Every one knew how laborious the usual Method is of attaining to Arts and Sciences; whereas by his Contrivance, the most ignorant Person at a reasonable Charge, and with a little bodily Labour, may write Books in Philosophy, Poetry, Politicks, Law, Mathematicks and Theology, without the least Assistance from Genius or Study.

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Gulliver's Travels:
Voyage to Laputa





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Fanciful. Preposterous. Absurd.
Archive for May 2006
These unripe things are now read by me in vain, Oy!


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.

The Phases of Venus

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.

Ptolemy's geocentric system as depicted by Andreas Cellarius in his lavishly illustrated Harmonia Macrocosmica

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:
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.

From Huygens' Systema Saturnium. Observations of Saturn by others prior to Huygens. I is an observation by Galileo in 1610. II is one by Scheiner in 1614. III is one by Riccioli from 1641-1643. IV-VII represent suggestions by Hevelius based on his theories. VIII and IX are observations by Riccioli from 1648-1650. X is an observation by Divini from 1646-1648. XI is one by Fontana in 1636. XII is one by Gassendi in 1646. XIII is from observations by Fontana and others from 1644-1645. Plate between pages 32-33

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]


[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
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
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.
Past Glory


Cornelis van Poelenburgh (1594-1667): Ruins in Rome

O thou new comer who seek'st Rome in Rome
And find'st in Rome no thing thou canst call Roman
Arches worn old and palaces made common,
Rome's name alone within these walls keeps home.

Behold how pride and ruin can befall
One who hath set the whole world 'neath her laws,
All-conquering, now conquered, because
She is Time's prey and Time consumeth all.

Rome that art Rome's one sole last monument,
Rome that alone hast conquered Rome the town,
Tiber alone, transient and seaward bent,

Remains of Rome. O world, thou unconstant mime!
That which stands firm in thee Time batters down,
And that which fleeteth doth outrun swift time.

— Ezra Pound [1].

Roman Ruins with Figures. Giovanni Paolo Panini 1730s
A fantasy amalgam featuring the astonishing but very real Pyramid of Cestius

Roman Ruins with the Arch of Titus. Giovanni Paolo Panini 1730s

Figures Discoursing Among Roman Ruins. Giovanni Paolo Panini 1730s

Capriccio: Ruins and Classic Buildings. Canaletto 1730s.

Capriccio: View with Ruins. Canaletto c 1740.

Rome as it was c 300 AD.
Model by Italian Gismondi (1887-1974) now housed at the Museo del la Civiltà Romana in Rome
(For more information see this post)

Other posts on ancient Rome:
The Marble Plan
Roma, Romolo, Remo
The Colours of White
Maps of the Roman Empire
[1] Time consumeth all — This is a poem made famous through its appropriation by a numerous authors. This Ezra Pond version was a translation from a French poem by Joachim du Bellay who in turn translated it from the original Latin by Giano Vitale (Janus Vitalus).
"At the turn of the sixteenth and seventeenth century, a Frenchman was able to read a poem on the ruins of Rome signed by Joachim du Bellay; a Pole knew the same poem as the work of Mikołaj Sęp-Szarzyński; a Spaniard, as the work of Francisco Quevedo; while the true author, whom the others adapted without scruple, was a little-known Latin humanist, Ianus [Janus] Vitalis of Palermo."

— Czeslaw Milosz, The Witness of Poetry, 1983
John Emerson (the Savant Formerly Known as Zizka) was prompted by this curious fact to follow the lingusitic journey this poem has made around Europe. Though its original author is hardly known today, the poem's sentiments about the transitory nature of power and glory strike a chord even today.


Here is an animation I made of the distribution of the world population from 1 AD until 2300 AD (projected) where the size of each country's territory is distorted so as to show its relative population size. These maps were obtained from the mind-boggling Worldmapper project at the University of Sheffield where you will find surprising maps of a wide range of demographic and economic indicators (such as refugees, tourists, chemicals, ores and computer exports (check out Singapore!)

Hat tip to the very estimable BLDGBLOG.

Administrator's note: this seems like a good time to declare a brief hiatus. Once again I'm running a bit out of puff and those time constraints still haven't gone away. So you might as well know now that there won't be any new posts here at Laputan Logic for at least a couple... well, let's just say four weeks.

