C O R N E L L    U N I V E R S I T Y

Center for Radiophysics and Space Research

SpaceSciencesBuilding

Ithaca,New York14853-6801

 

Telephone (607) 255-4971                                                Laboratory for Planetary Studies

Fax (607) 255-9888

February 17, 1994

Mr. Edip Yuksel

[address]

Dear Mr. Yuksel:

                Thanks for your recent letter, but I don’t think you have understood the distinction I was making between A PRIORI and A POSTERIORI judgements. Let’s take the example you’ve sent me. You have chosen the first verse of the Qur’an to do your numerology, but of course that is an arbitrary decision. You could, for example, have chosen the 19th sura, or any “code” index you wished and then tried to find it repeated throughout the Qur’an.

                I see many signs of arbitrary decisions in what you consider evidence; for example, why do you count from the missing “Bismillah” to the extra “Bismillah”, instead of from Chapter 1 to Chapter 9 or from Chapter 27 to the end? With a sufficient computer data base and absolutely no A PRIORI constraints a clever person should be able to find many regularities. If in addition the author and transcribers of the Qur’an consciously inserted a little numerology, I believe that the coincidences you describe can readily be understood. Of course I might be wrong.

                With best wishes,

Cordially,

[signature]

Carl Sagan

CS:lkp

 

***
*

EDIP YUKSEL

[Address omitted]

In the name of God, Gracious, Merciful

3/29/1994

 

Dear Dr. Sagan,

The conclusion of your concise letter was a brilliant skeptical hypothesis: “With a sufficient computer database and absolutely no a priori constraints a clever per­son should be able to find much regularity. If in addition the author and tran­scribers of the Qur’an consciously inserted a little numerology, I believe that the coincidences you describe can readily be understood.” Nevertheless, you, as a cautious scientist, did not forget to add “Of course I might be wrong.”

Unfortunately or fortunately, I can’t reciprocate your humble statement by say­ing “of course I too might be wrong!” On the contrary, I am obliged to say “of course, Dr. Sagan, you are wrong.” I am certain that the mathematical structure of the Quran is the work of the Supreme Mathematician, as you are certain that the planet earth is round and rotates around the sun. I hope you won’t get of­fended if I remind you of the possibility of having some “a priori constraints” that may force you not to see the inimitable signature of the Most Wise.

Before starting my counter argument, I want to tell you that I am impressed by your meticulousness in spelling the word “Qur’an” (The Book of Recitation) with its accurate translitera­tion. For convenience I prefer to write “Quran.” As for my misunderstanding of “a priori, and a posteriori statis­tics,” I can blame the different implications of this terminol­ogy in different fields.

Arbitrary Decisions

In order to provide a concrete base for our argument, in my previous letter, I had picked some mathematical patterns related to “Bismillah,” the opening statement of the Quran. You claim that it is arbitrary to focus on “Bismillah”.

I disagree, since I think “Bismillah” is the most appropriate candidate among all the options. If you ask people who are familiar with the Quran to choose an idiosyncratic or representative verse, I am sure that a great majority of them will pick the “Bismillah” without hesita­tion. It is not only the first verse of the Quran, it is also the opening statement of every chapter except Chapter 9. Furthermore, it is the most repeated verse in the Quran and the most popular verse among Muslims. We say “Bismi Allahi RaĤMaNi Rahim” (In the name of God, Most Gracious, Most Merciful) before eating and drinking, or be­fore starting our cars, etc. It is virtually a sacred password.

For the sake of argument, let’s assume that “Bismillah” is not special and we picked it arbitrarily. The probability of finding a verse in the Quran that exhibits ONLY six features of “Bismillah” is very low. If you consider the as­tounding inter­locking relation between the number of the occurrences of the words in “Bismillah” and the gematrical values of the names of God, then the probability will diminish dramatically. Please note that the re­lation between “Bismillah” and God’s names is not arbitrary but a necessity coming from the very meaning of “Bismillah.” Besides, we have discovered many more mathe­matical facts just about “Bismillah” which eventually reduce the probability to zero. Therefore, neither “arbitrary decisions” nor “a little nu­merology” nor “coincidences,” nor the combi­nation of the three can be candi­dates for a plausible explanation.

