Orkney and beyond

I used to believe that planes always landed on runways.

Orkney has a way of stopping you from taking things for granted.

I was up to speak for the second time at the Orkney International Science Festival, which is organised by Howie Firth – one of the most enthusiastic men I have ever met. He has a way of making you feel that each thing you say is the most interesting thing he’s ever heard. So it was with his usual infectious enthusiasm that I was invited up to speak about Botanica Mathematica and the links between maths and knitting.

With true Orcadian hospitality, Howie’s invitation didn’t mean that I came up to give my talk and then had to leave immediately after, but was an opportunity to have a holiday and time to explore the islands. Last year my companion Albert and I investigated the Mainland, seeing the amazing neolithic site of Skara Brae (the best-preserved prehistoric site I’ve ever seen), the stone circles of Brodgar and Stenness and the amazing coastline at Yesnaby. This year, it was time to venture further afield…

The weather forecast had promised an overcast but dry and mild day for flying to North Ronaldsay. Nothing could have been further from the truth. Morning broke to gale force winds and torrential rain, neither of which eased up for the entire day. Apparently a storm system had come in from the north east, bringing vengeance on Orkney and Shetland but leaving the rest of the UK to enjoy beautiful warm sunshine. Sigh.

To say that I was scared of the impending flight was an understatement. It was basically a flying minibus – notionally with 9 seats, but one of those seats being next to the pilot. The pilot in our case was Rebecca Simpson, a cheerful blonde woman of about 30 , who seemed amused at the terrified looks on our faces. We had a 30-second safety briefing, were told to buckle our seatbelts and then the propellers went to full throttle.

I can easily say that the flights that day were the best I have ever been on. The plane needed hardly any runway before it was in the air, buffeted by the winds and quickly gaining height to give us a spectacular view of the azure blue of Orkney’s various harbours. Our first stop was Papa Westray, which is mainly famous for having the shortest scheduled flight in the world – less than 2 minutes over to the neighbouring island of Westray – which comes with its own certificate.

The “airport” at Papa Westray

Despite my lack of certificate, I was glad that I was on the longer flight from Kirkwall, with time to enjoy the views and the feel the force of the weather blowing us around. Our landing on Papa Westray really showed off Rebecca’s skill; the winds forcing us to approach the runway facing about 45 degrees away from it, but turning at just the last moment to achieve a perfect landing. I was also incredibly amused at Papa Westray’s “airport” – bascially just someone’s house.

Five minutes later we had landed on North Ronaldsay, and were gratefully met by Tommy Muir, who was going to give us a tour of the island. Our original intention was to have a day of hiking about the island, but the weather meant that we didn’t want to be outside for more than a few minutes at a time, and were glad of the shelter of his van!

Seaweed eating sheep

North Ronaldsay is about 3 miles long and is mainly famed for two things: having the tallest land-based lighthouse in the UK, and for having seaweed eating sheep. In 1832 a dyke was built around the island and the native sheep were exiled there to make space on the island for more lucrative breeds of sheep and cow. The hardy creatures learnt how to survive on the seaweed and became renowned for their resilience, intelligence, tasty meat and soft wool. (Indeed, few sheep breeds have their own sheep fellowship!)

North Ronaldsay once had as many as 500 people living on it; today there are no more than 50. Climate change has meant that the land is no longer suitable for growing crops on, and so people have left as they realise there is no work for them to do. There is a school there, but only one child to attend it – teachers are flown in from the mainland to provide art, sports and history lessons. Some tourists do come, seeking the tranquility and remoteness of the place, and often to watch the seals and birds on the coast. Last year there was apparently a walrus who visited the island!

Despite a wet and windy day, we were sad to leave and were determined to visit again on a sunnier day.

Me with our amazing pilot Rebecca Simpson

Rebecca was there with her plane to take us home, and this time there was a dog occupying one of seats! He seemed completely nonplussed by the turbulence of the plane – he’d probably been on more flights in his life than me! Our stop in Sanday on the way home was another adventure. The direction of the wind made landing on the runway very difficult, so Rebecca simply landed at right-angles to the runway, into a field instead! She seemed to love the challenge of the weather conditions, but told us afterwards that the winds were quite mild compared to what she’d had to deal with before.

