Beyond Probability
God’s Message in Mathematics

By: Abdullah Arik (edited version)
.

"Mathematics is the language in which
God wrote the universe."
Galileo (1564-1642 AD)

Introduction

The Quran consists of 114 chapters, they are called Sura’s. Its original text is in Arabic. The shortest chapter (Sura) in the Quran contains three verses, whereas the longest chapter has 286 verses.
The Quran is a unique book in that some of its chapters start with a letter, or a group of letters, instead of the usual text. These letters will be called initials, and the chapters that start with initials will be called the initialled chapters throughout this research.
There are 29 initialled chapters in the Quran. These chapters are not found in any particular order. The first initialled chapter is Chapter 2, and the last one is Chapter 68. Some of these chapters contain the same initials, or a subset of the initials used in other chapters. There are a total of 14 different sets of initials which are made up of 14 different Arabic letters. Table 2 lists the 29 initialled chapters with the corresponding initials used. In this table, only the English equivalents of the Arabic letters are given. A cross reference table of Arabic letters versus their approximate English equivalents is provided in the next chapter.

Table 1.

The 114 chapters of the Quran with the

corresponding number of verses in each

Sura No.	Verses	Sura No.	Verses	Sura No.	Verses
1	7	39	75	77	50
2	286	40	85	78	40
3	200	41	54	79	46
4	176	42	53	80	42
5	120	43	89	81	29
6	165	44	59	82	19
7	206	45	37	83	36
8	75	46	35	84	25
9	127	47	38	85	22
10	109	48	29	86	17
11	123	49	18	87	19
12	111	50	45	88	26
13	43	51	60	89	30
14	52	52	49	90	20
15	99	53	62	91	15
16	128	54	55	92	21
17	111	55	78	93	11
18	110	56	96	94	8
19	98	57	29	95	8
20	135	58	22	96	19
21	112	59	24	97	5
22	78	60	13	98	8
23	118	61	14	99	8
24	64	62	11	100	11
25	77	63	11	101	11
26	227	64	18	102	8
27	93	65	12	103	3
28	88	66	12	104	9
29	69	67	30	105	5
30	60	68	52	106	4
31	34	69	52	107	7
32	30	70	44	108	3
33	73	71	28	109	6
34	54	72	28	110	3
35	45	73	20	111	5
36	83	74	56	112	4
37	182	75	40	113	5
38	88	76	31	114	6

Table 2.

The 29 initialled chapters, number of verses in each,

and the initials prefixing these chapters

Ch. No.	No. of Verses	Initials
2	286	A,L,M
3	200	A,L,M
7	206	A,L,M,S
10	109	A,L,M
11	123	A,L,R
12	111	A,L,R
13	43	A,L,M,R
14	52	A,L,R
15	99	A,L,R
19	98	K,H,Y,A,s
20	135	T,H
26	227	T,S,M
27	93	T,S
28	88	T,S,M
29	69	A,L,M
30	60	A,L,M
31	34	A,L,M
32	30	A,L,M
36	83	Y,S
38	88	S
40	85	H,M
41	54	H,M
42	53	H,M,A,S,Q
43	89	H,M
44	59	H,M
45	37	H,M
46	35	H,M
50	45	Q
68	52	N,N

Note: All initials occur in the first verse of these chapters with the exception of chapter 42. In this chapter, the first two initials occur in the first verse, then the last three initials occur in the second verse.

Ever since the revelation of the Quran, many scholars studying the Quran tried in vain to understand the significance of the initials and the initialled chapters. However, their significance remained a mystery until recently.

Discovery of the Mathematical System

An Egyptian-American biochemist and a Muslim scholar, Dr. Rashad Khalifa, started translating the Quran into English in the early 1970's. He was determined to find an explanation for the mysterious initials. With this in mind, he initiated an extensive research on these initials after feeding the Quranic text with the initialled chapters into a computer. His objective was to search if there is a mathematical pattern which would explain the significance of the initials, although he had no idea where and what to look for. After several years of research, Dr. Khalifa published his first findings in a book entitled "Miracle of the Quran: Significance of the Mysterious Aphabets" in 1973. Although his findings indicated a correlation between the frequency of the initials themselves, he did not relate these frequencies to any common denominator. By January 1974, he recognised 19 as a common denominator in the initials and throughout the Quran.

Continuing research after this discovery unveiled an intricate mathematical system which pervades the whole Quran and governs every possible element in it (Khalifa, R., 1981 and 1989).

Remarkable Design

The entire text of the Quran is mathematically composed with remarkable intricacy. The basis of this mathematical system is the number 19. Virtually every element of the Quran contains 19 as the common denominator.

