Circles and Stars Between Cosmology and Cosmography

The recently-opened Lisbon exhibition “The Emperor’s Gift: Circles of Knowledge” brings to light a recently-discovered 19th-century Arabic manuscript, a (literally) dizzying and (literally) encyclopaedic collection of circular diagrams and tables covering all the topics between heaven and earth. In fact, this Gulbenkian manuscript, called in Arabic Tuhfat al-Khaqan: Dawa’ir al-‘Ulum wa-Jadawil al-Ruqum (The Emperor’s Gift: Circles of the Sciences and Tables of the Numerals), is organized thematically in a way that reminds us of medieval encyclopaedias, notably from Ming China, following the tripartite arrangement of Heaven–Earth–Man (Tian–Di–Ren) or, roughly, cosmogony/cosmology–geography–beliefs/psychology.

The manuscript is literally dizzying because the convoluted paths of minuscule lettering force the reader to turn the head or turn the text in many ways to be able to follow: you actually have to “get your head round it”! And it is literally encyclopaedic because the great part of its contents is about transmitting a teaching (Gr. paideia) in a circular format (Gr. enkyklon): “a teaching in circles” is as literal a rendering of the Greek enkyklopaideia as we can get. This makes us think a lot about the conceptual and visual power of the circle.

Mirza Muhammad al-Akhbari, Tuhfat al-khaqan, 19th-c. MCG manuscript, fols. 2v-3r.

And in turn (how else?), from our particular RUTTER angle, thinking of navigation, orientation, windroses, and rhumb diagrams, we realise that this exhibition is at heart about one of the fundamental questions in philosophy of science: that of mathematical realism, in a Pythagorean and Galilean way, revived in our days by the mathematical universe hypothesis (MUH). The question, succinctly put, is, how can we explain that material reality be so adequately described by mathematical formulas and geometrical diagrams?

Sundial, courtyard of the Great Mosque of Kairouan.

Even only grazing this topic, needless to say, exceeds the scope of these brief lines, but let us suggest that a useful answer may be related, once again, to the Great Triad (三才 sancai) of Chinese cosmology, to a certain essential correspondence, a very familiar je ne sais quoi shared by Heaven, Earth and Man, that is, the physical order of the world beyond the earth, the order of our planet, and the properties of our mental apparatus, our consciousness. The key underlying “forms” to study, consider, and contemplate, are three: orthogonality (the grid), concentricity and radiality. This manuscript, and the extremely suggestive Gulbenkian exhibition are at once evocative, aesthetically delightful, and seriously provocative in the best philosophical way. They are welcome in every way in our times of sound bites and attention-stealing technology. [J. Acevedo]

Cosmic Navigation and Cosmic Pilots

As we embark on a new academic year with our Arabic reading group, we start more in earnest to tackle the pages of Sulayman al-Mahri’s Mir’at al-salak li-kurat al-aflak (Mirror of Travellers into the Heavenly Spheres), a primer of astronomy for the education of maritime pilots in the early 15th century. Not so much of a primer really, but more like an intermediate-level handbook of cosmography.

The first pages tell us about the order of the heavenly orbs, how the universe is conceived as… an onion (that’s my image, not al-Mahri’s!), or more elegantly, as a compound of concentric spheres, within each of which move the planets or other heavenly bodies. It all starts from the centre of the earth, with the description of the elemental spheres wrapped around it: water, air, fire. This cosmology is of course in all its basics an Aristotelian cosmology, found in numerous accounts over most of ancient and medieval Eurasia. Latin versions abound, including some beautifully illustrated.

Gautier de Metz, 13th century.

Approximately at the same time that al-Mahri was writing his works, Iberian nautical science was being revolutionised by the incorporation of astronomical precision techniques to the extensive tried and tested savoir-faire of the pilots. Long-distance oceanic navigation elicited, or rather forced, technoscientific developments which brought its practitioners to new levels of skill. And yet, East or West, either in Atlantic or Indian Ocean waters, there is the lingering question: Did they really need to know about the system of the cosmos in order to take a ship from A to B? And if they did not need to know those cosmic subtleties, why did they keep learning them? Why would such a practical pilot as al-Mahri, who wrote excruciatingly detailed route descriptions, care to elaborate so much on what was practically philosophical knowledge? Was it just didactic inertia, a superstitious repetition of old doctrines?

