Looping · Systematics · Terminology

Thinking outside the loop

In his book titled Ethnological Studies among the North-West-Central Queensland Aborigines, published in 1897, Walter E. Roth describes a man’s cap that includes both linked and looped structures.

roth-1897-hairnet
roth-1857-hairnet-detail

“Head-net…a sort of netted cap with a circular ring at the top from around which the body of the net is woven, the pattern of the stitch being shown in the diagram… It is manufactured, by men only… Another form of head-net, an undoubtedly modern innovation, is made by the women, though not necessarily worn by them alone, after the manner and of same mesh as a fishing net…”

Roth describes a further variant of looping with an inlaid thread as being typical of dilly bags. In a categorization of fabric structures that he would continue to develop, the three forms are juxtaposed in a single labeled illustration.

roth-1987-abc.jpg

“There are three kinds of mesh to be found in the weaving of a dilly-bag. The most common, what may be called the ‘type,’ is that marked A in the diagram: rarer forms are the ‘hair-net’ B, and its modification, the ‘twist’ C. The type-pattern may be alone used in the weaving of the bag throughout, and under such circumstances it would be pretty safe to infer that it had been made by women, who do not usually weave the other forms of mesh. The hair-net pattern has been so described because of its identity with what is met with in that particular article [in the preceding illustrations], of which can certainly only be made by males: there are generally two or three rows of this mesh connecting the type with the twist pattern surrounding the mouth of the bag. No dilly-bags made in their entirety with the hair-net or twist pattern are discoverable: these particular meshes would seem to be only subsidiary to the type one.” Continue reading “Thinking outside the loop”

Description · Looping · Structures

From loop to knots

The chain of loops illustrated in 1771 by Alexandre-Théophile Vandermonde (discussed in the preceding post) appears in another seminal text on knot theory. Peter Guthrie Tait presented a number of papers on that topic to the Royal Society of Edinburgh during its 1876–77 session, with a condensed version appearing as an article titled “On Knots” in the Society’s Transactions. vol. 38, 1849.

tait-chain.jpg

His comments on the first of the illustrated forms state:

“…the supposed number of loops may be any whatever. The free ends must, of course, be joined externally. If we make the crossings alternately + and – it will be seen at a glance that a change of one sign (i.e., that of the extreme crossing at either end) removes the whole knotting; so that there is but one degree of beknottedness. The crossings in this figure are in three rows. Those in the upper row are all copper (the last, of course, becomes silver when the sign is changed)…”

The free ends need to be joined since Tait presents the chain as a mathematical knot, which is closed by definition. All such constructs are analyzed in terms of the number of points where the closed element crosses over or under itself, the direction of each crossing, the effect of selectively changing those directions, and how the knot relates to its mirror image. He uses the the terms ‘copper’ and ‘silver’ to qualify the crossings further.

Tait’s explanation of the lower chain is:

“To give the greatest beknottedness to a knot with the same projection, it is obvious that all we have to do is make the copper crossings into silver ones, i.e., change the sign of each of the upper row of crossings. This gives fig. 9 [unnumbered here]. With five loops it has four degrees of beknottedness.”

In “On Knots. Part II” from 1884, he more clearly defines the concept of beknottedness and how its degrees are counted:

“I still consider that its proper measure is the smallest number of signs which will remove all knottiness.

The discussion then goes further into ‘locking’ and ‘linking,’ concepts introduced in the 1877 publication along with the undefined ‘knotfullness’ and ‘belinkedness.’ The 1884 volume includes On Knots, Part III, which similarly clarifies knottiness. Locking and linking are directly relevant to the description of looped fabric, and the concepts of  both beknottedness and belinkedness can usefully be applied to its structural analysis.

Knot theory is largely focused on reducing elaborate looped constructs to their minimum knottiness by eliminating as many extraneous loops as possible. At least one further besomethingedness is therefore needed to quantify the unravelable loops that are deliberately retained in actual fabric. In the spirit of florid Victorian coinage, I’m going to start by suggesting ‘beloopedness’ and pair that with ‘loopfullness.’ Depending on how far they can be taken, it may also prove useful to co-opt the colloquial term for unraveling a sequence of looped stitches by undoing the knot that secures it and pulling the freed end — frogging. This would add ‘degrees of befroggability’ to the extensions of the glossary.

