Arab Tridua: Three-Day “Weeks” in Arabia

This post is about a rather neglected aspect of time division in early Arabia. In his Fawā’id (IV, 7) Ibn Mājid explains: “Every month is divided in ten parts of three days each, and each part has its name.” Then he lists the ten triads or, more specifically, tridua: Ghurar, Nufal, Tusa‘, ‘Ushar, Buhr, Bīd, Durā‘, Muhāq, Hanādis, Ziyād, Surar. Most of the names are straightforward in meaning, relating to the appearance of the moon or to the date count, and the word “three” is implicit. For example, “The three of Tusa‘” (al-thalāth al-tusa‘) means something like “the three [days] of the ninth”, because this triad ends on the ninth day of the lunar month. Al-thalāth al-bīd means “the three of whiteness”, because they are near the full moon.

Keen-eyed readers will have noticed that the above list actually contains eleven tridua, not just ten. This means to reflect the garbled textual condition in which Ibn Mājid’s list reached his readers in the 15th century, with obvious ingrained misspellings and interpolations. The earlier references I can find for these names are Ibn Wādih al-Ya‘qūbī (9th century) and al-Bīrūnī (11th century), who give slightly different lists. In comparison to them, Ibn Mājid’s does look like the outcome of centuries of Chinese whispers.

Now, al-Bīrūnī explains first that the names are derived “from the distinctness revealed by the state and the curvature of the moon,” and shortly after that they are “taken from the faces of the moon and its curvature.” This is what I find warrants a thought on our concept of “week”. Our weeks derive in part from a division of the lunar cycle in quarters.

Let us leave aside for now the numerological relevance of the division in three, seven or ten, which we have discussed previously. We can see how the beautiful continuum of the lunation allows for as many divisions as our powers of observation allow us to determine distinct—hence nameable—units. How many nights do we need to appreciate each clearly distinct aspect of the moon?

Nama-rupa, in the Sanskrit philosophical terminology, “name-form”: mutually dependent and inseparable aspects of every phenomenon, everything that appears to then vanish “under the Sun.” The gentle and ever-so-fleeting light of the moon is perhaps the phenomenon par excellence, now there, now vanished… What is left to us, puny sublunary creatures is to wield our power to name, and thus, by naming, to create scientia, the knowability and the knowledge, a “possession for ever.” [JA]

The Spacetime of Early Modern Navigation

As we continue to read chapter 4 of the Fawā’id, about the nautical rhumbs, and as we go through detailed descriptions of time and distance measurements, we come across technical concepts which in their practicalities bring us, once again, to reflect on some of the principles of our modern technoscience.

The distance unit in early modern Arab navigation was the zām (pl. azwām). The technical concept is the taraffā or tirfa, called by early Portuguese explorers the “Rule of the Leagues” (regimento das leguas), the function between the distance travelled, the latitude progress, and the azimuth of the destination: e.g. if you travel straight up north, it takes you one hour to shift your position by one degree northwards, but if you travel towards the north-east, it will take you longer to advance that same degree northwards. A nice image of this concept is given by the triangle below, where A is the point of origin, and the latitude difference between A and B would be one degree. Simply put: the AB diagonal path takes longer to reach the same parallel.

Now, how to measure the advance without any points of reference on the flat surface of the ocean? The key point is: time is a function of movement. Something has to move for there to be a sign of time, because, as ordinary language teaches us: “time passes”, and we speak about “a space” or “an extension” of time, and we ask “how long?” as if we were speaking of a stretch of a road or a piece of string.

The solution: look up from the surface of the ocean and into the sky, where the positions and the continuous movement of the heavenly bodies show us directions and show us time. This relation between movement and time brings to mind Plato’s formulation: “time is the moving image of eternity” (Timaeus 37d). A sundial illustrates this too, being somehow “a moving shadow of eternity”. The passing stars were the necessary reference, and so, one of the definitions of zām reads, “the distance it takes to raise the Pole Star by one eighth of a finger if the ship sails due north”.

Sundial, courtyard of the Great Mosque of Kairouan.

Fundamental coexistence of space and time, and strikingly obvious continuity of their dimensions… What to make, in this light, of the complexities of the space-time formalism of contemporary physics, with their illustrious history and mathematical refinements? Is this yet another case of “nothing new under the sun”? The word itself, spacetime, goes perfectly well with the medieval perception of navigators—the consubstantiality of space and time was immediately obvious. Perhaps it is just a matter of continuing to deepen the dialogue, the centuries-old conversation between the depths of metaphysical speculation and the frontlines of physical enquiry. Time will tell. [JA]