Examples
The Quran being a book totally structured on the number 19, contains a vast of patterns and features that are too many to be able to mention them all, the following are only some of these examples:

• The number of chapters in the Quran is 114 = 19 x 6
• The total number of verses in the Quran is 6,346 = 19 x 334
• The occurrence of the word God (Allah) in the Quran is 2,698 = 19 x 142
• The sum of all the verse numbers where the word God occurs is 118,123 = 19 x 6,217
• There are 30 different numbers mentioned in the Quran (e.g. 1 God, 2 brothers, 7 heavens ... etc.), If we add the 30 numbers we get a total of 162146 = 19 x 8534
• The first statement in the Quran, "In the name of God, Most Gracious, Most Merciful" consists of 19 Arabic letters. It is known as the `Basmalah'
• If we look at the four words of the Basmalah separately, we find that each word occurs in the whole Quran in a number that is a multiple of 19
• The very first revelation that was given to the prophet was the first 19 words in sura 96
• The total number of letters making up the 19 words is 76 = 19 x 4
• The First revealed sura (96) has 19 verses
• Sura 96 consists of 304 Arabic letters = 19 x 16
• The last chapter revealed (Chapter 110) has 19 words, and its first verse has 19 letters
• The main message in the Quran is that there is only One God. The word “One” in Arabic is WAHED. The word WAHED appears in the Quran 19 times (when used to speak of God)
• The Geometrical Value (explained below) of the word WAHED is 19
• The word `Quran' occurs in 38 different chapters = 19 x 2
• The word "Quran" occurs in the Quran 58 times, however one of them, in 10:15, refers to "another quran". Thus, the frequency of the occurrence of God's "Quran" is 57 = 19 x 3
• If we add the numbers assigned to all the chapters in the Quran, plus the numbers assigned to all of the verses in the Quran, plus the total number of verses in the Quran, we get a total of 346199 = 19 x 19 x 959
• If we look at the chapters which start with Initials separately and add the chapter numbers, verse numbers and number of verses, the total is 190133 = 19 x 10007. It follows that the total for the un-initialled chapters, 156066, is also divisible by 19.
  
  

This was only a very small selection of 19 related features out of an almost infinite number of other features.

A totally independent feature of the mathematical structure of the book is the initialled letters which appear in the beginning of the initialled suras, and their occurrence inside their chapters. All the initials occur in their corresponding chapters in multiples of 19, when looked at as individual sets. For example, there are two chapters that are initialled with the letter Q. The number of occurrence of the letter Q in each of these chapters is 57 or 19 x 3.
All the details of the initialled letters and their occurrence, plus more details of the miracle of 19, can be found at:
Miracle of the Quran

Geometrical Value (G.V.)

Another aspect of the Quran's mathematical design is the use of the G.V. of the Arabic letters. The G.V. value of a letter is the numerical value assigned to it. When the Quran was revealed, fourteen centuries ago, numbers as we know them today did not exist. Instead, there was a universally accepted numerical system where the letters of the Arabic, Hebrew, Aramaic, and Greek alphabets were used as numerals. In actual fact this system is still used today, for example the Roman letters are used in Law Reference books … e.g. V = 5, X = 10 …. Etc.
The number assigned to each letter is considered to be its G.V.. Thus the G.V. of the letter V (in Roman) is 5 .. etc.
Table 3 gives the G.V. of each letter in the Arabic alphabet, which is listed in its original order. The choice of the English letters used for pronouncing each Arabic letter are based simply on the sounds of the Arabic letters.

Table 3.

The G.V. of

the Arabic alphabet

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10	9	8	7	6	5	4	3	2	1
(Y)	(Tta)	(Hha)	(Z)	(W)	(H)	(D)	(G)	(B)	(A)
100	90	80	70	60	50	40	30	20
(Q)	(S)	(F)	(Aa)	(S)	(N)	(M)	(L)	(K)
1000	900	800	700	600	500	400	300	200
(GH)	(DH)	(Dda)	(ZH)	(KH)	(TH)	(T)	(SH)	(R)

Why 19?

The mathematical coding of the scriptures with the number 19 makes one wander the divine reason for using the number 19 instead of some other number. Besides having unique mathematical properties, such as being a prime number, the number 19 is the G.V. of the word "ONE" in all scriptural languages Aramaic, Hebrew, and Arabic. For example, in Arabic, the word for "ONE" is "WAHD" (pronounced Wahid). Based on Table 4, the G.V. of the letters W, A, H, and D are 6, 1, 8, and 4, respectively.
These numbers add up to 19 (6 + 1 + 8 + 4 = 19).
Therefore, the number 19 can be looked at to signify the First Commandment in all scriptures that there is only ONE God.

In addition, the number 19 is made up of the two numerals 1 and 9, these are the first and last single numerals used in mathematics, thus the number 19 represents the First and Last, or the Alpha and Omega which is once again the attribute of God as confirmed in all scripture.

The Opening Statement

The first verse of the Quran is "In the name of God, Most Gracious, Most Merciful." In Arabic, it is pronounced as Bism Allah Al-Rahman Al-Raheem, and is commonly known as the Basmalah.

