Posted on Tuesday 2 May 2006

So said Galileo Galilei in 1610 in a letter to Johannes Kepler, "Haec immatura a me iam frustra leguntur oy".

It was not a lament about the wilful ignorance of his times [1] but in fact an important insight. Hidden within this odd sentence Galileo had placed a coded statement about his his recent discovery of the phases of Venus — i.e. that Venus waxed and waned just like the Moon.

This was a crucial piece of evidence confirming his belief that the Ptolemaic model of universe — one which had the Earth placed at its centre — was inherently flawed. If the Sun and the planets really did all orbit around the Earth then how would it have been possible for the planet Venus, which Ptolemy had placed closer to the Earth than the Sun, was able to show the complete range of phases from "new" to "full"? It had always been known that that Venus and the Sun never appeared far from each other in the sky and Ptolemy linked the orbital speeds of both Venus and Mercury to that of the Sun's to ensure this. The fact that Venus appeared at one time on one side of the Sun and then the other was explained with epicycles [2] but Ptolemy had never suspected the existence of phases on a body that he had assumed was both point-like and perfect.

Galileo, however, knew that Copernicus' system — which had Venus orbiting the Sun instead of the Earth — would be able to explain it because at some point in its orbit the planet would be on the opposite side of the Sun from the Earth. When he wrote to Kepler, he still considered this new finding provisional and requiring further observation. Nevertheless, he wanted to lock in his rights of priority to this discovery by sending it to Kepler in an encrypted form.

The form he chose was an anagram. Haec immatura a me iam frustra leguntur oy when the letter are rearranged means Cynthiae figuras aemulatur Mater Amorumor or "The Mother of Love imitates Cynthia". Assuming this still doesn't make things a lot clearer to you, consider that the the "Mother of Love" is a reference to the planet Venus and Cynthia refers to the Moon, i.e. that Venus copies the Moon. (Galileo certainly wasn't trying to make this easy!)

Earlier that same year, Galileo made another discovery with his telescope, this time it was about the planet Saturn. In another letter to Kepler he wrote down this catchy phase:

smaismrmilmepoetalevmibvnenvgttaviras

It was of course another anagram but one which was considerably less poetic than the one given above but, nevertheless also containing a dramatic discovery. Decoded it reads Altissimvm planetam tergeminvm obseravi or "I observed the highest planet in threefold shape".

As Galileo elucidated to Julian de' Medici

I discovered another very strange wonder, which I should like to make known to their Highnesses . . . , keeping it secret, however, until the time when my work is published . . . . the star of Saturn is not a single star, but is a composite of three, which almost touch each other, never change or move relative to each other, and are arranged in a row along the zodiac, the middle one being three times larger than the lateral ones, and they are situated in this form: oOo.

The "strange wonder" of Saturn and its companions, which as Galileo was to observe changed in shape from month to month would remain a mystery for half a century until it was answered by yet another anagram, this time by Christiaan Huygens.

We have finally discovered the reason why Saturn sometimes is flanked by two things that look like ears, sometimes by something that protrudes as two straight arms, and sometimes also is lacking all this and appears round, as it was seen in the year 1642 and now again for the last three months. And it will not be difficult to determine when these changes will happen again, if we will be allowed two more months of observation, during which we will be able to see if they [the observations] agree with our hypothesis.

For we expect that toward the end of April, or even a bit sooner, Saturn's arms will reappear, not curved, as you can see them in the illustrations of Francesco Fontana and Hevelius, but in a straight line that protrudes on both sides, provided you study them with a superior telescope because if you use ordinary telescopes they will represent them again as two little circles as they showed themselves the first time to Galileo...

