Things to Think With: Crochet Hyperbolic Planes and Computing

Do you sew? Knit? Weave? Crochet? Personally, I have rarely ventured beyond replacing buttons on shirts, but Sarah Kuhn, Professor in the Psychology Department at the University of Massachusetts Lowell, taught herself to crochet after being inspired to create hyperbolic planes by Daina Taimina's book "Crocheting Adventures with Hyperbolic Planes".

Sarah has been working for years at the intersection of art, sociology, computing and engineering education. This latest project is part of a new research area, part of her evolving investigation of ways to bring mathematics and computational concepts to life. When she first saw some of these crocheted hyperbolic planes she asked herself: are they more than models? Can these objects be used to discover things? To her, that is a key point for a successful learning environment.

The answer is yes. Creating a hyperbolic plane crochet 'object' (the best word I can think of, although it feels insufficient) provides opportunities to explore algorithms, patterns, emergent properties, and programming - for starters. How?

I asked Sarah to explain how it all works, and asked her to assume she was speaking to a completely clueless crocheter (as I am, having never even touched a pair of needles). She patiently stepped me through the "single crochet stitch", the basic stitch in crochet. She explained the ways this stitch can be used, with no other more complex stitches, to create an object such as the gray spherical object pictured above or the colorful object below. The process is indeed algorithmic. You start with a circle out of yarn and move outwards in a spiral one stitch at a time. There is also something called "increasing". I won't try to replicate the explanation for fear of completely butchering it, but suffice it to say, every creation is different because of variables (computing concept!) including how often you increase, the type of yarn, the quality of the yarn, the color, and the composition of the yarn.

Crochet hyperbolic planes provide a simple entry into the worlds of mathematics, computing, and analytical thinking in general. They are easy to make, fun, and small changes result in sometimes surprising outcomes. A little crochet tweak here and you have a different form of ruffle; another crochet tweak and the shape shifts. Another topic: Design patterns and the implementation decisions they lead to.

Highly portable, crochet hyperbolic planes are excellent conversation starters. Sarah summarizes a typical conversation:

Scene: The doctor's office. Personae Dramatae: Sarah in chair, Person Nearby in chair (perhaps bored).
Person Nearby: "What is that?"
Sarah: "This is a hyperbolic plane"
Person: "What's that?"
Sarah: "It is math"
Person: "Really? That's math! If someone had presented that to me as math in high school I would have liked it".
[Conversation continues....]

Voila. An aesthetic entrance into the world of the formerly abstract. More complex concepts wait to be tackled by progressing to a discussion of weaving; weaving has far greater complexity than crochet and an interesting history that we know includes the computational (ahem...Jacquard Loom?).

Fiber arts (which encompass sewing, knitting, weaving, crochet) cross cultural, age, geographic and social boundaries. In some societies they are associated with women's activities, in other societies with men's activities. As Sarah says "a STEM opportunity hiding in plain sight". Not surprisingly, she is developing several ambitious project ideas that will integrate fiber arts into a variety of classes and programs with the explicit goal of encouraging interest in STEM disciplines - computing included. 

Sign me up. I wanted to reach out and grab one of these crocheted hyperbolic planes the moment I saw their pictures. Wouldn't it be fascinating and fun to explore the world of computing while creating one's own personal weird masterpieces of yarn? Stepping stones to complexity. Sarah Kuhn is demonstrating that the arts and computing have a lot in common.