I recently bought a T-shirt with the Eye of Horus on it. I really just liked the way it looked, but since I knew people would ask what it meant, I poked around on the internet to find out.
I was surprised and pleased to discover that, in addition to its significance as a symbol of protection, it also had significance in commerce. Specifically, it was a fractional counting system. The eye consists of six pieces, each corresponding to a power of one-half: 1/2, 1/4, 1/8, 1/16, 1/32, and 1/64. All the pieces together add up to 63/64, which the Egyptians rounded up to 1. By drawing different combinations of eye-pieces, the Egyptians could represent various fractions (e.g., use the 1/2 and 1/8 pieces to get 5/8). These fractions were used to measure quantities of land, grain, medicine, etc.
What fascinates me about this is that it was a naturally occurring use of binary, as opposed to decimal, counting. And the Egyptians are not alone in having used such a binary system. The phrase “two bits” for one-quarter of a dollar, for instance, originated in the division of gold dollars into eight pieces; two “pieces of eight” (another old phrase indicative of the binary counting system) equal one quarter.
There’s also a great practical reason for dividing things in a binary fashion: it requires less reference to standardized measures. Try dividing a piece of paper into five equal pieces without using a ruler. Pretty hard, right? But dividing it into four pieces – or eight, or sixteen – is simple. Just keep folding it in half. Halves are easy to compare. For weights, all you need to do is make sure the scales are even on a simple balance. And you can use the balance repeatedly to get any fraction that’s a power of one-half.
So all this was going through my head this afternoon, as I walked to the Subway to get a sandwich, when I suddenly realized: this probably explains why traditional English weights and measures seem so strange. They are, in many cases, binary. In volume, for example, 1 gallon = 4 quarts = 8 pints = 16 cups = 32 gills. (Odd that there’s no specific name for 2 quarts.) [UPDATE: LP notes in the comments that 2 quarts = 1 "pottle," which makes the binary progression complete.] Since the English system evolved in a time when precise standardized measures were hard to come by, it made sense for people to rely on the comparability of halves. The metric system would not have worked well in ancient times. Another interesting parallel: according to this page, before 1824 a hogshead was equal to 63 wine gallons – probably a result of the same rounding that led the Egyptians to say 63/64 = 1.
Was this obvious to everyone but me? Somehow it had just never occurred to me that there was an underlying binary logic to English weights and measures, but in retrospect it makes perfect sense. Of course, this is all speculative, as I know nothing about the actual history of English weights and measures. And there are some things my theory doesn’t explain, such as the presence of twelves (e.g., 12 inches in a foot) and sevens (e.g., 7 pounds in a clove, 14 pounds in a stone). The twelves might have resulted from a willingness to divide things into thirds as well as halves; note that three feet = 1 yard and three hands = 1 foot. But I’m at a loss to explain the sevens. Maybe a real historian could shed some light here.