# Chapter 4 Rules & Probabilities

In this chapter, I will describe some of the rules on how to select numbers and how to test them, and also about computing the probabilities of observing the successful tests on these numbers by chance alone. I made this as a separate chapter as it contains information heavily referred and used in the chapters dedicated to the evidences.

## 4.1 Rules

I will describe here some of the general rules that will be applied to test on any number of interest. Basically, how a number is obtained and which tests applied to consider whether the number of interest is under the 19 based coding system in Quran or not. These may not be necessarily the complete universal coding rules of the text of Quran but the ones I observed from the data and my analysis and followed them to test my hypothesis on any new number with respect to those rules. This means, if any error of flaws exist in the analysis, it would be my own unintentional mistake and not about the text of Quran itself.

Setting rules in the beginning is important, otherwise, without establishing rules that limits the boundaries of the numbers set to be tested, one cannot really claim a 19 based coding system on the text of Quran. Also, the rules must be meaningful, simple and and as general as possible. Thus, I state that the first and most important rule is the numbers alone or combined must be obtained in a meaningful way. This is the most general principal for all the rules and approaches used in this book.

Basically, the specific rules I will describe below is about combining all the different category numbers (e.g. chapter, verse, word, letter) at the same time and the used mathematical tests on them. See the following subchapters for detailed descriptions.

### 4.1.1 Rule: Mathematical operations for testing

There are only two mathematical operations to be applied on the numbers. The primary and default mathematical operation that is applied to all the numbers of interest is to divide the numbers directly by 19. The second operation is secondary and applied in some specific categories only along with the default one, which is to divide the sum of the digits of the number of interest by 19. This separation is done exactly as follows: If the number to be tested has order information then digit sum divisibilty test can never be applied on such numbers as it does not take into account the order of the digits in the number. For example if the number to be tested is concatenatination of two or more numbers, then digit sum divisibility test cannot be applie on such numbers.

A) Divisibility by 19 Divisibility of any number of interest by 19 is the default, primary and global mathematical operation to test the numbers of the system. Whenever a new number of interest is obtained, first rule is always to check whether it is divisible by 19 or not. If it is divisible by 19 then it is the evidence that the number under consideration is coded by 19 based coding system in Quran. If this test is successful on a combined number of interest, it proves that the size and also the order of the combined numbers are designed together, in harmony and interconnected to each other and thus they are under the 19 based coding system of the text of Quran.

The probability of any number divisible by 19 by chance is 1/19 or ($$5.26$$%) as discussed in detail in Chapter 4.2.1, where this unique probability is denoted by Probability P1 throughout this book. For example, the number of chapters in Quran is 114 and it is divisible by 19. In summary, if any number of interest passes this rule, then the probability of observing this successful test by chance alone is 1/19 and I defined this specific probability as Probability P1 for future reference.

B) Digits sum divisibility by 19

In this test, the sum of the digits of a number of interest is divided by 19. This is the secondary mathematical operation and thus optional test. It is applied if the number has not any order information. The sum of the digits of a number of interest yields also another random number. Therefore, the probability of it being divisible by 19 can be approximately considered as Probability P1 (1/19) too. If this test is successful on a combined number of interest, it only proves that the size (but not the order) of the combined numbers are designed together, in harmony and interconnected to each other and thus they are under the 19 based coding system of the text of Quran.

In summary, I apply one main default test to all the numbers. I apply the additional digit sum test to each number of interest if the number of interest does not have order information in it. If any one of them holds, then this is considered as an evidence that the number of interest is under the 19 based coding system of the text of Quran. Namely, if we used both of the test for a number, we perform two tests and each has the probability of 1/19 to be successful by chance alone. Therefore in the probability calculations, if both are used at the same time, this is counted as two separate tests with each having the probability of 1/19 and thus increases the total probability as 2/19 in those cases.

### 4.1.2 Rule: Combining multiple numbers

Since the evidences might have different general purposes, the rules might slightly change regarding the purpose. You can see the sections of evidences for more details. Here I want to mention some basic rules that I simplified to make the system as simple as possible regarding the comprehension of the evidences. I simplified rules of the evidences as follows. As a rule, the system does not test the total count numbers of a category individually but the total number and the orderly concatenated combined number of all the main categories together. The order is always is the natural order in the text categories, which is from left to right as chapter, verse, word and letter. In the evidences, I do not test any other combinations among those the main categories of the text, which greatly simplifies the complexity of the system in general. For some other cases, for example the general verse indices that is not one of the 4 main categories of the text, additional rules explained in their related evidences.

Regarding the main totals of the 9 descriptive numbers, as described in Chapter 3.6.1, they alone, as a single number, are not tested. This means as a rule, we do not test the total counts of the descriptive numbers alone c, v, V,u,U, w, W, l, L that was presented in Chapter 3.6.1.

