It’s all “some beans” to me
In his new book, Alex’s Adventures in Numberland, Alex Bellos sheds fascinating light on the gap between our natural mathematical skills and what’s demanded of us in the modern world; a matter very dear to my heart and which should be occupying governments and financial regulators too.
Field research in the Amazon rainforest, performed by French linguist and anthropologist Pierre Pica, has found that our ‘natural’, instinctive grasp of quantity (ie, size, volume, distance) can differ greatly from what modern formal arithmetic requires of us.
By studying the remote Munduruku, Pica has sought to isolate whatever instinctive grasp of number humans might have before we begin to learn and assimilate the huge edifice of modern arithmetic and mathematics.
And what did he find?; that when we think quantitatively we naturally think in ratios. When asked to place the numbers one to ten along a line, most of us space them at even intervals. Not the Munduruku. They think that the intervals start large and become progressively smaller as the numbers increase. In other words, and to use the language of modern maths, they naturally visualise quantities along a logarithmic scale rather than the linear one most of us are used to. This also happens to be what kids do before we get them trained (according to Robert Siegler and Julie Booth at Carnegie Mellon University).
How come? The Munduruku (and kids) seem to be making decisions about where the numbers should lie by estimating ratios between the amounts. This makes it perfectly logical (whatever that means) for the distance from one to five (which is a five-fold increase) to be much longer than the distance from five to ten (which is only a doubling). Pica thinks this way of understanding quantities, using ‘guesstimated’ ratios, is a universal human intuition evolved as part of our basic cognitive toolkit. After all, in the time before accountants what mattered was not precisely how big, fast, long, numerous or high something was, but approximately which was the biggest, fastest, highest, longest or most numerous. In a sense, then, our ancestors lived (and the Munduruku still do live) in a binary world of more/less, bigger/smaller, longer/shorter, higher/lower, and since those societies lasted eons, but modern numbers are no more than 10,000 years old, we all carry that logarithmic instinct with us to this day.
Not convinced? Bellos provides us with a neat example involving perspective …
… if we see a tree 100 metres away and another 100 metres behind it, the second 100 metres looks shorter. To a Munduruku, the idea that every 100 metres represents an equal distance is a distortion of how he perceives the environment.
… and another one which better illustrates the potential consequences for how we apprehend quantities and make decisions in a world dominated by big, big numbers …
… we can all understand the difference between one and 10. It is unlikely we would confuse one pint of beer and 10 pints of beer. Yet what about the difference between a billion gallons of water and 10 billion gallons of water? Even though the difference is enormous, we tend to see both quantities as quite similar – very large amounts of water. Likewise, the terms millionaire and billionaire are thrown around almost as synonyms – as if there is not so much difference between being very rich and very, very rich.
Still not convinced? Remember when Blackadder tried to teach Baldrick to count using dried beans?
I rest my case. What do you think?