From aliens to bees via tattoos…

A short review of intern Joe Double’s work with Tom Rocks Maths over the summer of 2018. Written for the OUS East Kent branch who provided funding for the project. 

‘First of all, I must thank you again for the grant, and for the warmth and friendliness at your event; it was an absolute delight to give my presentation and talk to your members, as it has been interacting with you in general.

I had the opportunity to work with one of my tutors over the summer to produce pieces for a general audience about complex mathematical topics. Without the help of the OUS East Kent group, I couldn’t have taken up this opportunity – with their grant’s help, I was able to afford to live in Oxford through a large part of the summer, allowing me to work in close contact with my tutor and use his studio for creating the videos and audio pieces I worked on. The OUSEK grant can be put to use far more flexibly than those from bigger schemes (which always have preconditions to meet about how the project will apply to industry, say), so I couldn’t recommend applying more if you have an idea for a project for your time at Oxford which is on the unusual side!’

Pieces I produced during the project:

Why do Bees Build Hexagons? Honeycomb Conjecture explained by Thomas Hales

A video I edited of Tom (my tutor) interviewing Thomas Hales about the mathematics behind beehives.

Would Alien (Non-Euclidean) Geometry Break Our Brains?

My main video, written, filmed and edited by me, about demystifying non-Euclidean geometry.

Take me to your chalkboard

My main audio piece, where I interview Professor Adrian Moore (also of St Hugh’s) about what philosophy can tell us about how aliens might do maths.

Maths proves that maths isn’t boring

An article about Gödel’s incompleteness theorems, and how they show maths is always risky.

Getting tattooed for science…

An audio piece I edited about a tattoo Tom got of the Platonic solids.

Alien maths – we’re counting on it

An article about how we use the mathematics of prime numbers to send messages to the stars.

Play Nice!

An article about a game theory paper which could amongst other things help stop deforestation.

The original article was published on the OUS East Kent website here.

Play Nice!

Whoever said having fun is more important than winning was not a game theorist. Game theorists are mathematicians who study games, and how to win them. But they aren’t just interested in Snakes and Ladders – game theory also involves studying ‘games’ like nuclear standoffs, trade wars and even the competition of species as they evolve.

New research from the Institute of Science and Technology in Austria (http://dx.doi.org/10.1038/s41586-018-0277-x) might help us to use game theory for environmental good. Their findings look at perhaps the single most important problem we face in looking after the environment – ‘the tragedy of the commons’.

The tragedy of the commons plays out all around us, and relates to situations where everybody stands to benefit from damaging a useful shared resource. Everybody in the office exploits the ‘commons’ of the biscuit tin by taking a biscuit, but nobody can be bothered to go out and buy a new packet to keep the tin full. Eventually, the tin is empty, and everyone has to endure life without biscuits whilst someone looks for more. Such pointless suffering could have been avoided if only someone had acted sooner!

In a more serious setting, the tragedy of the commons can lead to catastrophic results. Take deforestation – the shrinking of the world’s forests as we use trees faster than they can grow back. It is in the individual interests of each logging company to spend all their time chopping down trees (which makes them money) and to waste none of it replanting them (which doesn’t). At least, in the short term. But over time, this clearly won’t work – the ‘commons’ of the world’s forests will be so damaged that everyone will lose out. Bad news for all you atmosphere fans out there.

The new research uses game theory to study the tragedy of the commons, to try and understand what we can do to prevent it. To stick with the logging example, the researchers treat logging companies as players competing in a series of very simple games, over and over, learning each other’s tactics. Each game is just a matter of choosing one of two options: Chop down trees without bothering to replant them, or take the time to replant them as well. Each time the choice is made, the company gets a reward depending on what they picked; they will get a bigger reward if they don’t use any of their time replanting. It looks like companies that are perfectly happy to drop-kick Dr Seuss’ orange defender-of-the-trees, the Lorax, are going to do better than their greener rivals.

At least, initially. The key to the new research is that in it, the games that have already been played affect the rewards up for grabs in the next game. If you keep choosing not to replant trees, then you may do better than your opponents in each game, but you’ll gradually make the rewards smaller and smaller as you start to run out of trees to cut down. So, you can’t just think about the profits to be won in today’s game – you have to think about what you’ll be playing for in tomorrow’s game too.

The researchers found that this makes a big difference to how companies will play. If previous games made no difference to the current game, then companies which don’t replant trees would do better than their replanting rivals. But, given that failing to replant the trees you cut down means worse prizes in the future, the companies which do replant end up doing a lot better than those that don’t bother. In other words, it pays to play nice.

The one catch to this is that the prizes have to get significantly worse when you choose not to replant. So, in practical terms, these findings suggest ways to make the ‘game’ of logging less environmentally devastating – by changing the rules. For instance, governments could pass laws which force any companies failing to replant trees to pay an increased tax on any future trees they cut down (or maybe pay for the Lorax’s extensive pension plan). This makes logging more like the game the researchers studied, where past choices quickly and significantly affect future rewards. So based on the researchers’ findings, such a law would make sure that doing the right thing and replanting trees is the better choice.

Yes, game theory is about winning. But by figuring out which rules reward the sort of people who go out and buy more biscuits for the tin, we can make sure the ‘winning tactic’ for the world’s most dangerous games is to play nice.

Joe Double

The Prisoner’s Dilemma

I demonstrate the classical game theory problem of the prisoner’s dilemma live on BBC Radio, with a short introduction to the subject from Sergey Gavrilets. You can listen to the full interview via the Naked Scientists here.

A lot of our decisions, although we may not realise it, rely on maths. Game Theory is the study of the decision-making process and it can be applied to almost any subject including economics, political science, psychology, and even biology. The last one is of particular interest to Sergey Gavrilets, a mathematician at the University of Tennessee, who uses game theory to model early human behaviour…

  • Game theory is the study of mathematical models of conflict and cooperation between intelligent rational decision-makers
  • An example would be if your phone was ringing in the next room whilst you are watching a movie with your family – the group benefits from answering the phone, but no-one wants to make the sacrifice themselves to do so
  • The prisoner’s dilemma looks at whether or not you should snitch on your friend and have a chance of going free, or stay quiet and hope your friend doesn’t snitch
  • Ultimately the best solution is for you both to stay silent, but it relies on trusting your friend for it to work!

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