Bible Code: Report

Section 2: What the Skeptics Can’t Explain

Section 3: Divine Patterns or Pure Chance?

Section 4: The Purpose of the Bible Codes

Section 5: Conclusion

Appendix: A Detailed Example Of A Statistical Analysis

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http://www.thebiblecodes.com/feature/index.htm

THE TRUTH ABOUT THE BIBLE CODES

Author: Keith York

This article is property of the author and may not be reprinted or distributed without permission.

March 4, 2000

Section 1: Introduction

1. What is an equidistant letter sequence?
2. What is a matrix?

Section 2: What the Skeptics Can’t Explain

1. What the skeptics have successfully refuted
2. What the skeptics continue to ignore

Section 3: Divine Patterns or Pure Chance?

    1. How much can be found by pure chance?
    2. The criteria for a significant code
    3. How do you know the codes are significant?

Section 4: The Purpose of the Bible Codes

    1. What is the purpose of the Bible Codes?
    2. Can the codes forewarn us of events to come, or be used to predict the future?
    3. Are there hidden theological teachings or messages?

Section 5: Conclusion

1. The implications of the Bible Codes
2. Summary

Appendix: A Detailed Example Of A Statistical Analysis

Section 1: Introduction

1. What is an equidistant letter sequence?

To understand the Bible codes one must first understand two fundamental concepts: (1) equidistant letter sequences and (2) arrays. The equidistant letter sequence (usually referred to as an ELS) is the method by which individual words or phrases are encoded in the Bible codes, whereas an array is a combination of ELS’s in a two-dimensional framework. We will start by defining and illustrating what an ELS is. As the name implies, an equidistant letter sequence is a sequence of letters that are equidistant from each other when written as a string without spaces or punctuation marks. An example is the following phrase.

HISEYESSEEMEDROUNDINGANDROUNDINGLIKE.

The underlined letters spell the word ‘York’. Each letter in the ELS ‘York’ is 10 letters further in the text than the preceding letter of the ELS. Therefore it is said that this ELS of ‘York’ has a +10 skip distance. The skip distance of an ELS can vary from 1 (which would be a surface text appearance of a word) to 2 (every other letter) to tens of thousands. Whenever a researcher reports a finding he should list the skip distance of every ELS that is shown in the array. This helps others to verify the researcher’s results.

2. What is an array?

Individual words and phrases are encoded as equidistant letter sequences. However, a code does not consist of a single ELS. In order to be considered to be a code, two or more ELS’s must together form an array. An array (also called a matrix) is a portion of text containing two or more ELS’s in which all spaces and punctuation have been removed and which contains a certain number of letters on each line. An array can consist of either deliberately encoded ELS’s or ELS’s produced by random chance. The criteria that distinguish between the two are examined in Section 3.2. An example of an array is given below. The software program CodeFinder contains an English text of “Moby Dick” for practice purposes. Since my name is Keith York, I searched for those three terms in “Moby Dick” to produce an example array. It is shown below. Needless to say, this is an example of an array consisting of ELS’s produced by random chance.

In the example above, ‘KEITH’ is -311 skip distance, ‘YORK’ is 10 skip distance, and ‘NAME’ is -309 skip distance. Note the meaning of the negative skip distance. It means that ‘Keith’ and ‘Name’ are seen going from bottom to top in the array instead of from top to bottom, as would be the case for a positive skip distance.

An array (or matrix) can be described in a number of ways. The line length is the number of letters in a line of the array. It is the width of the array that would be seen if the array was fully extended to the left and right. In the above example, the line length is 153. In other words, the H that is directly below the O of ‘York’ in the array is found 153 letters later in the surface text. The row split is the number of rows from one letter of the main term to the next. In this case, the main term is ‘Keith’ and each letter of the ELS is two rows below the preceding letter. Therefore the row split is said to be two. The size of the array is the area (length X width) of the array. The above example contains 31 columns and 17 rows. Therefore the area of the array is 31X17 = 527.

For a given line length, each ELS will have a fixed compactness. One measure of compactness, z-squared, is derived from the Pythagorean theorem. For ‘Keith’ in the above array, each letter is two rows below and one column to the left of the preceding letter. Thus 2X2 + 1X1 = 5, the z-squared value of ‘Keith’ for this array. The distance between the letters of ‘Keith’ is simply the square root of the z-squared value, or Squareroot of 5. For ‘York’, z-squared is 0X0 +10X10 = 100, and the distance between the letters is 10. For ‘Name’, z-squared is 2X2 + 3X3 = 13, and thus the distance between its letters is Squareroot of 13.

For a given line length, ELS’s will also have fixed distances from each other, defined as the nearest distance between a letter of one ELS and a letter of a second ELS. In the example above, ‘Keith’ and ‘York’ are Squareroot of 5 distance from each other, while ‘Name’ and ‘York’ are 3 distance from each other. These compactnesses and distances can be very important in statistical analyses of arrays, as will be shown in the Appendix of this paper.

Now that the fundamentals have been covered, the dispute between codes proponents and codes opponents or skeptics can be discussed.

