The math and physics of knitting

  

https://www.sciencenews.org/article/how-one-physicist-unraveling-mathematics-knitting

I know this wanders around a bit, but the bottom line is in the last paragraph.

 I would put good knitting up; not just with Knot Theory, but with advanced multidimensional  Manifold Theory.  Instead of a thousand page mathematical proof, the competent knitter produces a better and more useful object, likely a garment.

 

Moreover, folks doing knot theory/manifold theory, deal with continuous sets of numbers, while knitters deal with quantum stitches, that have sizes and locations that depend on a large number of variables. Quantum physics is more difficult than knot theory.

 

Mathematical knots and manifolds have abstract forms, such that a line has zero width and a plane has zero thickness. Yarns on the other hand  have real thickness which may not be constant during use, and yarns may change its length in use.  Some yarns material stretch in use and some shrink in the wash, or when you dry your wool socks too close to the campfire  : (   Some yarns (hemp, cotton) get shorter as they absorb water and many yarns get heavier as they absorb moisture, which changes their fit and drape.  And, some yarns tend to untwist and fall apart when they get wet.

 

Then, there is the nature of the yarn. Twist holds yarn together.  More twist, and the yarn is more durable, more elastic, and more stable. However, put a lot of twist in a thick yarn ply and you get “barbed wire”. Yarns designed to be durable have more and finer plies (with high twist), that are then plied together or plied and cabled  (plied yarns twisted together).  Twist is very expensive – mills competing on cost put less twist in their yarns. (And try to disguise their motive by bragging about how fluffy and soft their yarns are.)

 

Wool has scales that tend to lock the fibers together giving the fabric great durability. “Washable” wool yarns have the scales chemically removed, and have less durability.  Nylon is cheap, slippery, and strong. Wool does not grab on to nylon and nylon does not hold wool, so the addition of nylon reduces the durability of wool fabrics – the wool abrades off and you are left with a net of  nylon fibers, so you assume that nylon must add to the durability of the (sock).  No, it is a cheap filler that facilitates wear, so that you buy more socks.

 

All of that is theory before we get into practicality. I have 2 men’s sock patterns, one by a London fashion editor (Mary Thomas), and the other from a yarn mill (Briggs & Little) that caters to people knitting serviceable objects for people working in the cold. The patterns differ by 4 stitches in the heel. The slightly wider heel in the pattern from B&L  is MUCH, much more durable than the narrower heel from Mary Thomas. Small changes in a knitting pattern can result in large differences in the object’s serviceability and durability.

 

The use of different yarns can affect durability and comfort the as much as the stitch pattern.

Yarns with low twist plies tend to be soft and weak. They produce fabrics that are not particularly warm. They are for fashion. Fashion is not expected to endure. If one wants a sweater that is very warm and durable, knit it from a yarn built up from fine plies. If you want a sweater for a dramatic sportive look to wear in a centrally heated pub use a softer spun, more bulky yarn. The real sailor’s sweater will be too warm to wear in a (heated) pub.  (A weatherproof sweater can be designed to vent when the wearer is warm and not vent when the wearer’s skin is cold. These designs only work with weatherproof fabrics. Such venting can reduce the need to layer garments.)

 

 On the other hand, the less dramatic stitch-work in the real seaman’s sweater will be more effective padding when you are storm tossed against spars and rails at sea (or in the “slot” on SF Bay). And, the real fisherman’s sweater will be “weatherproof”.  You can wear it in the rain, and it will be warm and it will feel warm and comfortable. (If vented, the venting may allow a cold stream of water to run down your back.)  In heavy or wind blown rain, you may feel the rain, but such storms do not last long, and when the deluge diminishes to an ordinary rain, then within 15 minutes, you will feel warm and comfortable. Likewise a “garage sale” fall while skiing may allow snow under the sweater, but once the snow has been scraped out, a few minutes later the sweater is comfortable.   That is; a thin layer of fabric next to the skin has dried, and the garment again is warm and comfortable.

 

Such fabrics require wool fibers to be densely packed (e.g., ~spacing between wool fibers less than 40 microns). This slows air flow through the fabric and stops most liquid water.  If we think of a knitting needle as a lever for moving loops of yarn,  and  calculate the leverage available, and the muscles available to provide power; then, hand held needles (cable needles or single point needle or DPN)  have very limited leverage (e.g., 1:3) and are driven the small muscles of the hand via the fragile tendons of the wrist. However, if one end of the working needle is supported, than the available leverage is much higher (1:10).  In the picture of Elisabetta Matsumoto knitting, her working needle is supported by a knitting belt (not visible) and the work is driven by her shoulder muscles.  A knitting belt is the fastest proven technique for hand knitting.

 

The Fair Isle stitch pattern she is knitting has a second strand of yarn carried behind the fabric, which greatly increases warmth of the fabric, which advantage is offset by less stretch.  Traditional Shetland Fair Isle knitting was done with rather fine 2-ply yarns, and the fabrics were warm, light weight, very low bulk, and  well suited for the climate.  A similar knitting technique was used for “weaving” vests which produces a similarly warm fabric/weight with slightly more stretch.

 

The invention of the square rigged ship, some where in the vicinity of the Channel Islands circa 1,000 AD, demanded some way to keep active sailors warm above deck, even in foul weather.  Hence, what we know today as “fisherman’s sweaters”.  Production of such sweaters require the use of knitting sheaths to support the working needle. Knitting sheaths give the knitter more leverage, and allow tighter knitting.

 

Many of the traditional fisherman’s designs make use of the different properties of different stitch patterns used next to one another, to improve the over all characteristics of the object. For example basket stitch used between bands of purling to make a sweater that well suited to rowing or hauling a line.  It is also fast and easy to knit, so it was very popular and was known as “Lizard Lattice”. When such combinations are considered, there are a very large number of useful knitting stiches.

 

Such hand knit sweaters, kept Shackleton’s men warm in their year (1914 -1917) on the Antarctic ice.  And, they have enough stretch to allow sailors to preform acrobatic work. Objects hand knit with a knitting sheath can be truly “weatherproof”. The last large group of people to knit using knitting sheaths were men on British destroyers in the Pacific during WWII. They knit to pass the time while on battle stations. They hated that knitting because someone was about to try and kill them. They  loved it because, if they were still knitting, nobody was actually shooting at them.

 

In the period 2005 -2010, several of the old British mills producing the dense yarns used for the traditional fisherman’s sweater had failures of their 100-year old spinning equipment and they stopped producing such yarns.  When I started hand spinning such yarns, I was told it was impossible and had never been done.  In fact, such yarns had been spun in the past, and they can be seen in any museum with a good textile collection.

 

The standard text on modern knitting techniques is (The Principles of Knitting) , and the author teaches the history of knitting sheaths, but does not know how to use knitting sheaths. 

 

I think that from 1,000 AD, until ~ 1840 AD thousands of bright eyed, nimble fingered knitters somewhere between the Shetlands and Lisbon were doing what Elisabetta Matsumoto and her advisors would consider graduate level, university physics. Those knitters could run their hands over a departing fisherman, and when the fisherman returned, he would have a fisherman’s sweater well suited to his duties on board, the climate where his ship fished, durable enough to last a fishing season; and that sweater was knit to fit.  These are a set of skills we have lost.  Elisabetta Matsumoto does not even know that weatherproof wool fabrics can be knit.