Do numbers make you numb?
Way back in May 1982, Douglas Hofstadter (he of "Gödel, Escher, Bach" fame) wrote an article for Scientific American called "Number Numbness, or Why innumeracy may be just as dangerous as illiteracy". To provoke the readers to think about how they internalise big numbers, he concocted this scenario:
'The renowned cosmologist Professor Bignumska, lecturing on the future of the universe, had just stated that in about a billion years, according to her calculations, the earth would fall into the sun in a fiery death. In the back of the auditorium a tremulous voice piped up: "Excuse me, Professor", but h-h-how long did you say it would be?" Professor Bignumska calmly replied, "About a billion years." A sigh of relief was heard. "Whew! for a minute there, I thought you'd said a million years."
The absurdity of the comment arises because a million and a billion years are both so far beyond our lifespans as to make the difference meaningless from a personal point of view. In the article, he makes the case that most people have little real grasp of large numbers: not really being able to distinguish millions from billions from trillions, even though there is a thousand-fold difference between each.
But while this distinction may not give us sleepless nights when used in comparison to human lifespans, there are areas of life (national and corporate budgets, national population statistics, even hard disk sizes) where the billion vs million distinction DOES affect our lives, and many of us lack the "Number Sense" to be aware, instinctively, of the difference. Hofstadter argues that this "numbness" to numbers causes a loss of perspective, to the detriment of public debate.
Numbers in the News
The media themselves often fail to establish a proper context for the numbers in the news. Any number ending in "...illion" just ends up in a mental category called "big number".
In November 2015, the UK public sector net borrowing was around £14 billion; debt was around £1.5 trillion. Are those big numbers? Of course they are, but are they unexpectedly big? Are they alarmingly big? Are they big in context?
Lionel Messi earns around 25 million Euros a year. Is this a big number? Of course it is, but how big, in context? And what context should we use? Other footballers? Other sports people? Other individuals? Corporations?
I'm a huge fan of the BBC Radio 4 programme "More or Less". This programme tears apart statistical claims floating about current debates: I think it makes a vital contribution to understanding what's really going on, and debunking inaccurate claims. And one question they will often start with, when looking at some reported statistic is "Is that a big number?".
So, Is That A Big Number?
All this is by way of introducing an idea I am currently working on - an online service to answer just that question. Enter a number, any number, and it'll respond with a bunch of relevant comparisons, to put the number in context.
For example: in 2015, there were 72.4 million cars sold in the world. Is that a big number? the web service tells us: "One for every 100 people in the world". 17.5 million cars sold in the USA? That's "One for every 18 people in the USA" Big numbers? You can draw your own conclusions. And that's the point: to allow people to make informed judgements by putting things in context.
We'll throw in a few quirky measures too, just for fun. How long is an Imperial Star Destroyer, in terms of X-Wings? How long is a football pitch in terms of iPhones laid end to end?
It's very much in development but you can play around with what's been done here (www.isthatabignumber.com). As you can see from all the not-yet-live links there's a lot more to come. We're hoping to use this as a hub for a variety of numeracy-related services: a number-led blog, educational resources.
So, is 25 million Euros a big number? Click this link to see:
I'd love to think this could play some small role in helping people such as journalists, teachers or just the curious to better understand the numbers around us.