Assignment: Thought problem.

Here's a question I almost put on the exam. This picture is one you saw in my slide-show. It is often seen in books and on book covers, supposedly from a medieval or renaissance woodcut. For example, in the book The Astrologers and their Creed, An Historical Outline Praeger, 1969, we read next to this picture, facing page 94:

German woodcut of between 1520 and 1530, illustrating the idea that the sphere of the fixed stars was not the limit of the universe.
I found this book in a university library. Sounds authoritative, doesn't it? It even identifies it as of German origin and gives a 10 year range of dates, which is rather precise when dealing with medieval history. How many students would take this information at face value and quote it in their term papers? Yet it's a lie. Now how much would you trust anything else found in this book? Or any other book in the library? Moral: compare alleged facts carefully, with a skeptical eye. Never rely on a single source.

Actually the picture is from a 19th century textbook of astronomy. The coloring of this version is obviously a modern addition. We do not know whether this image had any earlier origins. But it certainly was made to illustrate the first scientific revolution of the 17th century. Remember that your textbook spent a couple of pages discussing "Plato's allegory of the cave" (p. 23; your textbook's index is terrible). Your task was to write a short essay relating this drawing to the scientific revolution and to Plato's allegory of the cave.

Things you might have discussed.

The picture is often reproduced in textbooks with various interpretations. Often it is colorized, as is this one. But its first known appearance was in black and white, in Camille Flammarion, L'Atmosphere: Météorologie Populaire (Paris, 1888), p. 163. See Kerry Macgruder's web page for a full accounting of its history and various interpreations. Flammarion was an astronomer and writer of popular books, written in a florid style, which was described by translators as "annoying", especially in the original French. There's second hand evidence that Flammarion had the picture prepared especially for this book, but I suspect it might have originated somewhat earlier than that. However, the border devices (dragons along the top, a scroll with no words along the bottom, decorative pillars at left and right, usually cropped off when the picture is reproduced today) suggest strongly that it is certainly not as early as 17th century in origin. It is unsigned, so we do not know the name of the artist.

The caption of the picture in Flammarion's book is "Un missionaire du moyen age raconte qu'il avait trouvé le point oû le ciel et la Terre se touchent...", which translates to something like "A missionary of the present age relates that he discovered the point where the sky and the Earth touch.." Flammarion's use of this picture is rather disappointing, for others have used the picture since then and have squeezed from it (or invented) far more significance than that. This suggests to me that the picture may have been a "stock" picture of somewhat earlier (but not much earlier) vintage than 1888, and was created for a far different purpose than Flammarion's book. It may have originally had a different interpetation than has been given to it since by others who have used the picture in text books. But that hunch has no supporting evidence whatever.

However, the assignment did not ask you to inquire about the picture's origins. Considering only on what is in the picture, we can ask "What might the artist have been trying to depict?" Several points seem clear enough.

  • The celestial sphere is shown with the stars upon it. This depiction is certainly in medieval style.
  • The artist is using, in the right portion of the picture, depictions of sun, moon and stars in the style that suggests medieval artistic conventions. This is surely intentional.
  • The earth shows slight curvature, indicating that this is not meant to depict the usual flat earth. In fact, the earth surface joins the celestial sphere, which would not make sense on either the round earth or flat earth models as they are usually understood.
  • The garment of the fellow at the lower left is not 19th century.
  • This fellow is holding a shepherd's staff. The artist was not depicting a "learned academic" here.
  • On close examination we see that the man has parted the "curtain" of the celestial sphere to push his head and shoulders through. (The fact that the earth joins the celestial sphere may have been the artist's way of making it possible for the man to reach and touch the celestial sphere.)
  • The upper left shows machinery, wheels and orbs.