Back in Kirkwall airport, the giant runway with all its lights seemed far too easy for Rebecca, and we knew that no flight we ever took would be quite as exciting again. My talk on Monday night was well received and I’m hopeful of getting some new binary bonsais and hyperbolic chanterelles to add to our collection. The hospitality and enthusiasm of everyone I’ve met in Orkney has meant that I will no doubt be back for many years to come, always finding a new adventure and wonders to explore.

And, if this story has inspired you to visit Orkney and talk about science, get in touch with Howie and he’ll no doubt be eager to have you visit to speak at his science festival!

Giant 4D buckyball sculpture

This is a model of a mathematical structure called a “Cantitruncated 600-cell”, colloquially known as a 4D buckyball. It took twenty people five hours to build and contains over 10,000 pieces of specialised plastic called Zometool. Such a model has never been seen in the UK before and I’m incredibly proud to have been able to organise its creation in Edinburgh last week.

The sculpture perches at the top of the main staircase in Summerhall, a great arts venue which used to be the University of Edinburgh’s veterinary school. The hall in which we put together those pieces of plastic was no doubt designed for dissecting cows or lecturing students about the removal of dogs’ testicles. Instead, Monday’s event (held as part of the University’s Innovative Learning Week) led our students into looking at the anatomy of geometry and playing with very different sorts of balls.

So what is a “Cantitruncated 600-cell”? The description on Wikipedia is less than enlightening. (It does, however, give some other cool names for this shape, including the “Cantitruncated polydodecahedron” and “Great rhombated hexacosichoron“.) Basically, the 600-cell is a shape made up of 600 tetrahedra (which in turn are 3D shapes made of 4 equilateral triangles) joined so that 20 of them meet at each corner. To ‘truncate’ means to ‘chop off the corners’. If we chop off a corner of the 600-cell, we see a shape which has 20 triangular sides – this is another regular 3D shape called an icosahedron.

Chop corners off an icosahedron, and you get a football, or buckyball.

‘Cantitruncation’ means ‘truncate, then truncate again’. Truncating the icosahedron leaves us with a shape colloquially known as a buckyball, or football (see left). Putting these facts together, we see that our model is a 4D shape made of 600 tetrahedra, but where each corner has been chopped off and replaced by a buckyball.

I have written a lengthier and much better explanation of this for the School of Mathematics website so recommend that you read that for more details! Otherwise just let your brain gently simmer in the crazy complexities of 4-dimensional geometry.

Photographer (and mathematician) Graeme Taylor was there on the day to do time-lapse photography of the build, and you can watch his final video at:

You can also see photos on Flickr by the University’s photographer Dong Ning Deng (scroll right for more!). Our students had to work very hard to not only put this giant jigsaw together, but also to cope with the engineering challenge of building enough of a framework to not let the model collapse under its own weight. I have to say that the sound of cracking plastic haunted my dreams for some nights afterwards…

Our 4D buckyball will stay in Summerhall until the end of the Edinburgh International Science Festival (20 April) and will (hopefully!) form part of the festival’s Art Trail. So go and see it while it’s there and tell me what you think of it!

The Valknut Challenge

I’ve been lacking in time and inspiration for blogging for a while now, but hopefully will get back into it again now that some of the chaos of Semester 2 has passed. As my come-back article I wanted to write about a fantastic evening I had at the RBS Museum Lates at the National Museum of Scotland just over a week ago.

The Museum Lates happen three times a year and are a chance for adults to get into the museum after hours to look at the collections whilst enjoying a cocktail and some live music. But they are much more than that! Each Late is themed in some way, and the theme this month was ‘Vikings’ to accompany the museum’s special exhibit. So guests were encouraged to dress up as Vikings, get their faces painted, touch Viking objects, make Viking paraphernalia (but NOT horned helmets – they aren’t Viking!), listen to Viking stories and eat Viking food. It was the perfect opportunity for us to get in some stealth maths engagement…

(From left) Joshua, Helene and Madeleine all Vikinged up and ready to go.