The Basmalah is so special and unique that it constitutes the foundation upon which the Quran's 19-based mathematical composition is built. It is the opening statement of the Quran, and is composed of four words and exactly 19 Arabic letters. These letters are given below in Table 4 with the approximate English equivalents and their corresponding G.V..

Table 4.

The 19 Arabic letters of the Basmalah and

their corresponding G.V.

Letter No.	Arabic Letter	English	G.V.
1	Baa'	B	2
2	Siin	S	60
3	Miim	M	40
4	'Alif	A	1
5	Laam	L	30
6	Laam	L	30
7	Haa'	H	5
8	'Alif	A	1
9	Laam	L	30
10	Raa'	R	200
11	H!aa'	Hha	8
12	Miim	M	40
13	Nuun	N	50
14	'Alif	A	1
15	Laam	L	30
16	Raa'	R	200
17	H!aa'	Hha	8
18	Yaa'	Y	10
19	Miim	M	40

Mathematical Design of the Basmalah

The four words and the 19 letters of the Basmalah are put together according to a mathematical system which is humanly impossible to compose. This remarkable system is based on the number and the G.V. of the letters that constitute the four words of the Basmalah. Let us first summarise the information we need to know about the Basmalah in Table 5 before we review this incredible mathematical system.

Table 5.

The four words of the Basmalah, the English translation,

the number of Arabic letters in each word, and their G.V.

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No.	Arabic	English	#Letters	G.V.	Total
1	Bism	In the name	3	2, 60, 40	102
2	Allah	God	4	1, 30, 3, 5	66
3	Al-Rahman	Most Gracious	6	1, 30, 200, 8, 40, 50	329
4	Al-Raheem	Most Merciful	6	1, 30, 200, 8, 10, 40	289

TOTAL

19

786

Using the data in Tables 4 and 5, we get the following 19-based mathematical facts:

FACT 1

The Basmalah consists of 19 Arabic letters.

FACT 2

The sequence number of each word in the Basmalah followed by the number of letters in it forms an 8-digit number which is a multiple of 19:

1 3 2 4 3 6 4 6 = 19 x 19 x 36686

FACT 3

Replace the number of letters in each word in Fact 2 by the total G.V. of that word. Thus, the sequence number of each word is followed by its total G.V., to form a 15-digit number which is a multiple of 19:

1 102 2 66 3 329 4 289 = 19 x 5801401752331

FACT 4

Replace the total G.V. of each word in Fact 3 by the G.V. of every letter in that word. For instance, the total G.V. of the first word, 102, is replaced by 2 60 40. Similarly, the total G.V. of the second word, 66, is replaced by 1 30 30 5, and so on. The result is a 37-digit number which is a multiple of 19:

1 2 60 40 2 1 30 30 5 3 1 30 200 8 40 50 4 1 30 200 8 10 40 = 19 x 66336954226595422109686863843162160

FACT 5

As Fact 4 but this time we substitute the G.V. of every letter with the cumulative total G. V. of all preceding letters. So for the first letter we write its G.V. which is 2, next we write the total G.V. of letters 1 + 2 which is 62, then 1 + 2 + 3 = 102. The total is imported to word 2 and so on.

We end up with the following number:

1 2 62 102 2 103 133 163 168 3 169 199 399 407 447 497 4 498 528 728 736 746 786 = 19 x .................

FACT 6

Insert the sequence number of each letter in the word before its G.V. in Fact 4. For example, the G.V. of the letters in first word are 2 60 40. When we insert the sequence numbers of the letters, we get 1 2 2 60 3 40, where the sequence numbers are in italics, the G.V. are in bold. Similarly, the G.V. of the letters in the second word are 1 30 30 5. When we insert the sequence numbers of the letters, we get 1 1 2 30 3 30 4 5, and so on. When all the numbers are put together, the result is a 56-digit number which is a multiple of 19:

1 1 2 2 60 3 40 2 1 1 2 30 3 30 4 5 3 1 1 2 30 3 200 4 8 5 40 6 50 4 1 1 2 30 3 200 4 8 5 10 6 40 = 19 x 590843895848580686595 . . .

FACT 7

Replace the total G.V. of each word in Fact 3 by the sum of the G.V. of the first and the last letter in that word. For instance, the total G.V. of the first word, 102, is replaced by 42. The number 42 is the sum of 2 and 40, which are the G.V. of the first and the last letter in the first word. Similarly, the total G.V. of the second word, 66, is replaced by 6, the sum of 1 and 5. Repeating this process for the four words of the Basmalah,we get an 11-digit number which is a multiple of 19:

1 42 2 6 3 51 4 41 = 19 x 748755339

(2+40) (1+5) (1+50) (1+40)

FACT 8

Consider the numbers used in Fact 2 and Fact 3. In Fact 2, the sequence number of each word is followed by the number of letters (3, 4, 6, and 6) in the word. In Fact 3, we replace the number of letters by the G.V. of the words (102, 66, 329, and 289). Now, for this case, the sequence number of each word will be followed by the sum of the number of letters and the gematrical value of the word. Therefore, the number we use for the first word will be 105 (3+102). It will be 70 (4+66) for the second word, 335 (6+329) for the third word, and 295 (6+289) for the fourth word.

