Woven cosmos and patterned number

Ancient textile technology and the emergence of Greek philosophy (Part 1)

One of the research questions grounding the PENELOPE project has to do with the nature and the extent of ancient textile technology’s contribution to the rise of early Greek thought on nature and the cosmos. We build here on previous work by Ellen Harlizius-Klück, who has explored in her doctoral dissertation (https://zenodo.org/record/848661#.XFitOc17nIU) the connections between the rise of dyadic arithmetic in archaic Greece, early cosmology, and ancient weaving by a novel interpretation of the function of the paradigm of weaving in Plato’s Statesman as an instance of epistēmē (‘science’).

The warp-weighted loom

The focus of our current work is to look at ways in which the distinctive logic of generating patterns in weaving, and particularly on the warp-weighted loom in use in ancient Greece, may have represented an especially fitting model for thinking about the structure of the physical world, the kosmos (a Greek word whose original meaning is ‘ordered structure’).

Creating geometrical patterns on a fabric implies conceiving of forms in terms of numbers, since every line emerging on the design of the weave results from the particular combination of odd and even threads, and pattern repeats are regulated by numerical relationships. In turn, our investigation encompasses the interconnected aspect of early Pythagorean ‘pebble arithmetic’, i.e. a way of arranging pebbles in shapes so as to discover properties of (even and odd, square, etc..) numbers – in other words, a way of thinking of numbers in terms of shape. (You can find a pebble argumentation and even play around with pebbles a bit here: http://www.praetexta.de/psephoi/e_start.html; use the Go-stone in the lower right corner for going forward).

Pebble arithmetic

There are a number of remarkable texts in early Greek cosmology where textile technology seems to play a significant role in defining and illustrating features and mechanisms of the functioning and structure of the physical world. In the few transmitted lines of what a number of ancient sources report as the first prose book in Greek literature (with a competing tradition assigning such a price to Anaximander’s book), Pherecydes of Syros describes an act of cosmic generation in terms of weaving in the frame of the narration of the wedding of the supreme divinities Zās and Chtoniē: in a section of the Grenfell-Hunt papyrus bearing Pherecydes’ text, the craftsman god Zās offers as a wedding gift to Chtoniē a robe (phāros in Greek), in which he in-weaves (poikillein is the Greek verb used) “Earth (Gē), the Ocean, and the Ocean’s dwellings”.

This is not, we think, an allegory or simply some kind of literary imagery; the act of cosmic generation that is here, for the first time in Greek thought, illustrated in terms of craft, features weaving for precise reasons: the structure of discrete elements that forms the cosmos is best conceived of in terms of a technology that is able to generate order, symmetry, regularity and at the same time preserves variegation, multi-coloured effects, and let any kind of shape appear on the fabric as the result of construction.

In arguing that specific (techno)logical features of ancient weaving as a technē (a Greek notion encompassing craft, art and technology) are at the core of Pherecydes’s model of cosmic order, we aim at fully re-integrating Pherecydes as a thinker, rather than as a mythographer, within the emergence of Greek philosophy in sixth century BC Ionia: the choice of weaving on the part of Pherecydes, in particular, should be brought to comparison with Anaximander’s architectural model of the world as two different answers to a common concern for serious investigations into nature and the cosmos – rather than, as the critical vulgata has perpetuated (from Aristotle to modern scholarship), mythical vs. philosophical thinking. At the same time, we think that bringing up ancient weaving technology as one (among other) conceptual paradigm suggesting a specific mode of generating structures may enrich the scholarly debate on the factors determining the so-called ‘revolution’ of early Greek natural philosophy; a number of different answers have been suggested for the rise of Ionian thinkers in just that region at just that time: historical causes like Greek urbanization, or the contribution of specific technologies, either new (like monetization) or significantly improved (architecture). We believe that weaving should also be brought into the wider picture, especially since evidence of ‘weaving knowledge’ providing a consistent analogical model for different modes of compositions (in poetic performance, dance, rhythms) is conspicuous in archaic Greece.

Less explicit, at least in literary sources, is the connection between weaving and the so-called Pythagorean number theory: numbers, in the forms of ratios of musical harmonies, being at the core of Pythagorean cosmology, they seem to be granted as well an epistemological function, at least in the extant fragments of the 5^th century thinker Philolaus of Croton, where things in the world ‘possess number’ and thus they can be known as far as one is able to grasp their numerical relationship. Numbers, that is, can be seen as constituting the structure of things, and things in turn may be seen as made of numbers in the sense of ‘ordered plurality’, possibly patterns. Philolaus is also defining some basic notions of dyadic arithmetic by dividing the species of numbers in even, odd, and odd-even (possibly referring to the unit). A practical way of finding out the properties of odd and even numbers is by arranging pebbles on a surface, a practice that a couple of ancient sources associate with Pythagorean thinkers; disposing pebbles in the so-called ‘gnomon’ for, among other things, measuring the difference of successive square numbers, was another practice that early sources trace back to early Pythagoreanism.

Gnomoi

When we bring this together with Aristotle’s and Theophrastus’ mention of the way the Pythagorean Eurytus arranged numbers in pebbles so as to assigning specific shapes to particular numbers (‘… Eurytus assigned what is the number of what, for instance this one of man, and this one of horse, … reproducing with pebbles the shape of natural creatures’, Arist. Met. 1092b8-13), a practice that Aristotle compare to ‘those who arrange numbers into figures, the triangle and squares’, we might come close to what ancient Greek weavers in fact did when constructing woven patterns and images. The fundamental division of warp threads into even and odd, and the logical and arithmetical constraints of pattern repeats (the total amount of warp threads cannot be a prime number, for instance, and it must be divisible for odd/even times the number of threads of the single pattern) imply knowledge of dyadic arithmetic on the part of the weaver: in turn, arranging pebbles into shapes and geometrical patterns would allow a weaver to think of geometry in terms of arithmetic, each pebble/unit representing a crossing of warp- and weft-thread.

Our plan is to explore the topics that we have sketched here in the coming spring and summer: we will keep you updated on upcoming publications and presentations via our blog!

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