My co-conspirator in this project was Madeleine Shepherd (who you may remember from lots of previous projects, including the last Alice In Wonderland themed museum late and also the Mathematicians’ Shirts project), and on the night we had two lovely assistants: Helene Frossling (Madeleine’s colleague at ICMS) and Joshua Prettyman (an undergraduate on my maths outreach team). Together we presented the public with…The Valknut Challenge!

In Viking mythology, the Valknut was the special symbol of Odin, king of the gods. It consisted of three interlocking circles, but if you removed any one of the circles then the other two would fall apart and would not be linked together at all. The Valknut Challenge is: can you draw/make the symbol? If you haven’t seen this before, you should have a go before scrolling down to see the picture.

The Valknut symbol is often found on Viking stones where Odin is depicted going into battle or standing over fallen warriors. It’s not hard to see why the symbol would be synonymous with strength in battle: the three interlocking circles symbolise the strength we have in acting together which falls apart when we go it alone. The same symbol has been found in many civilisations – for example, signifying the Trinity in Christianity.

The Stora Hammars stone showing a Valknut above a scene of human sacrifice and next to some warriors. Powerful stuff.

Mathematically the symbol is called the Borromean rings (named for the Italian Borromeo family who used the symbol on their coat of arms). There are actually infinitely many different ways of solving the puzzle, and the Valknut is a special case of a more general puzzle where you have n circles and have to interlink them so that removing one ring makes the rest fall apart. Such a link is called a Brunnian link and they are particularly cool topological objects. 🙂

The standard Borromean rings.

A different solution to the Valknut challenge.

And another solution!

Most people have created a Valknut/Brunnian link in the course of their lives without ever realising it. Every knot or link can be drawn as a braid, and the Valknut is actually the standard 3-stranded braid that girls do in their hair all the time. Try making one and pulling out a strand – you’ll find that the other two strands become instantly untangled. This means you can quickly make a braid and harness the power of Odin whenever you need it – handy to remember next time you find yourself in battle.

The next Museum Late will be on 17th May with the theme of ‘Dinosaurs’.  If you missed out this time around then make sure you get tickets early for the next one! Anyone have any ideas for some surreptitious Jurassic mathematics that we can do?

Wizard or mathematician?

“You’re not a mathematician – you’re a wizard!”

This was the verdict delivered yesterday by a group of Dungeons & Dragons fans who had come to ICMS for Doors Open Day, after being treated to some maths busking by me. I also think they went away convinced that I was a geomancer instead of a geometer – I really must work on my enunciation…

Spatulamancy: the art of using a humble spatula to predict the future?

[An interesting aside, geomancy is apparently one of the seven “forbidden arts,” along with necromancy, hydromancy, aeromancy, pyromancy, chiromancy (palmistry), and spatulamancy. Ah, I love Wikipedia.]

It’s been a stressful week for me, but culminated in a totally wonderful day of maths communication yesterday. In the morning I gave the first Edinburgh masterclass of the season to a group of 82 enthusiastic 13-year-olds, and some equally enthusiastic student helpers. When I commiserated with them on having to get up early on a Saturday morning, the response was “We’d always get up early for lectures if they were as interesting as this!”. Which is lovely and flattering for me, but really makes me sad that we aren’t doing enough in university to bring our subject alive. Of course not every lecture can be as fun as a masterclass, but there are far too many researchers for whom lecturing is a chore and who never make an effort to bring enthusiasm or interest to their subject.

I digress, but there was an interesting blog post on a related theme by Peter Rowlett this week. He asked whether it was possible to pursue a career in university teaching and lecturing whilst not being a researcher – a question I have full sympathy with as someone in exactly that position. For me the story has a happy ending: after a year and a half of trying to persuade the university that a full time outreach/teaching position was a Good Thing, I have finally got my contract extended to 3 years. It is great to know that the department and university value the things I do, but I would despair of being able to find a similar position were I ever to change universities. While good teaching and public engagement are listed as promotion criteria in many places, in practice they are rarely rewarded when compared with research output.