When combining the 4 main totals of the descriptive numbers of both text type of Quran by pairing, we pair them by concatentaing in both directions if their lengths are equal. If their lengths are not equal as in the verse resolution case, then while pairing the longer vector is located at the begining and test is perferomed only in one direction. This shows if all the four of the descriptive numbers of both of the text types are all in harmony and designed together and represent the whole text of Quran. This gives us for example two numbers to be tested cvwlcVWL or cVWLcvwl at the total counts level.

We have to set rules that define the way we can combine multiple descriptive numbers. Otherwise, the potential numbers of combinations becomes too large to follow for readers and also would be difficult to define in a system of rules. Therefore, here I aim to set only the most meaningful rules, which are simple to understand and follow along with the evidences. I observed the combinations of the numbers and inferred these meaningful rules. I decided to make sure that the combinations are meaningful and did not include many other combinations that were also divisible by 19 but not fall into the defined system of rules. Here are the other general rules for combining multiple descriptive numbers in more detail:

A) There are two representation categories of the text of Quran: First of all there are two representation categories of the text of Quran, which is with and without unnumbered Basmala verses. In particular, first category is the one that includes the numbered verses and also the unnumbered 112 Basmala verses that appears in front of each chapter without a verse number. The second one is only with numbered verses. In literature, scholars refer to either categories depends on their choice. Because, everyone already knows all the chapters begins with the unnumbered Basmala verses except chapter 9. So, some scholars prefer to mention the unnumbered Basmalas as well and say there are 6348 verses in Quran and some scholars prefer to mention only the numbered verses, assuming that there is no need to include the unnumbered verses into numbered verses in counting, and say there are 6236 verses in Quran. In my analysis of the text of Quran regarding the number 19, I observed that both are together is the correct representation. It means, as long as one mentions one of the two numbers along with its distinct property without excluding the other, then it is correct.

B) Combining the 4 main descriptive numbers:

The descriptive numbers can only be combined within its own text type in the given natural order. The combination of the combined numbers by all the other associated categories can be done in any order.

Each of the two text types described in point A has, 4 different main descriptors, which are chapter, verse, word and letter numbers in order. This order is the natural order of concatenating these numbers and I use this order as a general rule in combining these numbers. This means for instance, I can never concatenate first, letters and then words in combining the multiple descriptive numbers. Also, when using these 4 descriptive numbers, they must be combined together. Also, any combination attempt needs to be meaningful and should test a meaningful property of the text. I also generated an independent verse index (denoted by VerseI in text data) from 1 to 6236 or from 1 to 6348 for both of the text types. This especially helps to correctly refer to the order of the unnumbered Basmalas in calculations in some tests. In concatenations, the natural order of this independent descriptive number is before the chapter as it can independently point any verse without needing the chapter or verse number. In a special case, I may have to use this general verse index instead of the special verse index of each verse within chapters, in which case I provide an additional explanation in that evidence. Basically, unnumbered Basmala verses has no special verse indices and in such cases we might utilize from the general verse indices.

Also, when combining the numbers of the two text types of Quran, they can be concatenated in either order. So, in that attempt both order is tested and this needs to be included in the probability calculations. At the verse resolution, 6348 is longer than 6236 and thus while pairing such unequal cases, we take only one direction, where the longer is at the begining.

C) Combining the totals of the descriptive numbers:

When testing the totals of the main descriptive numbers provided in Chapter 3.6.1, all the 4 main numbers for each of the two categories must be concatenated at the same time together. There is no other combinations tested. This already tests the harmony and integrity of the totals of all the main descriptive numbers together and provides a tractable evidence that can simply be perceived by any and represent all the main descriptive numbers as follows.

The 4 main descriptive numbers of first text category as shown in Chapter 3.6.1 is concatenated as $$c, v, w, l$$ and similarly the other one is concatenated as $$c,V, W, L$$. As a rule we do not test them alone but we must concatenate them as in these two forms:

$c, v, w, l, c,V, W, L$

$c,V, W, L,c, v, w, l,$

These letters are the symbol characters that I use to represent the 7 main descriptive numbers of the text of Quran as described in Chapter 3.6.1. Regarding the rule described, we have two possible numbers to test on the main descriptive numbers. If statistically significantly successful, this will show us that all the totals of the main descriptive numbers of the text of Quran was designed together.

As the second combination approach, we also test the sums of these 4 main descriptive numbers for each text type and at evry text resolution. This shows evidences with respect to totality of all those descriptive numbers.

Evidence 5.1, Evidence 5.2, Evidence 5.3, which are all the evidences about the descriptive numbers, are tested by only the default divisibility by 19 test as there is order information in the numbers. This tests the order along with the size and integrity and harmony of those numbers among each other.