The answer is most likely “No, they did not need to know,” just as a mechanic fixing a carburetor does not need to know the laws of physics, or a butcher the details of embryology. A more interesting question may be asked, though, especially in our times, when all the cosmology and astronomy of the nautical sciences has been encapsulated in little devices which use satellite geo-positioning technology, like GPS. The question, and we are only left to ponder, is How did that knowledge impact their navigation? Did it have any practical influence, or was it just a matter of “depth”, of ”taste” (sapere, saber, dhawq) added to the mental framework of the pilots? Next time you meet a 15th-century pilot, we know what to ask him! [JA]

A Planet-Less Nautical Astronomy

From the RUTTER crew conversations logbook, preserved for posterity: We have been wondering at the early modern pilots of the Indian Ocean, who famously used complex combinations of stars to navigate by night—a catalogue of about 150 celestial bodies was in their treatises— but, and here’s the question, without ever even bothering to mention the planets. By this I mean the five known at the time, Mercury, Venus, Mars, Jupiter and Saturn. The same planets without which Ptolemy’s astronomy would have been reduced to nothing, and the same planets without which astrology would have been unimaginable.

The reason for this absence is obvious, and it is a nice etymological lesson. A planet, as is well known, means in the original Greek a “wanderer”, a “vagabond”. Now, if you are going to depend on guidance through the night and through the vast expanse of the ocean, you cannot rely on something changeable. You need fixed, unchanging points of reference, and this is exactly what was provided by the night sky, those wanderers excepted.

How bright they are, and unflickering! We have just been witnessing in Lisbon the approach and conjunction of Venus and Jupiter, every day, in the sunset sky, very impressive. And yet for all their steady light, they are not good for navigation: one day they are here, next day there, one day going straight, next day retrograding… They are strong, but fickle. The importance that they have in the astrological view of the cosmos is quite indicative of the variable state of the world: matters of the world and we are not ruled by stars, which would make us constant, but by those wandering bright lights.

Photo: Jorge Rodrigues da Silva

The lack of importance that the planets have in navigation is, in turn, quite indicative of the nature of this craft, and of how special is the state of being at sea and being in transit to a destination: there is peril, and there is the urgency to reach a place, and so all the variable concerns of the pilot are subordinate to accomplishing his task, as Ibn Mājid says, “going and returning with the passengers and the cargo safe.” [JA]

Ostriches? What Ostriches!?

The early Arabic sky has some ostriches running through it: one of the lunar stations of early Bedouin astronomy is called The Ostriches (al-Na‘ā’im), and two of the brightest stars in the sky, Fomalhaut (α PisA) and Hadar (β Centauri), are also called “ostriches”, zilmān. We have been reading about these ostriches for long months now and, busy with astronomical and nautical details, we missed the question obvious to any contemporary reader: what ostriches in Arabia?

It is a historically well-known fact that we humans, as cultural and mythical beings, always project on the night sky our lives, including both what surrounds us everyday and what informs our minds. This is how the Greeks had the Ship Argo and their deities and fabled animals above, while in Patagonia they had rheas in the sky, and in Australia emus. Of course, you could say that if the Greeks had a winged horse, the Arab bedouins could very well have had their ostriches and an ice cream cart too, but… is there something missing?

An old picture, and an ancient mosaic from Petra.

As it turns out—and this is the beauty of how uranography and astronomy intertwine with very down-to-earth disciplines across the natural sciences—there were ostriches in Asia Minor and Arabia, but they were hunted to extinction by the middle of the 20th century. The Arabian ostrich (Struthio camelus syriacus) was very close genetically to its North-African cousins, and it had an important place in the culture of the Middle East since prehistoric times, but alas, it could not survive the arrival of firearms and motor vehicles.

