Roman Numerals | | DJS

Roman Numerals

Roman numbering is still used in the 21st century for indicating dates in films and books. it exists on the face of some clocks. This system is interesting for combining two aspects of counting forwards and backwards but at the same time it has no regard for the resulting length of a number in terms of counting characters. Yet underneath it remains a base ten system.

Basic characters are one and five, thence ten and fifty, hundred and five hundred, thousand. In order, I,V, X,L,C,D,M.

Numbers start off in base one; I, II, III. Four could be IIII but is usually shown as IV, ‘one less than five”

Around the value of ten we have VIII, IX, X, XI, XII; rising to near fifty we have, similarly, XLVII, XLVIX, XLIX, L. You might expect forty-nine to be IL, but here is an implicit rule that left-placing a smaller character can only be done with the adjacent letter in the series. Similarly forty-five is NOT VL but XLV, ninety-five is XCV not VC. The typical number IX, subtracting one from ten, is called the subtractive form.

For those who think all of this is way too easy:


1.  What is the longest (most characters used) in numbers less than a hundred?

2.  What comes before one?  Can you do fractions?

3.   What numbers are meant by (i)  EIX  (ii) HII (iii) FII  (iv) ZXL ?

Either show off that you know this ("Well done!"), go find out,  read on —or use a combination of those actions.

Quite clearly the Romans did not have a standardised approach. Even if Rome made a decree, the time for any new ruling to spread across the empire would be measured in years. It is not hard to find examples in which four identical adjacent characters are used—many clocks show four as IIII)—so nine and forty might be written VIIII and XXXX. Admiralty Arch in London (says Wikipedia) shows 1910 as MDCCCCX, (not MCMX as we would now).

In an old dictionary I found reference to the use of other letters and I remember discovering back in the early 70s that N was 90 and P 400. Research is much easier with the wonderful internet and I record the usable medieval (Middle Ages) characters F 40; R 80; N 90; Y 150; H 200; E 250; B300 P (or G) 400; Z 2000. The wikipedia article explains a little more.

I think it is self-evident that a V represents an opened hand. Similarly L and C are shapes easily made with hands. I imagine a real need to be able to communicate numbers across a distance that could not be shouted, such as a noisy market.

To indicate fractions a collection of dots was used, generally counting twelfths, with S for 6/12. Thus S: was "six plus two twelfths", 8/12 or 2/3. Here subtraction was not used. four dots could be in row or square, so :: would be 4/12 = ⅓. Where five dots were needed they were arranged as on a die, ⁙, called a quincunx.

To represent large numbers there were two systems:

(i)   the vinculum simply puts a continuous line above the number to multiply by a thousand  īṽ = 4000  ī = 6000  (hard to type).

(ii)  the apostrophus used C shaped brackets, with the reversed form Ↄ to indicate more zeroes.

   I❩ = IↃ = D = 500,             I❩❩ = IↃↃ =  ↁ = 5000,             I❩❩❩ =  IↃↃↃ = 50000,

   ❨I❩ = ⅭIↃ = ↀ =1000,     ❨❨I❩❩ = ⅭⅭIↃↃ = ↂ =10000,     ❨❨❨I❩❩❩ = ⅭⅭⅭIↃↃↃ = 100000.   

   It is suggested that D followed on from I❩ and that M followed on from ❨I❩, which I find entirely plausible,    though I wondered whether 𝚽 (capital phi) was in use at the time.

DJS 20151211

Typing issues 

Those interested in the problems of typing these characters are directed to unicode characters 2160 to 2188.    Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅶ Ⅷ Ⅸ Ⅹ Ⅺ Ⅻ Ⅼ Ⅽ Ⅾ Ⅿ       ⅰ ⅱ ⅲ ⅳ ⅴ ⅵ ⅶ ⅷ ⅸ ⅹ ⅺ  ⅼ ⅽ ⅾ ⅿ     ↀ ↁ ↂ Ↄ ↄ ↅ ↆ

where ↅ  is a late form of six  and ↆ an early form of fifty. Another excellent wiki article here. [And yes. I have supported them with money again this year].

Here’s a quincunx ⁙    Unicode  U+2059.

⚄ U-2584  ⁙  U2059    ⵘ U2D58

There’s a very similar system counting with rods, sometimes called the Suzhou counting rod system (Suzhou, Jiangsu, west of Shanghai, city of canals and biting insects). Characters in rows 1D360 and 1D370:

𝍡 𝍢 𝍣 𝍤 𝍥 𝍦 𝍧 𝍨     𝍩 𝍪 𝍫 𝍬  𝍮 𝍯 𝍰 𝍱    these count from 1 to 9 in the vertical and horizontal forms


1.   38 is XXXVIII, 83 is LXXXIII but 88 is LXXXVIII, eight characters long

2.   We can dispute whether anything comes before one. Read about zero, and its several uses as a character. Placeholder? Integer? I think we might credit Brahmagupta with the integer, who wrote long after Rome had collapsed as an empire.

3.i)    EI = 251     (ii)   HII = 202      (iii) FII = 42      (iv) ZXL = 2045

Fun that breaks the rules: A seen as V upside-down and still a five. Add to those shown above O=onze=11, S=seventy rather than a half, T=160 (four forties?) and Q=D=500.

HAVVAII   200+4x5+2 = 222

QVEBEC  500+5+250+300+250+100=1405

NEVVCASTLE = 90+250+5+5+100+5+160+50+250=665

BRISTOL = 300+80+1+70+11+50 = 512

NY = 90+150=240 or perhaps -90+150=60 since these characters are adjacent in the longer medieval list

BRITAIN = 300+80+1+160+5+1+90=637

Go on, find some names that do fit the rules!  If we stretch to allow IC=99, VC=95, IL=49 then IS=69 AN=85, IN=89, IR=79, IB=201, IP=399, VP=395, AQ=496 and so on. We might use the overline (or underline) to shift numbers to the left and so generate 4-letter combinations, such as IRAN = 7985 (two underlines on the IR) and IRAQ = 79496 (three underlines needed); but in area Iran is 4x bigger than Iraq. Have fun!!

LIRA=51085,   RAIL=85049,  NYNY=60060,   MANIC=1085099

I’ve mentioned elsewhere that Rome’s most famous town crier, he who shouted out the trivia posted at the crossroads, and aware of the famous Socrates, Aristophanes, etc. was a Greek by the name of Radiotimes. [Radd ee ohh ti meez] Of course he was.

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