Odd-Even Mathematical Miracle
This article takes a look at the 6555 surah, 6236 ayat, odd-even mathematical "miracle" in the Qur’an.
Contents |
[edit] Introduction to the “miracle”
There is a widely spread claim, circulating on the web at least since 1998,[1] that there is a “mathematical miracle” in the Qur’an concerning the sums of the surah numbers, and the sums of the ayats, or verses. It is sometimes called a binary, odd-even, or checksum miracle. It consists of two apparently remarkable coincidences. If you look at the Excel spreadsheet after you’ve read this article, you can see them for yourself and verify what is said.
If you add up all the surah numbers from 1 to 114 (1 + 2 + 3 + … + 112 + 113 + 114), the total is 6555. If you add up the number of ayats for each surah in the Qur’an (7 + 286 + 200 + … + 4 + 5 + 6), the total is 6236.
Now, for each surah, you can add its surah number to the number of ayats it has (e.g. 1 + 7 = 8 for the first surah, 2 + 286 = 288 for the next surah), and we can call the result its “s+a number”.
If you add up all the odd s+a numbers the result is 6555, which as we saw is the sum of the surah numbers in the Qur’an. If you add up all the even s+a numbers, the result is 6236, which is the sum of all the ayats in the Qur’an. Apparently we have a pair of amazing coincidences. Someone might imagine the odds are thousands to one, but are they?
[edit] 2 coincidences or 1?
Before beginning, it’s worth mentioning that the number of ayats into which the Qur’an is divided was a matter of dispute from the early days of Islam, and the 6236 divisions of the Kufah school simply became most popular.[2]
The first thing to notice is that added together, the odd and even totals must contain the sum of all the surahs and all the ayats in the Qur’an (since every surah belongs to one of the two groups). Thus if one group = the sum of the surahs, the other group must = the sum of the ayats. We can deconstruct things a bit further. We can simply state the “miracle” as follows:
1. Total s+a (odd) = total surah numbers
6555 = 6555
2. Total s+a (even) = total ayats
6236 = 6236
Each sura belongs either to the odd s+a group or the even s+a group. If we subtract all the suras numbers belonging to the odd s+a group from both sides of the first equation, we can see that it becomes:
Total ayats in the odd s+a group = total sura numbers in the even s+a group
If we then subtract all the ayats belonging to surahs in the even s+a group from both sides of the second equation we can see that it becomes:
Total surah numbers in the even s+a group = total ayats in the odd s+a group
Swap the sides of this equation round and you’ll see that it is identical to the other equation.
Thus both apparent coincidences in reality simplify to a single one: Total ayats in the odd s+a group = total surah numbers in the even s+a group. Specifically, that number is 3303. And no, 3303 is not divisible by 19 in case you were wondering.
It is sometimes claimed that if the distribution of ayats was changed in any way, the pattern will disappear. However, there are many ways you could alter the distribution of ayat numbers without affecting this property and which you can easily verify with the spreadsheet. For example, you could add/subtract any multiple of 2 to the number of ayats of any sura in the even s+a group. For 2 even numbered suras, you could swap their number of ayats if both are even or both are odd. The same for 2 odd numbered surahs.
[edit] How remarkable is this coincidence?
Obviously, it is vastly less remarkable that one coincidence of this magnitude should occur than two independant such coincidences (you would have needed to multiply the two probabilities and would have arrived at a rather small number).
The sum of the ayats (which range from 3 to 286, skewed such that the higher numbers are less frequent) is approximately the same as the sum of the surah numbers (which range from 1 to 114, uniformly distributed), 6236 and 6555 respectively. It is not particularly remarkable that you can use some criteria to select approximately half the surahs (as this process does – exactly half as it happens), and find that the sum of those surah numbers = the sum of the other half’s ayats (3303 is approximately half of 6236 or 6555).
Even if your selection turns out to be weighted toward the higher numbered surahs, then the ayats of the other surahs will similarly be weighted toward the higher numbers (since the surahs tend to be ordered such that as the surah number increases, the number of ayats per surah decreases). So there is a rough correlation – they are not independant variables. Almost whatever your selection of half the surahs, the sum of their numbers will roughly correlate with the sum of the other surah’s ayats.
We should also bear in mind that for each way of dividing the surahs into two halves, you have two chances to find a match: your “odd” group might = the sum of all surahs and the “even” group = the sum of all ayats, or alternatively, your “odd” group might = the sum of all ayats and the “even” group = the sum of all surahs.
If the selection criteria that is used hadn’t produced a coincidence, there are many other options for selecting half the surahs and people could have tried them (for example odd numbered surahs, surahs with an odd number of ayats, or words, or letters etc.).
Using computer simulations with random numbers and a similar distribution of ayats as we have in the Qur’an, you'll see that the odds of finding a match after randomly selecting half the surahs are approximately 1 in 170. See the footnotes for the vbscript used.[3] If there is a 169 in 170 chance that a selection criteria will not give a match, then 1 – (169/170)^n gives the probability that you will find a match with n attempts using random selection criteria. For example, there is a 0.057 probablity (1 in 17 chance) of getting a match trying 10 selection criteria. Of course, if you succeed that does not mean that there is a 16 in 17 chance that you have found a miracle. Otherwise every unlikely event would be a miracle. Unlikely things happen all the time.
We must consider that huge amounts of man-hours have been spent looking for numerical patterns in religious books, so try hundreds or thousands of possible patterns and coincidences, including this kind, and it is likely that you will find some.
[edit] See Also
- Mathematical Miracles - A hub page that leads to other articles related to Mathematical Miracles
[edit] External Links
- So-called Binary Checksum Miracle - XLS file
[edit] References
- ↑ It seems to have first appeared online at discoveringislam.org and comes from a book by a Jordanian researcher named Abdullah Jalghoom.
- ↑ Qurʾān - Encyclopædia Britannica, accessed March 29, 2011
- ↑ The vbscript code can be found at the quranspotlight website.
