Mathematics, my father and me

Throughout these years I visited my father regularly, and regaled him with what I was doing, where that bore on mathematics. And it regularly did. My honours and masters degree theses involved what today we would call data analysis, pretty simple stuff, from the vantage point of 2017, but unusual in their day for someone trained in history and moving into political science. I had been taught elementary statistics in psychology in my first year at university, but what I was dealing with now were large numbers - entire election results, and at every level, nation, state, region, electorate, sub-division, polling place. I could see patterns there, I said, explaining my interest, and asked him for advice. 'You'll work it out for yourself,' he said, and I did.

One of the things I had noticed in my work was that in politics people often equated 'most' with 'all'. For example, 'workers' or 'the working class' voted Labor. It couldn't be absolutely true, because something like three quarters of the workforce were employees. If they had all voted Labor that party would have been in power since Federation. So what did it mean? When I looked at what passed for data, it seemed that at best about two thirds of the working class voted Labor, however you defined the working class. I thought about it, and some of Dad's common-sense approach to numbers came to me. If half the workers voted Labor, and the other half Liberal, that meant there was no connection between class and party at all. If all the workers voted Labor, that would mean class and party were the same thing. Where did 'two-thirds' fit in that scheme? Well, a good deal close to 50 per cent than 100 per cent. Once you saw politics that way, the narrowness of Australian election results in over a century became clearer. All this did not come to me in a flash, though today it just seems obvious. It came as a puzzle that needed to be solved. When I explained the issue at an academic conference I was not loudly applauded, for I was disturbing fondly-held beliefs, and that does not make you a hero. It still doesn't.

Some years later, dealing now with several million bits of information in two national surveys for some 2000 people who had found themselves talking for an hour and a half or so, I had to learn how to construct a simultaneous equations model of forty years of national electoral activity that suggested strongly how Australia had become more and more 'national' in election outcomes.

At first I knew nothing about simultaneous equations, since they had not been part of what I had learned at school. But, like the bookie's penciller Dad had once taught, I needed to know, and I needed to know quickly. It proved quite straightforward. By now it was routine for me to check my own work. Yes, it is best practice for any academic, for it is much less embarrassing to detect the flaws in your own work before it is published than to have others point them out when your article or book is in print. But some of my caution went back to that early advice from my father: 'Go back and check! You're bound to have made errors. Find them and fix them!'

Later again, I read a paper about the use of Markov chains, and saw at once a use for them in my own work. A Markov chain, named after its Russian inventor, is a way of making predictions about a future (or past) state from the information you have at a given moment. My interest was in how long it took for children to acquire the political leanings of their parents. Remember, the modern party system in Australia started in 1910, when almost all the votes and all the seats went to the Labor and Liberal parties. I had to learn about conditional probabilities, but then I could suggest that Australia by the late 1920s was most likely characterised by party loyalties passed on by about three quarters of the electorate. Again, the bookie's penciller had showed the way.

I did not get to love mathematics in the way my father did, or in the style of my next brother, who is a professor of mathematical statistics. But I learned two great things from my father in this domain. One is the basic truth that mathematics is not hard if you have a good reason for wishing to employ it. The other is that checking your work is always important. The skilled trades have a phrase for it: 'measure twice, cut once!'

Too many of us fear mathematics, probably because of the way we were taught in primary school. That is a great pity, because it is a most useful tool in everyday life, and it can be fun. Long live the teachers who teach it that way!