The permutation clock

I recently had an idea: map the Unix time (seconds since 1st January 1970) to shufflings of a deck of cards. Each second would correspond to a different ordering of the 52 cards.

I wanted to think about how mind-bogglingly huge $52!$ is: $52!$ seconds is more than $2 \times 10^{60}$ years. So even if you spent your entire life watching this thing, you’d leave this world having seen basically none of the possible permutations. Happily, Wikipedia reckons that the heat death of the universe will happen in about $10^{100}$ years, so there’s plenty of time for me to enact my plan.

My adventures in 3D printing: Write Angles Cube

At work we’ve got a 3D printer. In this series of posts I’ll share some of the designs I’ve made.

This is one of the first ‘proper’ things I’ve designed – I wanted to have a go at making something based on an object I already had. A colleague asked if I could make some props to explain coordinate systems, and I was holding a whiteboard pen at the time, so I decided to make a set of orthogonal axes out of whiteboard pens.

Tessellating Tricurves

Tricurves were introduced to the Aperiodical audience via Tim Lexen‘s posts Bending the Law of Sines, Combining Tricurves, Phantom Tiling, and (joint with Katie Steckles) Making Tricurves. Like Tim and Katie in that last post, when introduced to a new concept I like to play around with it to see it from different perspectives. Tiling is a topic in maths that is near enough to my speciality that I feel I should be able to understand it, but far enough that I don’t feel any pressure to be an expert – perfect conditions for playing with the concepts.

Sir Michael Atiyah has died

Over the weekend we heard the sad news that mathematician Sir Michael Atiyah has passed away on 11th January. One of the few mathematicians to have been awarded both a Fields medal and an Abel prize, Atiyah leaves behind an extensive mathematical legacy and will be missed by many.

A tribute to former President of the Royal Society Sir Michael Atiyah OM FRS (1929 – 2019), on the Royal Society website

Mathematician Sir Michael Atiyah dies aged 89, at BBC News

Michael Atiyah, Mathematician in Newton’s Footsteps, Dies at 89 at the New York Times

The Sound of Proof

Marcus du Sautoy has tweeted about a mathematics and music project he’s involved in, called The Sound of Proof. Five classical proofs from Euclid’s Elements have been interpreted by composer Jamie Perera into musical pieces, and they’ve put together an app/game to see if you can work out which one corresponds to which.

They’ll be announcing the results at an event as part of Manchester Science Festival in October. The project is a collaboration with PRiSM, the research arm of the Royal Northern College of Music in Manchester.

The Sound of Proof, at RNCM PRiSM

2017 London Mathematical Society Popular Lectures now online

The London Mathematical Society Popular Lectures present exciting topics in mathematics and its applications to a wide audience. The 2017 Popular Lectures were Adventures in the 7th Dimension (Dr Jason Lotay, University College London) and The Unreasonable Effectiveness of Physics in Maths (Professor David Tong, University of Cambridge).

The Lectures are now available on the LMS’s YouTube channel, along with many of the previous years’ videos.

Progress on billiard table problem

Quanta Magazine reports progress on what its headline calls the “Infinite Pool-Table Problem”. The problem is explained in the article as follows:

Strike a billiard ball on a frictionless table with no pockets so that it never stops bouncing off the table walls. If you returned years later, what would you find? Would the ball have settled into some repeating orbit, like a planet circling the sun, or would it be continually tracing new paths in a ceaseless exploration of its felt-covered plane?

The article describes progress on the problem via study of ‘optimal’ billiard tables, “shapes whose particular angles make it possible to understand every billiard path that could occur within them”.