It is likely that the additional terms would have met with Tait’s approval. He took delight in artful terminology and was surely aware of the way his ‘knottiness’ otherwise sounded, adding ‘perversion’ (“deformed into its own perversion”) and ‘screwing’ (“of all kinds”) to his labels for other attributes of knots. Although ‘loopiness’ had yet to acquire the connotations it now has, its latter sense would surely have added to the delight. (His terminology has all been streamlined in the recent literature of knot theory, and I’ll also be making that shift — but not quite yet.)

Other knots that parallel looped fabric structures appear in Tait’s drawings. He provides direct justification for the present excursion by stating that “Some are closely connected with knitting, &c,” explicitly using the following three as examples.

tait-hourglass.jpg

It is further worth noting that the least complex structure beyond a simple ring —  ‘the unknot’ — to qualify as a mathematical knot is the ‘trefoil.’ This is also a quintessential loop in the craft sense, rendered mechanically secure by drawing its free end(s) through the middle as described below.

Here is Tait’s illustration of it.tait-trefoil

He doesn’t show anything equivalent to the stocking stitch in Vandermonde’s mathematical framework. However, given Tait’s own mention of knitting, and since the number of loops in a chain “may be any whatever,” he would doubtless have been comfortable seeing his analytic procedures extended to any looped structure found in fabric. The mathematical rigor that was his intent can also be relaxed when adapting his method to such description.

In craft terms, if a loop is added to a fabric structure by leading the end of the working thread into the preceding loop and pulling it entirely through the new loop — as with an eyed needle — the result is a knot. (That’s why calling nalbinding ‘knotless netting’ is fundamentally incorrect; ‘loose-knot netting’ would be far better.) If instead, the thread is pulled into an old loop to form a new one, but the end of the thread is not drawn entirely through it — as with a knitting needle or crochet hook — there will be no knot in the structure until the thread is pulled fully through a subsequent loop. It is also possible to work end-led around a preceding loop but not through it.

Plain knitting (stocking stitch) is loop-led through the penultimate row in the fabric, which is followed with a row of crochet-type slip stitches that successively reduce the number of workable loops to a single one. The end of the thread is then pulled through it to form a knot. (There are alternative ‘bind offs’ but the end effect remains the same.)

A loop-in-loop structure where only the final loop is secured in this way has “but one degree of beknottedness” regardless of how extensive the preceding looping is. A looped structure that is punctuated with knots at regular intervals has greater degrees of beknottedness than one that is homogeneously looped throughout, but again, that does not describe any further detail in its looped component.

However Tait might have felt about any of this, the concept of loopfullness can be used to quantify differences between various forms of looped fabric, based on properties of the individual loops. As counted by Vandermonde, an open-knit loop has four crossover points with the one it’s worked into, two in front and two in back:

vandermonde-stocking

Closing the loop adds one more crossover point, thus making the loopfullness of closed-knit fabric 20% greater than that of open-knit fabric.

iso-closed-loop

Working a second row of chains asymmetrically into the one illustrated by Tait produces a structure that is normally seen as plain crochet but also illustrates (left-handedly) the final row of plain knitting.

patent-ss

The first and last loops in this drawing deviate from the configuration of the others in order to set up the free ends for fusing into a mathematical knot (alternating + and – crossings over the join). Otherwise, each of the four complete chains in the second row starts out as an open-knit loop, with its characteristic four crossover points. Another loop is then worked into it laterally, adding four further crossover points, and imparting double the loopfullness to plain crochet than plain knitting has.

Another way of stating this is that plain knitting involves a single loop being worked into another single loop. Plain crochet works one loop into two other loops, and the question is whether the difference between loop-in-loop and loop-in-loops should be taken to indicate different degrees of beloopedness. That distinction applies not just to crochet-type asymmetrical compound looping, but also to symmetrical compound looping as typified by the knit tubes that began to appear in the 5th century CE, and compound nalbinding.

The preceding illustration of plain crochet also seeds a discussion of belinkedness that I’ll continue in a separate post. Instructions for producing such fabric, through to early 20th century (summarized here), prescribe the addition of further rows by placing a knot at the end a completed row and starting the next row afresh from the other edge of the fabric. Although the rows may be identical, each is a separate mathematical knot that is linked to its predecessor. The mode of that linkage is as important to the characterization of the fabric structure as is the configuration of the individual rows, and may prove reasonable to quantify in degrees of belinkedness.

Folding this all back into Tait’s initial concept of beknottedness, nalbound fabric where each stitch is secured with its own knot, has as many degrees of beknottedness as there are stitches. Flatwork plain crochet with each row ending in a knot, has as many degrees of beknottedness as it has rows (discounting its alternate characterization as a sequence of linked knots). Plain knit fabric, as already noted, simply has one degree of beknottedness.

