Counting is somewhat fundamental to our lives. A key feature of Human intelligence is our ability to define the number of a given artifact with which we are presented. To my knowledge, no animal exhibits this capability to any significant extent. Indeed, I believe that an Amazonian tribe was discovered whose counting system went “one, two, many”.
But even we, in the Western world, can run into trouble with numbers …
Big numbers lead us astray. Scientists avoid the problem by always working in powers of ten, but most of us like words. Up to a million is OK, but then there is a problem. We now often hear references to billions and trillions – particularly with reference to national debts etc. How many is a billion? Most of us would say 1 followed by 9 zeros. However, this is not universal. Originally, the word “billion” was coined to replace “a million million” – “bi” being the prefix for 2. So, a billion then had 12 zeros. Later it was changed in some countries [e.g. US and UK], but elsewhere the old meaning has stuck. So, that is why scientists are so fussy.
I am good at counting. I can obviously do so indefinitely in English and I can make a brave effort in French, German and Italian. They do make it hard in some languages. In France, for example, everything is OK up to sixty, but seventy is “sixty-ten”, eighty is “four twenties” and ninety is “four twenties and ten”. All very complicated. In some other French speaking countries [e.g. Belgium and parts of Switzerland] they have fixed is and have proper words for seventy, eighty and ninety.
Number bases are interesting. We almost always use base 10. I assume this is just a consequence of human beings having 10 fingers and thumbs [does anyone know why we have this number?]. Computer people use binary [base 2], octal [base 8] or hexadecimal [base 16]. Ultimately it is arbitrary what number base is used in any context. I have often thought that, for everyday purposes, base 12 might be handy, but I cannot imagine people accepting the change. If you can move all your fingers and thumbs independently [I cannot do that], you can count in binary. That means that you can count up to 1023 on your fingers or up to 31 with one hand]. Neat trick eh?
I have got caught out with numbers from time to time. A few years ago, I was doing a seminar in Israel. Before the event, the technician was setting up the PA. He was walking around the room with the mike saying three words in various combinations. Being curious, I asked him what they meant. He answered: “One. One, two. One, two, three.” So, I can now say hello/goodbye and thank you and count to three in Hebrew.