In the meantime, don't forget to check out those archives. Cheers.


As my wife says never mess with the Hakka and she should know what she's talking about. Notable Hakkas include Lee Kuan Yew, Deng Xiaoping and, er, Naomi Campbell. 'Nuff said...
Contributing yet another strand to the patchwork of overseas Chinese speech and customs were the Hakkas, latecomers to the southernmost provinces, moving into Fukien and Kwngtung in two separate migrations: during the tenth century and the twelfth and thirteenth centuries. The Hakkas whose name means `guest families' have been described as the gypsies of China, people who live side by side with speakers of different dialects in enclaves scattered across six southern provinces, without a homeland of their own. They were a rugged lot, and even their women had to be hardy. Little wonder that the Hakkas were the only Chinese to refrain altogether from binding their daughters' feet into the `golden lilies' that were de rigueur everywhere else. One thing Hakka women were not was dainty.

Men moving across great distances into an unknown landscape, assailed by the hostility of settlers who have preceded them, band together; and if Hakkas were (and still are) thought a very clannish people, they had good reasons to be. The banding-together took a palpably defensive form, in communal living and communal housing Their dwellings, still to be seen today in a border area in Fukien province, are extraordinary constructions, rising out of the countryside like veritable fortresses, gigantic, multi-storied, round. They are built to a circular plan, with a thick outer wall of tamped earth pierced by tiny squint-holes, presenting a resolutely sealed and embattled look to the world. In the walled complex, an entire community, numbering six to seven hundred inhabitants, could be concentrated.

It was no easy matter to live among the Cantonese, to contend for land and water. Feuds were easily ignited in such an atmosphere, and there evolved a tradition of armed fighting between the migrant and the settler. We read of a period of prolonged fighting between the two in the years 1855-67, a war in which about half a million people are said to have lost their lives. It is not hard to see why the Hakkas emigrated to Nanyang [South-East Asia]. In China they were pushed on to marginal land, hilly country rejected by those who had got there first.

— from Sons of the Yellow Emperor : The Story of the Overseas Chinese by Lynn Pan, Mandarin Paperbacks 1991, page 16
And here area a few examples of these remarkable communal round houses cum fortresses.

This type of building is round in shape and divided into three classes, small, medium and big. The small ones are usually 2 to 3 stories tall with a single ring. The medium dwelling is usually 3 to 4 stories tall with a large inner open space (single ring) or double rings. The large round building is usually 4 to 5 stories tall consisting of as many as three rings. The very small round building has about 12 to 18 rooms, the small ones have 21 to 28 rooms, the medium ones have about 30 to 40 rooms, the large ones have about 42 to 58 rooms, and the super large round buildings have about 60 to 72 rooms.

Two-third of the round building are 3 stories high and hold roughly 20 families or 100 people. The round earth building is a "group-oriented" residence, usually with one main entrance. Its wall is usually around 1 meter thick. The main entrance door is padded with iron sheet and is locked by 2 horizontal wood bars. The wooden bars retract into the walls in order to open the door. In the event the wood bars are sawed through, the locking mechanism is still intact.

Inside the entrance is a huge central courtyard where all the doors of the rooms and inner windows are open to. At the ground level except the hall and the staircases, the rooms are used as kitchens and dining rooms. The rooms on the second floor are used for storage. The rooms on the 3rd level are used as bedrooms. The rooms in each level are identical. In front of each room, there is an open round hallway and usually there are 4 staircases to move from one level to another. Thus each family occupies one vertical units with lower level as kitchen, 2nd level for storage and miscellaneous use and 3rd level and above used as bedroom. Sometime there is no open round hallway. Instead, every family has its own private staircase. A typical room is about 10-13 square meter in size.

The larger round earth building has room around 15 square meters. The windows facing outside tends to be small, with the window size at the outer wall smaller and the window size at the inner wall larger enabling wider surveillance from the inside. It is extremely hard for outsiders to come in through the windows. There is usually no window at the ground level. While the round building is fairly large, it has an inner ring, which is like a round building within a round building. For round building that built earlier than 15th century, they have other defensive features that would counter siege. It is said that during Ming dynasty as Japanese pirates intruded the coastal areas, they always leave the Hakka's Earth Buildings area alone.

Hakka - An Important Element of Chinese Culture

See also
Wikipedia: Hakka architecture