In the Year 20878 AD/AH

I can still do basic Algebra! Hurray!

I discovered this recently as I attempted to solve a problem that had plagued me for literally minutes. That was this: The Islamic Calendar and the Gregorian (i.e. Christian Calendar) have different lengths. The Islamic Calendar is Lunar and has twelve months. It begins in what is 622 AD in the Western Calendar (on Thursday July 15, to be precise, according to some calculations). In 622, the nascent Muslim community in Mecca fled persecutions and took refuge in the city of Yathrib, thereafter renamed Medina. This flight is known in Arabic as the Hijra, an Arabic word meaning migration or flight.

Ten Lunar years later, in 10 AH (Anno Hegirae, Latin for In the Year of the Hijra), the Prophet Muhammad revealed that God told him that each year should have twelve months and that they should stop adding extra days every year (know as intercalation). The intercalation had been done to keep the months in the same seasons; however, Muhammad stopped this and Muslims today view this as a great blessing since Muslim feast days, such as the fasting of Ramadan and the Pilgrimage to Mecca, are calculated according to the Hijri calendar, the seasons of the festivals change over time.

Since that time, the Islamic world has followed this Hijri calendar. Days, as in the Jewish tradition, begin at sunset, and new months begin with the first viewing of the crescent moon. Today, rather than rely on plain eyesight, mathematical algorithms are done to determine the phases of the moon. This concern for the phases of the moon and the necessity to determine the direction to Mecca for prayer drove Islamic scholars to become masters at astronomy and it was through their work that the world got the astrolabe and the compass; those inestimable tools of navigation.

The problem becomes, however, in this global world, that going between these two systems can be difficult and complex. The following formulas help one convert dates:

AH = 1.030684(CE-621.5643)

CE = 0.970229AH + 621.5643

Where CE equals the Common Era (or the Christian Calendar) date and AH equals the Hijri or Islamic date.

There are difficulties in this calculation though and dates are frequently disputed. An Islamic date recorded in a manuscript in the middle ages, for example, can be extremely tricky to determine precisely in the Western calendar for a variety of reasons. Firstly, in those times, determinations of new months required visually seeing the new crescent moon; though mathematical formulae existed even then. Furthermore, there have been, over the centuries, different Islamic calendars in use in different parts of the Islamic world. This, of course, is not surprising. Europe has only had a unified calendar for a few centuries. In the middle ages, some regions had their own calculations and there were constant debates about which one was best even though there was general agreement on the months (holdovers from Roman times). I can also through another wrench in the gears: namely, that the moon recedes from the earth every year by a couple of centimeters and hence the length of its rotations subtly change. Of course, this has virtually no impact in the short run even including centuries, but over millenia this might affect things. And let's not even discuss the horrors of leap years which exist in both systems!

So, the other day, my coworker and I were discussing these facts. He asked me what year it was in the Islamic system and I replied: 1429 AH. That means that 1429 lunar years have passed since the Hijra; however 1386 solar years have passed (2008-622=1386). Furthermore, in the first year of the Islamic Calendar, the difference between the two systems was 621 (a thoroughly meaningless number by itself since it is a combinations of two systems). Today, the difference is 579. The Islamic calendar is catching up to the Christian calender at a very slow rate. Indeed, it has gained by only 42 in 1386 solar years. Eventually, the years would be the same, I realized. But when? So, I did the following math:

Let x=CE
Let y=AH
x=0.970229y=621.5643
y=1.030684(x-621.5643)

Since I wanted to find the point at which x=y I substituted x for y and set the two equations as equal, hence:

0.970229x + 621.5643 = 1.030684(x - 621.5643)

I proceeded to calculated as follows:

0.970229x + 621.5643 = 1.030684(x - 621.5643)
0.970229x + 621.5643 = 1.038684x - 640.6363789812
0.970229x + 1262.2006789812 = 1.038684x
1262.2006789812 = .060455x
0.060455x = 1262.2006789812
x= 20878.350492

That means that in the year 20,878 AD it will also be the year 20,878 AH. Christianity and Islam will finally come together and peace will reign upon the earth. Now we need only wait 18,870 years (19,449 lunar!) for peace. At the current rate of the peace process in the Middle East, this might be early.