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By Root 673 0

world, did not share the Indian hunger for jumbo numbers. The highest-value number word they had was myriad, meaning 10,000, which they wrote as a capital M.

Roman numerals were also alphabetic, although their system had more ancient roots than those of either the Greeks or the Jews. The symbol for one was I, probably a relic of a notch on a tally stick. Five was V, maybe because it looked like a hand. The other numbers were X, L, C, D and M for 10, 50, 100, 500 and 1000. All the other numbers were generated using these seven capital letters. The Roman system’s provenance from the tally stick made it a very intuitive way of writing out numbers. It was also efficient – using just seven symbols compared to 22 in Hebrew and 27 in Greek – and Roman numerals were the predominant number system in Europe for well over a thousand years.

Roman numerals, however, were very poorly suited to arithmetic. Let’s try to calculate 57×43. The best way to do this is with a method known as Egyptian or peasant multiplication, because it dates back at least to ancient Egypt. It is an ingenious method, though slow.

You first decompose one of the numbers being multiplied into powers of two (which are 1, 2, 4, 8, 16, 32 and so on, doubling each time) and make a table of the doubles of the other number. So, for the example 57×43, let us decompose 57 and draw up a table of doubles of 43. I’m using Arabic numerals to show how it’s done, and will translate into Roman numerals afterwards.

Decomposition: 57 = 32 + 16 + 8 + 1

Table of doubles:

1×43 =

43

2×43 =

86

4×43 =

172

8×43 =

344

16×43 =

688

32×43 =

1376

The multiplication of 57×43 is equivalent to the addition of the numbers in the table of doubles that correspond to amounts in the decomposition. This sounds like a mouthful but is fairly straightforward. The decomposition contains a 32, a 16, an 8 and a 1. In the table, 32 corresponds to 1376, 16 corresponds to 688, 8 corresponds to 344 and 1 corresponds to 43. So, we can rewrite the initial multiplication as 1376 + 688 + 344 + 43, which equals 2451.

Now for the Roman numerals: 57 is LVII and 43 is XLIII. The decomposition and the table becomes:

LVII = XXXII + XVI + VIII + I

and

XLIII

LXXXVI

CLXXII

CCCXLIV

DCLXXXVIII

MCCCLXXVI

so,

LVII×XLIII = MCCCLXXVI + DCLXXXVIII + CCCXLIV + XLIII = MMCDLI

Oof! By breaking down the calculation into digestible morsels involving only doubling and adding, Roman numerals are just about up to the task. Still, we did much more work than we needed to. I mentioned earlier that the Roman system was intuitive and efficient. I’m taking that back. The Roman system quickly becomes counter-intuitive since the length of the number is not dependent on value. MMCDLI is larger than DCLXXXVIII, but uses fewer numerals, which goes against common sense. And any efficiency gained by using only seven symbols is forfeited by the inefficiency of how they are used. Often long strings are required to signify small numbers: LXXXVI uses six symbols, compared to the Arabic equivalent, 86, which uses two.

Compare the calculation above with the method of ‘long’ multiplication we all learned at school:

There is a very simple reason why our method is easier and quicker. Neither the Romans nor the Greeks or Jews had a symbol for zero. When it comes to sums, nothing makes all the difference.

The Vedas are Hinduism’s sacred texts. They have been passed down orally for generations until being transcribed into Sanskrit about 2000 years ago. In one of the Vedas a passage about the construction of altars lists the following number words:

Dasa

10

Sata

100

Sahasra

1000

Ayuta

10,000

Niyuta

100,000

Prayuta

1,000,000

Arbuda

10,000,000

Nyarbuda

100,000,000

Samudra

1,000,000,000

Madhya

10,000,000,000

Anta

100,000,000,000

Parârdha

1,000,000,000,000

With names for every multiple of ten, large numbers can be described very efficiently, which provided astronomers and astrologers (and, presumably, altar builders) with a suitable