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”.
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]
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