Sunday, 30 June 2013

Maths does plants

Last week the BBC published a  cheerful article ‘Plants do maths…’, which began with ‘Plants have a built-in capacity to do maths’. Seeing that, I assumed that it was just a piece of inexact but eye-catching journalism. But reading on, I was surprised to read a quotation from Prof. Alison Smith of the John Innes Centre, saying ‘They’re actually doing maths in a simple, chemical way… this is pre-GCSE maths… but they’re doing maths.’ Later, there was a quotation from her colleague Prof. Martin Howard, saying that ‘This is the first concrete example in biology of such a sophisticated arithmetical calculation.’

Mathematics involves starting from a problem statement (expressed as a pattern of symbols) and by various legitimate transformations and manipulations arriving at the result (another pattern of symbols). Sometimes, though not always, the symbols could be said to represent, more or less imperfectly, some situation in the concrete world.

It transpires (as in another sense the plants do) that the article’s about the chemical mechanism that regulates starch metabolism in some plants, and that the rate of a particular reaction is proportional to the quotient of the concentrations of two chemicals in the plants' cells: in other words, it’s proportional to the concentration of A divided by the concentration of B. Presumably the John Innes team were struck by how precisely the rate of reaction correlated with the quotient, though the article doesn’t tell us how strong the correlation was.

But even if the correlation were perfect, it still wouldn’t be plants doing maths. It would be something equally amazing: a simple mathematical expression representing something that happens in a biological system.

One of the greatest triumphs of mathematics was the model of celestial mechanics developed by Newton and others, in which the motions of planets were shown to be very closely modelled by mathematical formulae that many schoolchildren can work with. From there has sprung a widespread belief that mathematics can, given time, precisely represent and analyse all of nature, and a sense that mathematics is on a higher plane than the muddle of nature. Thence that article’s headline, and those professors’ remarks.

Yet it’s a belief that’s hopelessly false. Even in the simple world of celestial mechanics, the n-body problem (modelling the motions of more than a few planets at one time) has no practical exact solution in mathematics. In the world of complex systems (especially biological systems), mathematics often has to use complex and difficult formulae to model even approximately what’s going on in nature.

So there is cause to celebrate: the people at John Innes have found one instance where nature can be modelled accurately by simple mathematics. Whatever its other limitations, then in one case at least, Maths does plants.

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