While they remain undisturbed in the night sky, though, they help us on several fronts. They bring to mind the frailty of life on this sublunar place, and they can make us wonder at how we relate to the configuration of the night sky: while we obviously project parts of our lives on those glittering lights, what do we receive from them? What is the quid pro quo we have with the stars? What does their “life” project on earth? As readers of this blog will remember, there are very early and strong arguments to say that every systematic, controlled, “mathematical” way of pursuing knowledge here below derives from the observation of those ostriches and their celestial companions. There seems to be, in a very strict etymological sense, a dialogue between the stars and men: logos going through between high and low and low and high, for the advancement of science. [JA]

If You Are Patient…

Speaking of celestial rhumbs, Ibn Mājid is constantly going back to fine points of astronomical observations, how one star is “fettered” to another and how each one pertains to a rich interplay of positions. “Look at it when it is rising, then what is at the zenith and four fingers to the north at the same level. Then look at it when it is culminating, and check what is level with it and what is setting and rising at the same time…” and so on and so forth to a point of baffling complexity. It was the business of the pilots, who watched through the night and recognised the different configurations, as is encapsulated in the following advice:

If you persevere from its rising to its setting, from the beginning to the end of the night, you will see how all the configurations of its altitude measurements take shape through the sky.

Shapes seen in the sky by more than thirty different civilizations.
Design by Eleanor Lutz.

We had had occasion to comment on this “figurative” view of the stars, including its artisanal aspects and some of its more abstract associations. What is peculiar here is the emphasis on the prolonged observation to get “the full picture”, the direct relation between the tenacity of the practitioner and the access to the whole of the material, as it where.

In a few words we get a vivid and timeless picture of the Indian Ocean pilot’s discipline: watching through the night, patiently, registering the manyfold complexity that made wayfinding possible. I wonder to what extent this applies to the proficiency in other arts and techniques: the relentless attention, watching while everyone else sleeps, absorbing those guiding, principial forms—in the end, this is as good an image as it gets of what “in-formation“ used to mean; not just being exposed to data, but imbibing knowledge through the night with diligent eyes, to find a way. [JA]

Canopus: Gentle Celestial Key

Known in Arabic as Suhayl, Canopus is the second-brightest star in the night sky, second only to Sirius, and it has a cultural importance which it would be hard to exaggerate. In Islamic civilisation in particular, it is notable because the major axis of the Kaaba is aligned with its rising point.

As we read on through the nautical rhumbs, Suhayl has a prominent place, forming part of a diametrical pair which is closest to the poles. Suhayl would be practically a South Pole indicator, while its complementary opposites (al-Na‘sh, the Plough) would be North Pole indicators. Ibn Mājid explains: “Young and old among the people of the desert and the people of the sea, everyone knows Suhayl by sight.” And he adds: “Nothing is better than Suhayl to take altitude measures among what has been set in motion by the Turner of the Spheres (Tornator Caelorum, al-Dawwār). Southern peoples use it to unlock the routes to all of India and Arabia.”

Finding the South Pole,
approx. below the word “Cross” in the image,
between Canopus, Achernar and the Cross.

It is remarkable that the name Suhayl, a star of such mighty practical importance, should mean literally “the little easy-going one”. As a diminutive of sahl, it has a range of related meanings, all familiar names of gentleness. As we had seen with the Pleiades (Thurayyā, Soraya, Zorayda?), Suhayl has also the discreet yet pervasive distinction of being used as a personal given name; it is a common male name not only in Arabic, but in Urdu, Persian and Turkish as well.

