What is my greatest influence in writing a book? (or – what are Grandsire Doubles?)

I’ve always wanted to write a book, at least I think I’ve always wanted to. There are lots of reasons: the new challenge, the satisfaction and “legacy” of a physical publication, and, specifically, a productive use of my time during a difficult year or two as I enter the second half of my first decade in the data visualisation field. Mostly, they are all based around the challenge of legitimising my own experience and standing.

But it was reading this brief summary of academic author Hugh Neill, on an Amazon summary of one of his books, that most resonated with me. 

About the Author
Hugh Neill is a maths teacher who has also been an inspector and chief examiner. His books have helped over 100,000 people improve their mathematics.

Why do I love this simple explanation so much? I should explain. Hugh was my uncle, who passed away a couple of weeks ago, aged 85. He was a Mathematics lecturer and professor, before becoming chief examiner of Mathematics for the Inner London Education Authority (when it existed). As a life-long mathematician, I can’t say he alone inspired me to study mathematics for my degree, since I felt that desire and love of numbers and patterns in me was innate, but I’m sure I can thank him for sharing some of the same genetic predisposition towards the subject. 

And once he had retired, I knew that he did “a bit of writing”. What I didn’t know, was just how much writing! Hugh has written or co-written about 60 mathematics books. Now I know that he didn’t do this in order to live a retirement life of riches and luxury! But he saw it as an opportunity to continue working in the field that he loved, and as an opportunity to continue sharing his knowledge in that subject, as he had done for so many years as a teacher and lecturer.

Our paths did cross in later years – when we met a couple of years ago and I explained what I did these days in the field of data visualisation, he went to his study and returned with a smile, having found two books he thought I might enjoy. He was loathe to lend them to me because he loved to read books, just as he loved to write them! But he trusted that they would be material that I would find useful, and understood how relevant they were to me and my field, more so than they were to him. These were the books, you may recognise them …

He was right – Tufte’s books are (or were) the perfect crossover between mathematics/academia and data visualisation. And, I’ll be honest, it was refreshing to explain data visualisation to a relative outside the field, and for them to perfectly understand what I meant straight away! I didn’t have the heart to say that much as I appreciate the correctness and principles behind Tufte’s work, I often then eschew these principles. They were two books I had never owned up until then, but I knew and appreciated that complemented my collection perfectly. I have now read them, and, more than that, I have cited them, fairly I hope, in my new book.

And so, at our most recent family gathering only weeks ago, it was Hugh who I most wanted to share my book publication news with. I was proud to continue a family tradition of knowledge sharing and book publication, and he was the man I wanted to share that pride with. What’s more, the Tufte books that he leant me had played a small but important part in my upcoming publication. And although the conversation was short and Hugh’s health was fading then, we both knew and acknowledged why we go through the process of book writing, understanding the rigours and rewards.

I’m proud that my uncle Hugh has helped 100,000 people improve their mathematics. Like him, I love my subject area and I want to do exactly the same with data visualisation, that is our shared inspiration. You can substitute “improve” with “think more”. And you can remove at least two zeros, maybe three, for my personal ambition. But I want to help [a much smaller quantity] people think more about their data visualisation. 


The above is very much a “part 1” of this post. I wrote it in draft, but didn’t publish. It felt light on dataviz content, and more personal to me than it might be to my readers. I gained a lot personally from the process of writing the post, even if I didn’t click “publish”, and that was enough for me. However, a week on from writing the post, was Hugh’s funeral and service of commemoration. And this leads onto the seemingly unrelated second question in this post:

What are Grandsire Doubles?

A few days ago, I had no idea – I had never heard of the term. Grandsire Doubles are a particular change ringing method used in church bell-ringing. After the church service, a Grandsire Doubles quarter-peal was rung by Hugh’s friends, in tribute to him. I knew he had been a passionate bell-ringer for many years (having accompanied him one Christmas to see him in action at a local church), but knew little else. But one thing I did know is that bell-ringing relies on numbers, mathematics, sequences, permutations and patterns. I resolved to learn more and to explain it in the way I know best – in visual form. So there’s my connection, and my opportunity to pay my own small tribute. 

This blog (and, spoiler alert, the book!) already celebrates some of the possibilities of numbers and number sequences for data visualisations, and it seems like the field of campanology is an additional option I hadn’t considered until now.

My understanding is that change-ringing has two main principles. Firstly, that every possible combination of the church’s bells must be rung once, and only once. Straight away, there’s the maths … a five-bell peal leads to 5! combinations (that’s five factorial, which is 1 x 2 x 3 x 4 x 5 = 120 – not the number 5 expressed with surprise). The second rule is that each bell’s position in the arrangement of five bells can only change by one (or not at all) each time. You couldn’t go from last to first, for example, there’s not enough time for the bell to ring and the rope to return to position to be rung again immediately after.

Grandsire Doubles – diagrammatic form

The diagrams and explanations for bell ringers are visualisations in themselves! I can’t promise to understand a “bob”, a “dodge” or a “course” – the diagrams already assume a certain amount of campanology expertise. But what I can do is go fully visual. And because all change ringing starts and ends in the same place, the perfect option was to choose radial.

My visualisation is below, and the online version can be found here and includes a musical animation (courtesy of experimentation with the freely-available Sonic Pi software app, and free downloadable tubular bell chimes of five different pitches). It’s simple, but I hope it goes some way to explaining change-ringing in general, and Grandsire Doubles in particular, in a pleasing visual manner.

The musical animation element is separately available on YouTube and shown below

Grandsire Doubles with ringing bells – animation

I hope you enjoy this. I do think Hugh would have enjoyed this. Maybe between us we can get 100000 people to improve their mathematics, 100 people to think more about data visualisation, and a handful of people to show more interest in campanology? That would be a pretty satisfying combination.

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