Saturday, 16 September 2017

Craters on the Moon (or Science in Very Unlikely Places)



In the Tudor period nobody talked of, or wrote of, craters on the Moon. Leonardo DaVinci mentions only spots (macchie) but his drawing of the first quarter Moon from 1511 does not show any spots.

Even in 1611 Galileo still used expressions like "large or ancient spots" although he does use the word cavity to describe a large round depression on the lunar surface which is thought to be the crater Albategnius. The term crater was not used much later until 1700 by Allard. However, even before the Tudor period people were aware of light and dark spots on the Moon and descriptions and an image of them turn up in the most unlikely of places. Jan van Eyck in his 1440/41 diptych Crucifixion/Last Judgement includes a small image of the Moon. However, not much detail can be seen just five darker coloured patches on a bright background.See

However, even more interesting is Dante's Divine Comedy. Dante's long poem about Heaven, Hell and Purgatory includes some very interesting science. In the Paradise Section 2, verses 46 to 105 Dante's guide Beatrice explains to him the reason for the dark non reflective patches that are clearly visible on the Moon to an observer on Earth.

Paradiso Canto II:46-105 The Shadows on the Moon "I replied to her: ‘Lady, I thank Him who has raised me from the mortal world, as devoutly as I can, but tell me what are those dark marks on this planet, that make the people down there on earth make fables about Cain?’ She smiled a moment, and then said: ‘If human opinion errs, where the key of the senses cannot unlock it, the arrows of amazement should certainly not pierce you, since you see that Reason’s wings are too short, even when the senses can take the lead. But tell me what you yourself think about it.’ And I: ‘I think what appears variegated to us up here, is caused by dense and rare bodies.’ And she: ‘You will see that your thought is truly submerged in error, if you listen attentively to the argument I will make against it. The eighth sphere, the Stellar Heaven, shows many lights to you, which can be seen to have diverse appearance, in quantity and quality. If rarity and density alone produced that effect, there would be one quality in all of them, more or less equally distributed. Different qualities must be the result of different formal principles, and on your reasoning, only one could exist. Again, if rarity were the cause of those dark non-reflecting patches you ask about, this planet would be short of matter in one part, right through: or, as a body layers fat and lean, it would have alternate pages in its volume. If the first were true, it would be revealed by solar eclipses, when the light would shine, through the less dense parts, as it does when falling on anything else that is translucent. That is not so: so we must consider the second case, and if I can show this is false also, your idea will have been refuted. If this less dense matter does not go right through, there must be a boundary, beyond which its denser opposite must prevent light travelling on, and from that boundary the rays would be reflected, as coloured light returns from glass that hides lead behind it. Now you will say that the ray is darker here than elsewhere because it is reflected from further back. Experiment can untangle you from that suggestion, if you will try it, which is always the spring that feeds the rivers of your science. Take three mirrors, and set two equidistant from you, and let the third, further away, be visible to your eyes, between the other two. Turn towards them, and have a light behind you, reflected from the three mirrors, back towards you. Though the more distant has a smaller area, you will see it shine as brightly as the others.’

Ottavio Fabrizio Mossotti an Italian physicist who lived between 1791-1863 and who is known for the Clausius–Mossotti equation wrote, “It seems to me that Dante, by the experiment of the three mirrors, wanted to point out the principle that flat surfaces, which emit or are illuminated in equal degree, appear to have the same brightness at any distance they are placed. This happens because the size of their image and the amount of light that receives the eye from each point are both decreasing as the inverse of the square of the distance. Therefore, there is a compensation, and each element of equal apparent extension of the image is always represented by the same amount of light reaching the eye at any distance you observe the surface. ... (The light source must be supposed to be at a large distance, comparatively to that at which the mirrors are between them). ... The theoretical principle of Dante is right, and for that time had to be a sublime truth and not common knowledge”.

So Mossotti’s brightness is defined by the ratio of the light reaching the eye to the apparent size of the object. These both diminish with the square of the distance, so the apparent brightness remains constant. Therefore the bright and dark patches on the Moon's surface can be explained by simple optics. Later in the Divine Comedy Dante shows that he understands the law of reflection in Purgatory Section 25 Verses 1 to 36.

Purgatorio Canto XV:1-36 The Angel of Fraternal Love "Just as when a ray of light bounces from the water’s surface towards the opposite direction, ascending at an equal angle to that at which it falls, and travelling as far from the perpendicular line of a falling stone, in an equal distance, as science and experiment show, so I seemed struck by reflected light, in front of me, from which my eyes were quick to hide".

Dante is informing us that the incident and reflected light beams are at equal angles to the purpendicular as defined from the falling of a stone “dal cader della pietra”. This is the law of reflection which was studied by Euclid and Ptolemy but only defined mathematically much later by Ibn Sahl in 984 CE. Unfortunately Dante's Divine Comedy was little read in the renaissance and its importance was only rediscovered in the 19th century by William Blake.

So it is certain that the Tudors were aware of the presence of light and dark spots on the Moon. The Tudors thought that the Moon was either made of the fifth element Quintessence, or was Earth-like with seas and islands. William Gilbert in 1600 thought that the dark areas on the Moon were islands and the lighter areas were water. The Tudors saw an images of an old man carrying sticks, a thorn bush and a dog in the Moon. German and Danish folklore gives us accounts that the man in the Moon was either caught stealing cabbages, or collecting firewood on the Sabbath and so was exiled to the Moon as punishment, there was also a belief that if a pregnant woman stared at the Moon for too long her unborn child would be born mad. William Gilbert in his book “De Mundo Nostro Sublunari Philosophia Nova” commented that it was a shame no images of the Moon have come down to us through antiquity. Centuries later Dan Brown in “The Lost Symbol” writes that “if you want to hide something put it in plain sight”. Perhaps because the Moon was always in plain sight no one bothered to draw the surface features. We know that Harriot took a Digges-Bourne telescope with him to Virginia. We also know that he was a keen scientist and collector of scientific instruments. He surely must have looked at the Moon through his telescope at some point during his voyage. My guess is that if he had announced that he could see walled cavities on the lunar surface he would have been ridiculed for being driven mad from prolonged observation of the Moon, or at the least his findings would have been dismissed as being a result of poor optics. However, there is substantive written evidence that Tudor astronomers did look at the night sky through primitive telescopes well before Galileo and this evidence is indeed hidden in plain sight in the plays of William Shakespeare.

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