This might be extended into the similar enumeration of degrees of beloopedness by taking ‘one loop in one loop’ structures to have  one degree of beloopedness, ‘one loop with multiple loops’ structures to have two degrees of beloopedness, and any such compound structure that encapsulates yet another looped structure as having three degrees of beloopedness.

One illustration of that third case is seen in the family of crochet stitches that interpose multi-looped vertical separators between the anchor loop in the preceding row, and the loop that closes the current stitch. These are normally termed ‘posts’ and their ‘length’ defines the difference between plain crochet and the double, triple, and other modified forms. This attribute of looped fabric is the one that corresponds most directly to Tait’s knottiness, and is would therefore be most correctly designated as loopiness.

That concept also applies to the suggestion that Tait’s conceptual model is applicable to the practice of loop-based crafts. However, I do believe that the methods he developed for analyzing mathematical knots can be useful in the investigation of what Vandermonde called “difficult questions about fabric.”

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Here are a few particularly clickworthy links to additional material about Tait.

  • A lecture about his academic career and the context in which he developed knot theory can be streamed here.
  • His brother-in-law, Alexander Crum Brown, also a prominent scientist, knit an intricate three-layer model of one of the other knots illustrated by Tait. That model is currently in the collections of the National Museums of Scotland and can be seen here. The museum also posted a two-part blog with background detail about Crum Brown and his method for knitting the model.
  • James Clerk Maxwell, a close friend of Tait’s, commented on the latter’s florid terminology in a poem titled “(Cats) Cradle Song.”
Description · Looping · Structures

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.

vandermonde-plait.jpg

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-stocking.jpg

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.
History · Looping · Structures · Tools

Crochet isn’t for the birds

Hooks and needles have been around immeasurably longer than any evidence of either being used in the production of looped fabric, and looping without tools all but certainly predates the use of any such implements for that craft. In fact, there’s no way even to determine if our species was the first to figure out how to do any of this.

Tailorbirds know how to draw loose fiber into thread and sew with it.

Weaverbirds know how to gather uniform strips of vegetable fiber and loop and weave them into shaped structures.

A slender pointed beak that can both pierce and grasp is remarkably well suited to the sewing and looping seen here. It is also useful for converting a needle into a hook when needed.

From the perspective of sewing-tool design, the dual-purpose awl and tweezers provided by a beak is a more precise implement than the functionally equivalent index finger and opposable thumb on a human hand. There is no reason to assume that these birds developed their needlecraft and toolmaking skills before we started doing similar things but Homo sapiens can’t even claim credit for the oldest known eyed needle.

It’s a fair guess that this needle was used to pierce fabric and pull some kind of fiber through the resulting hole but that doesn’t preclude similar action at the site of the needle’s manufacture or elsewhere with other tools. It would be more of a stretch to see the needle as evidence of tool-based looping but at some point eyed needles clearly did come into use for that purpose.

There is an obvious upshot to all this. Just as there are several basic looped structures that can readily be made without tools and are seen as universal constructs, appearing independently at uncountable times and places, a battery of ubiquitous tools has been available throughout to ease and extend the production and design of looped fabric. However much local applications might diverge and whatever degree of specialized complexity a craft might ultimately acquire, at least in principle, all can be traced back to one or more elements of the same initial set of structures and tools.

In the largest number of cases, the appearance of similar techniques at widely separated times and locations is therefore best treated as coincidental. However, there are situations where corroborating evidence indicates cultural cross-pollination, if not the outright transfer of technology. One possible such occurrence can be seen in previous posts about the parallels between Egyptian yarncraft and Viking wirecraft, with tubular knitting appearing in each. A similar parallel is found in the looped yarncraft of the two regions.

The eyed needle was used by both communities when working with yarn but the only evidence of a hook used with that material is Egyptian, assuming the practice of  knitting on a peg loom. The Vikings similarly appear likely to have used a hook for knitting wire but, again, there is no indication of their having used such tools to work yarn. That technique does appear in Northern Europe far later as “shepherd’s knitting” (the basic form of what is now called slip stitch crochet), where it is believed to have developed over an indeterminate period for producing the types of warm utilitarian garments that were also made in the same region by nalbinding.

