It fascinates me how traditional crafts such as knitting and crochet have now become highly useful tools for our understanding of science and mathematics.
Knitting actually involves a fair bit of arithmetic, from counting stitches, calculating the gauge of your tension square (that is the number of stitches and rows required to knit a 10cm square for a particular yarn), adapting a pattern to match your gauge, and if you choose to work a pattern with a different yarn than recommended in your pattern, you will need to work out just how many balls of yarn you need for your project.
But the relationship goes beyond simple counting and calculations.
Anybody who has ever tried to understand a knitting pattern knows that knitting is basically a form of code. The British Office of Censorship certainly understood this: During World War II, people were banned from sending knitting patterns abroad for fear they may contain coded messages.
Alan Turing, the famous British mathematician and computer scientist who broke the code of the German Enigma machine in World War II, was frequently seen knitting Möbius strips and other geometric shapes during his lunch break.
At the same time, in Belgium, the resistance movement during World War II used knitting to transmit coded messages: Women who lived in building with windows overlooking the railway yards were asked to note the trains in their knitting by choosing one type stitch for one kind train and another stitch for for another type of train.
An early appreciation for the link between geometry and knitting can be found in an essay by Nobel-price winning American theoretical physicist Richard Feynman titled “What is Science” from the collection The Pleasure of Finding Things Out.
Please note that the essay was based on a lecture Feynman gave in 1966, a time before feminism had become truly mainstream - when I read this I strongly felt that I am glad it's not the 1960s anymore!
Here is Feynman in his own words:
"When I was at Cornell, I was rather fascinated by the student body, which seems to me was a dilute mixture of some sensible people in a big mass of dumb people studying home economics, etc., including lots of girls. I used to sit in the cafeteria with the students and eat and try to overhear their conversations and see if there was one intelligent word coming out.
You can imagine my surprise when I discovered a tremendous thing, it seemed to me. I listened to a conversation between two girls, and one was explaining that if you want to make a straight line, you see, you go over a certain number to the right for each row you go up, that is, if you go over each time the same amount when you go up a row, you make a straight line. A deep principle of analytic geometry! It went on. I was rather amazed. I didn’t realize the female mind was capable of understanding analytic geometry.
She went on and said, “Suppose you have another line coming in from the other side and you want to figure out where they are going to intersect.” Suppose on one line you go over two to the right for every one you go up, and the other line goes over three to the right for every one that it goes up, and they start twenty steps apart, etc.–I was flabbergasted. She figured out where the intersection was! It turned out that one girl was explaining to the other how to knit argyle socks."
More recently, knitting and crochet have been used in making complex mathematical concepts tangible and understandable. This has largely been facilitated by women in science who were able to think outside the box.
Take, for example, the work of Daina Taimiņa, the Latvian born mathematician and Adjunct Associate Professor at Cornell University, who used crochet to create a model of a hyperbolic plane to demonstrate how hyperbolic geometry works. For a quick introduction, watch Glenys Stace explain what hyperbolic crochet is in the video below:
What makes knitting and crochet such a useful tool is the ability to create almost any shape, no matter how twisted or complex, with a ball of yarn and a pair of needles or a crochet hook. Compared to other materials (paper, plastic, metal), a knitted shape is easy to handle, can be folded and unfolded as often as you like without breaking, and it is cheap and easy to make at home - making this the ideal tool to visualise the complex geometrical structures our world is made of.
It is therefore no surprise that knit and crochet models of our atmosphere, coral reefs and the human brain have all been used to help our understanding of these structures.
If you are interested to delve further into the topic of mathematics and knitting, have a look at this fantastic book by Sarah-Marie Belcastro and Carolyn Yackel.
Belcastro and Yackel are two American professors for mathematics with a keen interested in the link between mathematics and craft.
"Making Mathematics with Needlework" is aimed at mathematicians, needleworkers and teachers of mathematics interested in thinking outside the box.