This archaic, indeed pre-Islamic, custom of using star names for children makes you wonder about similar practices across cultures. Apart from Spanish Sol and Luna, Sun and Moon, which are used as girls’ names (in Arabic, Shams is for men while Qamar is for women), I can only recall literary characters like Lyra Belacqua (His Dark Materials) and Sirius Black and his family of Harry Potter’s characters. I wonder if our readers can tell us about other people named after celestial bodies? Not sure Arthur would count… Any Betelgeuses or Achernars you are acquainted with!? [JA]

The Greeting Stars

When speaking of “stellar navigation”, “celestial navigation”, or “astronavigation”, the implicit understanding is that of a sophisticated observational system. Long nights, repetitive activities, meticulous recording and so on. But Ibn Majid tries to shows us a different aspect of the relation between the pilot and the stars when he says: “It would be fair to use the following image to speak about me,

The radiance of the stars became so fond of me
That they would ask about me whenever I went out of sight.
When arriving they would say hello to me,
And when departing they would wave goodbye.”

Joniton, fourth son of Noah, the First Astronomer
(World Chronicle, 15th c., J. Paul Getty Museum, Ms. 33, fol. 12)

Can we derive any lesson from such a poetic utterance, to further our understanding of early modern technoscience? Perhaps only this, which we had already touched upon when discussing embodied knowledge: the relation between the expert “artist” (harking back to the technical sense of Latin ars) is multilayered and multifaceted, and hard to fathom. It seems clear enough, in any case, that unwavering attention to an object of knowledge, even something as inconceivably distant and alien as the stars—they who know neither joy nor pain of birth and death—brings about an epistemological shift. The cold object is no longer that cold, the relation not so distant… suddenly, one day, that distant star may wink at you.

This is not quite unrelated to the observer effect in physics, playing out in subtle overtones which were accounted for in medieval science but are fundamentally dismissed nowadays. Somewhere between the detached and practical stargazing, and the loving company of the celestial bodies, a different kind of “objectivity” arises. The cosmos is no longer altogether distinct from the observer, but a “wondrous cosmos” in which “all observers, from the farmer to the astronomer to the monk, had something to learn from watching the sky.” [JA]

Forms of Knowledge in the Heart

From our reading last week, this is how Ibn Mājid speaks of the purpose of his astronomical descriptions and teachings,

…for the discerning pilot to find his way through the expanse and the compact of the heavenly spheres… to advance to the ultimate degree and thus picture the sciences in his heart; and to comprehend the turning and dimensions of the spheres through the stars as they rise and set.

The original of this curious “picturing the sciences in the heart” is well worth a closer look. It may be said that the Arabic wording, yusawwiru al-‘ulūm fī qalbihi, is medieval epistemology in a nutshell, particularly in relation to technoscientific knowledge. In describing an accomplished pilot and the perfection of his art, this formula has three components: 1–an object, what is acquired or obtained, al-‘ulūm—plural of ‘ilm, knowledge, often translated as “sciences” or “techniques”; 2–a manner of acquisition, or a process, the verb yusawwiru—a root (s-w-r) we had found used for the “shapes” of constellations, and which has to do with forms, and in particular the Platonic ideas/forms/shapes (suwar aflatuniyyah); 3–a recipient or container for the knowledge acquired, qalb—the “heart” as a centre of consciousness sometimes distinct and sometimes overlapping with ‘aql, “intelect” or “mind”.

So, let’s for now leave aside the first component, and let’s unpack the formula by making explicit some of its implicit nuances. First, like those brilliant shapes in the night sky, the Platonic ideas, or objects of real knowledge, had acquired in Arabic a certain tridimensionality; the root s-w-r has to do with sculpture and pottery: the “ideas” were more like bodies of concrete knowledge. Second, their locus was not so much a breath-like, airy subtance like spiritus, ruh, anima, etc., or an abstract ethereal intellectus or mens, but the liquid/solid fixed centre of the body and the seat of vitality, the heart.

