Some time ago I was wandering through the website Ravelry. It’s a place where knitters and others can show off their work or make patterns available to others, either for free or for money. The patterns are incredibly varied and Ravelry is a nice place to go if you like to knit. On this occasion I found a sweater pattern that said it had been designed with the new mathematical shape that was the successor of Penrose tiles. That made me open my eyes. But I didn’t really go any further.

https://www.ravelry.com/patterns/library/einstein-tile-sweater

Then I read a book called A Piece of Justice by Jill Paton Walsh. And I am going to discuss the entire thing so if you don’t want spoilers, quit reading.

I had heard of Jill Paton Walsh because she was asked by Dorothy Sayers’ estate to finish a detective story that Sayers had started about Peter Wimsey and Harriet Vane. It was supposed to take place shortly after they were married. That book, Thrones and Dominions, came out in 1998? I read it, wasn’t excited, and moved on.

A Piece of Justice, published in 1995, is part of a series whose detective, Imogen Quy, is a nurse for one of the ‘colleges’ that make up Cambridge University; the college in the book is quite imaginary of course, but Walsh discusses doing research to make it as real as possible.

A Piece of Evidence has several threads running through it: Writing biographies, theories of how biographies should be written, piecing quilts, amateurs or towns people vs college intellectuals, honor, stubbornness, relationships, mathematics, and women’s rights. It’s quite an entertaining assortment of ideas. The quilting theme is vital, and Walsh had taken the liberty of imagining a successor to the geometric idea of Penrose tiles.

Penrose tiles are ways to cover a two dimensional surface, that is a flat surface, with designs that don’t repeat. Repeating designs have parts that can be moved up, down, or sideways and find a perfect match under them. Penrose tiles have five fold symmetry. They can be rotated 72º to find a match, but not simply slipped across a surface.

Penrose got his tiling down to two shapes …

and then found a more elegant set of two shapes.

Mathematically, and aesthetically, this is fascinating stuff but it’s way beyond me to explain. I can’t even explain why anyone cares, although architecture people love the elegance of this kind of surface coverage and have used it to great effect in various modern buildings.

The Holy Grail of all this coverage of a flat surface is ONE shape that can be endlessly laid down to cover a surface, but without repetition. Tessellation, of course, repeats instantly. In the book I mentioned at the beginning, a pretend solution of this tiling question is the central conceit of the book. A Welsh farm wife creates a quilt using her (pretend) single shape. A Cambridge professor stays at the farm as a Bed and Breakfast guest. He sees the quilt, understands what it is made of, thinks the farm wife just happened to do it, and steals the idea. He acquires a great mathematical reputation from the theft. Eventually bad stuff happens as a result.

One of the points the book makes over and over is that Cambridge, in 1995 at least, is full of women who got degrees and then became housewives. They no longer see their work as important and neither do a lot of others. At the end of the book Imogen, the detective, realizes that the Welsh farmwife had studied mathematics at Cambridge in the early 1920’s. It is reality that at the time, although Oxford granted degrees to women, Cambridge voted to refuse women the BA and had a riot about it. When the future farm wife got caught up in the riot fictionally, she decided that she hated Cambridge, and the pretend reverence for the life of the mind, and went off to marry a wealthy Welsh farmer and lived happily ever after. And invented this special shape for the quilting that she loved to do — the shape that got stolen.

The man who stole the idea didn’t see the farmwife as anything important so he never asked her where the idea came from, nor did he give her any credit. The ultimate murderer in the book also thought that farmwives, and incidentally, nurses, were inferior beings. The book ends with people around Imogen finding the farm wife and bringing her back to Cambridge, seventy years after she studied there, and giving her an honorary degree.

One of the many things that struck me while thinking about this book was, that in the 1980’s a woman, actually a nun, was honored by the mathematical societies of the world because, in the 1940’s she had made a discovery that seemed useless. But by the 1970’s it was the basis for a lot of the ways that computers were … doing something. Two mathematicians went looking for the ultimate originator of the idea and found Sister Mary Katherine Kelleher. And honored her. I don’t know if Walsh knew about Sister Mary Katherine, but she easily could have.

Further, in Gaudy Night, the Dorothy Sayers book about Oxford University (rather than Cambridge), Harriet Vane meets a woman who had taken a degree and then gone to Wales to marry a farmer, and it hadn’t turned out very well. Since Walsh was asked to write a sequel for Dorothy Sayers’ detective novels she would have been very familiar with this incident. In fact, she actually references Gaudy Night as part of a random conversation in her own book. But she had a completely different take on the idea of the Welsh farmwife.

As it happens, in 2023, thirty years after A Piece of Justice was written, someone did discover the Holy Grail of tiling, a single shape that could cover surfaces and not repeat. He was an amateur mathematician. And knitters on Ravelry created objects that used that shape.

https://www.ravelry.com/patterns/library/aperiodic-einstein-monotile

I went and looked to see if Walsh in 1995 had come close to the actual shape. The Einstein tile has fourteen sides and her imaginary tile had seven. Oh, well. By the way, here’s an example of knitting using the Penrose tiling.

https://www.ravelry.com/patterns/library/pentagonal-penrose-throw-blanket

In this particular case both truth and fiction are unexpected.