The tangled web of historical numeracy

By the Numbers: Numeracy, Religion, and the Quantitative Transformation of Early Modern England by Jessica Marie Otis.  Reviewed by Jay Hancock.

Why did some countries become wealthy after 1800? Historians argue about the relative influences of religion, climate, geography, slavery, colonialism, legal systems, and natural resources. But the key, famously shown by economist Robert Solow, who died in December, is technological innovation enabling more and more goods and services to be produced per worker and unit of capital. Innovation needs research, development, and engineering. All those require numbers and numeracy.

In the 1500s, the English began realizing that Arabic numbers, with place values and a zero symbol, are better for calculating than other methods. (Try adding up hundreds of fleeces and sacks of wool with Roman numerals.) But old habits persist. Otis goes into 16th-century account books and finds Roman notation for fixed quantities on the same pages with Arabic marks used for summing. The English used Roman numerals, tally sticks, and counting discs long after priests took up Arabic numerals to indicate the number of years since Christ was born.

People needed to learn the new “arithmetick.” But universities were busy teaching ancient Greek. Textbooks, paper, and even literacy were rare. From 1500 to 1700, however, math books and “cyphering schooles” multiplied. Lessons dropped Roman numerals and took up compound interest and decimal fractions. “Arithmetic” became synonymous with Arabic numbers.

Part of the change, explains the author, involved a retreat of religious fatalism. Once probability calculations started showing that gambling outcomes were not random, clergymen argued about whether God was still in charge. “Yes, but…” was the answer. At the same time, people got over the idea that national censuses were like King David’s sinful “numbering of the people” in the Bible. The English were already used to local parish registers. The stage was set for demography and population-data analysis.

Arabic numerals were so embedded in the commercial system by 1700 that it “would go near to ruine the Trade of the Nation” if merchants had to revert to Roman numerals, tally sticks, and other older systems, Otis quotes a Scottish physician and mathematician as saying. Like all good historians, though, she cautions readers against modernity bias, in this case assuming that Arabic notation seemed any more familiar to most early-modern Europeans than, say, Norse runes look to people today.

Sounds like an interesting book.

I have perhaps half a dozen or a dozen books on the history of numeracy which I find deeply interesting.  Reading, writing and arithmetic being the foundations of modernity.  

But sometimes you can know something without knowing it.

I do plenty of genealogical research and since a good portion of my ancestry came over as pilgrims and Puritans (1620-1640) they are smack in the middle of that transition Otis is discussing from Roman numerals to the Arabic numbering system.  

I have for some years been reading wills from 1630s onwards in which worldly chattels are spelled out and enumerated.  10 pigs, 20 sheep.  In some wills, it is quantities of things.  In others, it is quantities and values - 20 sheep worth 8 shilling 3 pence.  

And in all those years I never gave a thought to the fact that the implication is that the Pilgrims and Puritans who arrived in the American settlements were not only disproportionately literate (as they were) but that they were also apparently disproportionately numerate.  It is even possible that they had stolen a base and were already fully inculcated into the new numbering system and unencumbered by the challenges of Roman numerals.

I do not recall ever seeing Roman numerals in these early wills but I would not have been looking because I didn't even think to look.  

And now that I am thinking about it, I sort of suspect that some dates might have been rendered in Roman numerals but I am pretty certain I do not recall seeing any enumeration or calculation in Roman numerals.

I'll have to keep my eyes more open in the future.

But it is one of those challenges that end up biting you.  I knew the history of numerical writing transition and I knew the history of the Pilgrims and Puritans.  And I never linked the two conceptual categories together.