# 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.

1. The first and most important universal rule is that the numbers to be tested must be obtained in a meaningful way. This is the most general principal for all the rules and approaches used in this book. Also, the rules must be meaningful, simple and and as general as possible.

2. Another universal rule valid for all the relevant evidences is that the concatenations operation is always done in the natural order. Briefly, the natural numbers are concatenated in natural order. The natural order of the natural numbers of the text of Quran is from chapters, verses, words and letters.

3. Moreover, we have another two categories regarding the structure of the text of Quran. As mentioned in the earlier chapters, we have numbered verses and also unnumbered repetitive Basmala verses in the beginning of 112 chapters out of 114 chapters. I hypothesized that both represents the full text of Quran and therefore all the relevant coding patterns must be tested over the numbers from both text types regarding the applicability of a coding pattern. Thus, as a universal rule, any coding pattern is tested both of the text types of the text of Quran. This means, we need to test the numbers from all the 6348 verses and also from only numbered 6236 verses. Namely, we have to take into account all the possible trials that can come up from these categories. For example, if a single coding pattern is applicable to one of the categories alone, then we must test it for the other category too. Additionally, we also need to use the unique numbers that are derived from the used words and letters in the full text of Quran.

4. The primary goal of this book is to test the intactness of the full text of Quran. The evidences that test this main goal, testing the full text, must use either the 4 natural numbers of the text from chapters, verses, words and letters or the 3 natural numbers from chapters, verses, words. The former proves intactness up to the letters of the used text, whereas the latter proves intactness up to the words of the text of Quran. Both approaches can provide evidences for the intactness full text of Quran. This rule is applied while testing the intactness of the full text of Quran.

5. There are three levels of the text of Quran. We need to test any coding pattern in these levels if suitable to the tested coding pattern.
• First level is the total level, which shows the total number of chapters, verses, word and letters.
• Second level is at the chapter level sums of the numbers. For example, Chapter 1 has 7 verses, 29 words and 143 letters.
• Third level is at the verse level sums of the numbers. For examples Chapter 1 Verse 1 has 4 words and 19 letters.
1. The main and thus default testing operation on a number to be tested is to test whether it is multiple of 19 or not. As a general rule, if it is multiple of 19 then we designate it as under 19 based coding. The second but optional testing operation is to test the digit sum of the number, whic is used for facts but not for evidences. The only exception to this is for the coding patterns that are derived from the first chapter, Al-Fatihah, as described in the following coding patterns summary.

2. The followings are the summary of the primary coding patterns used in this book to test the intactness of the full text of Quran. Details can be found within the sections of the evidences. I summarized them here to be able to overview them together:

• The default coding pattern: The natural numbers are concatenated in the natural order.

• The pairing coding pattern: In this coding pattern, we pair two corresponding numbers. For example, between the numbers of the two text types of Quran. Namely, between the numbers of all the 6348 verses and the 6236 numbered verses.

• The coding patterns based on the first chapter, Al-Fatihah: The first chapter of Quran is named Al-Fatihah in Arabic and can be translated as The Opening or The Opener. It is considered as the most important chapter in Quran and memorized by all Muslims as it is considered to be required in the daily prayers. It is a short chapter with 7 verses. I realized that there are many independent 19 based codings available in Al-Fatihah. I then hypothesized that God might have left those special coding patterns of Al-Fatihah as clue, as The Opener, to discover the 19 based design in the full text of Quran, which mostly turned out to be true. Therefore, this particular rule instructs that whatever 19 based coding we observe in the first chapter, Al-Fatihah, we use that special coding pattern and apply it to the full text of Quran. Therefore this rule is only bound with the universal rules described above.

• The re-writing coding pattern: In this coding pattern, we attempt to re-write the full text of Quran with its ow natural numbers. This can only be done in two levels of numbers of the text of Quran. Namely, chapter and verse levels natural numbers. Since we are re-writing the text with its natural numbers, we replace the text parts with their numbers. Because the Arabic is written from right to left, the numbers replaced in those same positions as well. Therefore, concatenating numbers from right to left is only used in the evidences of the re-writing coding pattern.

• Special codings patterns: There are also some special coding patterns other than the above four and their details are described in their sections. Universal rules applied on all the evidences of this book.

