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 Parliamentâ€™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.
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 workmanâ€™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.
Cryptography
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.
Costumes
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.