Professor Smith European Studies Department Europe Studies 10 European History Course Code: 24000 ● Renaissance Art, God, Mathematics, and Anamorphosis ○ Mathematization of Painting ■ Painting, through linear perspective, could be potentially elevated to the status of science ■ Why does linear perspective provide this possibility for art to be considered a science? ■ The physical laws that govern how vision operates are the same laws used to create linear perspective art ■ To look at a canvas is now like looking through a glass window onto nature itself ■ Artists can now take part in the re-creation of nature ■ “The creator, the true first cause of geometry… as Plato says, always geometrizes… those laws [which govern the material world, including vision] lie within the power of the human mind: god wanted us to perceive them when he created us in his image in order that we may take part in his own thoughts” - Johannes Kepler 1599 ■ Thus, the rise of linear perspective in painting coincides with the rise of humanism in Europe ■ Through art and science human begins become “little creators” (imitating god as the Creator of the universe) ■ Art can now provide more than a mirror of nature; it is a window into nature ■ Through painting, we can learn to read the book of nature ■ What is the book of nature? ● “Book of Nature” ○ This is an old “trope”, i.e., a metaphorical expression ○ Goes back to the European Middle ages ■ If we learn about god by reading the books of scripture, then the parallel thought was that nature, also, can be understood like a “book” ■ As a “book”, it means that we need to “read” and “interpret” nature ■ But what is the “language” of this book? ● Galileo and the book of nature ○ “Mathematics is the language with which god has written the universe” ○ Although we will return to these ideas in the next lectures, for now the point is that Galileo is writing nearly 200 years after Brunelleschi and Alberti were writing on linear perspective ○ That is, renaissance art and the technique of linear perspective introduced a mathematical approach to seeing the world long before it became the provenance of science● Galileo and Perspective (Edgerton) ○ “...Galileo Galilei, the great astronomer and physicist… a direct descendant of his native city’s [Florence] illustrious artistic tradition” ○ “In fact, Galileo was both a talented draftsman and a teacher of perspective drawing and shadow rendering” ○ “The Geometry of its [the telescope’] function, as Galileo himself diagrammed it later, was essentially based on the same Euclidian optical model as Alberti’s perspective” ○ And not just Euclid ■ Also Al-Hasan ○ Linear perspective not just a technique, but a “symbolic form” as well ■ Transformation of western culture that also led to the rise of mathematically based science ● Representing the divine mathematically ○ If god wrote the book of nature in mathematics, how would god be made visible in mathematical representations of the natural world? ○ It’s easy for the vanishing point to be equated with the divine ○ It’s infinitely far away, not a physical place ○ The converging lines will never actually “touch” it ○ And yet, the vanishing point can make “objective” or representable (or visible through mathematics) what is “intangible” or unpresentable (the divine or truth) ○ It’s a way of bringing the infinite into the world ○ The renaissance was a time when theology started to treat the divine/infinite not so much as something beyond this world but, rather, as something that human beings could experience or bring into this world ● The infinite in the finite? The divine in the world? ○ Why address these questions? ○ Recall: edgerton’s thesis or claim was that it was under the particular conditions of Florence around 1400 that linear perspective emerged ○ These questions about the ability to experience the divine or infinite in the world were crucial religious issues ○ Thus, it makes sense that the technique of linear perspective emerged then and there ○ But this means that religious issues were in part behind the rise of a scientific development ● An Alternative to Representing the Divine in Perspective ○ Nicholas of Cusa ○ German philosopher, theologian, mathematician, and astronomer ○ Writing at the same time as Brunelleschi and Alberti, but he’s in Germany, not Italy ○ “On Learned Ignorance” (1453) ■ Explores the nature of the divine and what we can grasp of the divine nature ● Understanding the divine in with math ○ Two of the chapters have the titles:■ 11. Mathematics assists us very greatly in apprehending various drives [truths] ■ 12. The way in which mathematical signs ought to be used in our undertaking ○ God is infinite ○ As the maximum or greatest being, god contains everything ○ In god there is the “coincidence of opposites”, that is, in god opposites come together ● We can’t fully grasp god, but we can get a sense by reflecting on the infinite ○ The diameter of a circle is a straight line, and the circumference is a curved line which is greater than the diameter ○ So, if the curved line becomes less curved in proportion to the increased circumference the circle, then the circumference of the maximum circle, which cannot be greater, is minimally curved and therefore maximally straight ○ Hence, the minimum coincides with the maximum - to such an extent that we can visually recognized that is necessary for the maximum line to be maximally straight and minimally curved ○ Not even a scruple of doubt about this can remain when we see in the figure here at the side that arc CD of the larger circle is less curved than arc EF of the smaller circle, and that arc EF is less curved than arc GH of the still smaller circle ○ Hence, the straight line AB will be the arc of the maximum circle, which cannot be greater ○ And thus we see that a maximum, infinite line is, necessarily, the straightest, and to it no curvature is opposed ● Cusa one of the first thinkers of modernity ○ In a sense, nicholas of Cusa is still a medieval thinker: he says “there is no proportion/comparison” between god as infinite and human beings is finite ○ But on the other hand, it is telling that he turns to mathematics ■ The