## Archive for the ‘Edinburgh’ Category

### 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. 🙂

### Bright Club

When I told friends I was planning to spend the evening watching university academics doing stand-up comedy, the response was a look of confusion and a placatory “That should be…interesting.”

Academics and comedians normally form completely non-intersecting parts of a Venn diagram. After all, what is funny about a gamma ray burst, tree conservation or crayfish? When was the last time a seminar on genetics cracked you up with laughter? To be fair, I do often hear mathematicians making jokes, but normally they are so obscure that only the 3 other people in the room would have a clue why they were funny.

So I really didn’t know what to expect when I went along to Edinburgh’s first Bright Club at the City Cafe on Blair Street. I certainly didn’t expect there to be a long queue at the door because all the tickets were sold out! After a tense wait I was relieved to find myself inside, albeit with standing room only. In a stroke of luck, I spotted my colleague and fellow tweeter Karon McBride who squeezed me in on the seat beside her. She explained that she was quite interested at having a go at the comedy herself and was excited to see how the first session went.

Well, I don’t think that any of you readers are going to be surprised when I say that it was a fantastic evening.  Steve Cross, the founder of Bright Club, came all the way from London to start the proceedings, and we had the enthusiastically foul-mouthed Susan Morrison as our compère for the night. The first academic was none other than fellow mathematics PhD student Hari Srithkantha, which I’m very proud of because it was me who encouraged him to sign up for Bright Club! Hari is already making a name for himself in stand-up, taking part in the Chortle Student Comedy Awards and playing gigs around Edinburgh. However, it was great to listen to him making his research (into gamma ray bursts) the butt of his gags, which I think is something he hadn’t tried before. Even more than that, it was great to find out what he was actually researching! He is probably only the second person (after Matt Parker) to use a graph to make the audience laugh.