However, there is at least one instance of shepherd’s knitting in archaeologically recovered material claimed to be from Coptic Egypt. If that provenance is accepted, it raises a few interesting questions. It is entirely possible that the object is simply an isolated occurrence of a fairly obvious method of looping that would become commonplace at a significantly later date, both in North Africa and Northern Europe. On the other hand, if the parallels between the looping techniques in those two regions are a result of cultural interaction — of which there is otherwise ample evidence — it may be possible that the use of a hook to make crochet-type structures was communicated via those channels. I’ll get into the details of this by describing the Coptic object in a subsequent post.

History · Looping · Nalbinding · Terminology

More historical terminology

In the third volume of his Glysisvallur — a massive description of all aspects of the Swedish province of Hälsingland written circa 1730 — Olof Johan Broman includes the following description of yarncraft under the heading of sheep husbandry.

“Caps, mittens, stockings, and sweaters are knit [stickes] from both single and plied wool yarn. These are also stitched [sömes], especially the first named garments, but never sweaters. The difference between knit and stitched stockings, mittens, etc., is known. The latter practice is also called ‘to bind’ [binda] and the product, for example, bound [bundna] stockings, etc.”

The phrase ‘to bind stockings’ (binna strumpor) has its own entry in a Swedish Dialect Dictionary from 1766. This defines its use in the province of West Götaland as “to knit stockings” (sticka strumpor). Nothing else in that dictionary clarifies if knitting is distinct from binding, a synonym for it, or a generic term that subsumes both. These various senses are attested in other documents, where knitting and binding are used both to name specific crafts and as broader designations for other forms of looping.

The term knitting is used in that overarching sense in the definition of a name for slip-stitch crochet in the same West Bothnian dialect dictionary from which the definition of sömma presented at the outset of this excursion into Swedish lexicography was taken.

påta — v. (pōtă) … 2. to knit [sticka] caps, mittens, etc., with a small hook [krok].

This craft is commonly referred to as “shepherd’s knitting” in English texts. Written and illustrated descriptions of it began to appear in several European countries in the second half of the 18th century. All share one important attribute — they treat it as a form of knitting, or even binding. Prior to the 19th century, wherever the word crochet appears in a craft-related document, it designates the tool.

The word påta remains an accepted Swedish designation for traditional slip stitch crochet made with a flat hook. In the preceding post, we also saw it used to designate stitching with an eyed needle to make mittens. It appears in an intervening fictional narrative from 1907 consistent in all regards with the preceding dictionary definition.

She graciously took out a half-knitted [halfstickad] mitten. to which the white wool yarn was still attached. It was påtad as the women in Norrland used to do, who with a small bone hook [benkrok] put together [påtade ihop] splendid strong mittens.

The hook and the needle techniques also share contemporaneous dictionary definitions that categorize both as forms of knitting, and the 1790s dictionary says both were used to produce the same kinds of functional garments. A redundant array of names for techniques and crafts can be teased out of all this — binding, hooking, knitting, looping, needling, stitching, etc. They are all applied to the production of a more clearly defined number of warm utilitarian garments — caps, mittens, socks, and stockings.

Of these craft designations, knitting appears to be the one used in the broadest generic sense. However, the early sources differ on the other techniques they place in that category. All obviously agree that it includes knitting as a discrete craft, and slip-stitch crochet generally appears there as well.

The 1730s narrative unequivocally regards knitting and stitching as separate categories. Given the native Swedish terms for the implements fundamental to each — sticka and nål — the term ‘needling’ contrasts most clearly to knitting. In fact, nålning is used preferentially in Swedish scholarly texts through the 1960s, despite Margrethe Hald having introduced the term nålebinding into the vocabulary of Scandinavian textile research in 1945.

In 1963, Anne Marie Franzén published an article about a nalbound medieval sock, with the Swedish title En medeltida socka i nålning. The report on nalbound mittens Maria Collin published in 1917 noted that traditional practitioners called them nålade. Franzén cites Hald’s earlier work but does not mention nålbindning.

A Norwegian article headed Nålbinding, by Marta Hoffman in a volume of a pan-Scandinavian encyclopedia published in 1967, lists the corresponding Danish term as nålebinding and the Swedish as nålning or vantsöm — again without mention of nålbindning. Anna-Maja Nylén did adopt that term in her book from 1968 (perhaps having consulted the other sources noted above) but landed somewhere in the middle with ‘needle looping’ in its English translation in 1976.

I’ve taken the derivation of the various Swedish designations for nalbinding about as far as I can. One of these terms — virka — appeared in a previous post about looped purses (linked to above), and will be revisited in the contexts of chain-stitch embroidery and crochet. In the meanwhile, I’m going to consider the 1730s distinction between knitting and needling from a technical perspective and set etymology aside.