Humans evolved with ten digits on our hands, and that’s likely the reason we have ten digits in our number system. Counting on your fingers feels like such a natural and obvious thing to do that you might assume everyone does it in the same way. But, if you are in the UK or Europe, there’s a good chance you start counting with your left thumb. While in the US and Canada they start with the index finger, and finish with the thumb. And in parts of the Middle East like Iran, they start on the right hand, withe the pinky. But even though there are slight differences, these are all variations on the same basic system.
And that system, basically is for every new number, you add a new finger. What researchers call a linear system. And that makes it easier to understand some principles that are relevant for counting, like this one-to-one correspondence between the things that you want to count and the representations for the number.
This way of finger counting seems like it could be innate or universal – and in the past, that’s what some psychologists thought too.
Those researchers assumed that children basically need finger counting as a tool for learning to grasp the concept of number but also to learn counting. Question is whether that’s really true, whether there’s really just one way of counting.
For example, in Japan you start with fingers extended, and curl them in as you count upwards. But in other places, things diverge more – for example, the system used by speakers of some Bantu languages in Eastern Africa.
They try to make symmetric representations as much as possible. And so they continue in this symmetric pattern, which is very important to them culturally.
The big limitation with these methods is they quickly run out of fingers – but that’s not an issue everywhere.
Indian School System, for example, instead of counting complete or entire fingers’ you count the lines between the segments, which give you four different numbers for each finger. So you’ll reach much further than with the Western system.
These linear systems are all what researchers call one- dimensional. But there are also two-dimensional systems – like the one reportedly used by merchants in another part of India, Maharastra. Here, the left hand counts up to five, and the right hand keeps track of how many sets of five have been counted – so these fingers represent a different dimension, multiples of 5.
It’s also possible to combine these methods together – for example, using the Indian system in two-dimensions would allow you to keep track of 20 sets of 20 – or up to 400! But there’s a third category of finger counting where things get really interesting – symbolic.
In China, counting from one of five is the same as in the West. But after six, they keep counting on the same hand, and instead of using quantities to represent number, they use symbols.
So this type of system works perfectly well as long as you master it. But in order to learn it, it takes much more time.
One system that was difficult to master was a symbolic system used by the ancient Romans to count into the thousands. These three fingers on the left hand were used to count “units” – for example, this would be seven. The thumb and forefinger made shapes to represent the “tens” – so this would be 97. Adding the right hand lets you keep track of “hundreds” and thousands in the same way – so this would be 597, and this would be 1,597!
So – what does all this mean for our relationship with numbers? Well finger counting clearly has a huge cultural dimension. Natural as it feels, it’s a behaviour we learn as children, rather than something we do instinctively.
What cognitive implications, or what consequences do these differences have? How do children that grow up in different contexts and have different finger counting systems and different representations for numbers, how to they learn counting? Then finally, at some point in the past, our ancestors started counting and started designing counting systems. And which role did finger counting play in the process? We are talking about 100,00 years in the past and probably longer. So it’s a challenging task.But hopefully we get closer to an answer to it.
Let us know how do you count using your hands in the comments below.