Next we look at Flagellation by Piero della Francesca (c. 1458-59), which is meant to reveal something to us about how images were read in this time (What Dr. Herbert calls the period eye). In the figure, there are 15th century Italian men in the right half of the image. In the left half of the image, there is a scene of Jesus being whipped. To the person viewing this image at the time it was painted, both halves of the scene were very familiar. An important detail about the painting is the way in which the tiled floor of the plaza is depicted. Dr. Herbert's point is that in order to thrive in a merchant economy, people had to have a good ability to judge measurements and shapes just by looking at something at a distance. This requires the ability to recognize ratios and proportions. The tiles are painted in a way meant to imitate the way that tiles look at a distance. The distance between the white bands of tile in real life would be the same. In the image, the distance between the white bands decreases. Painters could use mathematic ratios to calculate how to depict this perspective.
Next we look at Christ Handing the Keys to Saint Peter by Perugino. This image is a great example of the vanishing point. The idea is that on the surface of the image, the distance between two points is finite and measurable. However, as a depiction of real space, the lines that go towards the vanishing point are parallel and will never meet. In this way, what is infinite is portrayed by means of a finite line. Imagine, for example, a picture of railroad tracks that extend out into infinity. Perhaps these railroad tracks go into space forever. In actuality, the distance is infinite. Yet when portrayed in a 2D image, the tracks will meet at the vanishing point. The vanishing point is a finite, concrete place in the painting which portrays something that is infinite. In this way, the vanishing point is both finite and infinite.
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