Section 2: What the Skeptics Can’t Explain

1. What the skeptics have successfully refuted

Skeptics’ attacks against the Bible codes generally fall into three categories. First there are the simplistic technical objections against the codes. These will be answered in this section. Secondly, there are the much more rigorous objections represented by a paper published in the May 1999 issue of Statistical Science. This paper is dealt with in Section 3.3. Thirdly, there are theological/doctrinal objections to the Bible codes based on a misunderstanding of the true purpose of the Bible codes. These misunderstandings of the Bible code’s true purpose are covered in Section 4.

As mentioned, there have been many simplistic technical objections to the Bible codes. These typically represent either a misunderstanding of the nature of the codes or a deliberate creation of a “straw man” description of the codes which can be easily demolished. The difference between the two is a matter of the skeptic’s knowledge and/or intentions. However, whether the mischaracterizations of the codes are a result of genuine misunderstanding or deliberate deception caused by hostile intent is irrelevant to the answering of these particular objections. Therefore we will not make any negative assumptions about the motives behind any particular skeptic’s objections, but simply focus on the facts. This is done by stating each proposed objection, followed by our response. If the skeptics can be said to have successfully refuted anything, it is their own “straw man” misunderstandings and mischaracterizations they have refuted, not the Bible code itself.

Proposed “straw man” objection #1: Codes proponents claim that the codes consist of equidistant letter sequences (ELS’s). ELS’s can be found in any text. Thus there is nothing significant about finding ELS’s in the Bible. It is true that ELS’s can be found in any text of any language, but codes proponents have never claimed otherwise. In fact, ELS’s of shorter words occur very frequently in a text, as is described in further detail in Section 3.1. It is not the occurrence of ELS’s that is important; it is how they are structured.

Proposed “straw man” objection #2: Words are found as ELS’s in the Bible at the same frequency as in other books, that is, the probability that is expected by chance. Thus there is nothing significant about the ELS’s in the Bible. There have been a few cases in which a word can be found as an ELS more frequently than expected by chance in a small localized part of the text when that word is particularly relevant to the passage in question. (An example can be seen in A Review of “Cracking The Bible Codes”.) However, in the vast majority of cases, words can be found as ELS’s at the same frequency of occurrence in the Bible as in other texts. Again, it is not the frequency of occurrence of ELS’s that is important; it is how they are structured.

Proposed “straw man” objection #3: Okay, so it is the structure of ELS’s that is important. Codes proponents show two-dimensional arrays of ELS’s. However, such two-dimensional arrays have also been found in books such as “War and Peace”. Thus there is nothing significant about the code arrays proponents have found in the Bible. True, two-dimensional arrays of ELS’s have been found in secular books like “War and Peace”. However, the simple existence of a two-dimensional array does not mean that the ELS’s it contains are significant. A valid Bible code array must meet certain criteria, which are listed and discussed in Section 3.2. To our knowledge, while the “code arrays” found in books such as “War and Peace” and others outside the Bible may meet some of the criteria and thus look like a valid array, none of them containing several ELS’s meet every criterion that codes experts agree are necessary to be met for an array to be valid. For example, in the Section 1 example from “Moby Dick”, ‘name’ is found at -309 skip distance. There are 10,158 occurrences of ‘Name’ in the -309 to +309 skip distance range in the 924,956 letters of “Moby Dick”. Thus this ELS of ‘Name’ is not near-minimal in skip distance; the array does not meet every criterion listed in Section 3.2; and therefore, the example array is not a statistically valid array.

Proposed “straw man” objection #4: Maybe there’s something about the Hebrew language that makes codes look significant. After all, Hebrew does not have vowels and therefore the Hebrew word for something is typically shorter than its English equivalent, meaning a word in Hebrew can be found as an ELS more frequently than that same word in English. This difference in language accounts for the “codes” found in the Bible. Again, there is partial truth in this charge. Hebrew does have some letters that act as vowels either all the time (such as aleph), or part of the time (such as vav and yod), but most times vowels in Hebrew are unrepresented in “unscripted” writing. (In Hebrew, vowel points can be found under consonants representing the vowel sound that follows that consonant. This is called “scripted” Hebrew. In “unscripted” Hebrew, the vowel points are omitted and the reader remembers the vowel sounds needed for each word as part of his vocabulary.) However, it is an effect that has already been tested for and controlled. In the experiment by Witztum, Rips, and Rosenberg (discussed in Section 3.3), their data set was tested and found to be statistically very significant in Genesis, but not significant in Hebrew translations of “War and Peace” nor in randomly scrambled texts of Genesis. If the effect was due only to the Hebrew language, significant results would have been found in Hebrew control texts, not just in the Biblical text of Genesis.

Proposed “straw man” objection #5: Michael Drosnin, author of The Bible Code, failed in many of his predictions. This shows that the Bible code is not valid. First of all, we (and others) do not consider Michael Drosnin to be an expert codes researcher. He is a journalist who developed an interest in the Bible codes, saw (and reported) a number of valid arrays developed by others, and then decided to try developing arrays himself. Apparently, he made a few accurate predictions based on the codes, such as the assassination of Yitzhak Rabin and election of Benjamin Netanyahu. (We see no reason to doubt the veracity of these claims.) However, he then “found” arrays that appeared to predict a number of future occurrences. Many of the dates that he named have passed without his predictions coming true. This is not a failure of the Bible codes, but a misuse of the codes. As will be explained in Section 4, the codes were never meant for us to use to predict the future, but only to verify God’s foreknowledge of events that have taken place in our past, but thousands of years after the Bible was written. This validates God’s authorship of the Scriptures while preventing the codes from being used as a crystal ball.