I think we might now rephrase and appropriately paraphrase Ibn Mājid’s formula: “the ultimate degree of your craft is when the knowledges acquired take shape like concrete constellations in the life-giving centre of your existence.” It may sound a bit grandiose, but it does express quite well something that takes place in the day-to-day practice of artisans everywhere: embodied knowledge is not just in the muscles and tendons that know the habitual movements, but also deep down in a central locus from where springs (like blood) the existential knowing joy of a work well made. [JA]

Sewing Paterns in the Sky

In the beginning of this journey through Kitāb al-Fawā’id, we dedicated one of our very first posts to the idea of mimesis. We were reading about navigation history in the first fā’idah, and about how Noah’s ark resembled the Big Dipper. Now, nearly two chapters later, this same idea reappears in relation to the 26th and 27th lunar mansions, al-far‘ān.

In ancient Bedouin tradition, the stars of the great square of Pegasus were imagined to be the upper open end of a well bucket, from which water would be poured. Seen in the night sky, its shape resembles a square where two parallel sides—one southern, the other northern—are the two lunar mansions called al-far‘ān.

However, neither Ibn Mājid nor Indian craftsmanship considered the four stars to form a perfect square. In fact, the difference between the lengths of the southern and northern sides was a crucial one, for it was the pattern upon which were cut the leech (al-dāmān) and the luff (al-jūsh) of a ship’s sail. Following Ibn Mājid, in Indian traditional craft, such a proportional resemblance was no coincidence. The cutting of the sails (tafsīl) was taken directly from the relative positions of these stars—that is, from the lines imagined in al-far‘ān or the great square of Pegasus. [IB]

The African Colleagues

A passing commentary by Ibn Mājid last week draws my attention to some aspects of his relation to Africa: “According to the ancients, this mansion (he is referring to Sa‘d al-su‘ūd, mansion 24) is found within the sign of Capricorn, but the people of Zanj (roughly what we know as the Swahili coast) consider that, as of the date of this book, it belongs in Aquarius.”

The intensity and historical importance of the maritime traffic between the west coast of India, the Arabian Peninsula, and the east coast of Africa, has been the subject of much international research, and it has elicited from medieval legends to modern soap operas shared across cultural and national boundaries. This sort of Oceanic triangle, comprising the historical areas of the Arabian Sea and the Sea of Zanj, bears testimony archaeologically, linguistically, religiously, economically and in other domains to perennial cultural exchange. So this is not new, and recent scholarship keeps stretching the historical boundaries of this fascinating record.

A second takeaway from our initial citation is the reference to those Zanji astronomers whom he obviously considered as interlocutors, or who were at least into the details of the overlapping between solar and lunar zodiacs. This amounts to saying they had an interest in both theoretical and practical astronomy, including awareness of precessional shifts. It is an enticing testimony to the collegial relations across the waters, and to the state of astronomical study on the Swahili Coast during the 15th century.

Finally, note the ring of immediacy and adventure when he implies that his book is informed by contemporaneous scientific dialogue between Africa and Arabia, and naturally Persia, Gujarat, Malabar… It makes you wonder to what extent our many new exciting initiatives of Indian Ocean Studies are simply picking up the torch, restarting a tradition of generous exchange which became dormant only a few centuries ago. [JA]

Star-Magical Charm of Scorpio

Reading about the eighteenth lunar mansion, al-Qalb, “The Heart” (of Scorpio), we find once again, but concentrated in one single little passage, several of the themes, the literary and cosmological threads that make the Fawā’id so illuminating and appealing.

On the theme of celestial complementarity, of ever-paired rising and descending stars, which is crucial for the navigational use of the skies, we first find some verses. As earlier in the book, the relations between heavenly bodies are used as pattern and subject of love poetry:

I came across her, when the wind,
Blew on her cheek a curl like the heart of Scorpio.
I asked her for a kiss when we were together,
And she hid from me with a heart of scorpion.

This is presented in the context of Aldebaran (“the eye of the Bull”), just mentioned as the diametrical opposite of this Heart (Antares), and of how both stars are alike in their ill-omened character. But it is Ibn Mājid’s own commentary which brings everything into play: “This poem belongs to permitted magic for love and magnetic attraction of the innermost hearts of men, because of its power, its subtlety, its symbolism, and its correspondence.”

