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How clever were the Romans?

24 August 2021

I was chatting with a friend this morning and during that conversation I began to realise just how clever the Romans were.

Allow me to elaborate...

We are all familiar with numerics, arithmetic and the representation of quantitative values by way of numbers.

Those of us who've done any amount of low-level computer programming are also familiar with using different bases to represent numbers. Digital systems use binary (base 2) and because of this we also sometimes use hexadecimal (base 16) to represent values when programming.

Once you wrap your head around it, using different bases for numerical representation is pretty simple stuff and the key to most of this is the use of columns to represent orders of magnitude (powers) of the base being used.

Unless you're using Roman numerals to represent values.

The use of Roman numerals (RN) to represent numeric values is fascinating.

The most obvious omission from the RN system is that there is no symbol for zero.

Perhaps the Romans wanted for nothing and had at least one of everything?

Sadly, no and eventually they figured out the omission and began to use the word "nulla" (Latin for "none") to represent a value of zero.

However, because the RN system is not column-based, there is no need for a zero, other than to denote the total absence of something. By comparison, the zero in our column-ordered represntative systems is used as a place-holder and thus is essential.

Obviously the RN system has huge deficiencies when it comes to any attempt to perform maths on the values represented by it -- but it really wasn't designed as part of a mathematical system, that's what systems based on column ordered powers of the base are designed for.

However, despite its drawbacks, the RN system is still alive and well today in some niches. Check out the copyright notice at the end of many movies and TV shows for instance, and you will find roman numerals are still used extensively. Why?

Well I googled for some info on this and found nothing particularly convincing.

Some references indicated that it was just a fashion at one stage and that style has persisted so as to create a consistency across the decades.

Other sources suggested that it was so that stupid (non-RN-literate) people wouldn't figure out that the material they were watching was much older than they might otherwise assume.

To be honest, the most engaging part of some of the movies and TV shows I've watched recently has been the challenge of decoding the copyright date shown in RN for just a brief second or two at the end of the credits.

Here are questions for readers: How familiar are YOU with the RN system? Can you read even complex RN values in the blink of an eye, or do you have to sit down and work it out? Do you know the values for all the RN symbols such as I V X L C etc?

Ah... isn't amazing what idle minds will come up with during a lock-down :-)

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