As another example of “arbitrary decisions” you mention the relation be­tween the missing “Bismillah” and the extra “Bismillah.”  You ask: “why do you count from the missing ‘Bismillah’ to the extra ‘Bismillah’, instead of from Chapter 1 to Chapter 9 or from Chapter 27 to the end? ”

I have at least four answers for this objection:

1. Just look at two adjectives of the “Bismillah” you mention in your question: MISSING and EXTRA. Isn’t it more logical to look for a relation between the MISSING and EXTRA, instead of the FIRST and MISSING, or the EXTRA and LAST?

2. The number of chapters from Chapter 1 to Chapter 9 AND from Chapter 27 to the end is also a multiple of 19:[, which is] 95 (19×5), since the number of all Chapters are multiple of 19.

3. The author of the Quran obviously has willed to hide the implication of the code 19 in Chapter 74 (The Hidden Secret) until 1974. It is a message reserved for the computer generation. If the missing “Bismillah” or the extra “Bismillah” had been in Chapter 19, as you suggest, then the code of the Quran could be easily discovered prematurely, since many previous Sunni and Shiite scholars were aware of the fact that “Bismillah” consists of 19 letters. The relation of “Bismillah” with another 19 could easily lead them to search for its mathematical function in the Quran. I believe that there are many reasons behind the timing of this discov­ery. If God Almighty did not want the corrupt Sunni and Shiite clergymen to discover and abuse this miraculous phenomenon, then it is understandable to see why the simple facts of Quran’s mathematical system are hidden from oblivious eyes.

4. Besides, if there was a conscious effort to insert a little numerology in the Quran, as you suspect, then satisfying your suggestions would be very easy.  Arranging the Chapter with missing “Bismillah” as the 19th chapter and the Chapter with the extra one as the 37th chapter would eliminate at least one objec­tion of skeptics. Why should Muhammad ignore this very simple arrangement while wasting his time and energy on arranging more complicated ones? If you claim that he was not smart enough to do this simple task, you will loose your main argument regarding more clever and complex patterns; because then you cannot say that Muhammad was a clever mathematician etc.

From your criticism, it seems you are not sure whether the claimed mathematical pattern is intentional or not. You seem to want to have it both ways. You have a two-sided judgment ready at your dis­posal: either it is ENTIRELY coincidence, OR it is semi-conscious and semi-coinci­dence. This is a very sure way of discarding anything you disagree with. You can jump be­tween these two preconceived judgments whenever you want. For instance, you can refute my answer above in number 4, by claiming that the mathematical structure of the Quran is entirely coincidental. On the other hand, when the word “coincidence” is too improbable to reject my argument, you can seek refuge in the other side of the label by claiming that it is a little deliberate numerology. I think, for a healthier argument you should clarify your position. Refuting a thesis by oscillating between a contradictory disjunction indicates prejudice.

Is Every Scientific Experiment Arbitrary?

Narrow Inductive Model of Scientific Investigation requires the following:

1. Observe and record all facts.
2. Classify and analyze without prior hypothesis.
3. Induce generalizations from observed facts.

But scientists never follow these utopic principles when they conduct their exper­iments. They do not observe and record all facts. How can they?  Their previous observations, reflections and expectations determine the relevant facts and exper­iments.

You must be familiar withNewton’s “Experimentation Cruces” on the nature of light and colors. A skeptic could object to his findings by claiming that he started his experiment with an a priori hypothesis and with arbitrary decisions: “Why didn’tNewtonmeasure the temperature of the room? Why didn’t he consider the distance of the source of light? Why did he ignore the role of the type of the mir­ror? etc….” As you know,Newtonhad a better intuition than any of his contem­porary scientists about which phenomena were relevant and which were not in searching for the nature of light.