Proposed objection #6: The text of the Bible that we have today is far from being the same as the original manuscript. It is filled with changes that have resulted from errors in the copying and re-copying of the text over a period of thousands of years. Since accurate codes depend upon the accurate preservation of the original text, even if there had been codes in the original text they would have long since been destroyed. Notice that I did not call this a “straw man” objection. The other objections were based upon a misunderstanding of the mechanics of how the Bible code works. This objection is based upon a challenge of the accuracy of the Hebrew manuscripts we possess today, which is a different line of attack altogether. Actually, there is strong evidence that the Hebrew Scriptures we have today, and especially the Torah (the five books of Moses), contains at best a minuscule number of disputed letters. For more on this subject, see the article by Harold Gans, A Primer on the Torah Codes Controversy for Laymen, which contains in its Appendix A an article by Rabbi Dovid Lichtman, “The Accuracy Of Our Written Torah”.

To repeat what was stated initially, skeptics who use the above arguments can be said to have only refuted their own misunderstandings and mischaracterizations of the Bible code, not the Bible code itself. This then leads to the next topic: what the skeptics continue to ignore.

2. What the skeptics continue to ignore

While certainly not true of every skeptic of the Bible codes, many skeptics ignore the true nature of the Bible codes and propound the “straw man” objections listed above. Another common feature of articles that attack the Bible codes is to ignore the evidence that has been gathered on the subject. One such article I remember reading two years ago in a Christian publication focused its attack on Michael Drosnin’s book and its shortcomings. The article did not once mention the work that had been published in Statistical Science by Witztum, Rips, and Rosenberg. If the reader is not even informed of this key piece of evidence, how is he supposed to make an unbiased judgment? Likewise, if a reader of such a critical article is never presented with the types of arrays such as found on this site, how is he supposed to make an unbiased judgment? That is why this site contains links to other Web pages that both defend and attack the Bible code phenomenon. We are unafraid of our readers looking at both sides of the story.

Section 3: Divine Patterns or Pure Chance?

1. How much can be found by pure chance?

This question can be broken down into two separate, but related questions: (1) How common are ELS’s of a particular word? and (2) What criteria distinguish an array consisting of a random pattern of ELS’s occurring by chance from an array consisting of deliberately encoded ELS’s?

The answer to the first question is a matter of word length and letter frequencies. The use of some English examples may clarify this. In an English text, ‘musical’ would occur very infrequently as an ELS because it is seven letters long. In comparison, ‘then’ would be found very, very often as an ELS because it is only four letters long and its four letters (t,h,e, and n) are all commonly appearing letters. In contrast, ‘jazz’ would be rare as an ELS. Although it is only four letters in length, three of its letters (j, z, and z) are uncommonly appearing letters.

This is what is actually found. CodeFinder allows one to conduct searches on many different texts, including an English edition of the King James Version Old Testament and New Testament. (This particular feature is for educational and practice purposes only since neither the publisher of the CodeFinder software nor the staff at this site nor any Bible codes expert believes that valid codes can be found in an English translation of the original Biblical texts.) To illustrate the above, ‘musical’ is found only once as an ELS in the KJVOT skip distance range 2 to 10,000; ‘jazz’ is found 36 times as an ELS in the KJVOT skip distance range 2 to 10,000. However, in the much smaller skip distance range of 2 to 10, ‘then’ is found as an ELS in the KJVOT 1438 times. If one had searched for ‘then’ at a range of 2 to 10,000 there probably would have been approximately 1.4 million occurrences. The four letters in ‘rock’ are more common than those in ‘jazz’, but less common than those in ‘then’, so one would expect it to occur as an ELS more frequently than ‘jazz’ but less frequently than ‘then’. Indeed this is what happens. ‘Rock’ is found 11,365 times as an ELS in the KJVOT skip distance range 2 to 10,000.

Looking at the Hebrew, the Torah has 304,805 letters. As a rough estimate, if one looked at a skip distance range of 2 to 10,000, there would be 3 billion possible ELS’s of any particular length. If one assumed that each of the 22 Hebrew letters is of equally occurring frequency, there would be 3,000,000,000/(22X22X22X22) = 12,800 occurrences of the average four-letter ELS in that skip distance range. There would be 3,000,000,000/(22X22X22X22X22X22) = 26 occurrences of the average six-letter ELS in that skip distance range. There would be 3,000,000,000/(22X22X22X22X22X22X22X22) = 0.05 occurrences of the average eight-letter ELS in that skip distance range. Of course, the exact number of occurrences for an ELS of given length will vary, depending on the letter frequencies of its component letters. Still, these calculations are illustrative and point to an important consideration in Bible codes research. The simple appearance of a word as an ELS by itself without other ELS’s in an array means nothing. This is particularly so for words of five letters or less. It is only when ELS’s of related words are found together in an array, or when an ELS of several letters is found in a particularly relevant passage, that it is possible that they might be deliberately encoded rather than chance occurrences. (One example of a lengthy ELS found in a particularly relevant passage is the finding of ‘Yeshua is My name’, seven letters in Hebrew, in the messianic prophecy of Isaiah 53. Grant Jeffrey reports this term and others found by Yacov Rambsel in Isaiah 53 in chapter 7 of his book The Mysterious Bible Codes, 1998, Word Publishing. The site www.biblecodecritic.com features statistical analyses of these terms found in Isaiah 53 which relate to the death of Jesus, finding the cluster of codes relating to Jesus’ crucifixion to be very highly significant. For analyses of other occurrences of the ELS ‘Yeshua is My name’ in the Tanach, see www.angelfire.com/ky/yeshuashmi.)

