The post after the previous post

Some interesting things happened as a result of my previous post. For example, several people did a dude-i-have-a-better-method-than-yours with me on Gtalk and also, Robin Kothari claimed that you can actually spend 50 hours in a single day on earth, as opposed to 48. I am going to elaborate upon these two things in the next few paragraphs.

The people who said they had a better method, had the following method in mind. You sit just east of the IDL for one complete day, and a very small number of seconds before midnight, step to the west, the place where the day you are currently at the end of, is actually about to start. So then after spending 24 hours in a day, you are once again at the start of the same day and hence, have another 24 hours in hand. This method has a shortcoming, which, I realized after answering a few buzzes on Gtalk, should have been mentioned in the post itself. The reason is simple. If you step to the west x seconds before midnight, you will first have to spend x seconds in a wrong day. If you step x seconds after midnight, you will again spend x seconds in a wrong day, only this time before stepping over the line. So the only way to achieve our aim would be to cross the line exactly at midnight. This can be accepted as a solution depending on the sloppiness you want to allow. This won’t fit in if you are a perfectionist.

The point raised by Robin is quite interesting. As it turns out, the IDL is not a straight line, as one would have expected. It has kinks in it, the biggest one being directed eastward at a place called Kiritimati. Until about 1994, the line bisected the group of islands, but then, the people got annoyed because the eastern part of the republic was always 24 hours ahead of the western part and hence there were only four days in a week in which official business could be conducted between the two parts. Hence they pushed a part of the line towards east, which led to the following two very weird things, which I quote directly from wikipedia –

  1. “However, for two hours every day—Coordinated Universal Time (UTC) 10:00–11:59, there are actually three different days observed at the same time. For example, at UTC time Thursday 10:15, it is Wednesday 23:15 in Samoa, which is eleven hours behind UTC, and it is Friday 00:15 in Kiritimati, which is fourteen hours ahead of UTC.” And also,
  2. “Because the earliest and latest time zones are 26 hours apart, any given calendar date exists at some point on the globe for 50 hours. For example, April 11 begins in time zone UTC+14 at 10:00 UTC April 10, and ends in time zone UTC-12 at 12:00 UTC April 12.”

(If the term UTC scares you, you can assume for the present post that UTC is actually GMT.)

Although it seems that wikipedia has directly answered our original question (just keep traveling to the point where it is still April 11), several other questions have been raised in the whole process. For example, “What do you mean by shifting a part of the IDL towards east?”, “Shouldn’t the IDL always be a straight line?”, “Who decides what the IDL should look like?”, “Can we arbitrarily give it any shape whatsoever?”

I am going to try to answer all these questions and hence fit everything into place now.

Suppose for the moment that we do not have such discrete time zones as we have now and that each longitude has its own individual time. If you are unclear about how to assign time to different longitudes, just assume that we say it is 12 noon at a particular longitude whenever the sun is directly above it and we say it is 12 midnight when the sun is directly opposite it. Since the earth completes one rotation in 24 hours, there will be a difference of 24 hours between two consecutive midnights (or noons) at a particular longitude. Also, at any given moment, different longitudes will have different times. So now we have a scheme to assign a unique time to each longitude. Note that by counting the number of times it has been 12 midnight at a particular place, we can assign unique dates to each longitude too. So initially, all the longitudes except the one exactly opposite to the place the sun is currently pointing at, have seen zero midnights. So all the places except this one place has the date 0. As the sun moves towards west, more and more places start seeing midnights and hence their dates increase to 1. After one complete rotation, all the places have seen exactly one midnight, except, of course, the longitude we started with. So this particular longitude has the date 2 and the rest have date 1.

Since we are going to refer to this longitude again and again, let’s give it a name, for example, The Longitude. Now consider a snapshot of the earth taken at a time when, say, it is 11 am of day 3 at The Longitude. The time at a place a bit west of it at this moment will be a little less than 11 am, a bit more to the west, a bit more less than 11 am and so on until you reach a place where the time is 12:01 am of day 3. If you travel further to the west, you will find yourself in day 2 and when you are just short of completing a full round of the earth, you will be at a place where it is just before 11 am of day 2. So whereas it is 11 am of day 3 at The Longitude, it is just less than 11 am of day 2 at the point immediately east to it. So notice that The Longitude, apart from being the place where each calender date arrives first, also happens to be a line, which, if you cross at any point of the day, you will encounter a sudden jump in the date, which will be an increment if you have travel from west to east and a decrement otherwise. Notice that we have a reference to the time when earth started rotating in the definition of The Longitude. Evidently, the earth started rotating a really long time ago, at least much before life became complicated enough that one would require the concept of date and time. So now, when we do require these concepts, we are free to assume that a particular longitude is the one where the sun shone first. This longitude is an approximate version of what we call the International Date Line. However, we are not done yet.