• There are three levels of the numbers that can be derived from the full text of Quran. Each level provides a different level of resolution of the design and thus intactness of the full text of Quran. First level is the total level, where sum of the total numbers of units in each components of the full text. Namely, each of the total numbers of chapters, verses, words and letters as explained in Chapter 3. The second level is the chapter level numbers, where total numbers of verses, words and letters counted for each chapter. The third level is the verse level numbers, where total numbers of words and letters counted for each verse of each chapter. There is no further resolution of the text we can zoom into with the natural numbers of the text. As a general rule, any relevant coding pattern must be tested over all the numbers that can be derived from each of those three levels of the full text of Quran. Also, for a coding to be designated as evidence, it must exist in at least two of these levels if this coding pattern considered independently. If coding exist in a single level but considered out of a special rule such as the case of Al-Fatiha based codings, then they do not have to exist in multiple levels but following the special rules is sufficient to consider them as evidence.

• All the numbers that might represent the full text of Quran with content information needs to be used if relevant to a coding pattern. Therefore, we have two cases with and without letters information, regarding the categories of the numbers. The first case is as follows: the numbers of chapters, verses, words and letters. The second case is without letters information as follows: the numbers of chapters, verses, words. As we see, both categories contain content information of the full text of Quran along with the structural, chapter and verse, information of the full text. Moreover, we have another two categories regarding the structure of the text of Quran. As mentioned in the earlier chapters, we have numbered verses and also unnumbered repetitive Basmala verses in the beginning of 112 chapters out of 114 chapters. I hypothesized that both represents the full text of Quran and therefore all the relevant coding patterns must be tested over the numbers from both text types regarding the applicability of a coding pattern. This means, we have to take into account all the possible trials that can come up from these categories. For example, if a single coding pattern is applicable to one of the categories alone, then we must test it for all the four total categories of th numbers described in this specific rule. Additionally, we also need to use the unique numbers that are derived from the used words and letters in the full text of Quran.

• In order to test the full text of Quran with number 19, I discovered three different coding patterns. We will apply all these three coding patterns to all the natural numbers described in the above rules. This means we will perform and count all the possible tests based on the rules described in this section for this chapter. This way, we will be able to accurately calculate the probability of our observation of successes statistically with a scientific approach. This will void and respond to any classical memorized objections of an average ignorant who might say that "one can find patterns in any book". My claim in this has been measured statistically with a scientific approach but the ignorant objections would not be able to give any statistical value for their claim.

These rules reduces the number of tests dramatically and allow us to test a small set of meaningful numbers to test for the general 19 based system. The codings designated as evidences must obey these rules. Only these evidences will be counted to calculate the probability of the general system presented in this book. Any other potential coding examples will be presented as strong or weak facts only and they are not considered under 19 based system presented in this book. I will present them as facts because some of them still looks interesting and also in the future someone else might consider them as evidence if additional information is realized with them. While I was writing this book, I had designated some codings as facts that later turned out to be evidences as I discovered additional information on them.

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 information related to the rules for combining multiple descriptive numbers:

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, repetitively, in front of each chapter without a verse number. The second category 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 repetitive unnumbered verses into numbered verses in counting, and they say there are 6236 verses in Quran. In my analysis of the text of Quran regarding the number 19, I observed that both together are the correct representations. It means, as long as one mentions one of the two numbers along with its distinct property without excluding the other, then it should be correct. Thus I tested both categories together.

B) Combining the main descriptive numbers and the general verse index::

The descriptive numbers can only be combined within its own text type in the given natural order. Each of the two text types 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. I also generated an independent verse index (denoted by VerseI in text data tables) 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 codings. In a special use case of these numbers is in the the pairing coding pattern:. Because, while pairing two corresponding categories, the numbered and unnumbered special verse indexes should also pair. However, since there is no number to represent unnumbered Basmala verses, while pairing the correspondence on this special verse indexes might have missing information. Therefore, as a special rule to the codings with the pairing coding pattern:, we always use the general verse indexes instead of the special verse indexes in the evidences.

### 4.1.1 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 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 access online for example from tanzil.net or quran.com. 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 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 About the 19 system presented in this book

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 probability of it. 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 along with their codes so that anyone who has doubt can also easily test, reproduce and witnesses to the truth by heart. In the end, we observe a coding system in the text of Quran and in this book I introduce this system that I discovered in the text of Quran in 2019. 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. 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 presented in this book is that, I do not change nor touch any text data, not even a single letter, of Quran that Muslims use. This point is important to repeatedly emphasize, as there is an older acclaimed 19 system claim 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 to have success. 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 codings with Test 19 individually, I will also calculate the overall probability including this event. 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 $$0.05$$%.