Another side of the story is that there are many people who do public engagement in their spare time who are not recognised for it. A job title such as mine (Mathematics Engagement Officer) can count for a lot, as my friend and collaborator Madeleine Shepherd has found many times. Although we’ve worked on many projects together, with her often the brains behind the ideas, emails proposing new engagement opportunities are often sent to me and rarely to her.

It was wonderful to see ICMS, where Madeleine works, being open to the public yesterday for Doors Open Day. The building, on South College Street, is a converted church and still has an original stained glass window, among other interesting features.

Doors Open Day at ICMS, featuring Penrose tiles, chaotic pendulum and magnets, Tantrix, and me busking to three D&D fans. Click photo for more ICMS images.

This was the first year it had opened as part of Doors Open Day and we had no idea how many visitors would turn up. In the end I think the count was at 229, most of whom were lured in by the promise of maths puzzles rather than an interest in the building itself. I was only able to attend in the afternoon (due to the masterclass in the morning) and had a huge amount of fun showing people my favourite topological tricks, card tricks and mathematical puzzles. Even those of the public who proclaimed they were bad at maths went away enthused by what they had learnt and wanting to share their new knowledge with friends and family. I hope that we can run such events more frequently instead of waiting for Doors Open Day every year!

This hope is not a forlorn one, as I have big plans brewing… I am currently recruiting undergraduates and postgraduates to be on my new Maths Outreach Team (with unfortunate acronym MOT), and hope to have a team of 10 people trained up and ready to engage by the middle of October. Once they are unleashed on the unsuspecting city of Edinburgh, there will be no end to the school workshops, festival exhibitions, website articles and puzzles, public lectures and impromptu maths busking. At least, that is the plan. If you know of any maths undergrads who would be interested in this, please spread the word!

On that note, it is time for me to head off and hatch more nefarious outreach plans. Please do leave a comment if you were at Doors Open Day, my masterclass, or if you have comments on the difficulties of being rewarded for good outreach and lecturing. Until next time…

A Night in Wonderland

On 18th May I was lucky enough to get involved with my first RBS Museum Lates at the National Museum of Scotland. These events happen about 3 times a year and are a chance for the (over 18) public to come back into the museum after hours and to get cosy with the exhibits with a cocktail and live band. It’s also a chance for science (and arts!) communicators like me to run an activity and get some surreptitious education into the evening.

The theme for this month’s Museum Late was “A Night in Wonderland”, so there were lots of top hats, white rabbits and red queens! (See lots of photos of the event on the Museum’s Flickr page.) Knowing that Lewis Carroll (real name Charles Dodgson) was a mathematician and logician as well as nonsense-poem writer, it seemed wrong for there not to be a mathematical component to the evening so I got together with Madeleine Shepherd (from ICMS) to brainstorm some ideas…

Our first idea was to get the public to make some Fortunatus’ purses. A Fortunatus’ purse appears in the novel Sylvie and Bruno by Lewis Carroll and is based on the old tale of Fortunatus, who has a purse which replenishes itself with money as often as coins are drawn from it. If you read the book you’ll find instructions for making such a purse by sewing together the edges of 3 handkerchiefs in an unexpected way.

‘You shall first,’ said Mein Herr, possessing himself of two of the handkerchiefs, spreading one upon the other, and holding them up by two corners, ‘you shall first join together these upper corners, the right to the right, the left to the left; and the opening between them shall be the mouth of the Purse.’

Now, this third handkerchief,’ Mein Herr proceeded, ‘has four edges, which you can trace continuously round and round: all you need do is to join its four edges to the four edges of the opening…’

The mathematical object created is one which has no inside or outside – it is called non-orientable, and is (of course) not possible to make in 3 dimensions without part of the purse intersecting itself. Some of you may be thinking that this is a Klein Bottle, but it is actually a different creature called a Projective Plane.

However, whilst doing the practice run for the purse-making, we found that it took quite a long time, was fairly fiddly and would involve giving drunk people sharp needles. Probably not the best idea. (But we might do this in a future maths/craft event!)