The above scheme would work really well if the only inhabitants of earth were dead cows in a pond. Unfortunately, there are several other occupants of this planet, most notably, living human beings. These are creatures with emotions and (hence?) a large tendency to screw things up. They came up with the idea of segregating the whole of their population into groups they called “countries” and since it was “inconvenient” for people in one country to follow different times, they decided to form discrete time zones. So people formed groups, called time zones and assigned a longitude to each of them, so that everyone in a particular time zone would follow the time at the assigned longitude. Also, for the sake of convenience, they came up with a naming scheme for the time zones. They named a particular longitude (and the time zone which followed its time) the Greenwich Mean Time, or GMT, and named each time zone on the basis of the number of hours each were ahead, or behind of the GMT. So a time zone which was called GMT + 5, was the one which was 5 hours ahead of GMT, and so on. Also, it just so happened, that the longitude they called GMT, was the one exactly opposite the one they called IDL. As a result, the time zones on earth all lied between GMT – 12 and GMT + 12, because if it was GMT + 13, it would be on the other side of the IDL and hence, because of the jump of date, would be called GMT – 11.

We can now answer the questions we started with.

What do you mean by shifting a part of the IDL towards east?

Let’s first understand what it means by shifting the whole of the IDL towards east. It just means that we are ascribing the name IDL to a new longitude. And if we don’t change the position of the GMT, it means we want to divide the earth into time zones from, say, GMT – 10 to GMT + 14, instead of the usual GMT – 12 to GMT + 12. So what does it mean by shifting only a part? It means there will be one small part of the world that will believe that the earth is divided into time zones from GMT – 10 to GMT + 14 and the rest will believe its GMT – 12 to GMT + 12.

Shouldn’t the IDL always be a straight line?

It would at least be simpler that way, but because of problems such as the one faced by the people at Kiritimati, let’s keep it as it is until someone thinks of a more elegant solution.

Who decides what the IDL should look like?

I don’t really know, but this place may give you some idea.

Can we arbitrarily give it any shape whatsoever?

Yes. We are the ones who defined it after all. In fact, it may be fun to think on the following – Is there some shape we can assign to the IDL so that it is always your birthday at some point or the other on earth?


How to spend the longest day of your life

I have to say that 4th May, 2008 was the longest day of my life till now, not just because it never seemed to get over, but also because I actually spent more than 24 hours (28.5, to be precise) in it. Well, the reason, of course, was that I started and ended the day in two different countries (India and Scotland, respectively). However it did make me think on two rather interesting questions – 1. Can one spend a day longer than this? 2. What would be the length of the longest day one can possibly spend being on earth? Obviously, the answer to the first one should be “yes”. It would be too much of a coincidence to unknowingly do something which cannot be outdone as long as you are on earth.

In any case, I did think on the aforementioned questions and after a cup of coffee and some discussions with Eliot Gehrt Setzer, it turned out that the interesting question had a simple answer. The answer, first of all, is 48 hours. Secondly, there are several ways to spend a 48 hours day, an approximate but intuitive way being as follows –

Go to this place called the International Date Line, which, according to wikipedia, “is an imaginary line on the surface of the Earth opposite the Prime Meridian which offsets the date as one travels east or west across it.” Wait there till the start of a new day and start traveling towards west as soon as a fresh day arrives. Remember to keep your speed equal to the speed of the sun (figuratively speaking, of course). This will ensure that its always midnight in the country you are presently in. After just a little less than 24 hours, you will be at a place just a little east of the International Date Line, where it will still be midnight and the date, surprisingly, the same as the one it was when you started. So now you stop and spend your next 24 hours there. At the end you will have spent 48 hours in the same day.

Starting at midnight isn’t really a necessity. The key idea is that you should spend some 24 hours of your 48 hours day without changing the time. This happened to be your first 24 hours in the previous case. It can be the last 24 hours too, or it can be just spread randomly across the day.

Starting at the IDL is a necessity though. That’s because if you don’t start there, then at some point of time you will end up crossing it, resulting in a sudden change of date. Of course, you will have progressed by only one day at the end of your 48 hours in this case too, but you won’t spend all of those 48 hours in the same day.

The above is definitely a good solution as long as you do not mind occasionally traveling to the past. Since the time zones change in a discrete way rather than continuously, even though you are traveling with the sun, so to speak, you will not always remain at midnight (in case you decided to choose the first of the ways described above). You will, depending on the width of the time zones you travel through, keep going back in time by a few hours every now and then. You can however, choose only very narrow time zones to keep such occurrences to the minimum.

Another interesting question arises if you restrict your idea of a “day” to only the time between a sunrise and the next sunset or a date change, whichever happens first. Realize that with this new definition of the day, normal days are less than 24 hours long. They can easily be made equal to 24 hours though, by being at one of the poles during summer. Can we do better? By being just south of the north pole (or north of the south pole) and doing the circle starting at the IDL will do the trick. Being exactly at the pole may lead to some elegant trick, but thinking about the date and time at the pole is scary and I will refrain from getting into it.