Flammarion's commentary about this picture is disappointing, especially after one reads the far more profound interpretations of other later sources who felt the picture was worth using and "explaining". Some see it as a metaphor for Renaissance and 17th century science, finally breaking away from the Ptolemaic planetary system, confined as it was within the celestial sphere of the "fixed" stars. Perhaps it represents man striving to "look behind or beyond the appearances" to discover the mechanism that makes everything work. This image recurs frequently in books, plays, and even movies. In the classic film "Wizard of Oz" we see it when Dorothy and her companions enter the great hall of the Wizard of Oz and see his huge face speaking at them with a booming voice But someone looks behind a curtain and sees the very ordinary Wizard working machinery to make the illusion work, and speaking into a microphone to amplify his voice. We then hear the booming voice: "The Great Oz has spoken! Pay no attention to that man behind the curtain!"

The person shown in the picture is looking at things beyond the celestial sphere of fixed stars. In the Ptolemaic universe there was nothing beyond this sphere except the "realm of the gods". Medieval artistic depictions of the cosmos showed only god and angels beyond the sphere. No gods or angels are shown in this picture, only—machinery! This is surely intentional on the part of the artist, and is the basis of most interpretations of the picture. On the simplest level, the picture shows mankind gaining a vision of the cosmos radically different from that of the ancient Greeks and the medieval Scholastics. However, commentators have various interpretations of the wheels and orbs shown in the picture.

The idea of the universe as a giant machine was arising in the 17th century. See my document on The Mechanical Universe. Most commentators credit this concept to both Descartes and Newton. Descartes' mechanics was thoroughly mechanistic, imagining even the vacuum to be made up of particles, and gave each of these particles a functional shape. Newton's mechanics was more abstract, but nonetheless he supposed that his laws of mechanics were the laws of operation of a deterministic mechanism. For those of religious inclination, it was machinery made by the Creator, working like clockwork, wound up by the Creator, and capable of running itself without intervention forever, determining everything that we observe in nature. [Newton did acknowledge that his mechanical equations did not fully account for some of the small and subtle apparent deviations of planetary motions. But Laplace later showed that they were due to gravitational interactions between the planets.]

One wonders if the artist may also have had in mind the old idea (dating to the Ancient Greeks, of 'Deux ex Machina', which literally means 'God in the machine'. We frequently hear this phrase to denote a lame plot device in which the hero is saved from a dire predicament when a God (or some other miraculous intervention) saves him. In Greek plays such miracles were often accomplished with stage machinery, for example a mechanical crane, to pluck the hero from the jaws of certain death.

Indeed, this machinery in the picture also reminds me of the 17th (and later) stagecraft that used machinery to produce the effects such as a ship being tossed in the waves of a violent storm. The stagehands working the machinery were, of course, hidden behind the curtains.

And finally, we might recall "Plato's Allegory of the Cave". It envisioned people shackled and confined in a cave, with a wall behind and in front of them, but their shackles only allow them to see one wall, on which shadows are seen. They had been there all of their lives. The shadows come from people walking behind the slaves carrying verious objects. The people in the cave have never experienced anything but these shadows in their entire lives. One of them is released (for reasons not given, and not important to the story), and allowed to walk out into the "real" world, with sunlight, trees, rocks and rivers. After some time he adapts to this, and desires to return to the cave to teach the others what the real world is like. They, of course, do not believe him, thinking he's making up fantasies. This is certainly a reasonable reaction. Plato likens this to the role of the philosopher who inquires what really underlies the world of simple appearances. Is our artist, in this picture, likening "peering outside" the celestial sphere to someone emerging from Plato's cave, to view the real world behind the simple appearances?

One commentator suggests that the picture shows someone looking beyond the appearances of the heavens to see the Ptolemaic epicycles that make it all "go". I find that hard to swallow. In the Ptolemaic model the planets and epicycles were nearer to us than the sphere of "fixed" stars, and this picture has the reverse. The two wheels with spokes at the very top left certainly are nothing like Ptolemy's epicycles.

I find it interesting that the sun and moon are depictred correctly, in relation to each other, in spite of the artistic embellishment of the face of the "man in the moon" which clearly is echoing the medieval depictions of the moon. Many artists never get the crescent moon drawn properly, and many make the same mistake that's in this picture, showing stars within the illuminated crescent of the moon. In fact, stars there would be hidden from view by the moon. But clearly this picture was not intended to be a faithful literal representation of the earth and heavens, for it shows many stars when it's still daylight (the sun is still above the horizon).