Thus the sequence number of each word in the Basmalah is followed by the numbers 105, 70, 335, and 295 respectively to form a 15-digit number which is also a multiple of 19:

1 105 2 70 3 335 4 295 = 19 x 5817212281805

(3+102) (4+66) (6+329) (6+289)

FACT 9

Consider Fact 2, where the sequence number of each word in the Basmalah is followed by the number of letters in the word. In this case, the sequence number of each word will be followed by the total number of letters up to and including that word (cumulative total). For example, the number of letters in the Basmalah's four words are 3, 4, 6 and 6, respectively. Then the cumulative total number of letters will be 3 for the first word. It will be 7 (3+4) for the second word, 13 (3+4+6) for the third word, and finally 19 (3+4+6+6) for the last word. Therefore, we write down the sequence numbers of the words followed by the cumulative total number of letters corresponding to the word. The result is a 10-digit number which is also a multiple of 19:

1 3 2 7 3 13 4 19 = 19 x 69858601

(3) (3+4) (3+4+6) (3+4+6+6)

FACT 10

This fact is very similar to Fact 8. In this fact, instead of using the cumulative total number of letters for each word, we use the cumulative total of the G.V. of the letters corresponding to the word. For example, the G.V. of the letters in the Basmalah's four words are 102, 66, 329 and 289, respectively. Then the cumulative total of the G.V. of the letters will be 102 for the first word. It will be 168 (102+66) for the second word, 497 (102+66+329) for the third word, and finally 786 (102+66+329+289) for the last word.

Therefore, we write down the sequence numbers of the words followed by the cumulative total of the G.V. of the letters corresponding to the word. The resultant 16-digit number is a multiple of 19:

1 102 2 168 3 497 4 786 = 19 x 58011412367094

(102) (102+66) (102+66+329) (102+66+329+289)

FACT 11

Insert the sequence number of each word (1, 2, 3, and 4) at the end of the underlined numbers in Fact 10 while keeping all the numbers the same. The result is a 66-digit number that is a multiple of 19. The sequence numbers of the words are printed in italics:

2 1 60 2 40 3 1 1 4 30 5 30 6 5 7 2 1 8 30 9 200 10 8 11 40 12 50 13 3

1 14 30 15 200 16 8 17 10 18 40 19 4 = 19 x 1136968584963 . . .

FACT 12

The G.V. of each letter is followed by its sequence number (1 through 19) in the Basmalah to form a 62-digit number that is a multiple of 19. The sequence numbers are printed enlarged:

2 1 60 2 40 3 1 4 30 5 30 6 5 7 1 8 30 9 200 10 8 11 40 12 50 13

1 14 30 15 200 16 8 17 10 18 40 19 = 19 x 113696858647647 . . .

In this fact, each one of the four words of the Basmalah is underlined to show the numbers representing these words. This information will be helpful to understand the next fact.

FACT 13

Consider the numbers in Fact 11, and replace the sequence numbers of the words (1, 2, 3, and 4) with their G.V. (102, 66, 329, and 289), while keeping all the other numbers the same. The result is a 73-digit number, also a multiple of 19:

2 1 60 2 40 3 102 1 4 30 5 30 6 5 7 66 1 8 30 9 200 10 8 11 40 12 50 13 329 1 14 30 15 200 16 8 17 10 18 40 19 289 = 19 x 113696858432 . . .

FACT 14

This time let us change the position of the G.V. of the words (102, 66, 329, and 289) in Fact 12, and put them preceeding the words, instead of following them. The resultant number, still 73 digits, is also a multiple of 19:

102 2 1 60 2 40 3 66 1 4 30 5 30 6 5 7 329 1 8 30 9 200 10 8 11 40 12 50 13 289 1 14 30 15 200 16 8 17 10 18 40 19 = 19 x 5379790738 . . .

FACT 15

For each word of the Basmalah, write down the following:

a) Number of letters in the word

b) The total G.V. of the word

c) The G.V. of each letter in the word

For example, consider the first word of the Basmalah. It has three letters. The total G.V. of these letters is 102. The individual G.V. of each letter are 2, 60, and 40 respectively. Therefore, we write 3 102 2 60 40 for the first word, and so on. The entire number is 48 digits long, and is a multiple of 19. It is given below with the numbers for each word underlined.

3 102 2 60 40 4 66 1 30 30 5 6 329 1 30 200 8 40 50 6 289 1 30 200 8 10 40

= 19 x 16327686340 . . .

FACT 16

In Fact 14, the total G.V. of the words are printed in bold. Now, we draw your attention to these bold numbers as we place them as the last item in each underlined word. The resultant number, still 48 digits long, is also a multiple of 19:

3 2 60 40 102 4 1 30 30 5 66 6 1 30 200 8 40 50 329 6 1 30 200 8 10 40 289

= 19 x 17160005390 . . .

