry Witham
2.Piero’s On Perspective, quoted in Judith V. Field, Piero Della Francesca: A Mathematician’s Art (New Haven, CT: Yale University Press, 2005), 130.
3.Johann Wolfgang von Goethe, Theory of Colors, notes by Charles Lock Eastlake (Cambridge, MA: MIT Press, 1970 [London: John Murray, 1840]). See also Dennis L. Sepper, Goethe Contra Newton: Polemics and the Project for a New Science of Color (New York: Cambridge University Press, 1988). The famous Newton-Goethe debate has often been taken as the first sign of the split between the humanities and the natural sciences, which widened after the era of Hermann von Helmholtz, who also engaged the debate with Goethe.
4.Hermann von Helmholtz, “An Autobiographical Sketch,” Selected Writings of Hermann von Helmholtz, ed. Russell Kahl (Middletown, CT: Wesleyan University Press, 1971), 472.
5.For the Renaissance tools see Hermann von Helmholtz, “The Relation of Optics to Painting [1871],” Selected Writings, 299-306. These include linear perspective and shadow, and space and form created by magnitude or how one object obscures another. There is also the effect of atmosphere on distant colors, which artists simulate by using “aerial perspective.” The artist also can deliver to the eye the effect of the brightest sunlight by a contrast of painted colors, when in fact the luminosity of the Sun is infinitely more than white paint.
6.For example, the system sees a red apple as red all the time, even though the eye can interpret red by a few possible combinations: by a direct red wave, by a contrast with another color wave, or by the momentary fatigue of nerve cells.
7.Hermann von Helmholtz, “Recent Progress of the Theory of Vision,” Selected Writings, 175-77. Helmholtz clarified that each of the three had subtle features: 1) Hue puts a color in one of the seven or so categories of the light spectrum; 2) Intensity is the purity of color. In paint, it is a color with no mixture of light or dark, and in the visual spectrum, it is the more precise wavelength for the pure color; 3) Brightness is also called luminosity, which, as it turns out, is a measure of dark or light relative only to the eye (and not to an electronic device, for example).
8.Hermann von Helmholtz, “Goethe’s Anticipation of Subsequent Scientific Ideas [1892],” Selected Writings, 487.
9.Helmholtz, “The Relation of Optics to Painting [1871],” Selected Writings, 313, 323. In the generation after Helmholtz, the art historian Heinrich Wölfflin (1864-1945), seeking a scientific basis for art interpretation, emphasized the role of the physical, biological “eye” in perceiving stylistic changes in paintings.
10.Linda Dalrymple Henderson, The Fourth Dimension and Non-Euclidean Geometry in Modern Art (Princeton, NJ: Princeton University Press, 1983), 70.
11.Some of the Cubists, for example, were attentive to the late-nineteenth-century revival of interest in Leonardo da Vinci as a geometer, and to the Renaissance concept of the “golden section,” with its roots in Pythagorean and Platonist mysticism. It would turn out, however, that the golden ratio—a proportion of 1 to 1.6—has never been found in a Renaissance painting or one that was done by the Cubists. This would have required, for example, to put those exact proportions into a painted composition, and no such precise dimensions were really pursued, it seems. It was long believed that Leonardo used the golden section, but research has looked in vain. (See Ross King, Leonardo and the Last Supper [New York: Walker and Company, 2012], 170-74.) Either way, the Cubists were attracted by the idea, as illustrated by their use of the term “golden section.” When the term “Cubism” was getting worn out in popular and media usage, the Parisian Cubists named their famous 1912 exhibition Section d’Or, the Golden Section, a synonym for the golden ratio as an alternative.
2.For a history of the science of light and its relationship to psychology and religion see Arthur Zajonc, Catching the Light: The Entwined History of Light and Mind (New York: Bantam, 1993).
13.There are a few models for how the brain produces “mind.” The prevailing scientific one today is the computer “parallel processing” model. Related to this—and adopted by both scientists and some theologians—is the idea that “mind” is a higher “emergent property” of the brain’s unfathomable physical complexity. Thirdly, in the tradition of dualism, the mind is something independent of the brain, or working in parallel with it. This kind of dualism originated in the Platonist and Christian idea of soul and, modernly, in René Descartes’s “thinking substance.” Dualism has had modern advocates in such people as the Nobelist neuroscientist John Eccles, but it primarily is a theological argument that questions how human identity is maintained if all brain cells are replaced several times in a lifetime, or that acknowledges the testimony of people’s transcendent experiences. See Owen Flanagan, The Problem of the Soul (New York: Basic Books, 2002); Ric Machuga, In Defense of the Soul (Grand Rapids, MI: Brazos Press, 2002); and Warren S. Brown, Nancey Murphy, H. Newton Malony, eds., Whatever Happened to the Soul? Scientific and Theological Portraits of Human Nature (Minneapolis, MN: Fortress Press, 1998).