2. The criteria for a significant code

This brings us to our second question. What criteria distinguish an array consisting of a random pattern of ELS’s occurring by chance from an array consisting of deliberately encoded ELS’s? There is a general consensus among Bible code experts that significant or valid arrays share the following characteristics. They consist of two or more related words that demonstrate the foreknowledge of God, where these words are both compact and in close proximity to each other in a two-dimensional array. In addition, near-minimality in skip distance of an ELS is considered significant. A simple example containing two ELS’s is shown below.

In red ovals is ‘Mein Kampf’ at 9832 skip distance, the fourth shortest skip distance occurrence of this ELS in the Torah. In green squares is ‘Hitler’ at -3 skip distance, the shortest skip distance occurrence of this ELS in the Torah. The array contains 1966 letters per line. This example is mentioned on p. 12 of Grant Jeffrey’s The Mysterious Bible Codes, although he does not show the actual array. Each characteristic mentioned above is found in this simple array. (1) The two words are definitely related. Adolph Hitler was the author of ‘Mein Kampf’. (2) The array demonstrates the foreknowledge of God. When the Torah was written, who but God could have known that thousands of years in the future an individual named Hitler would come to power, much less that he would write a book titled ‘Mein Kampf’? (3) The two terms are compact in this array. The letters of ‘Hitler’ are only 3 distance from each other. The letters of ‘Mein Kampf’ are only Sqareroot of 29 distance from each other. (From the Pythagorean theorem, 29 = 5X5 + 2X2.) (4) The two terms are in close proximity to each other. They are only two distance from each other. (5) Each term is near-minimal in skip distance. This occurrence of ‘Mein Kampf’ is the fourth shortest skip distance one in the Torah, while this occurrence of ‘Hitler’ is the shortest skip distance one in the Torah.

Actually, this same -3 skip distance occurrence of ‘Hitler’ also forms a good array with the second shortest skip distance occurrence (-7009 skip distance) of ‘Mein Kampf’ in the Torah, as shown below. This array has a line length of 1402 letters per line. As a brief aside, this second pairing illustrates a tendency within the Bible codes that researchers have noticed. God appears to have built in a certain degree of redundancy into the codes. While this is not true for every topic or event, it appears that certain especially important topics or events are described by more than one array. Oftentimes, different arrays focus on different aspects of a particular subject. This redundancy may be God’s way of highlighting certain subjects and/or ensuring that arrays about those subjects are found. For a statistical analysis showing the significance of these two arrays, see Appendix A.

3. How do you know the codes are significant?

As mentioned above, significant code arrays are those which meet the described criteria. However, that still leaves open some questions. How compact must ELS’s be in order to be considered significant? How near must ELS’s be to each other to be considered significant? The answers to these questions depend upon the specific words and skip distances involved, but a skilled researcher who has much experience examining arrays (in both the Scriptures and control texts) can oftentimes “eyeball” an array and have a good idea whether it is significant or not. In the end, though, the only way to know that an array is significant is to do statistical analysis, a prospect often involving intensive calculations and computer searches of control texts or control words. However, even if one shows that an individual word pair array (such as one of the above) is statistically significant, that may not be enough to convince a skeptic. He may point out that such a pairing might be a lucky fluke. The more relevant question, then, is not if a particular array is significant but is the Bible codes a valid phenomenon or not? Does it simply involve playing word games with randomly produced patterns or is it proof that God did indeed write the Bible?

If isolated word pairings do not constitute proof of the validity of the Bible codes phenomenon, what does? Basically, the proof comes from the gathering of extra data, so much data that the skeptics cannot objectively ignore it. (Of course, they can still non-objectively ignore it, but that is a different story.) There have been two approaches to this gathering of extra data. The first is the approach used by Doron Witztum, Eliyahu Rips, and Yoav Rosenberg (WRR). If isolated word pairs are unconvincing, then design an experiment that examines a whole class of dozens of word pairs where in each pairing the first word and the second word have the same relationship to each other. A paper authored by WRR describing such an experiment was published in the August 1994 issue of the mathematical journal Statistical Science (click here ). As originally submitted, this experiment searched the book of Genesis for ELS’s of the names (and other appellations or titles) of 34 famous rabbis and ELS’s of their Hebrew dates of birth or death. These rabbis were determined by the rule that their biographical entries in a particular Jewish standard reference book be at least 3 columns long. A statistical measure for each word pairing was calculated and the aggregate results were compared with various control texts. The results were found to be very significant. The referees were baffled and asked the authors to perform the same tests on a fresh data set, 32 rabbis whose entries in this particular reference work were from 1.5 to 3 columns long. Very significant results were found again. The probability of Genesis producing by mere chance as good a pairing for the rabbis and their dates of birth or death as was seen was calculated to be only 1 in 62,500. It was the publication of these highly significant results in a professional statistics journal that first created a widespread excitement about the subject of the Bible codes. Popular books by authors such as Grant Jeffrey and Michael Drosnin helped spread awareness of the subject into the general populace, as have web sites such as this one and the ones listed in this site’s Links section.