So instead we came up with the “Snark Constellation Challenge”, inspired in equal parts by the Lewis Carroll poem The Hunting of the Snark and by a mathematical object in graph theory called a snark. Visitors were invited to play a game which involved colouring the lines between stars in a constellation, and were challenged to colour the lines using only 3 colours.

Can you colour the lines with 3 colours so that at each star, 3 different colours meet?

There were two games the visitors could play: working collaboratively to find a colouring of all the lines, or working competitively to be the last person to draw a valid line. Have a go at the puzzle and see if you can colour the lines before reading on!

Edinburgh Sci Fest 2012 (Part 2)

Welcome back to part 2 of my write up of our exhibit at the Edinburgh International Science Festival. As you may remember, we were running a series of games and activities to test people’s probability skills and to see how people would react to the stats in a courtroom. In this post I will go through the solutions to the various questions we asked, so if you haven’t had a go at them yet then make sure to have a go now!

Edinburgh Science Festival 2012

Hello maths fans!  It’s been a very busy semester for your favourite geek sheep: sorting out activities for undergrads in Innovative Learning Week, lecturing Y1 undergrads in Proofs & Problem Solving, organising business/academic networking events, doing an art/science exhibition, and running an exhibition at the Edinburgh International Science Festival. Hopefully now that I have some time, you can look forward to blog posts about all of these things. 🙂

Today’s post is about our science festival fun. We (the School of Maths) teamed up with the School of Chemistry and went for a CSI-themed activity.The premise was that a priceless Egyptian vase had been stolen from the Museum and the visitors had to work out whodunnit. Using chemistry they had to analyse fingerprints and blood samples, and use UV and infrared data to identify substances found at the scene of the crime. After deciding on their prime suspect, they came over to the maths section, which was the courtroom. Here they had to weigh up the probabilities and statistics and then decide on whether their suspect was innocent or guilty.

Just as in real life, we didn’t reveal who actually did it, because we often don’t know for sure. And actually, we hoped that (despite all the evidence) the visitors would vote ‘Innocent’ because the evidence certainly didn’t prove anything beyond all reasonable doubt.

Most £20 notes have traces of cocaine on them.

I’ve had my heart set on doing something like this for a while because I wanted to publicise the great work that our Forensic Statisticians (Colin Aitken and Amy Wilson) are doing right here in Edinburgh. They are analysing the occurence of drugs like cocaine on banknotes to help the police decide when someone is really a drug dealer. Apparently (and don’t quote me on this) most £20 notes (like, over 80%) have got traces of cocaine on them, so the police need help in deciding when the notes have been involved in drugs crime or when they have just accidently been placed next to the ‘dirty’ notes in a shop till.

Colin has also appeared as an expert witness in a few trials and has helped to write books to educate judges and lawyers about statistics. Like the general population, judges and lawyers often have a very bad intuition about probabilities. But unlike the general public, their decisions can really affect people’s lives. The classic example is the Sally Clark case. An expert witness for the prosecution claimed that there was a 1 in 73 million chance that two cot deaths could happen naturally in the same family, and therefore that Sally must have murdered her children. Not only was this statistic wildly wrong (the actual figure is about 1 in 100,000) but the conclusion of guilt is also wrong. Neither side took into account the probability of her innocence: despite the unlikelihood of double cot death, double murder is (statistically) even more unlikely. Such a mistake is called the Prosecutor’s Fallacy. In Sally’s case, it led to her spending 3 years in prison for a crime she never committed and then committing suicide a few years after she was freed.

So anyway, the idea behind our science festival exhibit was to show people how bad they were at judging probabilities and to introduce the idea of Bayesian Statistics (which is behind things like the Prosecutor’s Fallacy). Have a go at these questions and see if you can solve them! Answers will be provided in the next blog post.

The Monty Hall problem assumes you'd rather win a car than a goat. This is not true for everybody.

