## Notations and queries

### June 22, 2009

Went to Manchester at the weekend and picked up a CD of highlights from Richard Feynman’s lectures, so have been enjoying his masterful presentation of the fundamentals of physics in the car into work. The six CD set covers topics including general relativity and quantum theory, as well as examining the nature of mass and what it means for space to be curved.

In order to compare the relative strengths of gravity and electromagnetism, Feynman shows the ratio between them is of the order 10^{42} and goes on to express this figure in more conventional notation as 1,000,000,000,000, 000,000,000, 000,000,000, 000,000,000,000 … which is good reason, he observes, for employing scientific notation.

Now while scientific notation is pretty well essential for expressing very large (and very small) figures, it isn’t something journalists use in copy, and with good reason – for a start, it would scare off most readers. But that doesn’t mean journalists should be ignorant of what scientific notation means. They may well be presented with information in this form and need to be able to interpret it for their readers.

Scientific notation simply expresses numbers in powers of 10 – 100 is 10^{2} and a million is 10^{6}, so that the superscript is the number of noughts following the “1”.

In the same way, small numbers are expressed as reciprocals of powers of 10 – a tenth is 10^{-1} and a millionth is 10^{-6} (for consistency, 10^{0} is defined to be 1).

Hence journalists need to understand what is meant by numbers expressed in this way; but ought to report them in language with which the reader is more familiar. Often, the best way of doing this is by analogy. Say that the local medical college has discovered a new microbe and calculate there are around 10^{10} of these microbes on earth – you want to include this in your article, but who has any intuition of how large that number is?

Therefore you relate it to something readers are at home with:There are around 3×10^{9} seconds in a century, so that means if you counted three of these microbes every second, it would take you 100 years to count them all.

Bringing the very large and the very small into a context which humans can relate to is an essential part of journalism.

I admire Richard Dawkins’ classroom technique for bringing home to schoolchildren the vastness of geological time. On their desks he’d place a nailfile, and then ask the children to stretch out their arms. The length of their arm – from their shoulder to their fingertips – represented the lifetime of the earth, from the moment it formed to the present day. Where on such a scale, he asked, does recorded history lie? Some would point to their elbow, or wrist, or knuckle. “Lift up your nailfiles,” he’d say, “and run them along your nails.” It was the shaving from the tip of their fingernails that represented the entirety of human history.