The point is, non-relevant phenomena may seem relevant to an outsider, but a scientist familiar with a particular subject will have clear or vague reasons to de­cide on the relevancy of observations. We can have a hypothesis as long as they guide our observation but not determine the result of our observation. Why don’t you grant the following self-correcting scientific method for the study of the mathematical system of the Quran?:

Simple Hypothetico-Deductive Model:

[Diagram is omitted]

The Fir Cone Argument

You know that each term of Fibonacci sequence which runs: 1, 1, 2, 3, 5, 8, 13, 21, 34 …, is the sum of the two preceding terms. This numerical sequence appears in nature and plants, such as reproduction of rabbits, fir cones and petals of cer­tain flowers.

Let’s take fir cones. Observers claim that the pattern of scales in fir cones follows the order of Fibonacci series. This claim or phenomenon can be evaluated in two ways. Let’s have a hypothetical argument regarding the existence of Fibonacci pattern in fir cones. Simultaneously, we will consider it analogous to our argu­ment on the mathematical pattern of the Quran.

PROPONENT: There are thousands of other plants where Fibonacci sequence cannot be observed. It is entirely an arbitrary decision to choose fir cones as an example of this so-called pattern.  The ap­pearance of Fibonacci sequence in fir cones is only an interesting co­incidence. Of course, I might be wrong.

OPPONENT: Though when other plants are considered, the appear­ance of Fibonacci sequence in fir cones can be a coincidence but the very pattern in fir cones cannot be coincidence. There must be a reason behind this regularity in fir cones.

PROPONENT: I was just being sarcastic. I was trying to use your own argu­ment against you. The status of “Bismillah” in the Quran is much more prestigious and important than the status of fir cones in plant kingdom, let alone in all of nature. Second, there are many more examples of the 19-based mathematical pattern in the Quran, than the examples of Fibonacci Sequence in nature.

OPPONENT: You ignore something about fir cones. We can repeat our obser­vation millions of times on millions of different fir cones and come to the same conclusion. The repeated observation of a similar pattern makes a scientist to ac­cept the existence of that pat­tern. However, you have only one “Bismillah” with a pattern.

PROPONENT: Well, how many fir cones are enough to convince you that Fibonacci sequence exists in the nature of fir cones?

OPPONENT: I don’t know. Probably, ten or twenty observation would be enough.

PROPONENT: That means, after twenty observations you will general­ize your con­clusion on billions of fir cones that you haven’t ob­served. Why do you “believe” that the other fir cones also will show the same property?

OPPONENT: For two reasons: First, all my twenty observations con­firmed the pattern without a single exception. Indeed, after several observations we start predicting and each extra observation is a fulfill­ment of our prediction. Thus, there is no reason to suspect the 21’st fir cone will spoil this coherent orchestra. Second, our previ­ous ob­servations on many other cases have created a very strong belief that ap­parently similar things share similar internal structures. I mean that our previous observations, say, on mangos or bananas have created a faith in determinism.

PROPONENT: What if, similarly, my observation on different elements of the Quran has created a faith in the intention and style of its de­signer.

OPPONENT: Well, you can select anything that confirms your faith, and you can ig­nore or interpret any exception that contradicts your expectation.

PROPONENT: Ironically, I can say the same thing about your scientific method. You observe and predict. If any observation contradicts your prediction you will modify your theory or create a new for­mula. Your prediction can be “certain” only about the objects of your previous obser­vations. However, on new cases you cannot guarantee your predic­tion, since history is full of failures of scientific predictions. Nevertheless, I believe that the predictive power of science in­creases with every new observation. It is the same with our obser­vations on the mathematical struc­ture of the Quran. With every new discovery or observation we get much more comprehensive un­derstanding of it.

OPPONENT: You are undermining the predictive power of science. I can challenge you to bring as many as fir cones and examine their scales. You will find the Fibonacci sequence in all of them.

