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Gresham College Lecture: Notations, Patterns and New Discoveries (Juggling!)

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On a dark winter’s evening on 23 January 2014, I discovered a new part of London I had never been to before.  Dr Colin Wright gave a talk entitled ‘notations, patterns and new discoveries’ at the Museum of London.   The subject was intriguing in a number of different ways.  Firstly, it was all about the mathematics of juggling (which represented a combination of ideas that I had never come across before).  Secondly, it was about notations.

 The reason why I was ‘hooked’ by the notation part of the title is because my home discipline is computer science.  Computers are programmed using notation systems (programming languages), and when I was doing some research into software maintenance and object-oriented programming I discovered a series of fascinating papers that was about something called the ‘cognitive dimensions of notations’.  Roughly put, these were all about how we can efficiently work with (and think about) different types of notation system.

In its broadest sense, a notation is an abstraction or a representation.  It allows us to write stuff down.  Juggling (like dance) is an activity that is dynamic, almost ethereal; it exists and time and space, and then it can disappear or stop in an instant.  Notation allows us to write down or describe the transitory.  Computer programming languages allow us to describe sets of invisible instructions and sequences of calculations that exist nowhere except within digital circuits.  When we’re able to write things down, it turns out that we can more easily reason about what we’ve described, and make new discoveries too.

It took between eight and ten minutes to figure out how to get into the Museum of London.  It sits in the middle of a roundabout that I’ve passed a number of times before.  Eventually, I was ushered into a huge cavernous lecture theatre, which clearly suggested that this was going to be quite ‘an event’.  I was not to be disappointed.

Within minutes of the start of the lecture, we heard names of famous mathematicians: Gauss and Liebniz.  One view was that ‘truths (or proofs) should come from notions rather than notations’.  Colin, however, had a different view, that there is interplay between notions (or ideas) and notations.

During the lecture, I made a note of the following sentence: a notation represents a ‘specialist terminology allows rapid and accurate communication’, and then moved onto ask the question, ‘how can we describe a juggling pattern?’  This led to the creation of an abstraction that could then describe the movement of juggling balls. 

Whilst I was listening, I thought, ‘this is exactly what computer programmers do; we create one form of notation (a computer program), using another form of notation (a computer language) – the computer program is our abstraction of a problem that we’re trying to solve’.  Colin introduced us to juggling terms (or high level abstractions), such as the ‘shower’, ‘cascade’ and ‘mill’s mess’.  This led towards the more intellectually demanding domain of ‘theoretical juggling’ (with impossible number of balls).

 My words can’t really do the lecture justice.  I should add that it is one of those lectures that you would learn stuff by listening to it more than once.  Thankfully, for those who are interested, it was recorded, and it available on-line (Gresham College)

Whilst I was witnesses all these great tricks, one thought crossed my mind, which was, ‘how much time did you have to spend to figure out all this stuff and to learn all these juggling tricks?!  Surely there was something better you could have done with your time!’ (Admittedly, I write this partially in jest and with jealousy, since I can’t catch and I fear that doing ‘a cascade’ with three balls is, for me, a theoretical impossibility). 

It was a question that was implicitly answered by considering the importance of pure mathematics.  Doing and exploring stuff only because it is intellectually interesting may potentially lead to a real world practical use – the thing is that you don’t know what it might be and what new discoveries might emerge.  (A good example of this is number theory leading to the practical application of cryptography, which is used whenever we buy stuff over the internet). 

All in all, great fun.  Recommended.

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