Bedford's Law & Quran

Submitters Perspective
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ourtesy of www.masjidtucson.org

BEDFORD'S LAW & THE QURAN


According to Benford's discovery, if you count any collection of objects - whether it be pebbles on the beach, the number of words in a magazine article or dollars in your bank account - then the number you end up with is more likely to start with a "1" than any other digit. Somehow, nature has a soft spot for digit "1". Benford was not the first to make this astonishing observation. 19 years before the end of 19th century, the American astronomer and mathematician, Simon Newcomb, noticed that the pages of heavily used books of logarithms were much more worn and smudged at the beginning than at the end, suggesting that For some reason, people did more calculations involving numbers starting with 1 than 8 and 9.

(Newcomb, S. "Note on the frequency of the Use of Digits in natural Numbers." Amer. J. Math 4, 39-40, 1881)

He conjectured a simple formula: nature seems to have a tendency to arrange numbers so that the proportion starting with the digit D is equal to log10 of 1 + (1/D).

Newcomb`s observations were then virtually ignored until 57 years later when Frank Benford, a physicist with the General Electric Company, published his paper. (Bedford, F. "The Law of Anomalous Numbers." Proc. Amer. Phil. Soc. 78, 551-572, 1938). He rediscovered the phenomenon and came up with the same law as Newcomb. Conducting a monumental research, he analyzed 20229 set of numbers gathered from everywhere from listings of the areas of rivers to physical constants and death rates, he showed that they all adhere to the same law: around 30.1 per cent began with the digit 1, 17.6 per cent with 2, 12.5 per cent with 3, 9.7 per cent with 4, 7.9 percent with 5, 6.7 percent with 6, 5.8 per cent with 7, 5.1 percent with 8 and 4.6 percent with 9.

Benford's law is scale-invariant (the distribution of digits is unaffected by changes of units) and base-invariant. In fact in 1995, 114 years after Newcomb's discovery, Theodore Hill, proved that any universal law of digit distribution that is base invariant has to take the form of Benford's law ("Base invariance implies Benford's law", Proceedings of the American Mathematical Society, vol 123, p 887).

In applying Benford's law three rules should be observed: 

  • First the sample size should be big enough to give the predicted proportions a chance to show themselves so you will not find Benford's law in the ages of your family of 5 people. 
  • Second, the numbers should be free of artificial limits so obviously you cannot expect the telephone numbers in your neighborhood to follow Benford's law. 
  • Third, you don't want numbers that are truly random. By definition, in a random number, every digit from 0 to 9 has an equal chance of appearing in any position in that number.

  

 An excellent fraud-buster:

This fascinating mathematical theorem is a powerful and relatively simple tool for pointing suspicion at frauds, embezzlers, tax evaders and sloppy accountants.

The income tax agencies of several nations and several states have started using detection software based on Benford's Law to detect fabrication of data in financial documents and income tax returns.

The idea is that if the numbers in a set of data like sales figures, buying and selling prices, insurance claim costs and expense claims, more or less match the frequencies and ratios predicted by Benford's Law, the data are probably honest. But if a graph of such numbers is markedly different from the one predicted by Benford's Law, it arouses suspicion of fraud.

 

Application to the Quran:

The Quran is divided into chapters of unequal length, each of which is called a sura.

The shortest of the suras has ten words, and the longest placed second in the text, has over 6000 words. From the second sura onward, the suras gradually get shorter, although this is not a hard and fast rule. The last sixty suras take up about as much space as the second . This unconventional structure does not follow people's expectations as to what a book should be. However it appears to be a deliberate design on the part of the author of the Quran.

Let's verify the evidence:

Quran consists of 114 suras. Each sura is composed of a certain number of verses, for example sura 1 has 7 verses and sura 96 (the first sura revealed to Prophet Muhammad) has 19 verses. So we have a set of 114 data to which we can apply Benford's law. The result is shown in the following tables:

Group X includes All the suras containing a number of verses starting with the digit X

Group one. These are  30 Suras

Sura Number

4

5

6

9

10

11

12

16

17

18

Number of verses

176

120

165

127

 

123

111

128

111

110


Group one

Sura Number

20

21

23

37

49

60

61

62

63

64

Number of verses

135

112

118

182

18

13

14

11

11

18

Group one

Sura Number

65

66

82

86

87

91

93

96

100

101

Number of verses

12

12

19

17

19

15

11

19

11

11



Group two . These are 17 Suras

Sura
Number  
 

2

3

7

26    

48       

57       

58          

59      

71      

72       

Number
of
verses

286     

200    

206     

227         

29    

29

22

24

28

28


Group two

Sura
Number

73  

81    

84  

85  

88    

90  

92  

Number
of
verses        

20

29

25

22

26

20

21

Group three . These are 12 suras.