PROPONENT: Though I don’t think that induction provides us with cer­tainty, nevertheless, I believe that your prediction will be confirmed. But, my question will be this: Based on the observation on fir cones how accurately can you predict the pattern of fir branches, or sun­flower petals or corn kernels?

OPPONENT: Certain things can be observed and therefore predicted for all material objects. However, there are details which we cannot predict with certainty without sufficient observation.

PROPONENT: That is exactly the same for our observation on the mathematical structure of the Quran. We observe and discover. Each discovery increases our knowledge of the big picture.

The Accuracy or the Predictive Nature of Mathematical Code

Here I want to give two examples:

1. Correcting a Scribal Error

Three chapters of the Quran, chapter 7, 19 and 38 contains letter “Saad” in their initial letter combination. Curiously, in verse 7:69 we see a word with a unique spelling: “Basstatan” Over the letter “Saad” is written a small “Sin.” This word occurs in the Quran with two different spellings and it makes no difference to the meaning. Just like the English words skeptic or skeptic. Commentaries of the Quran interpret it as an instruction on how to read the word. They claim that though it is written with “Saad” it should be read as if it is “Sin.” They narrate three Hadiths (allegedly Muhammad’s words) to support this interpretation .

The total number of “Saad” with this word “Basstatan” becomes 153, and it is not multiple of 19. Therefore, we concluded that the letter “Saad” in the word “Basstatan” is an orthographic error and should be corrected.

Indeed, when I checked one of the oldest manuscripts of the Quran, I found that our prediction was confirmed. Please see the document below:

[The copy of the manuscript is omitted here since it is presented in another chapter of this book]

2. Symmetry in the Table of God’s Attributes

In my second letter I had attached a list of God’s attributes with their numerical values and frequencies in the Quran, and the mathematical relation between these names and “Bismillah.”

Symmetry In The Table Of God’s Attributes

In my second letter I had attached a list of God’s attributes with their numerical values and frequencies in the Quran, and the mathematical relation between these names and “basmalah.”

Dr. Cezar Edib Majul, in his book “The Names of Allah in Relation To The Mathematical Structure of Quran” discovered the following two facts:

1. Only four attributes of God have gematrical (numerical) values that are multiple of 19.
2. The numerical values of these four attributes exactly correspond to the frequency of the four words of “basmalah,” that is, 19, 2698, 57, and 114.

Here is the table of this observation:

ASM
Name

19

(19×1)

واحد

 

WAĤiD
Oneالله

ALLaH
God

2698

(19×142)

ذوالفضل العظيم

 

ŹuW AL- FaĎL AL-Â ŽYM Possessor of Great Blessingرحمن

RaĤMaN
Gracious

57

(19×3)

مجيد

 

MaJYD
(Glorious)رحيم

RaĤYM
Caring

114

(19×6)

جامع

 

JAMe Gatherer/Editor

While I studied this table I noticed an asymmetry. On the right side of the table there are four names of God, but on the left side there are only three. Obviously, “Ism” (Name) was not an attribute of God. Therefore, I made two predictions. There must be one attribute of God that must have a frequency of 19, and only four names of God must have frequencies of multiple of 19. When I examined the frequency of all the names of God, I found that ONLY four of them are repeated in the Quran as multiple of 19. We already had discovered three of them: Allah (God), Rahman (Gracious), and Raheem (Merciful). The fourth one was “Shaheed” (Witness). This attribute is mentioned in the Quran exactly 19 times and thus fills the empty space corresponding to the numerical value of “Wahed” (One) on the right side of the table. Now we can modify our tables of God’s attributes according to the fulfillment of our prediction:

ŞaHYD
Witness

19

(19×1)

واحد

 

WAĤiD
Oneالله

ALLaH
God

2698

(19×142)

ذوالفضل العظيم

 

ŹuW AL- FaĎL AL-Â ŽYM
Possessor of Great Blessingرحمن

RaĤMaN
Gracious

57

(19×3)