14.For an overview of the anatomical and hierarchical system of the “visual pathway” see David Hubel, Eye, Brain, Vision (New York: Scientific American Library, 1988), 26-28.
15.Francis Collins, director of the National Institutes of Health, speaking on the PBS “Newshour,” February 20, 2013: He said there are one hundred billion neurons and each one has about ten thousand connections. “That means there’s something like one thousand trillion connections inside your brain.”
16.Hubel, Eye, Brain, Vision, 3. Hubel notes that the clear anatomy of visual nerves and their arrival at the visual cortex in the back of the head have made vision easier to study: “The visual cortex is perhaps the best-understood part of the brain today and is certainly the best-known part of the cerebral cortex.”
17.The scientist who first formalized the color-opponent theory was Ewald Hering (1834-1918), who built upon the earlier intuitions of Aristotle and Goethe. In 1874, Hering contested the tricolor mixing theory and instead proposed that the visual brain had a three-“opponent” system: red versus green, yellow versus blue, and black versus white. This not only explained the origin of color, but also features of color blindness; some people can see red but not green; blue but not yellow. What Hering lacked was experimental or physiological evidence. Nevertheless, these two rival theories now dominated optics. The longstanding tricolor theory would hold the field, favored by physicists, knowledgeable as they are about tricolor experiments with light and color wheels. By contrast, the new field of psychology became supportive of Hering’s oppositional theory. Eventually, the two theories have been tentatively reconciled (as nerve cells were shown to be able to inhibit, or oppose, each other, as well as mix primary colors). On Hering see Hubel, Eye, Brain, Vision, 172-74.
18.Margaret Livingston, Vision and Art: The Biology of Seeing (New York: Abrams, 2002), 86.
19.Semir Zeki, Inner Vision: An Exploration of Art and the Brain (New York: Oxford University Press, 1999), 61.
20.Livingston, Vision and Art, 50-52, 64-65.
21.Ibid., 64-65.
22.Hubel, Eye, Brain, Vision, 86.
23.Ficino, quoted from his De amore in John Hendrix, Platonic Architectonics: Platonic Philosophies and the Visual Arts (New York: Peter Lang, 2004), 143.
24.Several philosophers of the mind have explained why there is an ultimate barrier to science’s locating and explaining human consciousness, including Thomas Nagel, John R. Searle, and Colin McGinn. They were famously called the “new mysterians” by the more optimistic materialist philosopher Owen Flanagan in his Science of the Mind (Cambridge, MA: MIT Press, 1991), 313. Flanagan said: “The old mysterians were dualists [like Plato]… . The new mysterians are naturalists” [like all materialists].
25.Helmholtz, “Recent Progress of the Theory of Vision,” 213.
26.For a summary of why and how the brain and visual arts seek constants and essences see Zeki, Inner Visi
on, 1-12. For the psychology of essences see Paul Bloom, How Pleasure Works (New York: Norton, 2010), 8-24, 205-17.
27.My overlapping of Platonism and neuroscience (that is, arguing that both say essentially the same thing, but disagree on the material v. transcendental nature of the universe), may seem implausible to neuroscience. However, it is neuroscience itself that constantly targets Plato as its enemy, keeping Plato very much in the game. The critics of Platonist dualism of mind and body say that the essences Plato talked about are not “out there,” but have now been found in brain functions: modules and cells. I am simply continuing to contrast these two historic rivals, supposing that the natural v. transcendental question about reality remains open, even in an “age of science.” For the consistent rejection of “Platonism” in favor of neuroscience, see the writings of neuroscientist Semir Zeki (Inner Vision) and art historian John Onians (Neuroarthistory). Meanwhile, one critic of neuroscience, the philosopher Alva Noë (Out of Our Heads), says that both Platonist idealism (by way of Descartes) and neuroscience share the identical problem of seeking reality inside the head, whereas the postmodernist view congenial to Noë’s school of thinking says that human thought and perception, and indeed personal identity, are “socially constructed” by external factors ranging from power structures to friendships and language.