Scorpius (al-‘aqrab) in the sky; a lock of hair (‘aqrab) as a loving memento.

The image of the magically charged lock of hair runs from antiquity in the Song of Songs through to St John of the Cross, and globally across cultures. To write these lines you need a peculiar knowledge of celestial mechanics, to be sure, but also of seemingly unrelated disciplines like prosody, lexicology, astrology, magic, and a keen sense of the concretely human. As Ibn Mājid likes to repeat, nautical knowledge is far from exclusively theoretical, and if anything, it is above all an experiential knowledge.

Traditional navigation skills, in the way they have been preserved by Indian Ocean nautical literature—be it in Arabic or any of the languages of Gujarat, or the Konkan and Malabar coasts—consists of a very synthetic, and not merely systematic, but organic, understanding of man’s situation in the cosmos. Early modern pilots in Ibn Mājid’s lineage were heirs of a tradition beyond our trite dichotomies of humanities vs. science, or arts vs. technology—it was all more roundly human, and for that, so much more enjoyable and rewarding! [JA]

“The Clouds” and Stellar Fraternity

Just a brief note this week, prompted by a passing remark by Louis Massignon in his article about the Magellanic Clouds, “Les nuages de Magellan et leur découverte par les arabes”. Apart from their astronomical interest, these two galaxies, called the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC), are especially notable for being about 20 degrees from the South Celestial Pole, and as such of great aid to navigation. Even more, their current and historical position bears echoes of an even greater archaic importance, for around 1000BC they were almost on the Pole.

Unknown to Ptolemy, these Two Clouds (al-Sahābatān) were first mentioned in writing by al-Sūfī in the 10th century, and as such they were known to Ibn Mājid, and a common fixture of Indian Ocean navigation. The Celestial Pole can be located at the vertex of an equilateral triangle based on them (or alternatively a larger triangle based on Canopus and Achernar)—see the illustration below, where the Pole is approximately within the blue circle, and the two faint Clouds show on the centre right.

View from Mossel Bay, South Africa, 3 February 1488,
around the time that Bartolomeu Dias first rounded the Cape.

Massignon comments on the warmth of the relation of southern hemisphere nations to the Two Clouds, comparing it to the relation with the Pleiades, and observing: “it is fraternal respect rather than worship.”

The word “government”, we tend to forget, is not directly related to force and to the “might is right” delusion, or to other delusions of imperial grandeur, but to the Greek root kubernao, “to steer”, “to pilot” on the authority of knowledge. That we can benefit from our elder siblings in the sky, all those guiding lights, and to do so fraternally, like a passenger approached a pilot in the middle of the night on board a ship, to have a chat and learn… this is a reassuring thought in stormy times, and as good pilots know, some times are stormier than others. [JA]

Be Practical: Learn Your Poems!

Once again, starting from a minimal astronomical excuse, Ibn Mājid takes us on a major literary digression about Arabic proverbs, including the horrible story of the poor milkmaid—well above the content rating allowed to our younger blog readers… and in any case bringing us again to the serious question of audience: who were these “Commentaries” written for? what for?

It is obvious that if you are a pilot in need of directions and practical nautical references, you won’t have time to read the lengthy excursus fancied by Ibn Mājid. You need straightforward data, concrete information to arrive safely to your harbour. In that case, what you need is to read Ibn Mājid’s poems.

In an interesting reversal of our contemporary views, this early nautical literature, or at least Ibn Mājid as its preeminent representative, used verse as the preferred medium for strictly technical contents. If you wanted to use metaphors and all the panoply of belletristic effects, and to ramble on in stories and anecdotes, then write prose. If, on the contrary, you wanted to convey highly technical and indeed vitally precise information, then write poems!

Still in our days, some old pilots on the shores of the Red Sea and the Gulf do remember their nautical verses for this or that orientation detail. It is a striking survival of a medieval and ancient tradition of “artisanal poetry”, of which the famous pre-Christian example is Aratus’ astronomical Phaenomena. It is also a testimony to the discreet relation between “music” in a broad sense and scientific and technological endeavours.