FACT 17

Let us represent each one of the four words of the Basmalah by the sequence number of the letters in it. For example, the first word is represented by 123, since it has the first three letters of the Basmalah. The second word is represented by 4567 since it contains the letters 4, 5, 6, and 7. Similarly, the third word is represented by 8910111213, and the fourth word by 141516171819, since they contain the letters 8-13 and 14-19 respectively. If we add these four numbers representing the words of the Basmalah, the result is a 12-digit number which is a multiple of 19:

123 + 4567 + 8910111213 + 141516171819= 150426287722 = 19 x 7917173038

FACT 18

Consider the numbers that represented each word of the Basmalah in

Fact 16. Instead of adding these numbers, we write each one down, followed by the sequence number of the word. For example, the first number, 123, which represents the first word, is followed by 1. The second number, 4567, which represents the second word, is followed by 2, and so on. The result is now a 33-digit number, also a multiple of 19:

1 2 3 1 4 5 6 7 2 8 9 10 11 12 13 3 14 15 16 17 18 19 4 = 19 x 64813512047900 . .

FACT 19

This fact is based on three numbers only. We know that the Basmalah consists of 4 words, 19 letters with a total G.V. of 786. Now, let us put these numbers together. The result is a 6-digit number, a multiple of 19:

4 19 786 = 19 x 22094

FACT 20

The Basmalah is Verse 1 of the Quran. It consists of 19 Arabic letters. These 19 letters constitute the four words with the number of letters in each word being 3, 4, 6, and 6 respectively. Based on this information, let us write down 1 for the verse number, followed by 19 for the number of letters, and followed by 3, 4, 6, and 6 for the letters in each word of the Basmalah. The result is a 7-digit number as follows:

1 19 3466 = 19 x 19 x 19 x 174

As we see, this number is not only once, or twice, but three times a multiple of 19. Is it feasible for such an intricate, interwoven, and absolutely awesome mathematical system to be nothing more than coincidence?

Coincidence or Divine Design?

It is very incredible for the four words and the 19 letters of the Basmalah to result in so many numerical combinations based on the number 19. These combinations do not seem to be haphazard either. They are very consistent. For instance, let us look at the numbers in Facts 2 through 9. As you may have noticed, the numbers in these facts are in the same format:

1 ? 2 ? 3 ? 4 ? = n

The numbers 1-4 represent the four words of the Basmalah. The question marks represent any integer number. The resultant number "n" is a multiple of 19. There are only two possible explanations for these numbers in Facts 2-9 being in this format. One explanation is that all this is coincidence. After all, miraculous things do occasionally occur that cannot be explained easily, if at all. The only other explanation is that the Basmalah has been deliberately structured in a certain way to result in this remarkable mathematical system. Let us try to figure out which explanation makes more sense based on probability theory.

First, what is the probability (chances) for the Basmalah's mathematical composition to occur by coincidence? Can we compute this probability? If we can, how? Based on our assumption of coincidental occurrence, we can treat each number in Facts 2-9 as a random number. The probability of several random numbers being not only in a certain format, but also forming a number "n" that is a multiple of 19, can be difficult to compute unless we make some assumptions to simplify the problem. For example, the highest probability (the best chance) of obtaining "n" will be when we assume that the four numbers represented by the question marks above are all single digit numbers (0-9). In that case, the resultant number nª will have 8 digits since we know that the other four numbers are also single digit (1-4). Then we can easily compute the probability of 8 random numbers resulting in the desired format. Let us see how we can do this.

Imagine that we are playing a lottery. This lottery requires that we draw 8 numbers that are between 0 and 9. Anyone who satisfies the following conditions wins the jackpot:

1. The first number must be 1.

2. The third number must be 2.

3. The fifth number must be 3.

4. The seventh number must be 4.

5. All the numbers when put side by side must form a number that is a multiple of 19.

The resultant 8-digit lottery numbers can vary anywhere from 00000000 to 99999999. This means there are 100 million possible outcomes or combinations. How many times will the above winning conditions be satisfied out of this many combinations? If we knew the answer, then we could determine the probability or the chances of winning the lottery. In order to answer this question, we wrote a computer program to go through every number from 0 to 99,999,999 and determine all the numbers that will satisfy the desired conditions. This program found only 527 such numbers which ranged from 10,203,247 (first possible combination) to 19,293,949 (last possible combination). Therefore, the chances of winning this lottery is 527 out of 100 million or 1 out of 189,753.