مجيد

 

MaJYD
Gloriousرحيم

RaĤYM
Caring

114

(19×6)

جامع

 

JAMe Gatherer/Editor

Finally,

Dear Dr. Sagan, I’m enclosing a discovery made by Milan Sulc of Switzerland on the frequency of HH and M letters. They are the initials of 7 chapters. The frequency of HH and M letters in those 7 chapters are 2147, that is 19 x 113. The probability of this fact is 1/19. There are four subgroups whose combinations result in a multiple of 19. This is obviously coincidence, since there are 112 possible combinations. If you add the digits of each frequency (the absolute value of each number) you will end up with 113, which is exactly equal to the multiplication factor. This is valid also for all the subgroups. The probability of this phenomenon for each subgroup is 1/9. Therefore, the combined probability of these phenomena occurring altogether is 1/19 x 9 x 9 x 9 x 9 x 9, or 1/1,121,931. (FN1)Please let me know what you think.

Is it merely a coincidence?

Is it a mathematical property?

Is it a little numerology?

Is it a combination of the above?

or

Is it a great mathematical art?

Chapter	ح Ĥ	م M	Absolute Values										SUM
40	64	380	6	+	4	+	3	+	8	+	0	=	21
41	48	276	4	+	8	+	2	+	7	+	6	=	27
42	53	300	5	+	3	+	3	+	0	+	0	=	11
43	44	324	4	+	4	+	3	+	2	+	4	=	17
44	16	150	1	+	6	+	1	+	5	+	0	=	13
45	31	200	3	+	1	+	2	+	0	+	0	=	6
46	36	225	3	+	6	+	2	+	2	+	5	=	18
TOTAL	2147(19x113)		26	+	32	+	16	+	24	+	15	=	113
			D1		D2		D3		D4		D5

Chapter	ح Ĥ	م M	Absolute Values										SUM
40	64	380		6	+	4	+	3	+	8	+	0	21
41	48	276		4	+	8	+	2	+	7	+	6	27
42	53	300		5	+	3	+	3	+	0	+	0	11
TOTAL	1121 (19x59)			15	+	15	+	8	+	15	+	6	59
				D1		D2		D3		D4		D5
43	44	324		4	+	4	+	3	+	2	+	4	17
44	16	150		1	+	6	+	1	+	5	+	0	13
45	31	200		3	+	1	+	2	+	0	+	0	6
46	36	225		3	+	6	+	2	+	2	+	5	18
TOTAL	1026 (19x54)			11	+	17	+	8	+	9	+	9	54
				D1		D2		D3		D4		D5
41	48	276		4	+	8	+	2	+	7	+	6	27
42	53	300		5	+	3	+	3	+	0	+	0	11
43	44	324		4	+	4	+	3	+	2	+	4	17
TOTAL	1045 (19x55)			13	+	15	+	8	+	9	+	10	55
				D1		D2		D3		D4		D5
40	64	380		6	+	4	+	3	+	8	+	0	21
44	16	150		1	+	6	+	1	+	5	+	0	13
45	31	200		3	+	1	+	2	+	0	+	0	6
46	36	225		3	+	6	+	2	+	2	+	5	18
TOTAL	1102 (19x58)			13	+	17	+	8	+	15	+	5	58
				D1		D2		D3		D4		D5

OVER IT NINETEEN (74:30)

 

(FN1) [This probability calculation was based on the formula of the tables, 9 (N3) = (N1 + N4) + 2 (N2 +N5), where N is abbreviation of the word Number. N1 stands for the sum of the first column, that is the absolute value of the numbers in the tenth place of the frequency of letter H. For instance, the sum of each column in the TOTAL raw of the biggest group (where the total is 2147) satisfies this formula: 9 (16) = (26 + 24) + 2 (32 + 15). Years later, I noticed that my probability calculation above was wrong. The real probability is much less than I stated above. March, 2002. Edip Yuksel]