C) Combining the descriptive and unique numbers:

In this case there are two categories to combine. First the combination of the main numbers of point B and second the combinations of the unique numbers, uU. This would show if the unique numbers are in harmony and designed together with the main numbers of both of the text types and also intact until today. Then, as I described in point B, we have 4 possible combinations as presented in detail in Evidence 5.3. I will not write them here again to save space.

### 4.1.3 Rule: Obtaining the numbers from text

All the descriptive numbers must be obtained blindly from the text of Quran. One cannot change any of these numbers for any reason, which will be used to test 19 based coding system of the text of Quran. Here, the word blindly refers to the approach that we do not look at any content of the verses at all and just count whatever we have have in the text of the verses of Quran that represents Quran that we can buy from any book store. Please read Chapter 3 to read further details on how I got the final text document of Quran. However, I again declare that I did not make any single change to the text of Quran and it represents the same Quran as any traditional copy you can get from any book store. Although, I mentioned this very important point many times before, it is essential to include it in the rules again and formally include it into the tests.

Since I used computer friendly version of the text from tanzil.net/download, all the characters are counted as letters. Blank character is used to separate words.

## 4.2 Probabilities

I present some of the probabilities that I used to compute the probability of observing the successful tests that I provide in this book.

### 4.2.1 Probability P1:

The probability of a number being divisible by a particular number n is 1/n. For scientific explanations, see wikipedia.org/wiki/Natural_density. Therefore, the probability of a number being divisible by 19 is 1/19 or in other words $$5.26$$%. As a reference, I will refer to this particular probability as Probability P1 in the rest of the book.

P1 <- 1/19
cat(P1)
## 0.05263158

### 4.2.2 Probability P2:

Given that there is only one number n (e.g. 19) specifically written in a special way in a book but no other such case exist, what is the probability of such an event? To make the calculation simple, we should consider the possible numbers that we expect to be mentioned in that book as in between 1 and m. Then, the probability of observing a particular number n being written in the book would be 1/m. As an example, if m is equal to 100 then the probability of observing a particular number in this range is 0.01 or 1%.

When the book under consideration is Quran, we can have better approximation on the number that we might expect to be mentioned in it. In Quran, chapter 74, verse 30, there is this special verse “74:30. Over it is Nineteen” and it is not explicit for what exactly it refers as an independent verse. Scholars guess its meaning from the context but it might also mean something else as it is also not explicitly given regarding the context too. For example, it might also mean that there is a coding system over the text of Quran and it is designed over number 19. Moreover, there is no similar verse that refers to another number in such a special way as this one and thus the number 19 is unique in this sense in Quran.

Since there is only one number mentioned in Quran in a special way, then the probability of 19 (or any other single number) being mentioned in Quran by random chance might be estimated approximately as 1/114. I took this probability as the practical highest probability using the lowest possibly observable number (114) out of all the other potential numbers that might be mentioned in Quran as the number of chapters of it is 114. For example, if we had seen in Quran a verse like “Over it is 114” then this would probably be interpreted to be referring to the number of chapters in Quran and would not be surprising to us. However, anything above it is less likely to expect though it is still possible. In fact, there is even higher number like 950 mentioned in a context but we know what exactly it was used for and let’s say it is en exception and take a more conservative number. So, I limit the random potential number that we might observe in a book by 114 to cutoff all the potential objections on this point. Otherwise, if I had taken this number to be 1000, probabilistically speaking, it would still be correct and it would be a stronger support to my argument. After the long discussion of reasons on deciding on 114, we can calculate the probability. The probability of any single number (less than or equal to 114), or in particular number 19, being mentioned in Quran in a unique way can be approximately taken as 1/114 ($$0.88$$%). As a reference, I will refer to this particular probability as Probability P2 for the rest of the book.

P2 <- 1/114
cat(P2)
## 0.00877193

This is an important probability to consider because the number 19 is not any random number but the number specially mentioned in the content of Quran. Basically, the verse “74:30. Over it is Nineteen” connects the content of Quran to the 19 based system of the text of Quran. Therefore, we have to incorporate this additional event when we compute overall probability of what we observe in this book as in the 19 base system of the text.

### 4.2.3 Probability P3:

The probability of observing two independent events occurring as successes together is the multiplications of the probabilities of these two events.

As an example, the probability of observing Probability P1 and Probability P2 together is calculated as $$(1/19 * 1/114) = 4.62\times 10^{-4}$$ or $$0.0462$$%.

