FROM UNITS TO UNITY Author: Guy Snelling Intercal 581 Lupton Drive, Halfway House, Midrand Email: [email protected] Phone: +27 11 315 4321 Fax: +27 86 515 2344 Abstract To the layman, metrologists may seem to be a strange lot indeed. They insist on precision and accuracy, not only in their measurements but also in every part of their work. They must know the exact value of a measurement and then they calculate by how much they don’t know the exact value! To call them ‘pedantic’ would be like calling William Shakespeare ‘that bloke that wrote a bit’. But then ask a Metrologist about the origin of the measurements he or she is making and they will spout forth about famous scientists like Kelvin, Watt and Ampere. They’ll tell you all about the SI Units and the inter-relationship between the seven base units and how the French put together the metric system. But then ask them to go further back in time and things start to get a little hazy. Ask them about some of the lesser known units of measurement, such as the ‘shake’, the ‘jiffy’, the ‘micromort’ and even the ‘quasihemidemisemiquaver’ and they will be looking for the nearest escape route or at the very least, the nearest stiff drink. In every field of science, it is often good to go back to the basics. We can get so wound up in all the theory that we sometimes need to sit back, open our minds and re-live the past in order to bring understanding to the present. This paper will take a look back over the eons to a time before metres, litres, minutes and miles. To a life dictated by the length of an arm and a foot; to food sold in baskets and beer sold in caskets and to a period where you slept when it was dark and ate when you were hungry. We will discover how rudimentary measurements were made and how they were refined into the units and standards that we know (and love) today. Join me on a journey through time, itself only an arbitrary measurement, and discover the roots of our ancient profession. The Ancients Everyone knows that the Egyptian pyramids are built to a precision that is difficult to match even today, but at around the same time other cultures were also building vast monuments; the Mayans were building their version of the pyramids in South America; the Nabataeans built the desert cliff city of Petra; the Neolithic inhabitants of early Britain fashioned slabs of rock into the 50-ton sarsen stones of Stonehenge and further North the Scandinavians built their burial cairns. Whatever the size and shape of these vast monuments, they all have one thing in common; they needed precise measurements to build them. Precise measurements of course needed a system of measurement consisting of some kind standard artefact as well as a divisible unit. A good ancient example of this is the Egyptian “cubit”. Traditionally this was based on the length of the prevailing Pharaoh’s forearm and was sub- divided into “palms” and “fingers” and “digits”. It should be noted that other cultures such as the Greeks, Romans and Hebrews had similar units of length also called the cubit along with the Chinese chi, the Japanese Shaku and the Indian hasta. Such standards of course are of little value unless their length can be transferred to secondary and working standards. After all, one cannot expect the great Pharaoh of Egypt to visit a half completed Pyramid to check the measurements with his arm. Thus calibration was invented and the Egyptian workers were required by law to present their working cubit to their supervisor once a month for calibration against a standard cubit. Failure to do so was punishable by death, which may seem severe but there are a number of QA managers in industry even now that wish that the law could be re-instated. Looking further into the measurement of length, we find more references to the human body. An obvious one is the “foot”, although this was not based on the length of the Pharaoh’s foot but is believed to be a multiple of fractions of the cubit. It does, however approximate the length of a human foot and the Roman foot was around 296 mm long. This was divided into 12 unciae (inches) and also 16 digits. The reference to the mile also comes from the Roman mille, being 1000 paces with a pace being 5 feet. It seems that this would explain the success of the Roman Empire since the Greek pace was only 2½ feet long and therefore the Romans must have been extremely tall. Of course this was not the case and the Roman pace of 5 feet was actually the distance travelled by one foot when walking; what we in fact would refer to as two paces. The Middle Ages When the Romans occupied England, the 5000 foot mile was used, however Queen Elizabeth I changed it to 5280 feet, this being exactly 40 furlongs. Maybe the furlong should be explained at this point. In the medieval strip farming system, each farmer had one or more strips of land 220 yards (40 rods) long and 22 yards (1 chain) wide; this being 1 acre in area. Since the farmer ploughed furrows the length of the field the strip was “a furrow long”, hence the term “furlong” for 220 yards. The yard itself initially had several possible lengths, such as the circumference of the waist or the distance from the finger-tip to the nose. It was divided by the binary method into 2, 4, 8 and 16 divisions being the half-yard, span, finger and nail respectively. Other measurements of length existed such as Rod, Poles and Perches. Staying with agricultural terms, there is a measurement of area called a “barn”, however it is unlikely that you could see this with the naked eye as it is the area of the Uranium nucleus, being 10-28 square metres. There is then also the kilo-barn and mega-barn, along with the milli-barn and the micro-barn, although this is more often called an “outhouse”. Getting even smaller is the yoctobarn, more commonly known as a “shed”. While sticking with terms for distance, physical exercise also came into the mix with such units as the “league” which is traditionally the distance a man or a horse can walk in one hour. There were also variations on the length of the mile with the Scottish mile being 5952 feet, the Irish mile being 6720 feet and the Country mile being a generally vague distance, often longer than any measured mile. One should also be wary of the Irish distance of “a mile and a bit” as the “bit” may be longer than the mile. Before we leave length, it is worth noting we may have come across the origins of the of a cricket pitch. The length of this is of course 22 yards, which is the same as the width of a farming strip. It is not beyond the realms of probability to picture then an early game of cricket being played across the middle strip of a number of farming strips and the batsmen defending the gates or wickets between the strips. Something for the workers to do after the harvest and before the planting season. Speaking of planting, we come to another method of proving a reasonably precise measurement. The volume of containers could be measured by filling them with seeds which were then counted. It turns out that seeds are generally consistent in their size so were a useful and easily obtained standard. Seeds were also used in weighing systems and one unit of that method survives today in the carat, the unit used to measure gold and gems, derived from the Greek word kerátion, that refers to the carob seed. Obviously it was easy to use a lump of metal to represent a certain number of grains, and such lumps were kept in temples as official standards. Copies of these lumps could then be made and checked against the standard using a precise balance. Unfortunately, history shows us that it is all too easy to deceive a customer about weight by adding or removing metal and so it was necessary to implement an inspectorate of weights and measures. This same system still exists today, with the standard lump (1 kg) kept in a temple (BIPM) and regular comparisons and inspection taking place throughout the world. Other units of mass have been used over the centuries, and in some cases they are still used by some die-hards. The pound is equivalent to 0.453 kilograms and the name comes from the Latin word pondus, meaning weight. Incidentally the unit (lb) comes from the Roman word “libra”, referring to a specific standard weight (around 325 g). The slug is a mass numerically equal to the acceleration of standard gravity of 32.174 feet per second per second. Thus a 1 slug mass (32.174 pounds) will accelerate at 1 foot per second per second when subjected to a force of 1 pound weight. The stone is another unit that may often be heard in England, being the equivalent of 14 pounds and decreed by Kind Edward III in 1340 when Flemish measures were adopted to aid England’s wool trade. More Time Passes Moving on, reliable and accurate time measurement has always been a practical necessity. In ancient times, it is probable that the difference between night from day and between morning from afternoon was sufficiently accurate for most purposes.