I was thinking today about things that we take for granted, things that are so familiar and so engrained that we never think about them at all; things like time and distance. Time seems so obvious and so immutable – it is how we measure the passage of our lives. As far as we can understand, time flows in only one dimension – forward as we perceive it. But what is time? And why do we mark its passage as we do?
First of all, time is a perception. Our limited human senses tell us that we are born, grow, have whatever joys or sorrows mark our life, grow old… then eventually die in an unbroken stream of time. The same sequence happens again, as far as we can understand, for everything on and off Earth – it happens to animals, plants, institutions, empires, mountains, seas, continents, and the planets, stars and galaxies. And what makes that progression sequential is what we call time.
We measure time on earth in years and days. But these measures are valid only here on earth, this third planet of an ordinary star well out on one of the arms of a spiral galaxy. A day is what we call the measure of one revolution of the earth around its axis. If it revolved at a different rate, a day would be a different quantity of time, but it would still be a day. A year is what we call the measure of our revolution of the earth around the sun. Again if the earth were a little closer or farther from the sun the rotation around our sun would be a different amount of time, but it would still be a year. As an aside the distance couldn’t vary much, since the Earth’s climate depends on energy from the sun; a lot closer and the surface would be too hot to support life like ours. A lot farther away, it would be too cold to support, probably, life like ours.
So what? If the planet revolved differently or rotated around the sun differently, the periods that we describe as a “day” or a “year” would be different. The apparently rigid fact of their duration is only due to an accident of planetary formation.
I am not even going to get into weeks or months. Named after the moon and sun, Norse gods and Roman gods and emperors. What a mess!
There are more measures of time: hours, minutes, and seconds. Why are there 24 hours in the day? Why are they measured in two 12-hour segments? The two 12-hour segments can be traced back to the ancient Middle East. The Egyptians, Babylonians, Sumerians and others measured the day in two segments. These segments were equal because, at that latitude, day and night are roughly equal throughout the year. But why 12 hours?
Take a look at your hand, either hand, and count the segments of your fingers. You will discover, if you didn’t know already, that there are 12. We speculate that counting off the hours on the segments of your hand would give you 12 units. If the ancients had chosen to include the thumb as well in their calculations, we would likely be using base 14. So if our hands were jointed differently, with one fewer joint, perhaps we would have two eight hour segments in a day and each segment would be longer than what we describe as an hour.
Why 60 seonds in a minute, 60 minutes in an hour? We know that the Sumerians used the base 60 system. We don’t know why but it might be because 60 is very convenient for expressing fractions, since 60 is the smallest number that can be divided by one, two, three, four, five and six as well as by 10, 12, 15, 20 and 30.
When we measure distance, the same kind of pragmatic approach seems to be involved. In the Imperial system, a foot is about the length of an adult male foot. My foot happens to be exactly 1 foot long – coincidence? I think not. A yard, which is 3 feet long, approximates the length of a human arm. The Imperial system has many other measures, too numerous to repeat here, which relate to agriculture.
The metric system, widely used in the Western world, makes more scientific sense, almost. It was defined as 1/10000000 of the distance from the equator to the North Pole measured through Paris. That was the French Academy of Sciences definition in 1791 ( it is now defined based on the speed of light). But it too is based on the size of the earth. Different size earth, different size meter.
Computers are based, so far, on three number systems; binary (base-2), octal (base-8) and hexadecimal (base-16). That’s because when we started using devices to compute, the only way was to store data was as on or off . Yes or no. True or false – a system based on two and two only options. This has been the premise on which every computer today is based. Octal has only 8 numerals: 1, 2, 3, 4, 5, 6, 7 and 0. A ten (10) in octal is an eight in our familiar base-10 system. Hexadecimal extends octal by adding 8, 9, A, B, C, D, E and F. An F in hexadecimal equals 15 in our base-10 counting. A ten (10) in hexadecimal equals 16 in base-10. (I am not going to get into quantum computing – I don’t understand it at all). When you are gaming on your iPad, you are manipulating huge groups of ones and zeroes.
But so what? All these givens that underpin, measure and regulate our lives are either accidental – because of the planet’s size or rotation – or else by tradition or decree. How much else in our lives is bounded artificially? What would be the impact if it were different? There’s some ideas for us to ponder.