The Cambridge Lovelace Hackathon 2016

John Wallis Workshop

A portrait of John Wallis by Sir Godfrey Kneller

The 23rd of November this year sees the 400th anniversary of the birth of John Wallis, the Cambridge mathematician who developed infinitesimal calculus, contributed to other mathematical fields, and was Parliament’s chief cryptographer. His insomnia led him to develop astonishing skills in mental arithmetic and he published letters on musical theory. This year's Cambridge Lovelace hackathon is held in celebration of his work.

Everybody is very welcome to come and join in with us in exploring ideas from mathematics and related areas. Every year we come together to give talks, hold discussions, develop ideas, program and test, or just play games, drink tea, and socialise. Wallis gives us a lot to think about, for example the idea of infinity, self-supporting structures, or exploring cryptosystems, linguistics or music. We have a broad range of suggested activities listed here, but in the spirit of a hackathon, everybody should try to come along with their own ideas and projects on the day, based on their individual interests and skills.

Getting there

The main session will take place on Sunday, 27th November 2016 between 13:00 and 18:00 in room MR3 at the Centre for Mathematical Sciences (CMS) at the University of Cambridge.

MR3 can be found in the basement of Pavilion A, near the foot of the stairs leading from the Reception. Disabled access is via a lift in Pavilion D. CMS provides a map of the meeting rooms as well as useful information about finding the centre. The Centre has a café, but it will be closed during the event. However, the CMS website suggests other options for food.

What's happening

We will use this website to publicise the hackathon projects as they form, in the hope that it'll help those proposing projects find those who want to contribute to them. You can also turn up to the event and refer to the blackboard to see who is working on what. We also invite people to create respositories for their project in our GitHub organisation, in order to keep everything in one place.

The following projects, activities and starting points have been proposed already:

Structural analysis of the reciprocating floor
In 1545, Sebastiano Serlio described a structural engineering problem, rendered as follows in the English translation of his book:
Many accidents like unto this may fall to a workman’s hand, which is, that a man should lay a ceiling of a house in a place which is fifteen foote long, and as many foote broad, & the rafters should be but fourteen foote long, and no more wood to be had...
In Wallis's 1695 Opera Mathematica, he provides an analysis of the forces in such a reciprocal grillage structure. In John Wallis and the Numerical Analysis of Structures (from which the above quote is lifted), Guy T. Houlsby describes analyses of the forces in a reciprocal grillage structure. We attempt to gain a better understanding of this work and, if time permits, construct computational models of the analysis.
Make reciprocating structures from lollipop sticks
The floor mentioned above is just one example of a reciprocating structure, where each piece rests on its neighbours. Let's build them out of lollipop sticks and Lego to get a good understanding of how they work.
The symbol ∞
Wallis is credited with introducing the symbol ∞ for infinity. What interesting ways can we use this symbol to make cool new objects or effects? Can we make it out of Lego, for example?
Making and cutting Möbius strips
In some configurations, the Möbius strip resembles an infinity symbol, as well as representing infinity by virtue of being a loop. It can also be cut in special ways to reveal surprises, or made into charming Christmas decorations. We explore this one-sided surface and see what we can learn.
Knitting and crochet
Handicrafts are a great way to explore beautiful mathematical objects. The Möbius strip can be knitted, and repeatedly crocheting an infinity symbol gives a Chen-Gackstatter surface. We take our crochet into a new dimension and try to get a handle (!) on these surfaces.
Hair braiding: theory and practice
Hair braids are complex structures or patterns formed by interlacing strands of hair. Braid theory is an abstract geometric theory studying braids and their generalisations. We make cool braids out of hair or textiles or wire, and explore the ideas that allow us to think about them mathematically.
What is nonstandard analysis?
Calculus is a millenium-long triumph of human thought. Wallis played a role in its development, specificially the development of infinitesimal calculus. He exploited an infinitesimal quantity he denoted 1/∞ in area calculations, preparing the ground for non-standard calculus. Ordinarily, the operations of calculus are defined with limits based on epsilon-delta ideas formalised by Weierstrass. Non-standard analysis instead arrives at logically rigorous formulations using infinitesimal numbers, numbers so small that there is no way to measure them, and in the process opens philosophical debates about their validity.
Alien mathematics
Far away on another planet, inquisitive and inventive aliens are doing calculus, cryptography and composing music. How might they be doing things differently?
Eigen-analysis: fixed points in dynamical systems
A dynamical system is one in which a function describes the time dependence of a point in a geometrical space. An example is the Lorenz attractor, a set of solutions to the Lorenz system which pleasingly looks like the infinity symbol. Fixed points of the system don't change in time. We learn about the role of the eigenvalues and eigenvectors of linearised dynamical systems, and play with some on the computer.
Exciting things that happen at infinity!
The study of sequences and series are foundational to the study of calculus. Simple ideas describing finite series reveal secrets when considered at infinity, where some converge to a limit and others do not. We play with some of these ideas, with no prior knowledge required.
Looping film
The Oscar-winning 1983 short film Tango by Zbigniew Rybczyński depicts a temporally reciprocating structure. In this pre-digital animation, characters appear in a looping film set in one room. Remarkably, Rybczyński drew and painted approximately sixteen thousand cels and worked for sixteen hours for seven months to make his film. Perhaps using modern technology, a green screen and a video camera, we can make a computer overlay each time round in a similar way, recording participants to see what they create.
Update! Tim has produced a homage to Tango using a Kinect sensor (instead of using green-screen technology). We can use this at the workshop!
Linguistics and grammar
Wallis also did work on English grammar. We explore the linguistic aspects of his work.
Wallis served as chief cryptographer for Parliament. We study techniques for secure communication in the presence of cunning adversaries! Perhaps we can consider cryptography as it might be understood in Wallis's time and explore the methods employed by cryptographers and cryptosystems of that period.
We encourage (though by no means require) those participants who would like to to come in a mathematics- or Wallis-related costume.
Mathematical baking competition
Inspired by the MathsJam baking competition, we invite participants to bake and bring a delicious and mathematically interesting cake, ideally with a Wallis theme. The competition will be judged by a randomly-selected panel. We require volunteers for this panel, who should be willing to rank the cakes decisively.

Some of these activities will be accompanied by a very informal, blackboard-style talk. We welcome informal talks on any related topic from participants.

This list isn't intended to be prescriptive. We'll also be doing anything that anyone wants to propose on the day or beforehand. Please update us with your suggestions, and we'll add them here! Alternatively, the GitHub wiki can be used to share your ideas.

Links elsewhere

Please feel free to get in touch via email, at