There are many websites that give the complete text of Plato's Allegory of the Cave, from Plato's Republic. I saw no evidence that any of you consulted the original. You should not rely on secondary acounts of something like this, for they may have misinterpreted it. One thing you would have noticed is that Plato did not have science in mind. His purpose was to discuss what sort of person is best as a political leader. In my view, the frequent use of this allegory to illustrate a concept of philosophy of science is an extension of the idea beyond what Plato may have had in mind. I'd have been pleased if any one had said that the picture has only tenuous relation to Platos' allegory, and justified your judgment with commentary. Yet we must acknowledge that an allegory or analogy sometimes has uses beyond those its original author had in mind.

A note on Flamarrion's interpretation.

As we noted above, Flamarrion uses this picture in his 1888 book, and used it in an unexpected way. His book is about things we see in the sky. Here's an English translation, from Kerry Macgruder's web page:

Whether the sky be clear or cloudy, it always seems to us to have the shape of an elliptic arch; far from having the form of a circular arch, it always seems flattened and depressed above our heads, and gradually to become farther removed toward the horizon. Our ancestors imagined that this blue vault was really what the eye would lead them to believe it to be; but, as Voltaire remarks, this is about as reasonable as if a silk-worm took his web for the limits of the universe. The Greek astronomers represented it as formed of a solid crystal substance; and so recently as Copernicus, a large number of astronomers thought it was as solid as plate-glass. The Latin poets placed the divinities of Olympus and the stately mythological court upon this vault, above the planets and the fixed stars. Previous to the knowledge that the Earth was moving in space, and that space is everywhere, theologians had installed the Trinity in the empyrean, the angelic hierarchy, the saints, and all the heavenly host.... A missionary of the Middle Ages even tells us that, in one of his voyages in search of the terrestrial paradise, he reached the horizon where the earth and the heavens met, and that he discovered a certain point where they were not joined together, and where, by stooping, he passed under the roof of the heavens.... And yet this vault has, in fact, no real existence! I have myself risen higher in a balloon than the Greek Olympus was supposed to be situated, without being able to reach this limit, which, of course, recedes in proportion as one travels in pursuit of it—like the apples of Tantalus.

Flamarrion begins by alluding to the famous "flattened-dome" sky illusion, a distortion of visual perception that gives rise to the moon illusion and related illusions of the sky.

One foot of the rainbow [NASA]

Macgruder notes that he could only trace the anecdote of the "missionary" back to Voltaire. One theme of this passage seems to be that what we perceive with unaided senses, such as the flattened dome of the sky, is often not the reality. Another theme is the literary allusion to something that is desirable but out of reach, or unattainable. Our word "tantalize" derives from the Tantalus myth. The "place where earth meets the sky" is another literary allusion of indeterminate origin, imagining that it's a place where things are much better than elsewhere, being where the heavens touch earth. You can "see" where sky meets earth at the horizon, but you cannot reach that place, for it recedes as fast as you move toward it, tantalizing you.

A comparable example is the rainbow. Legend has it that if one could reach the end of the rainbow (where it touches earth) you'd find a pot of gold. But you never can reach it, for the rainbow is at your visual infinity, and moves away from you as fast as you move toward it, and disappears when there's no water droplets in the air to disperse the light into colors. So "chasing rainbows" has become a metaphor for believing in illusions.

Flammarion's reference to his asending in a balloon is correct. He did make balloon flights for research purposes, and in the press he was often caricatured riding in the gondola of a balloon with a telescope in hand. He wrote a book about his balloon flights. One of these flights was his honeymoon trip in a hot air balloon with his new bride. He had invited the parish priest to come along, but he declined, having a lunch commitment with relatives in the Marne valley. An often-related coincidence occured. Hot air ballons are at the whim of the winds, but the winds that day happened to take Flammarion and his bride directly over the garden where the priest was having lunch.

Isn't it wonderful what richness can be revealed when one analyzes a picture, even a textbook picture, and follows all the leads? Here, from just one intriguing picture we have been stimulated to wander through history, science, and literary allegories. This is very much in the spirit of a liberal arts education.

    —Donald E. Simanek, Feb, 2005