Quran Violates Zipf’s Law, Unlike Any Human-Authored Book

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Quran written on Chinese paper.


For those who need scientific evidence that the Quran comes from Allah — whose signature is at the top of this evidence — look no further than the law that applies to ALL human languages and books: Zipf’s Law, which “states that given a large sample of words used, the frequency of any word is inversely proportional to its rank in the frequency table. So word number n has a frequency proportional to 1/n.” In other words, if the first word is used 100 times, the second word should be used half that many or 50 times, the third word a third as many times or 33.3 times, etc. (See the amazing video at the bottom of this page to learn how pervasive in all human language this law is. But the producers of that video did not know about the Quran…yet.)

The “large sample” could be a book, such as Moby Dick or the Bible, or all of Wikipedia. All of these follow Zipf’s Law. In fact, all languages follow Zipf’s law. But the Quran does not! Not only that, but Allah the Omniscient Almighty embedded the reason the Quran does not follow Zipf’s law in the actual word rankings compiled from its text: min Allah – which means “from Allah.” He literally signed the results!

The most frequently used words in the Quran are not inversely proportional to their rank in the Arabic language. So to prove this, we can compare the frequency of word usage in the Arabic language as compared with that of the Quran. The charts below do exactly that. Below you can see the top ten most frequently used of words used in Arabic:

This chart shows us the top ten most frequently used words in the Quran for comparison:

The first two words in this chart are min Allah – من الله – (as you can see on the chart as 1 and 2 most frequent words in that order) which means “from Allah.” Thus you can see graphically how the Exalted literally tells us why the Quran does not follow Zipf’s law: it comes from the Almighty Himself.

Note the ratios in the Quran frequency chart above: the ratio is barely changing in the first ten words, slowly decreasing to 2.55, whereas in the Arabic language chart, by the tenth word, the ratio increased to 4.06, a normal Zipf Law ratio. The Quran simply doesn’t follow that law. And the first rankings are more significant in that they relate to the core of the text.

The ratios in the Arabic language closely follow the “power” ratio predicated in Zipf’s Law; the ratios in the Quran do not. You can check the frequencies in the chart above for the Quran where the first word “min” has a frequency of 4.3523, so the 2nd number should be half that number. But exactly half would be 2.17615. Instead we find a much larger 2nd word frequency of 3.6413. We don’t get close to the 2.17615 number until word number 6, which should have been closer to 1/6 of the frequency number for the first word, not a little over half. No human-authored book, not even a text randomly typed by a chimpanzee, nothing breaks this law, except the Quran.

Comparing the two charts above, you can see the second-most frequently-used word in the Quran is the name Allah, which is not even in the top ten of the Arabic language chart. The chart below shows the frequency of the name Allah in the Arabic language, at number 35 ٣٥ (Arabic), highlighted in yellow:

The second word is nowhere near the most ffrequently-used Arabic words. And the word qaal – قال – was number 5 in the Quran chart, where it doesn’t appear until number 12 in the Arabic language chart. 

It is also interesting to see the bottom of the chart of word frequencies for the Quran, as shown below

Here as the reader gets farther away from the top words “from Allah”, let’s see how the words depict what happens to the five words farthest away from Allah’s name (at the beginning): “will break” — “cleft asunder” — “to part” — “to fall and lose luster” — and finally, “to collapse.” Long before such charts could have been made, before George Zipf (who discovered it) was born, before “statistics” even became known as a thing, the Quran came with words that, in this very ranking, give us the message of what it means to be away from Allah the All-Knowing, Al-Wudud, the Loving. This also could show us the approach of the Finality — Al-Akhira — where every word on this final page could refer to Judgment Day in some way. 

The line graph below gives us a more distinct comparison between the two. Note that the Arabic language itself does conform to Zipf’s Law (represented by the dotted “power” line showing the predicted ratio). It is the Quran that does not, visible in two distinct wobbles; not extremely, since it communicates using the Arabic language, but significantly, unlike every human-authored book, showing us that this final revelation is indeed from our Creator, the Almighty, All-Merciful Allah.

Note the Quran is in green; you can clearly see the deviations the green solid line makes from the dotted Zipf-related “power” line, as well as the differences between the Quranic word frequency and that of the Arabic language in red. 

A complete frequency list of words in the Quran can be found here

قُل لَّئِنِ ٱجۡتَمَعَتِ ٱلۡإِنسُ وَٱلۡجِنُّ عَلَىٰٓ أَن يَأۡتُواْ بِمِثۡلِ هَٰذَا ٱلۡقُرۡءَانِ لَا يَأۡتُونَ بِمِثۡلِهِۦ وَلَوۡ كَانَ بَعۡضُهُمۡ لِبَعۡضٍ ظَهِيرًا 

Say, “If ˹all˺ humans and jinn were to come together to produce the equivalent of this Quran, they could not produce its equal, no matter how they supported each other.”

Al-Isra’ 17:88

Although people have studied Zipf’s Law extensively since it was discovered in 1835 by George Kingsley Zipf, this study is explains a possible explanation for the phenomenon. Making the probability of its violation significant. A clear and interesting explanation is below:

For Muslims, the Quran needs no ”scientific proof; reading its ineffable truth and hearing its incomparable beauty is even greater evidence. It has been reverenced for centuries, as shown in the picture above of Mushaf’s (copies of the Quran, which refers to the message itself) printed on Chinese paper during the Timurid Dynasty in the 15th century.

For comparison, some other charts:

Zipf’s chart for English language
Zipf’s chart for Moby Dick

It’s easy to see how the above charts also generally follow Zipf’s law.
Source for some of the graphics and other info: this post on Quora.

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