The Flammarion Woodcut


I bet you have seen this picture before. If not in black and white, then perhaps you’ve seen in it in colour. This is a much recycled illustration, reprinted many times, with or without adaptation, in various books, on book and magazine covers, posters and adverts.  This illustration is famous on at least two accounts. First, it is famous on account of its uncertain date and origin. For instance, Ernst Zimmer, a German historian of astronomy, thinks that the woodcut goes back to the early 16th centuty, to the school of Albrecht Dürer. Owen Gingerich, the historian of astronomy of Harvard University and the Smithsonian, is convinced that it occurs for the first time in Ernst Kraemers five-volume popular science book Weltall und Menschheit from 1907. However, two scholars, Arthur Beer, an astrophysicist and historian of German science at Cambridge, and Bruno Weber, the curator of rare books at the Zürich central library, have independently traced the illustration back to Camille Flammarion’s popular science book L’atmosphère: météorologie populaire from 1888.

Second, the illustration is famous on account of its rich symbolism which is taken to represent the mediaeval world-view. The illustration depicts a flat Earth bounded by the sky. The man, dressed as a mediaeval pilgrim and carrying a pilgrim’s stick, peers through the boundary and sees the hidden workings of the universe. The prominent element of the cosmic machinery in the top left corner looks like the “wheel in the middle of a wheel” described in the visions of the Hebrew prophet Ezekiel (1:4-26). You can learn more about the woodcut’s symbolism from the wikipedia page dedicated to it and from Kerry Magruder’s page. What you cannot learn there, however, is the following.

Look at the pilgrim’s stick. Curious place to lay it down, don’t you think? Why would the stick be laid down half protruding through the curtain of the sky? Here is an explanation. The illustration is probably making reference to a famous passage from Simplicius’ commentary on Aristotle’s Physics, in which Simplicius refers to Eudemus’ report of Archytas’ thought experiment. (Eudemus of Rhodes was Aristotle’s pupil who wrote a history of astronomy, and Archytas was a Pythagorean philosopher whom Plato knew and from whom he probably learnt much of what he says in the Timaeus.) Anyway, here’s Archytas question:

“If I came to be at the edge, for example at the heaven of the fixed stars, could I stretch my hand or my stick outside, or not? That I should not stretch it out would be absurd, but if I do stretch it out, what is outside will be either body or place.”

“Thus Archytas will always go on,” Simplicius recounts, “in the same way to the freshly chosen limit, and will ask the same question. If it is always something different into which the stick is stretched, it will clearly be something infinite” (In Arist. Phys. 467.26-32).

The Epicureans and the Stoics used and elaborated on Archytas’ argument for the infinity of space or void. Also, it is found in slightly different versions in Locke, Newton and Kant. Modern physics would answer that space could be finite without having an edge, as presupposed by Archytas’ argument.

Be that as it may, I think we have an explanation for the protruding stick. Whoever was the author of the woodcut, he seems to have known the original Archytas’ formulation of the argument which mentions stretching out “hand or stick”.

Dürer’s Melancolia I


In 1513-14 Albrecht Dürer (1471-1528) produced three well-known engravings: Knight, Death and the Devil, St. Jerome in His Study and Melancolia I. Tons of literature have been written on them, together and individually. This is not to say that I read much of it. However, I’ve been impressed by Melancolia I, and I’d like to share a few modest observations about it. (1) There is something odd about the title of the picture; I suppose that the right way to transcribe the Greek word (‘black bile’), today as well as in Dürer’s age, would be melancholia. (2) The word melancholia has many different meanings, often incompatible ones. A gargantuan discussion of the notion of melancholy is found in Richard Burton’s The Anatomy of Melancholy from 1621. Given that the female character which represents melancholy is holding a compass, is surrounded by sculpting and carpenting tools, and is laureled, it is clear that Dürer took melancholy to be a creative force. “Why is it that all men who have become outstanding in philosophy, politics, poetry or the arts are melancholic?” This is the question with which Book XXX of Ps.-Aristotelian Problemata starts (953a10-12). This idea is picked up by Marsilio Ficino, who wrote in his De Vita, a popular book that Dürer knew in German translation: “All men of excellence in any art have been melancholics.” (3) The female character is winged, like an angel. Arguably, this suggests that melancholy is God-sent, or that it is God’s gift to humans. (4) Sand-clock on the wall (detail). Above it is the gnomon, or sun-dial. Curiously, the sun-dial does not cast a shadow, although it should, given the direction of light. The sand in the clock is running, and it seems (thogh I’m not sure) that about a half of it is left. Moreover, the design of the sand-clock is not symmetrical, which may suggest that it is not rotatable, and that may imply irreversibility of time. Interestingly, sand-clock is present on all three engravings from 1513. (5) The magic square (detail). The sum of the numbers in all rows, columns and on both diagonals, is 34. I’m not sure if this particular number has any special significance. However, the square contains the date of Dürer’s mother’s death: 16. 5. 1514. The first number top left is 16, the next two are 3 and 2 (3+2=5), and the middle two numbers in the bottom row are 15 and 14.

I would be interested to learn the significance of other details of this engraving, such as the bell and the scale on the wall, the pentagonal sculpture at which Melancholy looks, the curled animal next to her feet, the comet in the sky, etc.

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