28.Gilbert Ryle, The Concept of Mind (Chicago: University of Chicago Press, 2000 [1949]), 15-16.
29.Zeki, Inner Vision, 22; John Onians, Neuroarthistory: From Aristotle and Pliny to Baxandall and Zeki (New Haven, CT: Yale University Press, 2007), 183, 187. Zeki hypothesizes that, in neurological terms, “Great art can thus be defined … as that which comes closest to showing as many facets of the reality, rather than the appearance, as possible and thus satisfying the brain in its search for many essentials.” Onians cites the concept that compelling art stimulates the brain’s “proper perception” and thus produces pleasure.
30.For a summary of biological theories on contemplative beauty and “disinterested” pleasure see Jennifer Anne McMahon, “Beauty,” The Routledge Companion to Aesthetics, ed. Berys Gaut and Dominic McIver Lopes (London: Routledge, 2001), 227-238. This basic experience of mental pleasure obviously goes beyond art, but in all cases has similar contemplative and disinterested features as well as an aspect of perceiving essences: this happens with enjoyment of stories, discoveries of principles, or seeing a puzzle solved (and thus, for example, the pleasure of beauty is found in mathematics and scientific answers). For all of this broader interpretation of beauty see Bloom, How Pleasure Works, 227-238.
31.For counterintuitive theories of religion see Pascal Boyer, Religion Explained (New York: Basic Books, 2001), and Todd Tremlin, Minds and Gods: The Cognitive Foundations of Religion (New York: Oxford University Press, 2006).
32.For the ability of the brain to change, repair itself, and “rewire” damaged areas see Norman Doidge, The Brain That Changes Itself (New York: Viking, 2007); and Jeffrey M. Schwartz and Sharon Begley, The Mind and the Brain: Neuroplasticity and the Power of Mental Force (New York: Regan Books, 2003). The new research relates to the repair of lost brain faculties and the apparent ability of “mind,” separate from the brain’s machine-like biology, to alter brain patterns. The plasticity, however, does not suggest that the basic cognitive powers or limits of the physical brain can be altered. In the new fields of “neuroaesthetics” and “neuroarthistory,” it is presumed that the plasticity causes changes in art appreciation and perception. This remains to be tested: it would require comparative brain scans, for example, of people over a few generations in different countries and cultures to see how new neurological growth in the brain (that is, new patterns of neuron connections) are stimulated by culture and thus cause entirely new kinds of physical perceptions. Current science shows that attitudes, such as “positive thinking,” can indeed heal the brain, or that impairment of hearing, sight, or phobias can be altered by daily practice—but these are different sorts of changes from experiencing a high level of “notable pleasure” from beautiful art. Interestingly, the leading medieval commentator on optics, Erasmus Witelo, noted how art perception has both constancy (he was a Platonist) and variety: “Each person,” said Witelo, “makes his own estimate of beauty according to his own custom.” Quoted in Umberto Eco, Art and Beauty in the Middle Ages, trans. Hugh Bredin (New Haven, CT: Yale University Press, 2002 [1959]), 69. As seen in Witelo, Platonism acknowledges constancy and change.
33.Suzanne Nalbantian, “Neuroaesthetics: Neuroscientific Theory and Illustration from the Arts,” Interdisciplinary Science Reviews 33 (December 2008): 357-68. As Nalbantian notes, neuroaesthetics received its formal definition in 2002: “The scientific study of the neural bases for the contemplation and creation of a work of art.”
34.Michael Baxandall, Painting and Experience in Fifteenth-Century Italy (Oxford: Oxford University Press, 1972).
35.Quoted in Michael Baxandall, “Fixation and Distraction,” in Sight and Insight: Essays on Art and Culture in Honour of E. H. Gombrich, ed. John Onians (London: Phaidon, 1994), 413.
36.For a classic statement on the biological objectivity of visual linear perspective see James T. Gibson, “Perspective and Perception,” Daedalus 89 (Winter 1960): 216-27.
37.Zeki, Inner Vision, 22-29.
38.Livingston, Vision and Art, 71-73.
39.Zeki, Inner Vision, 205-208.
40.On Impressionism and Cubism see Livingston, Vision and Art, 74-76, 125-33, 153-60, 77.
41.Ibid., 115. See John Shearman’s study of Leonardo’s luminescence cited here.
