Cryptography is today one of the most popular applications of computer science, and we usually think of it as a modern way to hide a transaction behind a complex, machine-generated code. Cryptograms however have been used since the antiquity, to exchange e.g. protected military or financial information. (Not to be confused with riddles, of which the Delphic oracle was keen, see below.) The scientists of the past were also keen of hiding their results in riddles, anagrams, acrostics and other wordplays. For example, when Robert Hooke, discovered in 1675 the law of springs, he famously presented it with the anagram ceiiinosssttuv. The solution was published by Hooke himself only three years later, and was the Latin sentence Ut tensio, sic vis: “as [large] is the deflection, so it is the force”. A few years before, he had discovered that the line of an arch for supporting a given weight should be the inverted shape of the catenary curve that bears that weight. He apparently announced the discovery to the Royal Society of London around 1671, but he did not provide any details until 1675, and then the details were encrypted. In an appendix to his Description of Helioscopes, he stated that he had found “a true mathematical and mechanical form of all manner of arches for building” and the cryptogram containing it was:


Unlike the law of the spring, he did not provide a translation in his lifetime, but that was provided by his testamentary executor in 1705: Ut pendet continuum flexile, sic stabit contiguum rigidum inversum. “As it hangs a flexible cable, so inverted stand the touching pieces of an arch”.

Why, you may wonder, did Hooke and the other scientists of his time used to announce their findings in such bizarre a fashion? Before the existence of scientific journals, the only way to disseminate results was to publish very expensive books. Galileo had his first astronomical discoveries printed in the Sidereus Nuncius (1610) with the patronage of one of the richest men in the world, the Grand Duke of Tuscany Cosimo II de’ Medici: just 550 copies, of which today about 80 survive (for this reason the four moons of Jupiter discovered by Galileo are still called “Medicean satellites”). The more usual way of establishing priority was to write a letter about your discovery to another famous scientist, not rarely your direct rival. Of course, you had to phrase your letter carefully so as not to actually reveal the discovery explicitly, so that the other would take credit for the work. This ingenious method of “publication” established priority, while at the same time communicating it to the person most likely to snatch the priority from you. Moreover, they used to write at each other in Latin. It is often said that scientists used Latin because it was the universal language, with a role similar to English today. In reality, nothing could be more wrong. It was just the opposite. English is a common language today spoken by everybody in the world, and not just by some weird scientists, whereas Latin was the language of the elite. Only intellectuals, lawyers or high state officers could fluently read and write it, not even kings used it anymore in the XVII century. (According to his preceptor Cardinal Mazarino, Louis XIV the “Sun King” was a very bad student when it came to Latin and maths.) Galileo wrote in plain Italian his Dialogue on the Two World Systems just for the declared purpose of making his science readable to everybody.

On two occasions Galileo, at that time professor of mathematics in Padua, announced discoveries he had made with this telescope by mailing anagrams to Johannes Kepler. In July 1610 he wrote to the high commissioner Giovanni Bellisario in Florence the announcement of a stravagantissima meraviglia (a top extravagant wonder), but temporarily preferred to hide it under a mysterious sequence, which read:


Since in Latin U and V are the same letter, the correct solution of the anagram was to be Altissimum planetam tergeminum observavi. (“I have observed the highest planet to be a triplet”.) The highest planet known at the time was Saturn, and what Galileo had actually seen were the rings of Saturn. Unfortunately, with his primitive telescope the rings appeared like two moons, one blurred spot on each side. With the help of another Medici, Giuliano the archbishop of Pisa, he could send the same message to Kepler. The Czech astronomer and mathematician had become an instant admirer of Galileo, after receiving in April of the same year a personal copy of the Nuncius from the hands of the Tuscan ambassador in Prague, and had replied with a long letter to Galileo titled Conversation with the messenger of the stars. Besides seeking for confirmation (and admiration) the stratagem of hiding the discovery into an anagram was Galileo’s way of establishing priority: should anyone else announce that Saturn had two blobs next to it, Galileo could unscramble the anagram and show that he had seen them first, and Kepler himself would serve as his expert witness. However, Kepler unscrambled the anagram wrongly to Salve, umbistineum geminatum Martia proles, and interpreted this to mean “Mars has two moons.”

The translation is very bad since it contains a word, umbistineum, that does not even exist in Latin. But the funny thing is that today we know that Mars does indeed have two moons, but neither Kepler nor Galileo had any way of knowing that, since they were first observed only in 1877. However, just the idea that Mars could have two moons was not extraneous to the ancient astronomers: reasoning by symmetry arguments, Venus and Mercury had no moons, the Earth had one, and Jupiter four. So, it was “logical” that Mars inbetween should have two. Such a reasoning lasted long in European culture, for example Jonathan Swift in his Gulliver’s Travels (1726), has the Laputian astronomers to affirm that Mars has two satellites, and goes as far as telling that one has a period of 10 hours and the other of 21,5 hours. From where could he have got such a notion is unknown, but the figures are surprisingly close to the reality (7.66h for Phobos and 30.55h for Deimos)! The rings of Saturn would be actually observed by Huyghens, 45 years later, who also decided to hide such a wonder under an anagram,


which, properly unscrambled into gross Latin, gives: Anulo cingitur tenui, nusquam cohaerente, ad eclipticam inclinato, “A thin ring surrounds it without touching, inclined with respect to the ecliptic”. It was indeed a time during which speaking of “rings around a planet” could take you to the sanatorium, or in front of the Inquisition.

