Maths for all?

The school leaving age in Britain has just been raised to 18. All pupils will have to continue with maths. That has raised howls of protests from journalists. It is claimed to be akin to torture for those who are no good at maths. “What is the use of maths anyway for most people?” “ We are good at science so why bother with maths?” — as though maths and science were unrelated. I suspect that the journalists who complain so vehemently are not themselves good at maths. No one seems to mind saying, “I was hopeless at maths at school”, as though that was something almost to be proud of. I am a bad linguist but I am not proud of the fact.

Maths is undoubtedly of fundamental importance. Science and technology are overwhelmingly applied maths. I am as I have said not a true mathematician but I know a decent amount of maths. I would feel myself to be in some way inadequate otherwise.

Is maths something that anyone of reasonable intelligence should be able to learn or is mathematics a facility, almost like sight or smell, that many simply do not possess? Does it matter that many know little beyond simple arithmetic? And does it matter that lack of maths is a handicap in many jobs — or so employers claim?

I thought I might tell you a story about how knowing maths saved my job and my future. As you know I went to Australia to set up the Plague Locust Commission. Economists at the Treasury had made a study of the costs and benefits of the CSIRO Entomology Division and put the benefit or otherwise of the Commission against CSIRO research. (Nothing CSIRO had discovered was of any use to me but that is by the way.) A couple of weeks after my arrival- it was a Friday- Doug Waterhouse the Chief of Entomology rang me- CSIRO has Chiefs not Directors. “Phil”, he said” You’d better look at this Treasury report since it shows that the Commission is a total waste of money. It will finish the Commission. We are having a meeting here on Monday morning so you’d better come along.”The report was in essence an equation. At the meeting there were the two young economists who had written the report and their boss. After the presentation Doug asked me if I had any questions. “Just a couple,” I said. “In your equation is the cost of running the Commission multiplied by the frequency of not needing control in a year?” “Yes” they replied, “quite right”. “In that case” I said “ I would carry out control every year then I could run the Commission for nothing.” The boss said ,”Alright that is a mistake. Could we move on?” “I have one more matter I’d like cleared up first”, I said. “ The probabilities of a large, medium and small outbreak (in a year) add up to the probability of an outbreak. Is that correct?” “Yes that’s right”, the economists agreed. “But” I said, “probabilities must add up to one.” The two started to bluster but their boss cut them off. Doug said, “I suggest you meet Dr Symmons in his office on Wednesday to sort this out”. To show my point think about throwing a 2 with a die and then a head with a coin. The chance of a 2 (or a 4 or a 6) is 1/6, so as a head and a tail are equally likely the chance of each is 1/12 since 1/12+1/12 = 1/6. Hence the chance of rolling a 2 and tossing a head is 1/6*1/12, that is 1/72 . Right? No wrong. The chance of a head is 1/2 and of a tail1/2 and1/2+1/2=1; it has nothing to do with what went before. The chance of rolling a 2 and tossing a head is 1/6 *1/2=1/12 not 1/72. The two economists went a stage further by making each class of outbreak cause either heavy, average or light damage. I think they put the chance of an outbreak at one year in 4, so the chance of an outbreak being a large one, causing heavy damage they made as 1/4*1/12*1/36 namely once every 1728 years. The correct figure is once every 36 years (1/4*1/3*1/3); it makes a difference. Once every 36 years in fact agrees quite well with the record.

This exercise is an equation. I know that those who the report was directed at did not try to understand the equation, I assume because they thought that they couldn’t and perhaps that appearing to be maths it must be right. I did not need maths to spot the errors- anyone should have been able to see the mistakes. But knowing some maths I was not intimidated- and my job was at stake. It is though not just the errors but the lack of data and the arbitrariness of the relationships that no one questioned because it was maths. I suspect, and in a few cases I know, that models such as the one that says we should drink no alcohol at all are similarly not based on data and include arbitrary relationships, but in most cases I do not know. That is partly because the models are not published and partly because even if they were they would be too complex for me to unravel. One might wonder how two graduate economists came to make the howlers I have described but I fear in economics howlers are not uncommon. Black and Scholes got a Nobel for claiming to be able to predict the future. They set up a company to exploit their insight- it went bust. One could make a case for the 2008 financial crisis being down to the errors of economists.

I haven’t got to the points I started with but I think this will more than do for now.