Monday, 14 March 2016

In Praise of π

It was always going to be irresistible. When my daughter told me that today was a unique Pi Day 2016 (14 March, 3.14.16) I knew I would want to blog about it. Indeed, given the part mathematics has played in my life, I'm surprised I haven't blogged on it before.

I owe a lot to π. Not so much to the number itself, for all its irrational, transcendental qualities (those are technical mathematical terms by the way, not just the blogger's purple prose). But to what it symbolises and represents in the world of thought, in the structure of the universe, and not least in my own life.

For autobiography comes into things today. I can remember that even at a tender age I used to long to make sense of the arcane mathematical symbols that littered the books I pulled off the school library shelves: all those xs and ys and Σ signs and long swirly Ss which I can't do on this keyboard but which I later learned to know as symbols of integration, and dy/dx, and e and most of all, because it seemed to crop up everywhere, π. 

I think I fell in love with maths when I finally got to understand what π stood for. Calculating a circle's circumference and area was where it all began of course. But as I went on to do A level maths, it seemed to me miraculous that this innocent Greek letter could work so hard. It featured in places where I least expected it such as working out the period of a pendulum or the movements of the planets or how the hours of daylight change as we travel through the year. And more and more surprises the deeper I went.

I went on to read maths at university. There I began to penetrate the mysteries of algebra, analysis, geometry, topology, number theory and formal logic. (From this some readers will deduce that my inclinations were very much on the 'pure' side of mathematics. I was never much good at 'applied' maths or statistics, though of course π makes plenty of appearances in those areas too.) I loved what I was studying. I loved mathematics for itself, its elegance and beauty, its endless capacity to model worlds we know about and worlds we can never know. I loved it because it seemed to draw me into the deep structures of the universe itself. Was it an art or a science? I used to wonder. I still do. Maybe it doesn't matter. 

And I loved maths for how it was teaching me to think. There are various theories of what mathematics is in itself. Philosophers differ, for instance, about whether it has some 'eternal' (God-given?) existence outside ourselves, whether it is a product of the human mind and its patterns of thought, or whether it is an elaborate game played according to set rules or axioms that govern how we handle signs and formulae on the screen or page. But all agree that logic lies at the foundation of mathematics. And I was finding that my own habits of thinking and speaking, arguing and debating were being profoundly moulded by a desire at least to try to be rigorous. 

I wish that after I graduated with a (not very distinguished) maths degree, I'd kept up my love of the subject. I never did apart from reading popular books on the subject from time to time - which I still do. However by then my vocation to be a priest was beginning to change the way I was thinking about my future. So I turned to theology and took a second degree in what used to be called 'the queen of sciences'. I loved that too. (Perhaps I'm lucky enough to be one of those insatiably curious people who can love almost anything that is interesting enough.) And I realised, when I started to write my first faltering essays, that I owed a huge amount to my mathematical studies. 

When you study theology, you realise how easy it is to be careless about your assumptions and ways of working. Not all the textbooks were models of clear, disciplined, rigorous argument, I used to feel. As I said, maths taught me something of how to think. And as I now see, thought is so basic to who and what we are as human beings. There's much more to be said about Descartes' famous cogito ergo sum, 'I think, therefore I am'. There's more to human life than simply thinking. But he was on to something pretty important. And I reckon I started to glimpse it when I was studying maths as a schoolboy and a student. In that respect, π changed my life, if you'll allow the figure of speech. 

My daughter is about to marry a high school maths teacher. He loves what he does, both the subject itself, and the art of teaching it and exciting young people in their journey of mathematical discovery. I was fortunate to have teachers who lit up mathematics for me too. It's true: you never forget a good teacher. The shortage of good maths teachers in our schools today is worrying. Mathematical literacy (which is more than simply numeracy) is one of the basic foundations of education. As Einstein put it, the point of education is not to impart facts but to teach us how to think. There's no better discipline than maths for helping us to do that. Maybe Pi Day is a chance not only to celebrate mathematics and mathematicians, but also to think about how we are going to train up the next generation of children for whom π will be as alluring as it once was for me.


  1. I have always found maths and logical thought difficult. I remember going to see an uncle who tried to help me understand algebra, but to no avail. Carl Jung's theory of personality type has helped me feel less bad about this. It had helped me understand that thinking is my 'inferior function', which does not mean I can't think. I can and I do, but it is slow. There is a danger in being a psychotherapist and over-using feeling and intuition, and my stress coming out in irrational thinking. Perhaps I need to spend time in Sensing and Thinking types of prayer? It is said that God can get through to us through our least developed functions. But for some reason I don't understand, maths remains a mystery to me.

  2. Bad teaching! Sweeping statement, but I think that's very likely. Although I enjoyed maths and found much of it easy, I was taught, it didn't just happen. So, no, don't feel bad. I enjoyed languages, too, but my French and Italian are terribly rusty these days. You can't do everything.
    To Michael, I would say, I do think maths deals in absolutes, in a way science does not. If you have a smartie, and then another, you have two smarties. One plus one. They're real, and you can eat them! (I'm off chocolate, sorry) This is also twice as many smarties as before (one times two). And if you eat one (if you can stick at only one) you have taken one away! It's magic! Looking forward to Easter.