# ASCUS progress meeting 1

Last week Madeleine and I met up with Mark Eischeid and Julia Malle from ASCUS to talk about our shortlist of ideas for the project. Mark and Julia are artists from very different walks of life (Mark in landscape architecture and Julia in glasswork) so we were looking forward to getting new perspectives on our ideas from a non-mathematical viewpoint. ASCUS also have the job of finding a venue for our shirty sculptures and we needed to discuss the requirements that some of our sculptures would have. Hopefully we are not being too ambitious!

So, here’s our shortlist of sculptures that we hope to make; indeed, to get started on very shortly!

**Klein bottle shirt**

A Klein bottle is a famous topological object which has no inside or outside. It was first described in 1882 and only truly lives in 4 dimensions – if we try to draw it in 3 dimensions then it appears to intersect itself. A Klein bottle would be easy to make from a single shirt by passing a sleeve through the main fabric of the shirt and then sewing the cuff to the neck. The bottom of the shirt and the remaining cuff would also be sewn up so that there would be no edges to the sculpture.

**Alexander horned sphere shirt**

The Alexander Horned Sphere is another great object in topology. Normally when we draw a sphere, there is a clear inside and outside, and if we have a loop of string in either the inside or the outside then we can pull the string tight without encountering any difficulties. The horned sphere is a way of drawing a sphere so that loops of string **outside** of it *cannot* be pulled tight. Its invention came as a great surprise to the mathematical community and its construction highlights the crazy properties of infinity and fractals. We would like to make this sculpture using the sleeves of ever-smaller shirts as the ‘horns’, and hope we can do a few iterations before it gets too small!

**Patchwork geometry shirts**

The discovery of different kinds of geometry came as another surprise to mathematicians. For centuries, schoolchildren had been taught that there are always 180 degrees in a triangle and that Pythagoras’ Theorem is always true. Not so! Triangles on a sphere have angles that add up to more than 180 degrees and triangles in hyperbolic space (like a saddle shape) add up to less than 180 degrees. It is a great lesson in how mathematicians must always be aware of the axioms they build their theories upon. What things do we take for granted now which will be overturned in the next century? Madeleine and I will create these 3 geometries by attaching patchwork shapes to the bottom of the shirts: hexagons fit together to make flat space, pentagons will make a spherical shape and heptagons will fan out to make hyperbolic space.

**Illusion shirt**

Moving on to a slightly more philosophical work, we would like to create a sculpture which only looks correct from a certain direction. This might mean that it only looks like a shirt from a particular angle, or that a hidden message is seen when it is viewed a certain way. This would illustrate the nature of mathematics: that problems can look incredibly hard until they are seen in the right way and by someone with the right tools. A particular example is in the work of Edinburgh mathematicians in *integrable systems*, where there are very complex and often chaotic systems of equations, but these can become tractable when transformed into the correct coordinates.

**Compressed sensing shirt/image reconstruction shirt**

Finally, we had an ambitious idea to create a series of shirts which each had a small piece of an image on them, and the public would have to find a number of the shirts across the city in order to discover the whole image. The implementation could go in two different ways depending on the kind of mathematics we want to showcase. Firstly there is optimization, which tries to spot patterns in order to find relevant data quickly. For example, Google has to sort through millions of web pages every time it does a search, but it is very efficient at knowing where to look. We could implement this in shirt form by placing the shirts in locations with a common theme; for example, all the Tesco stores. A second piece of mathematics we could look at is the relatively new field of compressed sensing. In reconstructing an image this way, mathematicians take advantage of the fact that lots of data is replicated, so that a large image could be reconstructed by just sampling the pixels in a small number of places. We could have lots of shirts around the city, but only a small number of them need to be found in order to put the whole image together.

Our shirt-making will begin on the weekend of the 24/25th September, during an event at Inspace called Stitch Lounge. There’ll be free use of sewing machines, lots of people around experimenting with crafty ideas and, most importantly, afternoon tea. Come along and see what everyone is up to!

And please do leave comments to let us know which sculptures you are most looking forward to seeing, and why. We would love to hear from you!

Posted on September 14, 2011, in Uncategorized. Bookmark the permalink. 2 Comments.

How about 4d shirts?

Any suggestions on how to implement this? We did have thoughts on representing a 4D cube or something, but weren’t sure how it would work with shirts.