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In need of a number

1 Oct, 2012

Numbers...Adam Kucharski, who is studying for a PhD in maths at Cambridge, won the Professional Scientist category of the 2012 Wellcome Trust Science Writing Prize with his compelling account of the importance of estimates. 

In the words of Mark Henderson, Head of Communications at the Wellcome Trust and a judge in this year’s competition: “This was a fascinating piece that explained not only why estimation is much more than just guesswork, but that also demonstrated how important it can be to science”.

How many piano tuners are there in London? Someone asked me that in a job interview a few years ago. Dozens? Hundreds? Thousands? I had no idea either. And yet, in science, similar questions crop up all over the place. How many species are there on Earth? How many neurons does the brain have? How many planets are there in our galaxy?

Estimating quantities can be difficult. Take the piano tuners. The question is a classic example of a “Fermi problem“, which we must solve by combining a series of assumptions. In other words, if we know the approximate number of people in London, we can guess the number of households and hence number of pianos and so on.

The method is named after Enrico Fermi, a physicist who worked on the atomic bomb. While watching the first test detonation in the New Mexico desert, he estimated its strength by dropping torn strips of paper from his hand as the shockwave arrived. The pieces eventually landed 6ft away, which allowed Fermi to work out how much air had been displaced by the blast and how much energy this would require. He guessed 10 kilotons of TNT: half the true value. Still, not bad, considering his estimate was based – literally – on a handful of assumptions.

Scientists are still grappling with other Fermi problems. A particularly elusive one is the number of animal and plant species on Earth; previous estimates have ranged from 3m to 100m, which just shows how little we know about those we share our planet with. Researchers are partly to blame. Some parts of the tree of life are well documented – particularly our friends, the mammals and birds – but for other sections we barely have a sketch of the branches, let alone individual twigs. Last year, however, biologists at Dalhousie University in Canada found a new way to tackle the question.

They noticed that we know a good deal about the broad classifications near the base of the tree, like kingdoms and phyla, despite things getting patchy when we get down to the species level. And for the parts of the tree that were known, the number of species in each family, genus, order, class or phylum followed remarkably consistent patterns. Which meant that – assuming the patterns held for the lesser-studied parts – they could use what they knew about the structure of the tree to fill in the missing information. This method gave the researchers an estimate of 8.7m species, give or take a million.

It isn’t always that we don’t have a value. For years, the number of neurons in the human brain was said to be 100bn. Which, as estimates go, is certainly a neat, memorable figure. It’s just not clear where it came from.

Unable to track down its origins, researchers in Brazil used an ingenious – if grisly – method to come up with their own estimate. First, they got a brain and dissolved it to make an evenly mixed “brain soup”. Then they took a sample, counted the neurons and scaled up the value to give an estimate for the whole brain.

Because they didn’t just focus on one part of the brain, which might have a larger or smaller concentration of neurons compared to other parts, they got a more reliable number than other methods might have produced. In experiments, that number turned out to be around 86bn neurons, 14bn – about a baboon brain’s worth – fewer than we thought.

New techniques can also help researchers estimate things on a much larger scale, such as the number of planets in the Milky Way. Previous detection methods would often miss planets, so earlier this year a team of astronomers turned to an approach known as “microlensing“. This relies on the fact that a star’s gravitational field acts like a lens and magnifies the light of other background stars; if the star has a planet in orbit around it, the magnification will be even greater. Using this method, the researchers calculated that each star in our galaxy has on average 1.6 planets orbiting it, which means there must be billions of planets out there.

Estimates like these might make for good trivia, but they have some other important uses. One advantage of a reliable number is that it can help us comprehend the scale and complexity of a system – whether it be a brain, ecosystem or galaxy – and in turn understand how that system evolved. It also provides a reference when measuring damage, be it through Alzheimer’s disease or species extinction. What’s more, it gives us an idea of how much work is still to be done. (We have only identified around 1.5m species and 700 planets, so there is some way to go.)

Of course, not everything needs to be estimated. The number of piano tuners in London is a good example – I looked that up after the interview. There are 92, apparently. And how many did I say? I’m afraid you’ll have to guess that one.

Adam Kucharski

This is an edited version of Adam’s original essay. Views expressed are the author’s own.

Find out more about the Wellcome Trust Science Writing Prize in association with the Guardian and the Observer and read our ‘How I write about science‘ series of tips for aspiring science writers.

Over the next couple of months, we’re publishing the winners and shortlisted essays from the 2012 competition. Read all, and the 2011 essays, in our archive.

Image credit: Flickr/MervC
One Comment leave one →
  1. Hazel Lambert permalink
    1 Oct, 2012 10:17 am

    I’m looking forward to reading more from Adam Kucharski, he writes so neatly (though appreciate that may have been the editor!) can we have a part two?

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