Based on this information, we can say that the probability of the occurrence of the mathematical phenomenon described in Fact 2, is 189,753 to 1. The probability of the mathematical phenomenon in Fact 2 and Fact 3 occurring by coincidence is the same as winning our lottery twice. To determine the probability of winning the lottery twice, we multiply 189,753 by 189,753:

189,753 * 189,753 = 36,006,201,009

In other words, the probability of the mathematical phenomenon in Fact 2 and Fact 3 occurring by coincidence is less than 1 in 36 billion. In comparison, in the California state lottery where six numbers are drawn out of 51, someone has to buy about 18 million $1 tickets to cover every 6-number combination for the grand prize. Therefore, the chances of winning the California lottery, 1 in 18 million, is much better than the chances of the mathematical phenomenon in Fact 2 and Fact 3 occurring by coincidence.Now, let us try the same process once more, and pick another set of eight numbers that will also meet the winning conditions. To determine the probability of winning the lottery three times, or the probability of the mathematical phenomenon in Fact 2, Fact 3 and Fact 4 occurring by coincidence, we multiply 189,753 by itself three times:

189,753 * 189,753 * 189,753 = 6,832,284,660,060,777

The above number is close to seven quadrillion! If you are wondering what a quadrillion is, you are not alone. We had to look in the dictionary to find out what follows the trillions. Thus, there is an almost 1 in seven quadrillion probability that Fact 2, Fact 3, and Fact 4 will occur by coincidence. As you can see, by considering just three of several mathematical facts, we realise that the probability of such numerical combinations occurring by coincidence is extremely minuscule. It is very clear that this probability will approach zero as we take more and more mathematical facts into consideration. Therefore, one would be illogical to even suggest that the mathematical composition of the Basmalah is nothing more than a mere coincidence.

If we rule out the possibility of coincidence, then we have to accept the other explanation that the Basmalah has been deliberately structured in a particular way to result in this remarkable mathematical system. Can we also rule out the possibility for such an intricate system being designed by any other than God? All this will be discussed in the following sections and chapters of this book. It is up to the individual to draw his or her own conclusions from these presentations.

The Missing Basmalah

The Basmalah occupies a special position in the Quran. It is the opening statement in every one of the 114 chapters in the Quran, except Chapter 9. The absence of the Basmalah from Chapter 9 had puzzled generations of people who had studied the Quran for the last 14 centuries. In fact, many theories were advanced to explain this phenomenon. As it turns out, this is also a part of the mathematical composition that has been intricately built into the Quran.

Since the Quran consists of 114 (19 x 6) chapters, the Basmalah missing from Chapter 9 should result in a total of 113 Basmalahs in the Quran, a number that is not a multiple of 19. However, if we start counting from Chapter 9, we find that the missing Basmalah is compensated for, exactly 19 chapters later, in Chapter 27. This chapter contains two Basmalahs, one at the beginning and one in Verse 30. Thus, the total number of Basmalahs in the Quran is restored to 114, or 19 x 6, with the additional Basmalah in Chapter 27.

Not only is the missing Basmalah found 19 chapters later, but the chapter and the verse number in which the extra Basmalah occurs also adds up to 57 (27 + 30), or 19 x 3. This is quite remarkable, and it shows us how the whole Quran is like a jigsaw puzzle with all the pieces fit together in a 19-based mathematical system.

The connection between the missing and the extra Basmalah leads us to deliberate further on the mathematical design of the Quran. If we add the chapter numbers starting from Chapter 9 (with the missing Basmalah) up to Chapter 27 (with the extra Basmalah), the total is 342 (9 + 10 + 11 + ... + 27 = 342). This total is a multiple of 19, as it should be, since the sum of any 19 consecutive numbers is a multiple of 19. However, what is remarkable is that if we count the number of Arabic words from the first Basmalah in Chapter 27 to the second one in verse 30 of the same chapter, we find that the total is exactly the same as the number above, 342, or 19 x 18.

The summary of the mathematical facts reviewed in this section is given below:FACT 20. There are 114 (19 x 6) Basmalahs in the Quran.

FACT 21

There are 19 chapters from the missing Basmalah in Chapter 9 to the extra one found in Chapter 27 (both chapters inclusive).

FACT 22

The extra Basmalah is found in Chapter 27, verse 30. These two numbers add up to 57, or 19 x 3.

FACT 23

The number of Arabic words from the first Basmalah in Chapter 27 to the second one in verse 30 of the same chapter is 342, or 19 x 18. This is the same number obtained if we add all the chapter numbers from Chapter 9 (with the missing Basmalah) through Chapter 27.

A Unique Phenomenon

As stated earlier, every chapter in the Quran starts with a Basmalah, except Chapter 9. However, none of these Basmalahs are assigned a verse number, except in Chapter 1 where the Basmalah is in Verse 1. Yet, the unnumbered Basmalahs are part of the Quran. The fact that they are unnumbered is also part of the mathematical composition of the Quran. To demonstrate this point, we assign a verse number of zero to each one of the unnumbered Basmalahs so that they can be included in our study.

FACT 24

Let us combine (put together) the chapter number with the verse number where the Basmalah occurs, for each of the 114 Basmalahs in the Quran, and add up all the combined numbers. The concept of combined numbers will be explained below with the examples.