The second anagram that Galileo had sent out to Kepler, again with the help of Giuliano Medici, was in more plain Latin, Haec immatura a me iam frustra leguntur oy, meaning “These immature ones have already been read in vain by me” (with the meaningless “oy” appended to the end of the sentence, evidently because Galileo could not better fit it into the anagram). His intended solution, which he revealed after a few months, was: Cynthiae figuras aemulatur mater amorum, which translates to “The mother of love imitates the figures of Cynthia” Given that Cynthia is another name for the Moon, and that the mother of love is Venus, what this sentence proclaims is that Venus has phases like the Moon. This was another very dangerous thing to say, because the only explanation for Venus having phases like the Moon was that Venus orbits around the Sun, a scientific position that was heretical at the time. Once again, Kepler got it wrong, and unscrambled the anagram to “Macula rufa in Jove est gyratur mathem”. Kepler’s solution is again in very bad Latin, and even has a few letters left over. But if you ignore such minor errors, his solutions says: “There is a red spot in Jupiter, which rotates mathem[atically]”. Once again, Kepler was surprisingly right just by mistake! As we know, there is indeed a red spot on Jupiter, which rotates around as the planet rotates, but Kepler could not have known that, since Jupiter’s Great Red Spot was first seen only much later, in 1665.

Riddles could be another way of hiding precious information, and possibly more fun, since they could be more easily passed also to lay people and not restricted to scientists. A famous one was written again by Galileo, actually it is the very last writing we have from him before his death in 1642. Two years before, the Florentine literate Antonio Malatesti had published a collection of riddles (La Sfinge, the sphynx) in the form of sonnets, one of which, Con spoglia dorata, was dedicated to Galileo’s telescope. From his exile in the villa in Arcetri, outside Florence, Galileo was very pleased by the wordplay. Isolated from the human society since nine years, almost entirely blinded by an obscure illness, he could only dictate correspondence and other written arguments to the young pupil Vincenzo Viviani, the only other person that the Papal verdict admitted to his residence apart from family members and, in the very last months of his life, his old time admirer and friend Evangelista Torricelli. So, he replied with another sonnet to Malatesti, that he entitled Enimma (enigma) of which I give you my scant and non-poetic translation:

A monster am I, stranger in shape and form than a Harpy, a Siren or a Chimera. Nor has any beast on Earth, in air or in water, such varied forms of limbs as me. No part of mine to another does conform, more than if one were white and the other black. Often, I am followed by a herd of hunters that track my footprints. In the obscure darkness I sojourn, so that when I pass from the shadows to clear light, quickly my soul flees out, just as a dream flees out at the break of the day. And there my disjoined limbs I leave, and my whole being I lose, and my life and name.

The solution of this riddle has been the subject of a longstanding debate, and still today we have no definitive solution as to who is the monster (Mostro son io) Galileo is describing. In the Galileo biography by M. Camerota (2004) it was suggested that it could Galileo himself, although this solution is considered among the least probable even by his proponent. Antonio Daniele, a historian and philologist, suggested in 2009 a gambit: the solution could be the telescope itself, the same solution as for Malatesti’s sonnet. Another possible solution, proposed by the great astrophysicist Giovanni Bignami, is that it should be a comet; however, the sonnet does not refer to nor suggest anything about comets, despite Galileo’s extensive writings about comets. A recent arXiv post (May 2022) by the italian astronomers Busetto and De Angelis proposed that the answer is the Zodiac: the first few verses describe strange animals (the Greek work zoidiakòs literally means “the circle of small animals”); the “hunter” is the constellation of Orion, which outlies the ecliptic and is ‘behind’ the Zodiac; the last 6 verses clearly refer to the daily disappearance of the stars. However, for a great mind like Galileo, it all seems a little too obvious, doesn’t it?

The most interesting (at least to me) suggestion was formulated in 2021 by Mark Peterson, emeritus of mathematics and physics at Mount Holyhoke College (Massachusetts). The monster is the Ptolemaic system of the Universe. The Ptolemaic system does not determine the proportions, or the relative sizes, of the planetary orbits, which are instead calculated in the Copernican system. Orbits in Ptolemaic system are weird curves riddled with epicycles and deferents (the “strange and horrible beasts”), whereas Copernicus’ orbits are perfect circles (which Kepler corrected into tight ellipses). These “parts” do not conform to each other, like white against black, and such symmetry considerations must have been a compelling argument to Galileo, for whom the notion of proportion and its importance in natural phenomena was a recurrent theme throughout its work. The “hunters following the tracks” are the astrologers who compute the positions of the planets using the Ptolemaic model. To go “from the darkness into the light and disappear”, likely refers to the fact that planets (the ‘limbs’) are not visible in the daytime. But one could read it also as a bold restatement by the old and dying Galileo, his last cry from the darkness of a prison, of his irrepressible belief in the truer Copernican model: the older Ptolemaic model favored by the Roman Church fades away, the ‘disunited limbs’ give way to the unified orbits of Copernicus, the old model loses its status as a description of the universe, it is dead. Triumph the science.

Hiding science behind literature

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