Continuing with my hectic life in the last week of March…

**Tuesday** was a day for me to prove my worth as the next David Attenborough or Brian Cox.

The College of Science & Engineering had been successful in getting some money from the research council EPSRC to produce a series of 5-minute videos highlighting the work that was being done by scientists at Edinburgh. Each department was supposed to nominate one or two of their researchers to speak for the camera, highlighting the applications and benefits of their work.

Now, before you start thinking that I am a fame-hungry media-whore of a sheep, let me stress that I (and my maths colleagues) did what we could to find ourselves a real bona fide applied mathematician to do this. At the beginning of the year we approached Jacek Gondzio, who works in an area of maths called optimization. Jacek made it into the *Guardian *in 2008 for using Britain’s fastest supercomputer to solve problems relating to financial mathematics and risk modelling. Clearly his work is more important now, in our financial crisis, than it has ever been, and it would have been great for him to have the chance to get on camera and explain it to the wider community. Sadly, despite our urging, Jacek was just too shy to take up the opportunity.

This reminds me a little of a joke: How do you spot an extroverted mathematician? Answer: They look at *your* shoes when they’re talking to you.

Of course not all mathematicians are shy and socially inept, but it was certainly going to be a challenge to find someone who was extroverted, articulate, passionate, and working on something useful. And in Edinburgh. And with an EPSRC grant. We ended up, with 2 weeks to go before the filming date, with a shortlist of 4 people, of whom one was out of the country, one was too quiet and another was too busy. We asked Joan Simon, a charismatic Catalonian who works on the theory of black holes, but after a few days’ consideration he decided that he was also too busy.

At this point, things were dire enough that I suggested to Julia that maybe *we* should do it. It was a bit of a long shot, seeing as we were no longer EPSRC funded and that our research had barely a sniff of real-life about it, but it still seemed better for us to do it than for the opportunity to be wasted. And we had loads of great props that really deserved to make it onto the big screen. đź™‚

Tuesday morning came and we didn’t really know what was happening. We’d submitted a script to the producers and booked a room, but nobody had confirmed that we were doing it. Julia had some quite impressive bags under her eyes from staying up late to rehearse the script and I had specially combed my quiff, just in case. Finally, an email! “Be there at 11:30.”

The film ‘crew’ were two PhD film students, one of whom (Alastair Cole) had his own documentary company specialising in linguistic anthropology. Wow. I think they were a bit apprehensive about filming mathematicians, but after they caught sight of the sheep and knitted surfaces, the apprehension turned to curiosity and amusement. Sadly I wasn’t allowed to be in the film (and my quiff was so beautiful too!) but the video did not end entirely sheepless…

We (well, Julia) started off explaining what a topologist was: someone who looks at those properties of objects that don’t change after stretching and wiggling. This gave us the opportunity to stick in the classic joke that a topologist is someone who cannot tell the difference between a doughnut and a coffee cup, and to exhibit said objects. We then explained that what concerned knot theorists was not so much the objects themselves but how they sat in space (the *embedding*). All mathematical knots are intrinsically circles; it’s the way they sit inside 3D space which is interesting. And such work is going to have applications in looking at objects in our universe. For example, how do black holes sit in our 4D universe?

We then had to find a way to explain slice knots. That is, knots which are slices of spheres sitting in the 4th dimension. What even IS the 4th dimension? How can we visualise it? With more knitting, obviously. Every knot can be drawn as the edge of a surface, called a *Seifert surface*. It’s pretty easy to picture a surface for the simplest untangled knot: it’s just a disc, like a frisbee. Picturing a surface for the overhand knot, or trefoil, is already much harder. One surface which works is the 3-twisted MĂ¶bius strip, although this is not strictly allowed because it has only one side. You could also picture 2 discs, drawn one above the other, with three twisted strips joining them. (Pictures below courtesy of Seifertview.)

Or, if you had the time, you could crochet them!

Each of these surfaces is very different from the frisbee because there are holes in the surface. Sometimes there is a way of pushing the surfaces into another dimension so that the holes go away – such knots are exactly the slice knots. We demonstrated this rather abstract concept using a 3-dimensional analogy…and a sheep! You’ll just have to wait for the final video to see how we did it.

Hopefully the film will be edited and put online (on the University’s Youtube channel) within the next month. When it is, you lucky readers will be the first to know!

I’m looking forward to getting other mathematicians on board in the next round of filming. Hopefully they will be less daunted by the prospect when they see somebody else doing it. And hopefully seeing the finished edited film will help me in starting to do some filming of my own.

Look out for future blog posts about mathematical knitting – it’s all the rage these days! We’ll be using knitted torii to play noughts & crosses at the Edinburgh International Science Festival and I’m hoping to make some (slightly better) Seifert surfaces for different knots. If you have ideas for other projects, let me know!

Posted by Changing Perspectives « Modulo Errors on April 4, 2011 at 11:10 pm

[…] Today’s post by Haggis the Sheep demonstrates how crochet can help understand some topologically-interesting surfaces, so I felt I should mention a similar piece of fibre art I encountered this weekend. The object on the left is a Lorenz Manifold made out of over 25,000 stitches (plus three wires), and took Bristol mathematician 85 hours to assemble. Hinke (along with Bernd Krauskopf) had been experimenting with computer visualisation of the manifold, and developed an algorithm which ‘grew’ the image from a small disc, adding layers with additional or fewer points at each step to specify the local features of the surface. This approach conveniently works just as well for wool as pixels – each row of a crochet pattern differs from the last by increasing or decreasing the number of stitches to alter the shape. […]