1) One of the most famous examples of conditional probability is called the Monty Hall problem, or the Car-Goat problem. You are on a gameshow, trying to win a car. You definitely don’t want to win a goat. There are three doors, behind which the host of the show has hidden 2 goats and a car. You choose the door which you think conceals the car. The host then opens a different door to reveal a goat. Finally, you get to choose: should you stick with your original choice of door, or should you swap? Or does it make no difference?

2) On very similar lines is the following queston. I flip two coins and tell you at least one of them is a head. What’s the chance that the other one is also showing a head?

3) In a lottery there are a 10 numbers in a bag and you win the jackpot if you correctly predict which 4 numbers get pulled out. What are the chances of winning the jackpot? What are the chances of predicting 3 out of the 4 numbers?

4) If 100 people each flip a fair coin 5 times, how many of them will we expect to flip 5 heads?

5) On the wall there is a calendar for 2012. Visitors to the museum put their birthday on the chart as they come in. After how many visitors do we expect to see the first shared birthday? (I.e. two people with the same birthday.)

Betty only sees what she thinks 2/3 of the time.

6) An eyewitness, Betty, says she saw a suspect leaving the scene of the crime, and that the suspect was wearing a hat. Betty is shortsighted and only correctly identifies hats 2 out of 3 times. That is, 1 time out of 3 she will think that someone is wearing a hat when they aren’t, and 1 time out of 3 she will think that someone isn’t wearing a hat when they are. If 10% of the Edinburgh population wears a hat, what are the chances that the suspect was really wearing a hat?

Needless to say, most visitors to the exhibit found these questions very difficult, but that was the point. We wanted to teach people not to trust their intuition when it comes to probability, and especially not if they are in a jury on a court case!

Many thanks to all who visited us in the Museum and played all our games with us! I hope you all had a good time and learnt something new. 🙂

A week in the life: Wednesday

After another last minute call for help, I found myself on Wednesday helping out with the Maths Extra day that the maths department at Edinburgh were trialling for the first time.

The department usually organises a couple of revision sessions per year for local students studying Higher and Advanced Higher maths. For the past couple of years we’ve used these sessions as an opportunity for a few postgraduates to do short (15 minute) talks on their research. This widens the students’ perspective on what mathematics is, what kind of people do it (for example, women! trendy people! non-bearded people!) and why it is useful.

This year our outreach coordinator, Lois, decided that it made more sense to have the postgraduate talks on a day of their own, together with a set of interesting maths problems that the students could work on in groups. They also got a lecture from our Director of Teaching, Toby Bailey, who worked through a seemingly simple geometry problem to show how an inquisitive nature can reveal many beautiful insights.

I was involved both in giving a talk (about knots in DNA) and in helping to design some of the problems that the students worked on. My favourite problem was one that I plagiarised from the Masterclass Training Day that I was at, where I heard it given by Demi Allen, an undergraduate at St Andrews.

Imagine a very long corridor of rooms, one for each number 1,2,3,4,… To begin with all the lights are turned off.The rule is that on the nth pass down the corridor, you flick the switch of every nth room. So on the first pass, you turn every light on. On the second pass, you turn every second light off. On the third pass, you flick the switch of every 3rd room, etc. The question is which lights are still turned on at the end, and why?

It’s a really neat problem – very easy to get stuck into, and a few different layers to the answer when it comes. I encourage you all to have a think!

My knotty DNA talk seemed to go ok, but the kids were pretty quiet and didn’t ask any questions or interrupt with any remarks. I guess 15 minutes is a bit too short to really explain an aspect of your work AND make it interactive. I’m also getting bored with knots these days and would really like to work on designing some talks in other areas. Longer ones perhaps, with more of an element of discussion around them. Like whether 0.999…=1, or whether Euclidean geometry is ‘wrong’ or just a specific way of thinking. I can feel myself being influenced in these thoughts by Eric Mazur’s lecture (which I’ll discuss in Friday’s post!) – that we don’t just want to impart information but we want students to really think deeply about them too. If anyone has good ideas for discussion points in maths I’d be glad to hear them!

