It’s the guest blogger handling ‘V’ today, a day later than usual…

FIVE!

Given that LLM is over in Italy as I write this post I thought I’d try and do something a bit Roman/Italian-ish. Of course, in the title, I mean the Roman numeral V which represents 5 in that counting system. I was watching a programme on TV recently in which someone had brought an antique grandfather clock in to be valued. The interesting thing was that in the “4” position it had “IIII” and not, as we might have expected, “IV”. They expert guy explained that it was more to do with the aesthetics of the clock face. The 4 position is the mirror of the 8 position and as 8 is represented by “VIII” makers wanted to display the face as symmetrical as possible so used “IIII” as an alternative to “IV”. Now just in case you didn’t realise, with Roman numerals the system is that symbols after V mean you add them on to V and symbols before V mean you take away (“VI” = V + I, “IV” = V – 1); similarly with the other main single letter numbers L (50), C (100) & M (1,000). If you think about it it’s very similar to our own way of representing numbers. If you take 32, for example, we know (but we don’t do it) that it is 30 + the 2 after the 3 and so on. 32 only has meaning because we know what it represents: 2 x 1 added to 3 x 10 meaning there are 32 “things”.

However it got me thinking about the “V”: why didn’t they use “IIIII” for instance? And carry on up to say 10 (their X) the base number of modern counting systems. How did they get from “IIIII” to “V”? It seems there are at least a couple of schools of thought: one, that the V came from an earlier system where 5 was represented by “Λ” and two, that the symbols came from tally stick markings. The tally marks were notches cut into a “counting stick”: “I” meant 1, “II” meant 2 and so on. In this system of cuts in the wood, for a number like 7 you would see “IIII ΛII” cut into the stick. I think you can easily see what could have developed next: once you got a “Λ” mark meaning the 5^{th} item had been counted you didn’t actually need the first four “IIII” because people knew they were kind of included in the “Λ”. Then at some point, whether the Romans themselves introduced it or not, the “Λ” was inverted to become the symbol we know today as five – “V”. Seems plausible to me but I won’t fall out with you if you disagree. And on the back of this there is a view that says when you got to 10 you had two of the symbol “Λ” carved into the stick and by inverting one and placing it on top of the other you got X for 10. Again a bit subjective but I like that one.

One further explanation suggests that way back in the beginning when humans were first developing the idea of counting or giving a value to a group of items they would have used the fingers of their own hands. Hold up your own hand and open the fingers and thumb and what shape is formed by the thumb and first finger – a V shape (although not completely symmetrical as the thumb is shorter). It’s not a great leap to see how by using two hands once you get more than 5 objects you could count up to 10. This also seems very plausible.

And that’s it for “V” is for five.

And finally – if you’re wondering when we stopped using the Roman numerals and started using our modern day 1,2,3,4,5 etc (called Arabic) – it was in the 13^{th} century. The strange thing is that in the purely Arabic system the number 5 looks much like our 0 and 0 itself is represented by a dot ( “.”). (The “V” and “Λ” are 7 & 8 in that system.) The guy who most people believe was responsible for the change from Latin to our current system was Leonardo Fibonacci; his book, in 1202, was called *Liber Abaci* (Book of Calculation). You might recognise his name as many will have heard of the expression “Fibonacci Numbers” named after him; he didn’t actually invent the concept, as it had been previously reported by Indian mathematicians, but gave an example in his book. A Fibonacci number, if you remember your maths lessons, is one which is the sum of the previous two. The start position is usually given as 0 followed by 1. This then generates the series 0,1,1,2,3,5,8,13 etc.