Sura
Number

31     

32    

45    

46    

47    

67    

76    

83    

89    

103    

108    

110  

Number
of
verses            

34

30

37

35

38

30

31

36

30

3

3

3


 

Group four

  These are 11 Suras

Sura Number

13

35

50

52

70

75

78

79

80

106

112

Number of verses

43

45

45

49

44

40

40

46

42

4

4



Group five

These are 14 Suras.

Sura Number

14

34

41

42

44

54

68

69

74

77

97

105

111

113

Number of verses

52

54

54

53

59

55

52

52

56

50

5

5

5

5

Group six

These are 7 Suras.

Sura Number

24

29

30

51

53

109

114

Number of verses

64

69

60

60

62

6

6

  Group seven

These are 8 Suras.

Sura Number

1

8

22

25

33

39

55

107

Number of verses

7

75

78

77

73

75

78

7

  Group eight

These are 10 Suras.

Sura Number

28

36

38

40

43

94

95

98

99

102

Number of verses

88

83

88

85

89

8

8

8

8

8



Group nine

These are 5 Suras.

Sura Number

15

19

27

56

104

Number of verses

99

98

93

96

9

 Thus, there are 30 suras in the Quran containing a number of verses starting with digit "1", 17 suras with digit "2", 12 suras with digit"3", 11 suras with digit "4", 14 suras with digit "5", 7 suras with digit "6", 8 suras with digit "7", 10 suras with digit "8" and 5 suras with digit "9". As it is seen on the graph, this digital distribution is remarkably close to Benford’s prediction.

This data also conforms to the Quran’s code:

30*1+17*2+3*12+4*11+5*14+6*7+7*8+8*10+9*5= 437 = 19 x 23

Is It A Mere Coincidence?

We observed that Group one contains 30 suras. Remember that number 30 is the 19th composite number. Number 30 appears to have a crucial role in Quran’s mathematical system. The only time that number 19 is mentioned in the Quran is verse 30 (sura 74). Also note that the number of suras (114=19*6) is immediately preceded with 30th prime number (113). Furthermore, the 19th prime is 67 and sura 67 happens to have 30 verses (Group three). Also see Editor’s Note#2 in The End of the World coded in the Quran.

Another fascinating feature of Group one reveals itself when we arrange the suras in the chronological order of revelation; Sura 82 with 19 verses fits into the 19th place.

Sura Number

96

87

93

100

91

101

86

20

17

10

11

12

6

37

18

Number of verses

19

19

11

11

15

11

17

135

111

109

123

111

165

182

110

Chronological order of revelation

1

8

11

14

26

30

36

45

50

51

52

53

55

56

69

 

Sura Number

16

21

23

82

60

4

65

63

49

66

64

61

62

5

9

Number of verses

128

112

118

19

13

176

12

11

18

12

18

14

11

120

127

Chronological order of revelation

70

73

74

82

91

92

99

104

106

107

108

109

110

112

113

  

Henri Poincare:* Mathematician, born in Nancy, France. He studied at Paris, where he became professor in 1881 (=19 x 99) . He was eminent in physics, mechanics, and astronomy, and contributed to many fields of mathematics. He created the theory of automorphic functions, using new ideas from group theory, non-Euclidean geometry, and complex function theory. The origins of the theory of chaos are in a famous paper of 1889 on real differential equations and celestial mechanics. Many of the basic ideas in modern topology, triangulation, and homology are due to him. He gave influential lecture courses on such topics as thermodynamics, and almost anticipated Einstein's theory of special relativity, showing that the Lorentz transformations form a group. In his last years he published several books on the philosophy of science and scientific method, and was also well known for his popular expositions of science.

 

BEDFORD’S LAW & The Quran

"If God speaks to man, he undoubtedly uses the language of mathematics."   Henri Poincare*

"You shall not accept any information, unless you verify it for yourself. I have given you the hearing, the eyesight, and the brain, and you are responsible for using them." Quran (17:36)

The Quran is intended to be an eternal miracle. The highly sophisticated mathematical system based on prime number 19 embedded into the fabric of the Quran ( decoded between 1969-1974 with the aid of computers), provided verifiable PHYSICAL evidence that "The Book is, without a doubt, a revelation from the Lord of the universe." (32:2), and incontrovertibly ruled out the possibility that it could be the product of a man living in the ignorant Arabian society of the 7th century. It also proved that no falsehood could enter into the Quran, as promised by God .

"To ascertain that they fully delivered their Lord's messages, He protectively enveloped what He entrusted them with and He counted the numbers of all things ." 72:28 (7+2+2+8)

Furthermore the mathematical miracle of the Quran shed new light on the exceptional style and structure of the book. Here, we will look into one of these aspects through Digital Analysis based on a modern mathematical theorem known as Benford’s Law which has proved strikingly effective in detecting frauds.


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