Loopography

The graphic representation of a looped fabric structure can provide a useful complement to its narrative or photographic description. When documenting fabric that includes a variety of stitches that are irregularly juxtaposed, a pattern diagram can provide clarity that is not possible by other means. Numerous systems of notation are based on square-grid diagrams, adapted to the needs of individual crafts. Others, such as ‘symbol crochet’ enable intricate patterns to be represented without the constraints imposed by a grid, and for them to be worked with little or no ability to read the language of the accompanying written instructions.

The structural analysis of, say, a fragment of archeologically recovered fabric is similarly eased by graphic support, and line drawings extrapolated from photographs are commonly included in site reports and independent object descriptions. However, in contrast to the defining aspect of drawings provided by pattern designers, an analytic drawing of an older object may reflect assumptions about details that are obscured by the fabric itself, or are not present in the fragment at all. The difficulty inherent in this is compounded by the ease with which errors can be injected into a drawing, and the low likelihood of their being recognized in the subsequent editorial process.

The earliest generalized illustrations of looped fabric structures appear in an essay by Alexandre-Théophile Vandermonde titled “Remarques sur les problèmes de situation” (Remarks on the problems of location), included in the Proceedings of the French Royal Academy of Sciences from 1771. This is frequently seen as a seminal step toward to the development of ‘knot theory’ later in the following century. In fact, however, the author’s own intention was for it to provide a framework for the description of loop-based yarncraft in both manufacturing and analytic contexts.

However one or more threads may encircle each other in space [circonvolutions], we can always find a mathematical formula for calculating their dimensions, but this expression would be of no use to the crafts. The worker who makes a plait [or braid, tresse], a mesh [or net, réseau], or knots [nœuds], does not design it on the basis of dimensional relationships, but rather by visually positioning the order in which they are interlaced [entrelacés]. It would therefore be useful to have a system of calculation more in accordance with the worker’s thought process; a notation that only represents the conceptualization of his work and would be sufficient for its reproduction in the same manner at any time…. My objective here is only to suggest the possibility of such a notation and its applicability to difficult questions about fabric.

Vandermonde’s notation describes the path a thread takes in a looped structure, by assigning numerical coordinates to the points where it crosses over itself. He illustrates this with two drawings. The label he applies to the first of them — tresse — designates a plaited or braided structure, which requires more than the single element it illustrates. However, the depicted structure is identical to the familiar looped chain that pervades many posts on this blog, and provides a more appropriate label for the underlying model. His treatment of it also presages the shorthand now commonly used in nalbinding, which characterizes a stitch by whether the thread crosses over or under itself when entering each successive preexisting loop.

The second drawing is the no less familiar stocking stitch — mailles de bas — as Vandermonde labels it, and one of the earliest appearances (if not the first) of that term in print, in any language.

Vandermonde recognizes that a numerical system for the description of looped structures can easily become complex enough to require adjunct text and drawings. Since the elimination of such need is his primary objective, he identifies each point where the thread crosses over itself with a simple three-digit figure. The coordinates are then presented in a grid paralleling their location in the drawings.

It is apparent that Vandermonde misappraised the potential utility of his system. It was cited extensively, including the two illustrations, in the section on industrial knitting in Platière’s Encyclopédie Méthodique from 1785, where the first illustration of slip stitch crochet is also found. However, the additional illustrations of knit structures there, which clone Vandermonde’s graphic style, dispense with the numerical coordinates altogether.

It is also apparent that the meaningful presentation of identifiers for the crossover points in fabric containing asymmetrical structures, or single loops worked into multiple other loops, will often require the use of drawings. Notwithstanding its limited utility in manufacture, an intriguing question remains about the extent to which the numerical mapping of the crossover points in a pre-existing piece of fabric can increase the accuracy of its structural analysis.

Recognizing the crossover points as an essential attribute and providing ready means for their quantification is reason in itself to see Vandermonde’s system as a watershed contribution to the study of “difficult questions about fabric.” Although likely less intentional, his exclusion of the selvedges and the starting and finishing structures from the primary description, provides additional useful focus to the analytic process.

The vertically interlooped stocking stitch does not require a separate indication of how a horizontal row is anchored to the preceding row. However, basic structures of crafts such as crochet and nalbinding cannot be described without an equally precise indication of how they are interlooped, not only vertically but also laterally. It remains to be determined how easily Vandermonde’s coordinates can be applied or adapted to this. If nothing else, the attention to detail needed for testing their viability may increase the accuracy of the drawings that are still essential to the analytic representation of any fabric structure.

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• The entire Vandermonde essay can be found here.
• He was quite an interesting figure and his biographical details can be found here and here.
• Further details about the 1785 text can be found here.