42.Michael Baxandall, Words for Pictures: Seven Papers on Renaissance Art and Criticism (New Haven, CT: Yale University Press, 2003), 148. He lists Piero’s psycho-visual techniques for creating depth as: 1) interposition: masking part of a familiar object by another; 2) foreshortening: familiar object at angles to picture plane; 3) discernible recession of ground plane: “texture gradient”; 4) height in relation to a horizon: the higher, the farther; 5) reduction of the known size of an object with distance; 6) the relative diminution of similar objects with distance; 7) cast shadows in discernible relation to the casting object; 8) the modeling of volumes by shading and self-shadow; 9) degradation of distinctness of color (or reduced acuity); and 10) degradation of distinctness or color (atmosphere).
43.E. H. Gombrich, Art and Illusion, second edition (Princeton, NJ: Princeton University Press, 1961 [1960]), 332.
44.Thomas Martone, “Spatial Games in the Art of Piero della Francesca and Jan Van Eyck,” in Emiliani, PDFSA, 95-109.
45.Typically, counterintutive events are anything that defies normal expectations, and thus it may be when action is frozen. On the counterintutive and transcendent belief see Boyer, Religion Explained, and Tremlin, Minds and Gods. The sociologist Peter Berger has written on this phenomenon in Peter L. Berger, A Rumor of Angels: Modern Society and the Rediscovery of the Supernatural (Garden City, NY, Doubleday, 1969); and Peter L. Berger, A Far Glory: The Quest for Faith in an Age of Credulity (New York: Free Press, 1992).
46.Zeki, Inner Vision, 205-208.
47.John Pope-Hennessy, The Piero della Francesca Trail (London: Thames and Hudson, 1991), 69.
48.Psychology and economics have accepted the way humans establish value for various objects. Those critical of this acceptance have been Karl Marx, who called such values “fetishes,” and the Marxist-leaning art theorist Walter Benjamin, who lamented that art with such an essence has an “aura” that is illusory.
CHAPTER 11
1.Banker, CSS, v.
2.Ibid., 136.
3.James R. Banker, “Three Geniuses and a Franciscan Friar,” lecture, The Frick Collection, New York City, March 20, 2013.
4.Anthony Molho, “The Italian Renaissance, Made in the USA,” in Imagined Histories: American Historians Interpret the Past, ed. Anthony Molho and Gordon S.
Wood (Princeton, NJ: Princeton University Press, 1998), 273. See Molho’s entire “The Italian Renaissance” chapter (263-94) for a survey of American views of the Renaissance, especially in scholarly circles, since the nineteenth century.
5.Important compatriots of Becker in this project abroad were Gene Brucker and Donald Weinstein. See Donald Weinstein, “Introduction,” Marvin Becker, Florentine Essays: Selected Writings of Marvin Becker, ed. James R. Banker and Carol Lansing (Ann Arbor, MI: University of Michigan Press, 2002), 1-10.
6.On the German approach and influence in the United States see Molho, “The Italian Renaissance,” 271-76.
7.See Becker’s recollections in “Afterword,” Becker, Florentine Essays, 308-12. As with the United States, each postwar nation had its characteristic approach to the Renaissance. In Italy, it was studied as part of modern history up to the Italian unification in 1870. Before the war, Italian historians looked mainly for antecedents in ancient Rome and the medieval commune—both ideals of Benito Mussolini’s fascist state. When Becker had arrived in the 1950s, Italy was sharply divided between extreme parties on the left and right, and the Renaissance was of no use, it seemed, to either side. In Germany, despite its rich contributions to art history, the Reformation still dominated historical studies. See Paul F. Grendler, Encyclopedia of the Renaissance, vol. 5 (New York: Charles Scribner’s Sons, 1999), 283-85.
8.For histories of the Warburg and Courtauld Institutes see their Web sites: (http:warburg.sas.ac.uk/home/) and (http:www.courtauld.ac.uk/about/history.shtml). For histories of the Courtauld see “About Us” at the Web site. On the Warburg-Courtauld alliance see Elizabeth McGrath, “A Short History of the Journal,” at (http:warburg.sas.ac.uk/publications/journal/short-history-of-the-journal/).
9.Historian Carl Becker, quoted in Wallace K. Ferguson, The Renaissance in Historical Thought: Five Centuries of Interpretation (Boston: Houghton Mifflin, 1948), 196.
