U is for Usury

German woodcut of Italian bankers. Photo from medium.com

Usury was denounced by the Catholic church in the Middle Ages, a potential route to heresy and excommunication. But royalty, the church, and the merchants needed bankers. The bankers found ways around restrictions. The Medici thrived on banking, but it proved to be their downfall, or their rise depending on how you look at it. Lending to people in charge seems to have an inherent risk, usury or not.

Criminal Interest

Usury is defined as charging an “exorbitant” interest according to Webster’s. But there’s that third dictionary definition, listed as Obsolete. Usury was once defined as charging any interest at all. It varied with the century.

There were banks in Rome, which might charge from 5-12% interest. There were banks in the 6th century Byzantine Empire, because Emperor Justinian set loan rates, which varied by the venture: 4% for “exalted personages,” 7% for business loans, and 12% for maritime loans. The Council at Nicea centuries earlier had banned interest but for clergy, not everybody.

Yet a few centuries later, between the time of Charlemagne (750 CE) to the Black Death (1350), usury was more strictly banned. First, the Catholic church said that usury was banned to everybody, that you could not have a transaction where more was returned than was given. Even in a simple transaction, like selling a cow, the farmers had to find a just price, where they would only receive what it cost.

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S is for Summa di Arithmetica

Pacioli also created a font. This Majuscule seems especially appropriate.

Having just spent the past two months analyzing a 1494 accounting textbook, it seems natural to devote one my alphabetic letters to the greatest math teacher of the Renaissance age–Luca Pacioli. I stumbled upon him and his work last year for the letter “P,” so I’m not going to rehash his biography.

Luca Pacioli woodcut from Summa, his 1494 600-page math textbook.

Nor will I tell you the secrets of my 35-page treatise on how this chapter on double-entry bookkeeping for Florentine wool merchants reveals their pious contract with heaven and the Catholic church. Feather Beds and Jesus may just be my next book, who knows? What I will talk about is why this work was so revolutionary, despite accusations of plagiarism and critics calling it of “little or no value.” Boo on them!

Free the Numbers!

If numbers give you a headache, I apologize in advance. But we have to talk about numbers. Perhaps you aren’t crazy about multiplying large numbers, like 9876 * 6789. That’s what calculators are for. Now imagine that it’s the year 1490 CE, and you’re still using Roman numerals, and you don’t have a calculator. You have to multiply IXDCCCLXXVI * VMDCCLXXXIX. Can you imagine? There were, apparently, ways to multiple Roman numerals that involved writing them in columns, doubling and halving, then crossing out odds and evens. You would be desperate to find an easier way. Welcome to Hindu-Arabic numerals.

Pacioli’s explanation on how to multiply 9876 & 6789, from Summa.
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Z is for Zero

The Hindu concept of zero, the void, the circle. Graphic from pparihar.com.

A circle is an infinite number of points all equally distant from a single center. That definition came from Euclid, a Greek, although the Greek’s didn’t use zero. Aristotle was afraid to divide by the void because it wasn’t descriptive of the real world.

The Chinese and the Sumerians used placeholders in their counting, adopting different marks for the tens and the 60s digit, since Babylonians used base 60. But they didn’t have a zero.

The Mayans had a zero–they used base 20–which allowed them to produce large astronomical calculations that generated accurate solar and lunar calendars using only sticks. But their isolation prevented trade, which limited their civilization.

The Romans had zero, of course! Nulla. The Romans had sophisticated plumbing and developed roads that lasted for millenia. But Romans disdained to use nulla in their numbering systems, so even though their business records were hierarchical and detailed, they were limited. Growth is limited if a number like 397,654 is CCCXCVMMDCLIV.

The Arabs developed zero; they developed algebra. But the Arabs learned it from the Hindus.

Graphic from Pparihar.com.
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