Since WRR’s paper came out, a “refutation” of their work by authors Brendan McKay, Dror Bar-Natan, Maya Bar-Hillel, and Gil Kalai (MBBK) was published in the May 1999 issue of Statistical Science (click here ). MBBK pointed out what they perceived to be flaws in WRR’s methodology and data set, flaws which they claimed disproved the existence of the Bible codes phenomenon.. Shortly after that paper came out, this site published a paper Statistics and the Bible Codes. Our paper included the following statements. “As far as the statistics go, even though McKay’s paper was convincing, we think we should wait for WRR to reply, because they are saying how terrible and off the MBBK paper was.” Also, “even if the MBBK paper successfully rebuts WRR’s paper, that does no harm to the Bible codes. The reason is because all this amounts to is two groups of statisticians arguing on methodology.” Since that time, Harold Gans, a highly qualified codes researcher (and former cryptanalyst with the National Security Agency) has written a A Primer on the Torah Codes Controversy for Laymen in which he addresses the points raised by MBBK. In this author’s opinion, Gans successfully demonstrates that MBBK have not refuted WRR’s work. In addition, Gans describes additional Bible codes experiments which have been performed by WRR and himself which continue to show statistically highly significant results. Rather than delving into the intricate details of the original WRR paper, the MBBK “refutation”, and the Gans response, readers are invited to use the provided links to read the primary sources themselves.

The second approach to gathering more data is the approach that has been taken by this web site. If arrays consisting of only two or three ELS’s can be called minor codes, our goal has been to find examples of major codes or arrays consisting of ELS’s of several related words. This is not to say that we at this site believe that minor codes with only two or three ELS’s are invalid. It is just that we do not believe them to be particularly convincing to many readers. This site has published numerous arrays on various subjects consisting of ELS’s of several related words. This site has also published a methodology for examining these major codes and published an article, Formal Control Experiment Reveals Significant Codes. In this article, several major codes were examined and control arrays from a control text were constructed. These control arrays were compared with the real arrays found in Scriptures and mathematical calculations were performed (taking into account several factors) to determine which major codes were significant. Though some arrays were found to be insignificant, more were found to be significant. It is important to restate that just because we take a different approach to the Bible codes than do WRR and their associates does not mean that we believe their work to be invalid. We believe that their work is valid. However, we also believe that the approach they have taken to the codes to be only one aspect of a larger phenomenon, and it is these other aspects of the codes that we seek to explore. Also, WRR and others have written to a target audience of professional mathematicians, as is appropriate given the formalized nature of their research. However, we seek to reach a broader audience, showing them the reality and wonder of the codes, and through that, the reality and wonder of our God.

A third approach to statistical analysis of the codes can be found at www.biblecodecritic.com. This site is run by professional mathematicians Ed Sherman and Dave Swaney. Their approach in the analysis of code clusters is to first choose the most improbably occurring ELS to be the focal code. Analysis of all other ELS’s is based on their relation to the focal code. If an ELS crosses the focal code, they compute the probability that an ELS of that term and of no greater than that skip distance would cross the focal code by chance. If an ELS does not cross the focal code, they compute the probability that it would come as close to the focal code in the text as it does. A full description of the method can be found in Mr. Sherman’s book “Breakthrough”, which can be purchased and downloaded at their site.

As can be seen, there are many different approaches to the statistical question. Whichever approach is taken, though, the goals are the same: first, to test the significance of individual arrays, but more importantly, to show that the Bible code phenomenon is real, that it cannot be explained by random chance, and therefore that God did indeed write the Bible.

Section 4: The Purpose of the Bible Codes

1. What is the purpose of the Bible Codes?

The purpose of the Bible codes has been alluded to in the previous sections, but it is now time to state it explicitly. An excellent summary statement can be found at The Purpose of the Bible Codes. “The Bible Codes are there to show that the God of the Bible inspired the writing of all scripture, by finding descriptions of people and events that happened after the Bible was written, encoded in the original texts. The codes serve as God’s signature”.

Is this conception of the Bible codes consistent with what we see in the Bible itself? Hebrews 6:18 tells us that “it is impossible for God to lie” [1]. John 17:17 states that God’s “word is truth”. Since God will not contradict Himself, then the true conception of the codes must be consistent with the Bible’s plain message.

The first question to ask, then, is whether ELS encoding is consistent with the Biblical view of the inspiration of Scripture? Deliberate ELS encoding is possible only if God inspired Scripture at the letter-by-letter level. If God simply inspired an author’s ideas, but not how he actually wrote the book, then the deliberate encoding of information by ELS’s would be impossible. Traditional Jewish views of Scriptural inspiration are that the Torah was dictated letter-by-letter to Moses from God, but that He only inspired the authors of the Writings and Prophets at the idea level, not at the letter-by-letter level. Therefore the Jewish view of the codes is that they will be found in the Torah, but not in the rest of the Tanach. Christian proponents of the codes, however, believe that valid codes can be found all throughout the Tanach (the Hebrew Scriptures or Christian Old Testament). Referring to all of the Tanach, 2 Timothy 3:16 states that “All Scripture is inspired by God”. The original Greek word translated “inspired by God” is theopneustos, meaning literally “God-breathed”. 2 Peter 1:20,21 states “But know this first of all, that no prophecy of Scripture is a matter of one’s own interpretation, for no prophecy was ever made by an act of human will, but men moved by the Holy Spirit spoke from God.” This also is consistent with God inspiring the human writers of Scripture at the letter-by-letter level, not only in the Torah but also in the rest of the Tanach.

