Today, we’re going to talk about time. Not time in the metaphysical sense, but the measurement of time. In most of the modern world, we use a number of common units of duration such as seconds, minutes, hours, days, months and years. Most of us have an intuitive feel for these units and are comfortable using them everyday to do things like setting alarm clocks, booking flights, paying for parking, remembering birth days etc. We even think of the system as a reasonably logical one – 60 seconds in a minute, 60 minutes in an hour, 24 hours in a days 365 days a year etc. Here, we shall take a look at how these intuitive models ignore some of the more bizarre aspects of time keeping. If not understood correctly, these mistakes creep into unexpected places, affecting everything from software systems, medical and aeronautical system to financial and legal frameworks.
What is a second?
So what is it really? We know intuitively how long a second it, albeit, very inaccurately. But how does one objectively define it. You could define it in terms of pendulums and metronomes. You could define it in terms of fractions of a day. But these are still highly variable systems. The sun rises and sets differently based on the season. Pendulums swing differently based on your altitude and your local geography. Scientists have agreed on a much more systematic definition of the second based on a highly reproducible (but complicated) atomic phenomenon. For those of you with a background in physics or chemistry, a second is defined as the duration of some 9.2 billion cycles of the radiation emitted during a particular ground-state hyperfine electronic transition of Cs-133 atoms held near absolute 0K. Excellent! But this unit of time utterly useless in helping us going about doing the things that we usually do – knowing when to wake up, when to sleep, making appointments, judging age etc. How do we reconcile our formal time unit of the second with the hours, days, months and years that we know?
While our definition of second is based on atomic phenomena, it is still useful to reason in terms of the rotational period of the Earth about its axis. We still define a day (more technically, the mean solar day) as the time taken by earth to rotate once around its axis. This can be measured quite accurately by timing when distant galaxies and quasars pass over a meridian. A mean solar hour is one 24th of a solar day. A mean solar minute is one 60th of that. A mean solar second is one 60th of that. But this solar second is not the same as the standardized second we defined previously. To reconcile this, we define multiple timescales and convert between them. One simple system is called TIA (International Atomic Time), which is simply measured as a progression of the standard second with no corrections for the rotation of the earth. It is a monotonic measure of the proper time on earth. Another timescale is called UT1 (Universal Time 1) which is based on the mean solar day. Noon under UT1 corresponds to noon under the older GMT (Greenwich Mean Time) system. A day in UT1 has exactly 86400 seconds. A third, commonly used timescale is called UTC (Coordinated Universal Time) which ticks seconds at the same rate as TIA, but tries to remain synchronous with UT1. It accomplishes this by occasionally adding or subtracting a leap second during the last minute of a day when the difference between UTC and UT1 is too high. Hence, during some days in UTC, a day has 86399 seconds and yet others have 86401 seconds, with the last second being repeated twice. These corrections are not predictable far in advance because events such as earthquakes, tsunamis, lunar tidal braking and even the melting of icecaps can change the speed at which the earth rotates. Any scientific system that deals with high precision location or time-keeping (such as GPS systems, aviation systems, military weapons systems) need to carefully account for these small changes in time.
We’ve made things a bit complicated now, but we now have a timescale that usefully measures the time with respect to Earth’s rotation around the sun. But this is only really useful if you were in Greenwich, UK. Most of us do not live there. Hence, the sun would rise and set at an uncomfortably differently time under UTC for the rest of us. Long long ago (well, in the 19th century), time was usually kept locally as communication between towns was limited and slow. But with the invention of faster modes of transportation such as trains and faster communication systems such as the telegraph and later the telephone, local times became increasingly annoying as time differences between towns were not simple offsets. Instead, countries started to standardize the time within certain geographical areas to be within a single time zone. Noon in a timezone occurs at some arbitrary time that is close to the local noon but is standard across the entire time zone. Nevertheless, these timezone created yet more interesting artifacts in our time keeping techniques. Since time-zones were designated based on legally and geographically convenient divisions, it was possible to travel south on a meridian and be in two or more different time-zones, each with a different time. Over time, people got used to these differences, but it is still an irritation that needs to be dealt with by travelers in today’s world. It creeps up in unexpected places such as in air travel, where computers need to carefully differentiate between local time and universal time when displaying information.
If the gerrymandering of time-zones did not create enough confusion for our systems of time-keeping, we need to deal with yet another issue – daylight savings time. Under the daylight savings system, clocks are set ahead by a certain amount of time during summer and brought back to normal during winter. The effect of doing this is to cause the sun to rise later in the day during summer, hence leaving more daylight time during the evening. This allows people to carry our recreational activities in the evening that require sunlight. There are various countries in the world that use daylight savings time – mostly countries in Europe and North America that tend to be further away from the equator. At the designated time during the spring (say 2 am), all clocks move from 1:59.99 am to 3:00.00 am. During the fall, the reverse happens with clocks moving from 1:59.99 am to 1:00.00 am. Customarily, the shift in time is a jump of one hour at some predetermined date during the fall and the spring – usually occurring at 2 am, but this is not universally the case. There have been countries that have used shifts of as much as two hours and as little as half an hour. Different time-zones within the same country have sometimes followed different rules. Hence, computerized clocks and critical systems maintain a list of the various rules for time-zones around the world and regularly update this list whenever the official rules of various countries change. A fundamental issue with daylight savings time is that times are no longer unique or continuous. On the day on which time shifts backwards, the time 1:30 am refers to two distinct times. This is again an issue in critical systems that need to handle time correctly.
Hops, Jumps And Leaps
And so it seems that we have finally accounted for all the subtle shifts in time at the second, minute and hour levels. But we still have days, months and years! Most of us don’t think of the minor adjustments we need to do to days – we were taught the rules when we were young and have memorized them (or ignored them). The most important correction of days is the leap year, which contains one extra day every four years to account for the different between the astronomical year and the calendar year. The earth revolves around the sun in about 365.2424 days. Since a calendar year has 365 days, every four years or so, an extra day is added to the end of February, giving it 29 days. This results in an over-correction in the length of calendar years and hence, years that are divisible by 100 are not leap years. That turns out to be an over-correction as well and hence we throw in a leap year if the year is divisible by 400. Phew! What happens to people born on Feb 29 or contracts signed on Feb 29? Depending on the country and the jurisdiction, they are usually fictitiously considered to have happened on Feb 28 or on Mar 1.
Let’s examine one final issue – our calendars themselves. Up till now, I’ve simply assumed that we were using the international civil calendar, also known as the Gregorian Calendar. There are numerous other calendars such as the Hebrew, Islamic, Chinese and Hindu calendars. Some of these are solar and others lunar. Dates measured in one will need to be carefully translated into the other accounting for jumps and gaps in time. The Gregorian calendar itself involved a jump in time. When Pope Gregory XIII introduced it on 24 Feb, 1582 to correct for the incorrect accounting of leap years in the previous Julian calendar, he decreed that 10 calendar days be skipped. Hence, there are days in our calendar (such as 26 Feb, 1582) which without them ever having occurred. Other artifacts of our calendaring system show up when we try to move from the year 1 BC to 1 AD. There is no 0 AD nor a 0 BC. Hence, three years would have passed between 2 BC and 2 AD (and not four as one might naïvely assume). Any system that deals with historical dates and documents has to accurately account for all of these edge cases that have become embedded into our notion of time keeping due to historical reasons.
Time-keeping is hard and has extremely complex rules. It is difficult to do it correctly. Anybody working on a system of a reasonable amount of complexity should simply use pre-designed and pre-validated components that correctly take the various calendaring issues into account lest they be condemned to repeat the mistakes of those who attempted to do the same before them.