We will publish the observations that we gathered last year and this year, which show the period of the moon, all together when we have completed the entire system of Saturn. In the meantime, I think it appropriate to hide the main point in the following anagram, so that anyone who perhaps thinks he has found the same will have the opportunity to come forward with it and it cannot be said that he got it from us or we from him.

aaaaaaa ccccc d eeeee g h iiiiiii llll mm nnnnnnnnn oooo pp q rr s ttttt uuuuu

— Christiaan Huygens, The Discovery of a Moon of Saturn, 1656

These letters, when placed in their proper order read: Annulo cingitur tenui plano, nusquam cohoerente, ad eclipticam inclinato. which means "It is surrounded by a thin, flat ring, nowhere attached to its surface, inclined to the ecliptic".

Anarchy, this genius! [3]

Notes:

[1] wilful ignorance - from a letter to Kepler in 1610

"My dear Kepler, what would you say of the learned here, who, replete with the pertinacity of the asp, have steadfastly refused to cast a glance through the telescope? What shall we make of this? Shall we laugh, or shall we cry?"

for more read False Doctrine, about the trial and abjuration of Galileo.

[2] epicycles - in the modern physicist's lexicon epicycle is synonymous with "kludge". For example, An Interview with Carver Mead)

...point particles are assumed to occupy no space, they have to be accompanied by infinite charge density, infinite mass density, infinite energy density. Then these infinities get removed once more by something called “renormalization.” It's all completely crazy. But our physics community has been hammering away at it for decades. Einstein called it Ptolemaic epicycles all over again.

Hold on...epicycles?

Ptolemaic astronomers assumed that the earth was at the center. But then it became more and more complex to calculate the orbits of visible planets. When you assume the earth is the center, you have to add epicycles to the existing orbits to adjust them. In the same way, when you assume photons are point particles, and all you can calculate is probability, you have to add epicycles of conceptual nonsense to “explain” even the simplest experiment.

But to be fair to Ptolemy, his system actually produced pretty good results, better, in fact, than the one Copernicus proposed. The original formulation of the Copernican system, like Ptolemy's, also used circular orbits and used epicycles.

[3] Anarchy, this genius! - this is, of course, also an anagram which in an earlier time I would have simply left as an exercise to the reader. However, as this is the Internet Age, I realise that Google is only a mouse click away.

Other 17th century scientific anagrams include

ceiiinosssttuv

Robert Hooke (1676).

In 1678, Hook revealed the solution: Ut tensio sic vis or "of the extension, so the force". In other words, Hooke's law "in an elastic material, strain is proportional to stress". The more you pull against a spring, the more it resists.

F = − kx

Also

The foundations of these operations is evident enough, in fact; but because I cannot proceed with the explanation of it now, I have preferred to conceal it thus: 6accdæ13eff7i3l9n4o4qrr4s8t12ux. On this foundation I have also tried to simplify the theories which concern the squaring of curves and I have arrived at certain general Theorems.

— Isaac Newton in a letter to Gottfried Wilhelm Leibniz (via Henry Oldenburg) in 1677

The numbers in the anagram represent the number of times the letter appears. It expands to

aaaaaa æ cc dd eeeeeeeeeeeee ff iiiiiii ll m nnnnnnnn oooo qqq rr ssss tttttttt vvvvvvvvvvvv x

The solution to this anagram was never revealed by Newton although it is believed to say Data æquatione quocunque fluentes quantitates involvente, fluxiones invenire; et vice versa which translated means "Given an equation involving any number of fluent quantities, to find the fluxions; and vice versa" which in Newton's terminology is principle behind "The Calculus". There is still room for doubt in this interpretation, however, because if it is correct then Newton must have made an error in transcription. The sentence would have needed 9 letter t's instead of 8.

This anagram is especially remarkable because in it Newton appears to reveal the existence of calculus to Leibniz, the priority over which would later became such a source of acrimony between the two men. The irony is that if only Newton had spoken plainly about his invention then he could have established his priority over Leibniz. Instead Newton chose to be cryptic.

[4] apropos of nothing:

Un drame interastral: a short 19th century science fiction love story between an Earth boy and a Venusian girl.
Up Yours: Galileo's finger on display.