The second question to ask is whether the content of Bible code arrays is consistent with how God has spoken in the surface text of the Bible? God’s foreknowledge of the future and His revelation of that foreknowledge to men through prophecy is a general theme throughout the whole Bible. One of the clearest statements concerning this is found in Isaiah 46:9,10. “Remember the former things long past, for I am God, and there is no other; I am God, and there is no one like Me, declaring the end from the beginning and from ancient times things which have not been done, saying ‘My purpose will be established, and I will accomplish all My good pleasure.’ “ This verse (and others) clearly shows that God does indeed have the foreknowledge to encode the details of future events as Bible code arrays. Furthermore, this is consistent with how God has spoken in the past in prophecies.

Having established that our conception of the Bible codes is indeed biblical, one further point must be made concerning verification. If a person sends a message via a courier to another individual, how can the recipient know that the message he has received is indeed from that person rather than from a forger whose intent is to deceive? One way is through verification. Although there are various means of verification, one method is to include in the message information known only to both the sender and the recipient. How does that translate into the situation regarding the Bible codes? In this case, God is the sender, the Bible is the message, and we are the recipients. What was known to God when He wrote the Bible were the details of all future events. What is known to us when we attempt to find a Bible code array is selected data from our past. Thus in this case what is only known to both the sender when He wrote and the recipient when he examines are the details of history between when the Bible was written and the present time. Finding code arrays with these details is evidence that the Bible was indeed written by God. This constitutes the subject matter of the Bible codes, and a proper grasp of this point can guard one from misuses and false interpretations of the codes.

2. Can the codes forewarn us of events to come, or be used to predict the future?

The answer to this question is no. To understand why, apply the principle in the preceding paragraph. What is in our future is known only to God, not yet by us. What is in our future is thus a proper subject for God to have encoded details concerning it, but not a proper subject for us to attempt to find an array about. To find an array with details of a past event serves to help substantiate God’s authorship of Scripture. To find an array with supposed details of a future event can only be speculative. Since we do not know the details of future events, we cannot know that what we have found is a valid code array. It may be that we have made a lucky guess, but there is no way to know that until after the event has occurred. Therefore the codes cannot be used to predict the future nor to warn us of events to come.

The Bible codes also do not encode alternate possible futures which may or may not happen. See Does The Bible Encode Alternate Possible Futures?. In addition to the points made by that article, the following can be stated. For the sake of argument, assume that the Bible codes do encode alternate futures which might or might not happen. If one found an array about a possible future event which might happen, and it did happen, this would be indistinguishable from an array which God encoded about an event which He knew would happen. If one found an array about a possible future event which might happen, and it did not happen, this would be indistinguishable from a random word pattern one found by chance. It all comes back to the fact that the codes can only be considered valid where we know the relevant details of an event, i.e. when it has already happened. Thus not only is the idea of God encoding details of events which might or might not happen unbiblical, it is also philosophically indefensible.

3. Are there hidden theological teachings or messages?

The answer to this question is also no for the same reason. Knowledge concerning historical events can be gained through natural means once that event has occurred. Theological truths can only be learned through God’s self-revelation, i.e. the Bible. A hidden theological teaching or message is one that by definition is not in the plain text of the Bible. If it is not in the plain text of the Bible it cannot be known by us to be true, even if it is true. An example should suffice to illustrate the point. The Bible is limited in its teachings concerning the hierarchy of angels. Let’s say that a person decided to find an array concerning the hierarchy of angels. What he concludes from his array might be true, but there would be no way for him to know that it is true. Again, what he concludes from his array might be false, but there would be no way for a third party to know that it is false. Since natural means cannot teach us about the hierarchy of angels and the Bible says very little on the subject, the array is useless. Since it cannot serve to verify God’s foreknowledge, whatever pattern of ELS’s he may find will remain just that, a pattern of ELS’s. It can never qualify to be a valid Bible code array.

These are just two questions which might be raised. For a discussion of many other proposed but false “purposes” of the codes, see the article mentioned above, The Purpose of the Bible Codes.

Section 4 endnotes:

Section 5: Conclusion

1. Implications of the Bible Codes

The Bible Code answers the question of God’s existence with a definite Yes. God does exist. Furthermore, since the Code is found in the Bible, the answer is even more specific. The God of the Bible does exist. If the God of the Bible does exist, and the Bible is His self-revelation to us, then we need to take the Bible’s message very seriously. We are His creation and are accountable to Him. What are the implications of the Bible Codes for the reader of this paper? They are fourfold, as stated in this site’s Mission Statement. (1) For the atheist or agnostic, the codes demonstrate not just the existence of God, but also His awesomeness, and show that it is He and He only who is God. We hope from this that they realize their need for a Savior. (2) For the “religious”, the codes forces them out of their comfort zone into the need for a personal relationship with God. (3) For the believer who doesn’t believe that ALL of the Bible is true, the codes let them know that everything they read in Scripture is true, thus strengthening their faith. (4) For the believer who believes in all of the Bible, but has been mislead about the Bible codes, we hope that the codes strengthen their faith in the Bible, and provide them with evidence they can use in witnessing to others.