Einstein and Planck at the piano.

We can picture the old sea dogs, retired at home after a lifetime of sailing, and now enjoying the crazy stories told by Ibn Mājid. They had all their music of science and skill inside their minds, and now they could sit back and enjoy the Fawā’id. [JA]

The Interplay of the Two Zodiacs

As we continue reading through al-‘Awwā’, Ibn Mājid tells us about the positions of the lunar mansions in the solar zodiac. “At the time of Alexander,” the first northern and southern mansions were al-Sharatān and al-Ghafr respectively—what this means is that, around the fourth century BC, al-Sharatān was the first mansion to be seen rising after the vernal equinox; and Al-Ghafr the first after the autumn equinox—“but they are different in our time, in respect to the zodiac.”

Unlike the mansions of the moon, which correspond to stars visible in the night sky, the solar zodiac was determined by the tropical year. The Babylonian system inherited by the Greeks divided the zodiac into twelve equal divisions of 30 degrees, starting near αβ Arietis, on which the equinoctial sun rose around the year 400 BC.

Aries rising with the sun in Baghdad,
21 March, year 401 BC (Stellarium rendition).

Nowadays, the zodiac is divided in the same way: the sun is said to be in Aries after the vernal equinox, to be in Taurus after 30 degrees, in Gemini after 60, and so on. However, due to the Earth’s axis movement (the precession movement), the equinoctial points have been slowly shifting to the west in relation to the stars in the background. Even though Aries conventionally begins after the spring equinox, the constellation actually seen rising at that period is Pisces. At the time of Ibn Mājid, “when the sun or the moon descend in al-Sharatān (αβ Arietis), only six degrees of Aries remain there, and all of al-Butayn (εδρ Arietis) is within Taurus.” The lunar zodiac remained throughout a sidereal system, and this is one of the reasons why it had, and still may have, very practical usages for navigation. [IB]

How Many Do We Need?

We have once again come across a mention of al-Sufi’s Book on the Shapes of Stars (Kitāb suwar al-kawākib, 10th century), considered by many as the the most important update on Ptolemy’s enormously influential Almagest (originally entitled Μαθηματικὴ Σύνταξις; the Syntaxis Mathematica, 2nd century).

The fascinating history of this relation has been explored time and again from many angles. Briefly, as regards uranography—the “cataloguing of stars” contained in books 7 and 8 of the Almagest—al-Sufi was the pivotal figure who revised the Alexandrian material and prepared it for further developments, culminating with Tycho Brahe’s Rudolphine Tables (1627).

Now, coming to our nautical context: when Ibn Mājid mentions al-Sufi, he invariably adds “and his forty-eight constellations,” a number which seems to go back to Ptolemy. Studying the lunar mansions has made palpable how arbitrary the division of the ecliptic is: you have a rotating circle dotted with shiny specks, you introduce some boundaries and project your lines. You can have 28 mansions or 12 signs or 36 decans or even 144 dodecatemoria. The division in 36 is easy to understand if we think of the rationale of the Babylonian “Three Stars Each” catalogues: for each twelfth of the ecliptic you select one equatorial, one southern and one northern star or asterism, so you cover a wider area and thus give more parameters for orientation (we are not going to waste all those stars!).

In a very useful summary of Ibn Mājid’s uranography, Ibrahim Khoury speaks of 24 major stars used in Indian Ocean navigation. Why 24? and why 48? These figures might be a Greek alphabetic reminiscence: the Greek alphabet has 24 letters, and using this number meant you were speaking of “the alpha and omega” of the stars, the “heavenly ABC.” It meant it was enough, that no other element was needed. I suspect some earlier source for this, perhaps Hipparchus… but the abiding and concrete question is how many stars do we really need to find our way. Right now, dear reader, when it is dark, how many stars in the sky do you need to know in order to find your way home? [JA]