The first Basmalah occurs in Chapter 1, Verse 1. The combined number for this Basmalah is 11 obtained by putting the two numbers (1 and 1) together. The second Basmalah occurs in Chapter 2, Verse 0. The combined number for this Basmalah is 20. If we add these two combined numbers, 11 and 20, we get 31. We continue this process for each chapter. We skip Chapter 9 since it does not have a Basmalah. On the other hand, we include Chapter 27 twice since there are two Basmalahs in this chapter; one in Verse 0, the other is in Verse 30. The combined numbers for this chapter are 270 and 2730, representing the two Basmalahs in this chapter.The last Basmalah occurs in Chapter 114, Verse 0. The combined number for this Basmalah is 1140. By adding up all of the 114 combined numbers, we get a total of 68,191 or 19 x 3,589. This process is demonstrated in Table 6.

Table 6.

Mathematical system of adding the combined numbers

of chapter and the verse number where the 114 Basmalahs occur

.

Chap. No.	Basmalah Verse No.	Combined No.
1	1	11
2	0	20
3	0	30
-	-	-
-	-	-
-	-	-
8	0	80
10	0	100
-	-	-
-	-	-
27	0	270
27	30	2730
-	-	-
-	-	-
112	0	1120
113	0	1130
114	0	1140

TOTAL

68191 = 19x3589

What is remarkable about the above phenomenon is that the 19-based mathematical relationship holds true also when we repeat the same process using only the odd or even numbered chapters. The resultant total for the odd numbered chapters is 35,131 or 19 x 1,849. The total for the even numbered chapters is 33,060 or 19 x 1,740.

The Four Words of the Basmalah

The frequency of occurrence of every (Arabic) word of the Basmalah in the entire Quran (excluding the unnumbered Basmalahs) is consistently a multiple of 19. These words are ISM, ALLAH, AL-RAHMAN, and AL-RAHEEM. Their English meanings are NAME, GOD, MOST GRACIOUS, and MOST MERCIFUL, respectively. Note that we are using ISM (Name) as the first word of the Basmalah, instead of the word BISM (In the name). In other words, we are using the root word without the prefix B (In the) in this counting. Table 7 below summarises the mathematical facts based on the number of occurrences of the Basmalah's words.

Table 7.

The four words of the Basmalah and

their number of occurrences in the Quran

.

Word No.	Arabic	English	No. of Occurence
1	Ism	Name	19
2	Allah	God	2698 (19x142)
3	Al-Rahman	Most Gracious	57 (19x3)
4	Al-Raheem	Most Merciful	114 (19x6)

.

Now, let us itemise the facts summarised in Table 7 with the additional facts that make the mathematical system in the Quran even more incredible:

FACT 25

The first word in the Basmalah, ISM (Name), occurs in the Quran exactly 19 times. The verses where this word is mentioned are given in Table 8.

FACT 26

Using the information in Table 8, let us write down the chapter number followed by the verse number in which the word ISM (Name) occurs for each one of its 19 occurrences, without repeating the chapter number if there are more than one ISM in that chapter. The resultant number is 58 digits and a multiple of 19. This is shown below with the chapter numbers printed in bold:

5 4 6 118 119 121 138 22 28 34 36 40 49 11 55 78 56 74 96 69 52 73 8 76 25 87 1 15 96 1 = 19 x 2874305890111 ...

Table 8.

The chapter and the verse numbers where

the word ISM (Name) occur in the Quran

.

No.	Chapter No.	Verse No.
1	5	4
2	6	118
3	6	119
4	6	121
5	6	138
6	22	28
7	22	34
8	22	36
9	22	40
10	49	11
11	55	78
12	56	74
13	56	96
14	69	52
15	73	8
16	76	25
17	87	1
18	87	15
19	96	1

FACT 27

The word ISM (Name) with the prefix B (In the) makes the word BISM (In the name). This word occurs in the Quran in this particular spelling only 3 times; in Chapter 1, Verse 1; Chapter 11, Verse 41 and Chapter 27, Verse 30. If we add the number of occurrence of this word (3), to the numbers of the chapters and the verses where the word is found, the total equals exactly to the number of chapters in the Quran:

3 + 1 + 1 + 11 + 41 + 27 + 30 = 114 (19 x 6)

FACT 28

The second word of the Basmalah, ALLAH (God), is mentioned in the Quran 2,698 (19 x 142) times.

FACT 29

The numbers of the verses where the word ALLAH (God) occurs add up to 118,123, or 19 x 6,217. To determine this, we start from the beginning of the Quran, and check each verse for the occurrence of the word "God." If "God" is mentioned in that verse, whether once or more than once, then we add the number of the verse to our total.

FACT 30

The third word of the Basmalah, AL-RAHMAN (Most Gracious), is mentioned in the Quran 57 (19 x 3) times.

FACT 31

The fourth and the last word of the Basmalah, AL-RAHEEM (Most Merciful), is mentioned in the Quran 114 (19 x 6) times.