However, when evaluated with other multiple events, we will use Binomial test to approximately calculate the probability of the overall system. Also, note that most of the evidences are dependent to each other and the expected exact probability would be lower. See Chapter 4.2 for further details in all the mentioned probabilities.

## 4.3 Tables of the numbers to be used

The followings are the two tables that show the total numbers of each category of the text per verse in all and also the numbered verses. I will use these numbers of both category in the evidences.

knitr::kable(head(unQuran), booktabs = TRUE,
caption = 'Table head of all verses of Quran.')
Table 4.1: Table head of all verses of Quran.
VerseI chapter verse vwords vletters text
1 1 1 4 19 بسم الله الرحمن الرحيم
2 1 2 4 18 الحمد لله رب العالمين
3 1 3 2 12 الرحمن الرحيم
4 1 4 3 12 مالك يوم الدين
5 1 5 4 19 إياك نعبد وإياك نستعين
6 1 6 3 19 اهدنا الصراط المستقيم
knitr::kable(head(nQuran), booktabs = TRUE,
caption = 'Table head of numbered verses of Quran.')
Table 4.1: Table head of numbered verses of Quran.
VerseI chapter verse vwords vletters text
1 1 1 4 19 بسم الله الرحمن الرحيم
2 1 2 4 18 الحمد لله رب العالمين
3 1 3 2 12 الرحمن الرحيم
4 1 4 3 12 مالك يوم الدين
5 1 5 4 19 إياك نعبد وإياك نستعين
6 1 6 3 19 اهدنا الصراط المستقيم

The followings are the two tables that show the total numbers of each category of the text per chapter in the numbered verses.

require(data.table)
nQuran <- data.table(nQuran)
cwords <- c()
cletters<-c()
for(i in 1:114){
cwords <- c(cwords,sum(nQuran[chapter==i]$vwords)) cletters <- c(cletters,sum(nQuran[chapter==i]$vletters))
}
dfVCwl <- cbind(dfVC[,c(1:2)], cwords, cletters)
# Let's print this table
require(DT)
datatable(dfVCwl,
caption = 'Total numbers of each category in numbered verses per chapter',
options = list(pageLength = 10,
autoWidth = TRUE),
rownames= FALSE)

Similarly, we can get a table that also includes the unnumbered Basmala verses into the above table. We need to be careful about the numbered Basmala of the first verse of the first chapter and the no Basmala situation of Chapter 9.

cWords <- cwords + nQuran$vwords[1] cLetters<-cletters + nQuran$vletters[1]
cWords[1] <- cWords[1]-nQuran$vwords[1] cLetters[1] <- cLetters[1]-nQuran$vletters[1]
cWords[9] <- cWords[9]-nQuran$vwords[1] cLetters[9] <- cLetters[9]-nQuran$vletters[1]

#add the one Basmala per chapter verse into the verse counts
dfVCWL <-cbind(dfVC[,c(1:2)],cWords, cLetters )
dfVCWL$Verse_sum <- dfVCWL$Verse_sum+1
dfVCWL$Verse_sum[1] <- dfVCWL$Verse_sum[1]-1
dfVCWL$Verse_sum[9] <- dfVCWL$Verse_sum[9]-1
# Let's print this table
datatable(dfVCWL,
caption = 'Total numbers of each category in all verses per chapter,
including the Basmala verses',
options = list(pageLength = 10,
autoWidth = TRUE),
rownames= FALSE)

## 4.4 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 'AbjadSeqofaWord' generates the sequence of Abjad numbers for an input word. The following function 'AbjadSeqofaWordSumValue' returns abjad value of each word of the verse that is input to the function.

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,""))
return(tmp)
}

# Abjad number of each word in a verse is the output
# usage: (a verse is input)
# AbjadSeqofaWordSumValue(unQuran$text[1]) # output: "102" "66" "329" "289" tmp <-as.character(xverse) tmp <- unlist(tokenize_words(tmp)) for(i1 in 1:length(tmp)){ tmp[i1] <-sum(AbjadSeqofaWord(tmp[i1],abjadL, abjadN)) } return(tmp) } ####### AbjadSeqofwordsperVerse <- function(xverse){ #usage: Abjad numbers are repalced with each letter in a verse. #AbjadSeqofaWordSindx(unQuran$text[1])
#result:
#"40602"       "530301"      "50408200301" "40108200301"
#use rev function to have them in Arabic order.
tmp <-as.character(xverse)
tmp <- unlist(tokenize_words(tmp))
for(i1 in 1:length(tmp)){
#####