Debunking the odd-even mathematical miracle in the Qur’an
By Martin Taverille
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Introduction to the “miracle”
The Qur’an contains 114 surahs, or chapters, and each surah is further divided up into ayats, or verses, so that all together, there are 6236 ayats in the Qur’an. There is a widely spread claim circulating on the web 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 supposedly consists of two apparently remarkable coincidences.
For each surah, I will call the sum of its surah number and the number of ayats it contains as the surah’s “s+a number”. The surahs whose s+a number is odd go into the odd s+a group and the surahs whose s+a number is even go into the even s+a group.
The sum of the s+a numbers in the odd group is 6555, the sum of the surah numbers in the Qur’an. The sum of the s+a numbers in the even group is 6236, the sum of the ayat numbers in the Qur’an.
In this article, I will show that these properties of the numbering of the Qur’an are in fact something much more simple and far less unlikely than it at first seems, and why it is perfectly plausible that it happened by chance, without any deliberate intention, whether divine or human.
1 coincidence, not 2
Before beginning, it’s well worth pointing out that the number of ayats into which the Qur’an is divided was not part of Muhammad’s “revelation” (I’m talking here about the numbering, not the text itself or its ordering). Rather there were different systems of dividing up the surahs into ayats (6204, 6226 etc.), and the 6236 divisions devised by the Kufah school simply became most popular. Even today, the number of ayats into which a Qur’anic text is divided depends on which of the 7 or 10 qira’at (variant readings of the Qur’an) is used. For example, while the Hafs transmission is most popular today with 6236, Warsh uses 6214.
The first thing to notice is that added together, the sum of the even s+a numbers plus the sum of the odd s+a numbers must equal the sum of all the surah numbers plus all the ayats in the Quran (since every surah belongs to one of the two groups). Thus if one group = the sum of the surahs, it just follows trivially that the other group must = the sum of the ayats. One half of the “miracle” automatically implies the other. We can further deconstruct things from another angle. We can simply state the “miracle” as follows:
1. Total surah numbers + ayats in odd s+a group = total surah numbers
6555 = 6555
2. Total surah numbers + ayats in even s+a group = total ayats
6236 = 6236
Each surah belongs either to the odd s+a group or the even s+a group. If we subtract all the surahs 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 surah 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. To illustrate visually:
Thus both apparent coincidences just simplify to a single one because both in fact count the same quantity as part of each side of its equation. They are not two independent coincidences. They both follow trivially from a single quite mundane coincidence: 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’s worth noticing that it makes no difference whether you define the two groups based on odd and even numbers or any other selection criteria so long as the total ayats in one group of surahs = total surah numbers for the rest of the surahs. The two apparent coincidences follow simply from that fact.
Incidentally, it is sometimes claimed that the distribution of ayats has to be exactly as it is for the “miracle” to work, and thus it supposedly has a useful function as a sort of checksum against change (in the numbering at least). However, there are many ways that the total number and distribution of ayat numbers could be different without affecting this property. For example, you could add or subtract any multiple of 2 to the number of ayats of any surah in the even s+a group. Another is that for 2 even numbered surahs, you could swap their number of ayats if both are even or both are odd. The same for 2 odd numbered surahs. I have created an Excel spreadsheet so you can try this for yourself if you wish.
How remarkable is this coincidence?
Even by the most basic consideration at the start of the previous section we saw that one half of the “miracle” automatically implies the other. We further saw by putting it another way that its proponents unwittingly count the same quantity within both sides of each equation so it is in fact just two versions of the same equation, the same single coincidence. And as we shall see due to various factors, the likelihood of its occurance by chance is not so low that anyone should be impressed by it and proclaim it a miracle!
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. Thus (and as further explained below) 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 surahs’ ayats.
If the selection criteria that is used by the miracle seekers hadn’t found a coincidence, there are many other options for selecting around half the surahs and people could have tried them instead (for example odd numbered surahs, surahs with an odd number of ayats, odd letters in the surah name, odd surah number multiplied by ayats etc.).
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.
Using computer simulations with random numbers and a similar distribution of ayats as we have in the Qur’an, I found that the odds of finding a match after randomly selecting half the surahs are approximately 1 in 170. See the endnotes for the vbscript I used. 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. If the numbering had been very different, then obsessive numerologists would have found some different numerical “miracles” instead. One should bare in mind that miracle seekers do not have any prior hypothesis predicting a specific pattern, but rather just that there will be *some* kind of numerical pattern, fulfilled prophecy etc., and thus they commit the Texas Sharpshooter Fallacy.
Addendum:Some of the commenters below completely misunderstood the point in this article and went off on a tangent that is beside the point, suggesting that it would be extremely complex for someone to have intentionally given the numbering of the Qur’an this feature. In fact, I actually said this feature of the Qur’an was simply an unintentional coincidence, (and explained factors that boost its likelihood of occurance) so the difficulty or otherwise of deliberately manufacturing it is therefore irrelevant. However, for the interest of these people I have explained below in a comment dated June 17 2012 a simple process that someone could follow to deliberately implement these properties, which as I demonstrated in the article, both follow trivially from a match between just a single pair of numbers. I explain in the comment a simple process (without at all changing the text itself) to adjust the number of ayats into which the surahs are divided to make the single pair of numbers match if they didn’t already, which would in turn thus give that Qur’an the 2 pairs of matching number feature.
I have just added this explanation in the comment for interested readers since all the comments that have attempted to contest the article have for some reason focused on how it could have been done by a human deliberately. I don’t argue that it was deliberate in my article. I regard that question as an interesting, but distracting irrelevance. If, as I argued, this property of the numbering system was an unintended coincidence, which is very plausible due to various conducive factors that I explained, then it is utterly irrelevant how hard it would have been for a human to implement it deliberately (though as I explain in the comment, it would be a surprisingly simple process).
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Endnotes and references
dim i dim s dim selection(56) dim ayats(113) dim c dim randomSura dim sumSelectedSuras dim totalAyats dim sumUnselectedAyats dim pass dim matches dim numPasses dim stats(3248) totalAyats = 0 matches = 0 numPasses = 10000 'populate array with similar skewed 'distribution of ayats to that of the Quran for i = 0 to UBound(ayats) ayats(i)=fix(((114-i)^2)/77)+1 'ayats(i)=114-i 'uncomment to test that there are 100% 'matches when ayats are a mirror image of suras totalAyats = totalAyats + ayats(i) next 'see if we get a match using random selection of suras for pass = 1 to numPasses s = 0 sumSelectedSuras = 0 sumUnselectedAyats = 0 'populate array with random distinct sura numbers do while s < 57 Randomize() randomSura = Int(114 * Rnd())+1 'check through array to avoid adding duplicates c = 0 do while c <= s - 1 if randomSura = selection(c) then exit do end if c = c + 1 loop if c = s then selection(s) = randomSura sumSelectedSuras = sumSelectedSuras + randomSura s = s + 1 end if loop s = 0 sumUnselectedAyats = totalAyats 'subtract ayats in the selected suras from the total 'to get the sum of ayats in unselected suras do while s 0 then wscript.echo matches & " matches out of " & numPasses & _ " = 1 in " & numPasses/matches else wscript.echo "0 matches out of " & numPasses end if