Correlation with the Attributes of God

There are over 400 attributes (names) of God mentioned in the Quran. Professor Cesar Majul (1983) looked at the G.V. of these attributes, and discovered that there are only four attributes of God whose G.V. are a multiple of 19. This is summarised in Table 9 below.

Table 9.

The attributes (names) of God whose

G.V. are a multiple of 19

	Attribute of God	G.V.
1	Waahed (One)	19
2	Zul Fadl Al-`Azim (Possessor of Infinite Grace)	2698 (19x142)
3	Majid (Glorious)	57 (19x3)
4	Jaami (Summoner, Gatherer, Editor)	114 (19x6)

We can see from Table 7 and Table 9 above that the only attributes of God whose G.V. are multiples of 19 correspond exactly to the frequencies of occurrences of the Basmalah's four words. Let us summarise these mathematical facts:

FACT 32

The first word of the Basmalah, ISM (Name), occurs in the Quran 19 times, and the number 19 represents God's attribute WAAHED (One). The G.V. of the four Arabic letters in the word WAAHED are 6, 1, 8, and 4. These numbers add up to 19. Thus,

6 + 1 + 8 + 4 = 19 = WAAHED (One)

FACT 33

The second word of the Basmalah, ALLAH (God), occurs in the Quran 2,698 or 19 x 142 times, and the number 2,698 represents God's attribute ZUL FADL AL-`AZIM (Possessor of Infinite Grace). The G.V. of the 13 Arabic letters in this attribute of God are 700, 6 , 1, 30, 80, 800, 30, 1, 30, 70, 900, 10 and 40. These numbers add up to 2,698. Thus,

700 + 6 + 1 + 30 + 80 + 800 + 30 + 1 + 70 + 900 + 10 + 40= 2698 (19 x 142) = ZUL FADL AL-`AZIM (Possessor of Infinite Grace)

FACT 34

The third word of the Basmalah, AL RAHMAN (Most Gracious), occurs in the Quran 57 or 19 x 3 times, and the number 57 represents God's attribute MAJID (Glorious). The G.V. of the four Arabic letters in the word MAJID are 40, 3, 10 and 4. These numbers add up to 57. Thus,

40 + 3 + 10 + 4 = 57 (19 x 3) = MAJID (Glorious)

FACT 35

The fourth and the last word of the Basmalah, AL RAHEEM (Most Merciful), occurs in the Quran 114 or 19 x 6 times, and the number 114 represents God's attribute JAAMI (Summoner, Gatherer, Editor). The G.V. of the four Arabic letters in the word JAAMI are 3, 1, 40 and 70. These numbers add up to 114. Thus,

3 + 1 + 40 + 70 = 114 (19 x 6) = JAAMI (Summoner, Gatherer, Editor)

Conclusion

The third attribute of God, Majid or Glorious, given in Fact 34 also refers to the Quran (Quran 50:1). Based on this, we can deduce the following conclusion from the remarkable phenomenon summarised in Facts 30-35 and all the other mathematical facts presented in this chapter: The author of the Quran is One who is the Possessor of Infinite Grace, who gathered the Quran into 114 chapters.

Thus, the Quran's intricate numerical code based on the number 19 starts at its very first verse with the opening statement, the Basmalah, indicating to the reader of the Quran at the outset that he is reading the word of God. However, what is presented to you so far is a small fraction of this indescribably vast, elaborate mathematical system which extends all the way to the end of the Quran. Next we will discuss this remarkable system in relation to the opening chapter of the Quran.

Acknowledgements

All praise and thanks are due to God who has allowed me to work on this project. I would like to acknowledge the work of Dr. Rashad Khalifa who discovered the existence of the 19-based mathematical system in the Quran.

Through his efforts and encouragement before he was killed on January 31, 1990, many individuals began research on the Quran's mathematical system. Based on this research, some individuals were blessed to discover different portions of this system by God's will. I would like to thank Professor Cesar Majul and brother Sharif of Egypt for their contribution to this particular volume.

For the editorial assistance, I am grateful to the the following individuals: Gatut Adisoma, Donna Arik, Douglas Brown, Shakira Karipineni, Lydia Kelly, Lisa Spray, and many others in Masjid Tucson. May God bless them all.

References

Dan, J. and Talmage, F., eds, (1982), STUDIES IN JEWISH MYSTICISM, Association for Jewish Studies, Cambridge, Massachusetts.

Khalifa, R., (1973), MIRACLE OF THE QURAN: Significance of the Mysterious Alphabets, Islamic Productions, St. Louis, Missouri.

Khalifa, R., (1981), THE COMPUTER SPEAKS: God's Message to the World, Renaissance Productions, Tucson, Arizona.

Khalifa, R., (1982), QURAN: Visual Presentation of the Miracle, Islamic Productions, Tucson, Arizona.

Khalifa, R., (1989), QURAN: The Final Testament, Islamic Productions, Tucson, Arizona.

Majul, C. A., (1983), The Names of Allah in Relation to the Mathematical Structure of Quran, Pamphlet, Islamic Productions, Tucson, Arizona.