2. Summary

The author has sought to give a good overview of the truth about the Bible codes in this paper. Section 1 explained what an equidistant letter sequence (ELS) and matrix are. Section 2 addressed some of the common mischaracterizations and misunderstandings of the codes that have been raised by skeptics. Section 3 listed the criteria for a valid Bible code array and discussed the difference between random ELS occurrences and significant codes. Section 4 stated the true purpose of the Bible codes and refuted some of the false proposed purposes of the codes. Section 5 has shown the implications of the Bible codes and what they mean for the individual reader. If we have given the reader a better understanding and appreciation of the codes and helped strengthen your faith in God, then we will consider our mission to be accomplished.

Appendix: A Detailed Example Of A Statistical Analysis

This appendix shows a detailed statistical analysis of two Bible code arrays presented in Section 3.2 of this paper. Those two arrays show a pairing of ‘Mein Kampf’ with ‘Hitler’. The ‘Hitler’ in each array is the same occurrence and, at -3 letter distance, is the shortest skip occurrence of this word in the Torah. The two occurrences of ‘Mein Kampf’ (at -7009 letter distance and 9832 letter distance) are the second and fourth shortest skip distance occurrences of this word in the Torah. It is hoped that this example will help lead the reader into a greater understanding of the Bible codes phenomenon and the methods of statistical analysis used to show their significance. I apologize beforehand for the technical jargon that follows, but given the importance of statistical analysis to Bible codes research I believe that is important to go into detail on the subject.

First it is necessary to define a term used by Witztum, Rips, and Rosenberg (WRR) in their 1994 Statistical Science article. For an array of given line length they define a term using the Greek letter delta, which we will simply call D. This term, D(e,e’), is the sum of three squared distances: (1) the squared distance between consecutive letters of ELS e; (2) the squared distance between consecutive letters of ELS e’; and (3) the squared minimal distance between a letter of e and a letter of e’. Designate ‘Mein Kampf’ as e and ‘Hitler’ as e’. Thus for the first array, the first squared distance is 29. This is calculated by squaring the 5 rows from one letter to another and adding the square of 2 columns from one letter to another (5X5 + 2X2 = 29). The second squared distance is 3X3=9. The third squared distance is 2X2=4. Therefore in the first array D(e,e’) = 29+9+4 = 42. In the second array, the first squared distance is 26 (5X5 + 1X1 = 26). The second squared distance is 3X3=9. The third squared distance is 18 (3X3 + 3X3 = 18). Therefore in the second array D(e,e’) = 26+9+18 = 53. Notice that the smaller D(e,e’) is for a particular pair of words, the better the array is for that pair of words. (It must be explicitly stated that delta values for one pair of words cannot be directly compared with delta values for another pair of words. A delta value pointing to a statistically significant array for two particular words may point to a statistically insignificant array for a different two words.)

Having defined D(e,e’) for the two arrays, we ask the following question. What is the probability that the shortest skip distance occurrence of ‘Hitler’ in the Torah would produce arrays with two of the four shortest skip distance occurrences of ‘Mein Kampf’ in the Torah where D(e,e’) < 53?

When WRR performed their experiment, they performed additional calculations on delta(e,e’) to come up with functions labeled mu and sigma of e and e’, and omega and c of w and w’. Those calculations, which are very complicated, were designed to produce aggregate statistical measures for the entire data set of 32 rabbis (each with different possible appellations) and their dates of birth and/or death (with three standard Hebrew date formats tested for each). They then performed an internal control test where the aggregate result for all correct pairings was compared with 999,999 randomized mismatched pairings (that is, where each rabbi’s name was paired with a different rabbi’s date of birth and/or death). These were then ranked from 1 to 1,000,000 with 1 being the matchings that gave the best result and 1,000,000 being the matchings that gave the worst result. If the Bible codes phenomenon does not exist, one would expect the correct name/date matchings to perform no better on average than incorrect name/date matchings. However, using four different statistical measures, the correct matches in Genesis ranged from 4th best out of 1,000,000 to 570th best out of 1,000,000. By any standard one might want to use, these are very significant results.

Our analysis will be quite simpler, needing only the delta function, D(e,e’), since only one word pair is involved. However, our analysis is conceptually similar. Where WRR used name/date mismatches, we will keep one ELS constant and permute the letters of the other. Namely, we will keep the four shortest skip distance occurrences in the Torah of ‘Mein Kampf’ (ELS e) constant while searching for arrays of it with e’, where e’ are the permuted spellings of ‘Hitler’. By permuting the letters of a word, one can create several “control” ELS’s which have exactly the same expected letter frequencies as the ELS being tested. Therefore, since ELS e is being kept constant and the letter frequencies for the test e’ and the “control” e’ ELS’s are the same, the D(e,e’) of the correct spelling and the permuted spellings can be directly compared. As it turns out, a 5-letter word where each letter is different has 120 spelling permutations. (The number of permutations equals “5 factorial”, which is written “5!”. 5! = 1X2X3X4X5 = 120.) However, half of these spelling permutations are simply the backwards spelling of the other half. Thus there are only 60 “reversal-independent permutations”. (As an example, abcde and edcba are considered as just one “reversal-independent permutation” since abcde at a skip distance of +n is the same as edcba at a skip distance of -n.) These 60 permutations are labeled H1 through H60, where H1 is the correct spelling of ‘Hitler’ and H2 through H60 are all other possible reversal-independent spelling permutations of the five Hebrew letters in ‘Hitler’.

