# How many?

By Colin Walls

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.

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• Dan S says:

You mentioned German. Although not a native speaker, I know enough to be dangerous…

German is interesting in that a number like 24 is said as “4 and 20” (remember “four and twenty blackbirds”?) To my native German-speaking wife that sounds perfectly normal, and to my bi-lingual daughters either the English or German approach sounds normal. But once you get over 100 in German, e.g. 224, the number would be “two-hundred four and twenty”. So it goes biggest-smallest-middle. Once you do it a lot it’s not so hard.

And the billion/million thing, also in German. In German, a million is the same (10 ^ 6), but a billion is (10 ^ 12) – as you’d said, “a million million”. A “milliard” is the German term for (10 ^ 9). When we’re discussing international economies & debts in our household, these orders of magnitude, and the terms we use with each other, become important. My billion is not my wife’s billion.

Last thing – dates. I’m one of the few Americans who writes all dates like 2011-11-03, always with the 4-digit year format. The typical American 11/03/11 can be confusing to some, especially when dealing with international customers. Of course you can remove all doubt by writing “November 3, 2011” when it’s critical.

• Fair comments Dan. I agree about German, but at least they’re consistent. I mainly use numbers in German for ordering beer, so I rarely get far into double figures [I don’t have that many friends!]. In Old English, I believe that numbers were different. There is a children’s song in which “four and twenty blackbirds were baked in a pie”.

I am with you on dates. I write them “readable and unambiguous” – i.e. 3 Nov 11, 3-nov-11, 3 November 2011 – or sortable and unambiguous – i.e. 20111103 – or maybe “sortable and logical if you’re smart” – i.e. 111103. I blogged about this a while back: https://blogs.mentor.com/colinwalls/blog/2010/09/16/what-date-is-it/

This article first appeared on the Siemens Digital Industries Software blog at https://blogs.sw.siemens.com/embedded-software/2011/11/03/how-many/