Look up at an old clock face and the Roman numerals seem completely at home. Their upright strokes hold the circle together; V opens like a small vessel; X makes a perfect crossing. They look deliberate, almost architectural. Yet place the same symbols in a merchant’s account book and ask them to carry a multiplication across the page, and their dignity becomes resistance. The marks are not wrong. The merchant is not incapable. The difficulty lies in a quieter mismatch: a notation made to preserve a number is being asked to help transform it.
One system for recording, another for reckoning
In the Fifth Great Lesson, Roman numerals offer a wonderfully tangible pause. Children already know some of them from clocks, book chapters or the names of rulers. I, V, X, L, C, D and M have travelled through many centuries because they are robust signs. A mason can cut them into stone. A copyist can repeat them. A merchant can recognise a familiar total at a glance. Long after the Roman Empire itself had gone, European traders continued to use these letters in records and labels. A useful convention does not disappear merely because a cleverer one exists somewhere else.
But Roman notation has no place value. The X in XX does not change its value because it stands in a different column, and there is no written zero holding an empty place. To add two Roman totals on paper, one can collect symbols, exchange five I’s for V, two V’s for X, and continue regrouping. It can be done. Subtraction, multiplication and division can also be done. What becomes tiresome is keeping the intermediate steps visible and orderly, especially when prices, weights and debts accumulate across a busy day.
The answer was often not a different mind but a different surface. On a counting board or abacus, pebbles and counters occupied lines for units, tens, hundreds and thousands. Their positions carried the value that the written letters did not. An empty line could remain empty without needing a numeral of its own. Counters could be moved, grouped and exchanged while the hands followed the calculation. When the work was finished, the result could be copied back into Roman signs for the ledger.
Imagine that merchant at a wooden table. On one side lies a permanent record: M, X and V, inked carefully so another person can read it later. On the other side lies a temporary model: loose counters that are continually shifted and cleared. One remembers; the other thinks. The two together form a complete technology. Calling Roman arithmetic impossible would miss the ingenuity of the people who made it work every day.
When the page itself learned to calculate
This distinction changes the usual story of “bad old numerals” being defeated by “good modern digits”. Roman numerals were exceptionally well suited to some purposes. We still choose them when we want a number to feel like a marker rather than an instruction: on a foundation stone, in a volume number, around a ceremonial clock. Their slowness is almost part of their beauty.
Positional decimal notation offered a different gift. With place value and zero, the paper could take over work previously performed by the board. A small set of digits could show not only a final quantity but each stage of an algorithm. Carries could be placed in columns; an empty position could be named; a calculation could be checked by someone far away. As written trade expanded, that portability mattered. The decisive change was not simply from letters to digits, but from a notation that stored results to one that also supported operations.
For a child, this is liberating. Number systems cease to be mysterious rules handed down by a textbook and become human tools, each shaped by a need. Rather than laughing at Roman merchants, we can ask what their tools did beautifully and where another tool served them better. That question belongs naturally in cosmic education: human beings inherit ideas, adjust them and pass them on, rarely noticing how much thought is hidden in the way they write an ordinary total.
Try a two-system market: make three price cards marked IX, XIV and XXVII, and set out dried beans or small counters beside a place-value mat. Let your child choose two goods. First build each price with counters; then combine and exchange ten units for one ten. Record the answer in our digits and, only afterwards, in Roman numerals. On a second round, try to keep every intermediate step in Roman notation alone. Do not race. Ask which surface helped the hands, which notation helped the page, and why a merchant might sensibly have wanted both.
Which tools in your own life are beautiful because they preserve something, and which are powerful because they let you change it? When do we mistake an unfamiliar tool for a foolish one simply because we cannot see the companion tool that once made it work?