My next speaking opportunity will be on 26th May at Linlithgow Academy, which is hopefully enough time to design a new hour-long masterclass as well as preparing for the science festival and revising for the thesis defence. Time goes so fast these days!

A week in the life: Tuesday

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.

A supercomputer

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.

A black hole of filmable mathematicians?

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. 🙂

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…

Knitted torus (aka doughnut) and sheepy coffee cup

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 Möbius 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.)

A trefoil knot bounding a 3-twisted Möbius strip

A trefoil knot bounding an orientable (2-sided) surface

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

Crocheted one-sided trefoil surface

Crocheted two-sided trefoil surface

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!

A week in the life: Monday

This week has been incredibly hectic. I’ve done 2 school workshops, helped Julia with some filming, FINISHED THE THESIS and learnt about peer instruction from the wonderful Eric Mazur. Each of these things is worth a blog post in itself so that’s what I’m going to do, releasing one post a day. As ever, your comments are very welcome!

Monday: I set off with Julia to Hutchesons’ Grammar School in Glasgow to deliver an hour long workshop on Möbius strips. 60-odd primary school (P7/Yr 6) pupils had come from all over the region to experience a day of masterclasses, and mine was the last session of the day so everyone was a bit rowdy! For anyone who knows anything about Möbius strips the class was quite predictable: we drew a line down the middle of the strip to see how it was different from a cylinder; we cut the strips in half; we cut them in half again; we cut the strips in thirds; we explored what happened with different numbers of twists, and we made Möbius hearts. The last one you may not have seen before… Take two oppositely oriented strips, glue them together at right-angles, then cut in half. A perfect thing to make for Mothers Day!

I had intended to lead the class through the first few steps and chat a bit about the one-sided nature of the strips, but as soon as the kids had started to make the Möbius strips there was no stopping them! Many an excited child came running up to me (well, Julia): “Miss miss! Look what I’ve made! I don’t understand. Have I done it wrong?” The wonder and confusion on their little faces was gratifying! It was also great to see the accompanying teachers getting equally excited about the activity, and I do hope they will take away the ideas to use in future classes.

The only disappointing thing was that only 2 of the children (and 1 teacher) stopped to ask “Why?” instead of just going “Ooh”. Surely the ability to question things is the first thing we should be trying to cultivate among our children? (For more on this, see “Friday’s” post on the lecture by Eric Mazur!) When something is interesting or unexpected, why don’t the majority of people want to know why it works like that, instead of being content thinking that it’s “magic”? Is this questioning nature what distinguishes a scientist from a non-scientist? I think it is at least what distinguishes maths/science from a magic trick: that knowing how it works makes the phenomena more exciting, not less.

Should we be doing outreach in private schools?

There was also a bit of a moral question that I got thinking about during this workshop. For those of you that don’t know, Hutchesons’ is a fairly expensive private school, and there were apparently some state primary schools that refused to attend for this reason. One of my Twitter followers also commented on the privileged nature of the students, intimating perhaps that I should not be concentrating my outreach efforts on children who already have an advantaged education.  My general principle is that I do not discriminate on any grounds: any school is welcome to invite me to speak or do a workshop for them. It seems unfair to be judging children by the backgrounds of their parents… And yet, having been brought up in the state education system, I also see the need for putting more effort into working with the less privileged among us.

I didn’t quite realise until I chatted to the teachers at Hutchesons how much harder state school teachers have to work than private ones (although on reflection this seems obvious). A state school teacher is generally expected to teach 22 hours per week, while a private one will only do about 16 hours. When you think how much preparation is required for each lesson, this is a huge amount more work. There are also more pupils to worry about in each class, fewer resources to tap into and more discipline problems to deal with. When the average person finishes their teacher training, what incentive do they have to go into the state sector, where they do a more difficult job for less pay? We should be applauding those that do make this choice and give them all the help we can to make their classes easier and more exciting.

What do you think? Should we discriminate against private school pupils and focus all our engagement efforts on helping state school pupils, or is this unfair? And why do you think some state school teachers refused to let their pupils come to the (free) masterclass day put on by Hutchesons’ school?