In the ninth century the Abbasid caliphate, like other burgeoning bureaucracies, needed an efficient and legible script in which to keep its documents in order. Ibn Muqla (885-939), geometer and vizier to the Abbasid court in Baghdad, created a standardized, proportioned Arabic writing based on geometry (al-khatt am-mansub or “proportioned writing”). This standardization was based on multiples of the smallest mark, namely the cross-section of a reed pen, as a point. This point becomes the basis of all other measurement. It is square or a rhombus.
As Abdel Ghani Alani discusses, L’Écriture de l’écriture: Traité de calligraphie arabo-musulmane, in Ibn Muqla’s systematized calligraphy, the straight line is defined as the trace that springs from a point, the source of curved lines being noqtat, the center of a circle. The line springs from the point, yet can also be considered a series of points. If the point is the mother of letters, the line (alif) is the father – less because of the alif’s verticality than because, rotated to form a circle, it describes the field of all possible letters in Ibn Muqla’s standardization of writing. Arabic writing shows well the line latent in any point, the line being, in essence, a point drawn out or acted upon in time. But in systematized writing, the point is as small as we can go.
Meanwhile, Islamic philosophers in Iraq in the 9th and 10th centuries were attempting to account for the smallest elements of matter, i.e. atoms, arguing that matter, space, time, and motion were all composed of indivisible minimal parts. The kalam atomists critiqued the versions they received of Greek atomism, reframing it in a theistic cosmology. They hotly debated whether atoms had magnitude and extension, generally concluding, following Epicurus’s doctrine of minimal parts, in the affirmative. At the turn of the 9th century, Ibn Mattawayah of Basra argued that atoms measure space by occupying it, and that they are not triangular or round, but square. [See Alnoor Dhahani, The Physical Theory of Kalam: Atoms, Space, and Void in Basrian Mu ‘tazili Cosmology] The smallest possible line is made of two atoms; the smallest possible surface holds four; and three-dimensional space is filled by 8 atoms. The atomists of Baghdad and Basra disagreed on whether atoms fill all space. The Baghdad view was that space is a two-dimensional container that envelops bodies like a skin; they generally argued, following Aristotle and his Greek commentators, that there is no void and that nature abhors a vacuum. The Basrian kalam philosophers, among them Ibn Mattawayah, argued that space is a three-dimensional expanse of void (Dhanani 67-68). Their debates are similar to the Greeks, who did not distinguish between physical and geometric space; hence Epicurus rejected Euclidean geometry because he could not support the Euclidean hypothesis of infinite divisibility.
In the 9th century, atomism reigned, not just across writing and philosophy buy also theology, fueling fiery debates. When God sustains the universe, went the argument of the radical atomist Al-Baqillani, He sustains it one atom at a time, one motion at a time, with the command “Kun!” – Be! Or not. Evidently the atomist philosophers held a radical perspective on performativity: if nothing can be counted on to endure, continued existence must indeed be performative; furthermore, its continuity is not due to some internal power but to divine grace.
The parallel concepts of square points in calligraphy and square atoms in philosophy raises specific questions concerning the existence of the square in time. We may wonder, for example, whether the form extends internally? But in the discrete worlds of standardized Islamic calligraphy and Islamic atomism, these questions are no longer posable. Standardization stops at the point; in fact, it is notable that the Arabic term for standardization is muqaf, to fix or stop. There is infinite extension outward from the minimal part, and an infinite possibility of embodied movement latent in the still point. No need to look for internal infinities – for the moment. Let us agree for now that minimal parts are indivisible and see what their doctrine might say to digital media.
Atomism translates well to the digital world. There is no question (is there?) that computers work with discrete, minimal parts: the on and off signals, the bit and byte of information. We may ignore for the moment that in a transistor-based digital computer each “on” signal represents a hurtling mass of hundreds of thousands of electrons, each “off” signal a relative dearth of electrons). The pixel is the visual minimal part that corresponds to a minimal part (actually a byte) of information. There’s no inside to the pixel.
However, time and infinity are implicit in the point or pixel because it is capable of drawing infinite iterations. This is beautifully illustrated in the classic computer-based work Every Icon (1997) by John F. Simon Jr: http://www.numeral.com/appletsoftware/eicon.html
In Every Icon, a near infinity of forms arises from an algorithm describing the action of 32×32 pixels over an unfathomably long time. Simon calculates that the second line would take 5.85 billion years to iterate all its possible variations. This modest-seeming artwork brings us into contact with infinity, or certainly with an awesomely long time, which in turn puts both our lives and planet into humbling perspective.
Laura U. Marks / Taking a line for a walk, from the Abbasid Caliphate to computer graphics, or, The Performativity of the Vector
As straight and narrow MIT scientist Vannevar Bush noted, in his critically important 1945essay “As We May Think” that: “The abacus, with its beads strung on parallel wires, led the Arabs to positional numeration and the concept of zero many centuries before the rest of the world; and it was a useful tool—so useful that it still exists.”
other islands in this text-fed stream