However, there is also another scenario of this case. If out of these two events, any one of them occurs and we conclude that overall global test passes then this is a different scenario in probability, which is a multiple testing problem. Basically, if we make two independent attempts to observe at least one success to pass a test then we need to calculate the probability by summing the probabilities of the success of each attempt. In our specific case, we test for two different rules (A and B) of the rule in Rule 4.1.1 on any numbers to be tested. Since we test two different rules on a number to test if it is under 19 based coding system or not, we take this into account and thus we sum the probabilities of these two rules. Both of the rules have the same probability, Probability P1, which is 1/19, as discussed in Chapter 4.2.1. Therefore the probability of at least one success of the test being true by chance is 2*P1 which is $$0.1053$$ or $$10.5263$$%. I will denote this probability as Probability P3 to refer to it throughout this book.

P3 <- round(2*P1, 4)
cat(P3)
## 0.1053

### 4.2.4 The Test 19

I already elaborated each of the specific rules that we apply on a number of interest to find out if the number is under the 19 based coding system of the text of Quran, which I observed and introduced in this book. However, I wrote this section to clarify how are they implemented together and what is the cumulative probability of testing. Also, in the book, to easily refer to the testing of any number regarding the rules described so far, I name it as Test 19.

God knows best and this is only my inference based on my analysis over the text data of Quran. The 19 based coding system I described here might or might not fully represent the real 19 based coding and only God knows best. However, the presented system is based on my personal observations and, in a few cases, observations of other people who worked on this subject but I tested and validated and thus included them in this book along with their reproducible codes so that anyone who has doubt can also easily test and witnesses to the truth by heart. In the end, we observe a coding system in the text of Quran and I introduce this system that we observe in the text of Quran. So, in conclusion, when I say ‘19 based coding system of the text of Quran’, this means the 19 based coding system of the text of Quran based on my reproducible tested and validated observations and inference, and also some of the few already available observations that I tested and provided their reproducible codes. Therefore, feel free to investigate more on this subject and see if you can find new unexplored parts of the system in Quran. The most important point of the 19 based coding system described in this book is that, I do not change nor touch any single letter of Quran that Muslims keep in their home or can buy from any book store. This point is important to repeatedly emphasize, as there is an older acclaimed 19 system that was ‘made up’ by modifying some parts of Quran (by R. Khalifa and his followers) and therefore almost all Muslims who know about the older claim have prejudices and put a distance between themselves and 19 based coding system claims about the text of Quran.

Back to the main topic, by default we apply the divisibility test and it has the probability 1/19. In some specific categories of hypothesis, I additionally apply, the optional test too along with the default test. Therefore, if we perform two independent tests on any number of interest, then we should consider this testing as multiple testing problem, which was explained in detail in Chapter 4.2.3 and we calculated the probability to be approximately equal to $$2*P1 = 0.1053$$ and denoted as Probability P3 to refer it in this book. So, whenever a number of interest passes Test 19 after only applying the default test, then the probability of this success occurring by chance alone is $$5.2632$$%. This probability is called as the probability of success of Test 19 on a single number of interest alone and independent of any other events when only the default test applied.

As explained in Chapter 4.2.2, we also have the event of the context of the text of Quran that mentions number 19. After evaluating all the numbers with Test 19 individually, I will also calculate the overall probability including this event. This event is important to consider because it causes even a single number event alone to be statistically to be very significant to consider as evidence regarding number 19.

Let’s exemplify it to clarify this point. For instance, let’s say we have only one number (out of one possible number) that passes Test 19. Then, the probability of it and Probability P2 together gives us the probability of observing an event that passes Test 19 (including the context event of mentioning number 19 in Quran) by chance and this probability is calculated approximately as $$P1*P2 = 5\times 10^{-4}$$ or $$0.05$$%.

# only default test
P3a <- (1/19)*(1/114)
P3a
## [1] 0.0004616805
# Including the  optional digit sum test
P3b <- (2/19)*(1/114)
P3b
## [1] 0.000923361

This probability will be denoted as Probability P3a (and Probability P3b when both tests applied) for future reference and whenever we present an evidence on a single number that passes Test 19, then, Probability P3a (or Probability P3b) is taken as its probability of occurring by chance alone assuming it is the only number of interest. However, when evaluated with other multiple events, we will have to use Binomial test, then I will use Probability P3 for one event of success and then in the end I will consider all of them and also use Probability P2 once for all. See Chapter 4.2 for further details in all the mentioned probabilities.

## 4.3 Some R Functions

This is the function to compute the sum of the digits of any integer number.

digitsum <- function(tmp_){
tmp_ <- unlist(strsplit(as.character(tmp_), split=""))
tmp_<- sum(as.numeric(tmp_))
return(tmp_)
}

#Example
cat(digitsum("1387"))
## 19

This R function generates the sequence of Abjad numbers for an input word.

require(stringr)
## Loading required package: stringr
##
## Attaching package: 'stringr'
## The following object is masked _by_ '.GlobalEnv':
##
##     words
AbjadSeqofaWord <- function(word, abjadL, abjadN){
word<-unlist(str_split(word,""))
}