Roman Numerals
Roman numerals were essentially a shorthand form of counting with fingers or notches on a stick: Useful for keeping a record of countable quantities, such as the number of sheep in a flock.
However, it was an inherently inefficient numbering notation prone to creating very long scripts and very difficult for use in mathematical operations.
As society advanced there was a growing need to describe increasingly large numbers; partly resolved through some “tricks” of shorthand notations.
In the western world, the step change to a better (middle-eastern) system only occurred in 1202.
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Through the ages Roman numerals have often been employed to mark dates or page numbers on books, monuments and buildings. We are literally surrounded by plenty of examples.
They were utilitarian in nature, just like the Romans. The purpose of Roman Numerals was to be able to record numbers and do simple arithmetic, just as you might do with an abacus – this was clearly essential to a nation which was so commercially oriented.
Modern numbers as we know and love them, including the number “0” are a medieval Arabic invention brought to Europe by the mathematician Fibonacci in 1202. After the Roman Empire the Middle East grew to be a great centre of scientific investigation and knowledge and pure mathematics was evidently essential. Basic arithmetic with unwieldy roman numerals is sufficient to undertake the amazing feats of ancient roman building and civil engineering such as the roman aqueducts. However they were relatively poor for advanced arithmetic or more evolved mathematics.
Roman numerals were written as a set of basic symbols governed by rules of addition and subtraction.
The numerals themselves were drawn from what you might see if you counted on your fingers: lines (letter “i”) to denote fingers and a “V” to denote an open hand. Two V’s make an X = 10 fingers. Larger multiples had their own capital letters stemming from the actual name of the number.
The various symbols were combined according to a few relatively simple rules of addition and subtraction in order to make up larger numbers. For example, 3= iii but 4 = iv. You can see that “one” short of the next lettered multiple is denoted by a simple effort of subtraction. This allows you to keep the roman numerals as short as possible. 9 = iX ie one short of 10.
The number 8 on the other hand would be made up of the largest symbols available: 5+3=viii. Just to give a last example, 50 is denoted by the letter “L”. 49= iL NOT XXXXiX and 45 would be VL. If C=100 then 90=XC, 95=VC and 99=iC. ie keep the roman numerals number as short as possible.
How did Roman numerals develop over time?
The Roman numbers symbols we commonly know were not the earliest forms used: Older forms were not related to the alphabet at all and gradually modified, starting from archaic versions of notches on a stick or fingers on a hand.
The larger number forms ‘L’, ‘D’, ‘M’ of the numbers 50, 500, 1000 are from around the 1st century BC only! ie >700 years later than the earliest founding of Rome by Romulus. The earliest ‘D’ & ‘M’ number forms date to an inscription in 89BC (CIL IV 590). The earliest ‘L’ equivalent to the number “50” is found in an inscription (CIL I 594) from 44BC in a law written out under the authority of Marc Anthony (and Julius Caesar) on bronze plaques found in Spain. Not surprisingly it relates to Roman trade and maintaining financial accounts.
“Quot cuique negotii publice in colonia de decurionum sententia datum erit, is cui negotium datum erit eius rei rationem decurionibus reddito referto que in diebus CL proximis quibus it negotium confecerit quibusve it negotium gerere desierit, quot eius fieri poterit sine dolo malo.”
Loosely translates to:
“Should the decurions grant any person the right to public trade in the colony, such person will maintain and make trustworthy accounts available to the decurions within 150 days of the business’ completion”
For a complete list of roman numerals have a look at the Roman Numerals Chart.
Going the extra mile towards larger numbers
The Roman Numeral system was obviously pretty unwieldy and an evident shortcoming of it is the lack of simple means of defining larger numbers, possibly suggesting that the Romans had little need for such large arithmetic. God knows how they managed to undertake those amazing feats of engineering! (Probably through geometry).
As Roman society developed it also required increasingly large numbers to be recorded. A number of means were devised to define larger numbers.
Various methods were available for large numbers, some also involving multiplication:
1) Pure multiplication of smaller units and thousands. For example VIM stands for 6000.
2) Multiplication by 10, achieved by enclosing within brackets. 10,000 would therefore be (M). Just to confuse you, the number 5000 could even be written D) rather than (D)
3) Multiplication of a number by 1000 by placing a bar across the top of the number. Eg 5000 would be V with a bar across the top. It’s my favourite for simplicity.
4) There were a variety of commonly accepted symbols for larger numbers:
This page was first written in MMVI.
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