Roman Numerals…not quite so simple

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Happy New Year!  And since the New Year is all about numbers (especially if you have come to look forward to Denise’s annual January 1 post on Let’s Play Math:  form all the integers from 1 to 100 using (exactly) the digits 2, 0, 1, 1 and common mathematical symbols), here’s a picture of a number that I meant to post in October November December.

LIIII

Recognize this number?  Even though it’s not written as LIV?  This is from the 54th entryway to the Colosseum in Rome, which was built almost 2000 years ago when Roman numerals didn’t always use the subtraction property that we’re taught, where 4 is written as IV instead of IIII.

I found that to be interesting in and of itself, since I’d heard that the subtraction was a later addition but never witnessed it.  But what’s weird?  It wasn’t a sudden change.  Here’s the forty-fifth gate:

XLV

The subtraction principle was used with 40, just not with 4.  Which leads to a natural question:  what about gate 44?

XLIIII

I’m bummed that we didn’t get a better picture of this, but you can kind of see all four Is after the L.  Apparently, according to our usual font of knowledge, the reluctance to use IV is because that was the standard abbreviation for Jupiter’s name in Rome (IVPPTER), and this mixture of sometimes using four symbols in a row continued for more than a thousand years:  in the 1390 English cookbook The Forme of Cury (here on Project Gutenberg) the author still uses IIII [as in the Table of Contents, where Section IIII is rapes in potage] and there are also some IV for section numbers and references to Edward, though those might be later additions.

Published under GNU-FDL

And even 100 years ago [last year, in 1910], the Admiralty Arch in London uses MDCCCCX instead of MCMX in the inscription

ANNO : DECIMO : EDWARDI : SEPTIMI : REGIS :
: VICTORIÆ : REGINÆ : CIVES : GRATISSIMI : MDCCCCX :

(In the tenth year of King Edward VII, to Queen Victoria, from most grateful citizens, 1910).

So what does all this mean?  Nothing much, except that Roman Numeral Rules were maybe not quite as hard and fast as I once believed.

12 Responses to “Roman Numerals…not quite so simple”

1. Berislav Lopac Says:

http://en.wikipedia.org/wiki/IIII#IIII_and_IV

2. 24hourtime Says:

Cool post. I’ve noticed little consistency in the use of numerals in the clocks I’ve been collecting at 24hourtime.info. If you look at the Europe page, it seems that additive only was the main standard in Venice. perhaps they all copied each other …

3. RevJATB Says:

I have always had Roman numeral wristwatches ever since I’ve been able to tell time. I just think they look nice. Every watch I’ve owned in my life has used IIII for the number four. And none of them have been antiques.

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5. Mandelbrot Video « 360 Says:

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6. Ξ Says:

It never occurred to me that clocks would have IIII; I think all the ones I’d seen have had IV, although now I’m questioning my memory of that. Maybe I just assumed it. In any case, I really like seeing all the examples at 24hourtime, so thanks!

7. Alan Says:

There is a very simple reason why ‘IIII’ is used and not ‘IV’;
quite simply the Romans did not EVER subtract in their numbers, irrespective of order, everything was always added;
it is a (relatively) new invention the idea of subtracting “roman” numbers.

Subtraction of numbers is correctly called “French Roman Numbers” because the idea of subtraction of these numbers was first invented by a French clock maker (forget the date – long time ago) who was having trouble fitting ‘VIIII’ in the position for 9 – so he decided to improvise. As clocks were publically displayed in town centres during the past 500 or more years people have simply become accustomed to this way of thinking of roman numerals – it was never how these were first used.

The Admarlty Arch in London is written correctly… not that many people now-a-days would realise that.

8. Ξ Says:

Alan, I don’t think it can be correct that the Romans didn’t ever subtract, because the carvings in the archway *do* show subtraction for 40 (written as XL) — it’s clear that it’s 40 and not 60 just from the location of the doors. That’s actually what I found so interesting, that they used subtraction in some cases, but not for all the cases that we use it today.

9. Weekend miscellany — The Endeavour Says:

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10. Scorpius Says:

Ref this site for a pretty good explanation of how the Romans generally used their number system, and how it has been inconsistently used over the centuries.

http://www.web40571.clarahost.co.uk/roman/howtheywork.htm

11. J Says:

The IVPITER explanation seems to have been dropped from Wikipedia, presumably due to a lack of any reliable citation for that explanation.

12. Alex-Constantin Brodoceanu Says:

they should have wrote MCMX instead