Each of the four occurrences of ‘Mein Kampf’ were searched for with the 60 permutations of ‘Hitler’ (12 at a time). Since we are only interested in those cases where D(e,e’) < 53, only skip distances -7 to +7 were searched for H1 to H60. (A +8 skip distance occurrence would have a squared distance of 8X8=64. Therefore regardless of how compact e was or how close e and e’ were, D(e,e’) would be greater than 64 in those cases.) Of H1 to H60, there were 37 permutations that produced 66 occurrences in the -7 to +7 skip distance range. Only one of these 66 was the correct spelling of ‘Hitler’. Row splits 1 through 7 were manually inspected in each case to see if any “good” arrays were formed. When a “good” array was formed, D(e,e’) was calculated. Of the 66 occurrences of the 60 permutations, the best was one of H21 and the -6164 skip distance ELS of ‘Mein Kampf’ at row split 5 with D(e,H21) = 29. The second best occurrence was one of H17 and the -7009 skip distance ELS of ‘Mein Kampf’ at row split 4 with D(e,H17) = 35. The correct spelling of ‘Hitler’ ranked 3rd best on two occurrences of ‘Mein Kampf’, D(e,H1) = 42 and D(e,H1) = 53.

This enables us to calculate the answer to the question that we first asked. What is the probability that the shortest skip distance occurrence of ‘Hitler’ in the Torah would produce arrays with two of the four shortest skip distance occurrences of ‘Mein Kampf’ in the Torah where D(e,e’) < 53? If H1 only ranked 3rd best out of 60 permuted spellings one time, P would be 3/60, or 5%. However, since H1 ranks 3rd best of the 60 permutations with two different occurrences of ‘Mein Kampf’, P = (3/60)(3/60) = 1/400. In other words, the probability that this would happen by mere chance is only 1 out of 400, or 0.25%. As we can see, the evidence of both arrays taken together is much greater than the evidence of either considered by itself.

Actually, the above is a slight understatement of the actual probabilities, for WRR’s paradigm would have us consider one other factor, the domains of minimality of ‘Mein Kampf’ and of ‘Hitler’ (H1), as well as H2 through H60. A “domain of minimality” (w) is simply the fraction of the text (in this case, the Torah) for which a particular occurrence of an ELS is the shortest skip distance. Thus the shortest skip distance occurrence of an ELS will have a domain of minimality of 1 (w = 1), whereas longer skip distance occurrences of that same ELS will have a domain of minimality of less than 1 (w < 1). One can also speak of a “domain of simultaneous minimality” of particular skip distances of the two terms e and e’, designated as w(e,e’). This is the overlap of the domain of minimality for the given occurrence of e and the domain of minimality for the given occurrence of e’. D(e,e’)/w(e,e’) gives a delta value [compactness and proximity of the two ELS’s] that is modified by a measure of how near-minimal each ELS is. Since we are keeping the four occurrences of ‘Mein Kampf’ (e) fixed and permuting the spelling of ‘Hitler’ (e’), we can consider only the effect of w(e’), that is, the domain of minimality of terms H1 through H60.

Since ‘Hitler’ (H1) at -3 skip distance is minimal for the entire Torah, w(H1) = 1. Therefore, D(e,H1)/w(H1) = D(e,H1) = 42 for one case and 53 for the other case. The occurrence of H21 that produces D(e,H21) = 29 is minimal for the entire Torah and thus w(H21) = 1. Thus D(e,H21)/w(H21) is still 29, and still ranked best. However, the occurrence of H17 that gave D(e,H17) = 35 has a much smaller domain of minimality, only 493 of the 304,805 letters of the Torah. (This is because it is found in a phrase that is repeated both a few verses before and a few verses after.) Thus in this case w(H21) = 0.00162 and D(e,H21)/w(H21) = 21,640. What was second best when domains of minimality were not considered is far from second best when domains of minimality are considered. This would make H1 2nd best twice from this perspective and P would be (2/60)(2/60) = 1 chance out of 900.

The two preceding paragraphs demonstrate how “domains of minimality” are taken into account when performing statistical analysis. The example also illustrates how this can sometimes produce strange results when compared with results that do not use domains of minimality. This is a rather extreme example, though, since multiply repeated phrases only a few verses apart occur only a handful of times. Therefore in most situations the use of domains of minimality will produce valid results. In any event, regardless of whether one accepts the probability of 1 out of 900 or 1 out of 400, the evidence is strong that rather than it occurring by random chance, God deliberately encoded this pairing.

As was stated in the introductory paragraph, it is hoped that this detailed example has led the reader both into a greater understanding of the Bible codes phenomenon as well as the methods of statistical analysis used to show their significance. If it has done this, this appendix has served its purpose.

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