The Mystery of Roman Numerals, or Why Your Watch Says IIII

Look at a Roman-numeral clock, a real one, the kind you find on a railway station or an old church. Stop at the 4. You will almost never see IV, the form they taught you at school. You will see IIII. Four strokes in a row, like a child counting on their fingers. That small detail has driven people mad for centuries, and nobody has a definitive answer. We will get back to it, promise.

First, let us start the system up again, because it is cleverer than it looks.

Seven letters to write everything

The Romans had only seven symbols: I is 1, V is 5, X is 10, L is 50, C is 100, D is 500, and M is 1000. Everything else is built by stacking or subtracting.

The basic principle is addition. You lay the letters out from largest to smallest and add them up. VIII is 5 plus 3, so 8. MDCLXVI, if you take each letter in descending order, gives 1666, the year of the Great Fire of London and a rather neat way to remember it.

The trick is subtraction. To avoid lining up four I's or four X's, you place a small symbol in front of a larger one to say "take this away". IV is 5 minus 1, so 4. IX is 10 minus 1, so 9. XL is 40, CM is 900. It is elegant, it shortens the writing. 1999 becomes MCMXCIX, which looks like a number plate but stays readable once you have the knack.

One little rule of the game, often forgotten: you only subtract with I, X or C, and only in front of the two rungs just above. I goes only before V and X, never before L or C. So 49 is written XLIX, not IL, tempting as that shortcut is.

The black hole: no zero

Here is the real dizziness. In Roman numerals, zero does not exist. No symbol for "nothing". And this is not an absent-minded oversight, it is a way of seeing the world. To count sheep, soldiers or amphorae, you do not need to write "zero sheep". You look at the empty pen and the matter is settled.

Zero as a fully-fledged digit, the one that holds a place inside a number and changes everything, comes to us from India, then passed through the Arab world before reaching Europe in the Middle Ages. It is what makes the magic of position possible: in 205, the 0 shouts "there are no tens here", and without it you would confuse 25 and 205.

Roman numerals, on the other hand, know nothing of position. An X is worth 10 whether it sits at the start or the end, it carries its value stuck to its skin. Handy for carving a date on a monument, far less so for keeping accounts.

Why nobody did sums with them

Try setting out a multiplication the Roman way. Take XXIV times LVII. You have no column to line up the units, no carry to bring down, nothing. The system describes numbers but refuses to handle them.

So how did they manage? They did the maths on the side, with their hands or on an abacus, a counting board where each row stood for the units, the tens, the hundreds. Fingers and pebbles did the work, the letters were just there to record the result. The word "calculate" comes from the Latin calculus, which means a little pebble. The Romans literally reckoned with pebbles.

That is why the move to so-called Arabic numerals, around the end of the Middle Ages, was a quiet revolution. Suddenly merchants and bookkeepers could add on paper instead of lugging a counting frame about. Arithmetic climbed down from the counting board and into the pen.

So, IV or IIII?

Back to your watch. Theories abound, none commands agreement, and it is almost more fun that way.

The most seductive one talks of visual balance. On a dial, IIII sits opposite the VIII on the other side, two nicely weighty blocks answering each other, whereas a thin little IV would break the symmetry. Another invokes Jupiter: in Latin the god was spelled IVPPITER, and carving IV on an everyday object would have seemed cheeky, rather like writing the first letters of a god's name on the kitchen clock. There is also a tale that a king of France, irritated, ruled in favour of IIII, but the story smells of a legend patched together after the fact.

The likeliest truth is more down to earth: clockmakers liked IIII because it made the dial more regular to build and to read. Tradition did the rest, and nobody ever dared touch it.

Next time you pass an old clock, glance at the 4. If there are four strokes, you will know it is not a mistake, but an old craftsman's whim that twelve centuries have failed to correct.