Too much data can mean league of folly

Human beings are exceedingly well equipped to act upon visual information.

We are not so clever, though, at charting a course through the overload of written and numerical data that the modern world bombards us with.

Britain's education system is probably the most measured in the world.

Because examinations and Sats results can be turned into numbers, there is a belief that such data offers some objective measure of the quality of a school.

But interpreting what the plethora of numbers is really saying about the system is not so straightforward. Witness how often the same data is used to demonstrate whatever particular prejudice a pundit is pushing.

The blind faith that people put in maths and numbers results in us being swayed easily by the league tables. But our ignorance of what maths can and cannot do hinders our ability to make informed judgements.

We feel much more at home assessing how good a school is at drama or music without someone measuring this for us and putting it in a league table.

Maths is certainly successful at finding ways to see structure, pattern and meaning in the complex world that surrounds us. Based on that understanding, we can often make choices with the security of knowing what will happen next. The differential equations that describe a moving body translate into our ability to fly safely from one side of the world to the other. But is it possible to master league tables to predict the course of our children's education?

Mathematicians face frighteningly complex situations to analyse. But by twisting and turning the problem, one can find ways to comprehend and master the figures. Maths looks at data in many ways: statistics, geometrical pictures, differential equations. Some perspectives reveal hidden information which otherwise might lie buried.

But others might provide no insights or misleading ways of seeing structure. The art is finding the best way to look. For example, a statistical analysis of the Hebrew text of the Bible claimed that the Torah contained predictions of future events.

Called the Bible Code, the prophecies arose from the fascinating art of Gematria, part of the Kabbalah. By counting out every 15th or 60th letter, say, the resulting text foretold the rise of Hitler and the assassination of Kennedy.

The significance of this discovery was supported by statistical evidence meant to illustrate that a random text would not contain such hidden messages. But subsequent analysis has shown that the scientists who generated the statistics had skewed their data by taking a biased viewpoint.

Graphs and pictures are also a good way to achieve some impression of detailed data. Then again, you only need look at the paradoxical pictures of the Dutch artist M.C. Escher to be reminded that what you see is not always what you get.

For example, looking at the two-dimensional shadow of a three-dimensional body gives a partial view. Choose the right perspective and that image might be enough for us to identify the person making the shadow. A two-dimensional silhouette of Hitchcock in profile is sufficient for most of us to name the director. But take a silhouette face on and we have lost too much information.

Tables of examination results represent too much data for our brains to process. But the simple league tables with which we are presented have lost too much information to be useful. Assessing a sixth-form college just by its final results reveals nothing of what the school has contributed to the education of the child.

A measure of how much pupils' results have improved from GCSE to A-level is surely a much better perspective on the quality of the school, even if the final results overall are lower than those of the neighbouring sixth form, where students came in with good GCSE results and simply coasted.

It took millions of years for us to evolve the ability to process the visual world. But it will be those who develop the maths skills to assess data who will be the fittest to survive the 21st century.

Marcus du Sautoy is professor of mathematics at Oxford university and author of The Music of the Primes (Harper Perennial)

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