Models, mostly based on mathematics of one kind or another, are used everywhere to help organizations make decisions about their design, policies, investment, and operations. They are indispensable.
But if modelling is such a great idea, and such a great help, why do so many things go wrong? Well, there’s good modelling and less good modelling. And it’s hard for the consumers of models — in companies, the Civil Service, government agencies — to know when they’re getting the good stuff. Worse, there’s a lot of comment and advice out there which at best doesn’t help, and perhaps makes things worse.
In 1959, the celebrated scientist and novelist C. P. Snow delivered the Rede Lecture on ‘The Two Cultures’. Snow later published a book developing the ideas as ‘The Two Cultures and the Scientific Revolution’.
A famous passage from Snow’s lecture is the following (it can be found in Wikipedia):
‘A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is the scientific equivalent of: Have you read a work of Shakespeare’s?
‘I now believe that if I had asked an even simpler question — such as, What do you mean by mass, or acceleration, which is the scientific equivalent of saying, Can you read? — not more than one in ten of the highly educated would have felt that I was speaking the same language. So the great edifice of modern physics goes up, and the majority of the cleverest people in the western world have about as much insight into it as their neolithic ancestors would have had.’
Over the decades since, society has come to depend upon mathematics, and on mathematical models in particular, to a very great extent. Alas, the mathematical sophistication of the great majority of consumers of models has not really improved. Perhaps it has even deteriorated.
So, as mathematicians and modellers, we need to make things work. The starting point for good modelling is communication with the client.