Unpicking the Big in Big Numbers

It’s election season, and so big numbers are everywhere. Some of them may even be accurate, But as politicians promise £millions here and criticise £billion cuts there, distinctions between these numbers blur. I think of it as £M and £bn both amounting to what Daniel Kahneman might term the ‘prototypical image’ of a great heap of cash, with no further disaggregation required. But distinctions are important.

The wonderful Hans Rosling was typically, insistently clear on this point. For instance, interviewed by BBC More or Less, he railed against the tendency to divide the world in two (from about 5min43):

"We can no longer have two boxes in our head, one labeled ‘Western World’, the other labeled ‘Developing World’… we have to realise that countries are on a line from at one end Singapore and Norway, and at the other end Congo and Afghanistan. And in that distance… most people live in the middle… In Africa, something bad happens in one country and you generalise to the whole of the continent. [In terms of life expectancy and fertility] Ghana is half way between Great Britain and Mali."

Or in his superb documentary on the world’s population, he talks (from around 35min40) about the distinctions between the world’s richest billion people, living on around $100 a day, the middle billion ($10 a day), and the poorest billion ($1 a day):  

"The most important to remember is this… the problem for us living on $100 a day is that when we look down on those who have $10, or $1, they look equally poor. We can’t see the difference…We say ‘Oh they are all poor’… But the people down here, they know very well how much better life would be if they move from $1 to $10… this is a huge difference…"

It’s appropriate that Rosling was talking about population, as I started thinking about these distinctions between big numbers when we were planning our interdisciplinary 10bn programme here in Sheffield last year (see also http://10bn.sheffield.ac.uk/). A colleague had the idea of representing 10bn people with grains of sand, stacking builders’ bags until we reached 10bn grains. I was somewhat sceptical that we’d need multiple bags, and set about some back-of-the-envelope scribblings to convince myself. And I did convince myself. My colleague, Roger, then passed on this statistic to emphasise just how much bigger a billion is than a million: a million seconds is about eleven and a half days.

A billion seconds is nearly 32 years…

In data, too, there is big data, Big Data, and BIG DATA!!!! The increasing ability of software packages to rapidly process huge data files is fantastic, but because any largish dataset becomes something we only ever ‘see’ at one step removed - as summary statistics, visualisations, the outputs of quality control measures - again perhaps we lose touch with degrees of bigness.

Scrolling down through a spreadsheet at a reasonable rate, it takes me about 15 seconds to reach the 1000th row. It would thus take me around 4 hours of constant scrolling to reach the bottom of the list of 250,000 or so recognised marine species listed in the World Register of Marine Species. If I wanted to scroll through each of the 45 million or so marine species occurrence records in the Ocean Biogeographic Information System, on the other hand, it would take nearly 8 days.

A billion records? Almost six months.

So it is useful, I think, when considering public finances and election pledges, to remind ourselves that what looks from a normal human standpoint as equally enormous piles of (often fictional) money, in fact £1bn is to £1M what £10,000 is to £10.