Reprinted from *Meridian Magazine* (25 Jan 2006).

©2006 by John P. Pratt. All rights Reserved.

1. Dizzy Bear |

2. History of Bible Codes |

2.1 Code Breakers |

2.2 Criticisms |

2.3 State of the Art |

2.4 Weaknesses |

3. New Approach |

4. Torah Tutorial |

4.1 CELS encoding |

4.2 Two Witnesses |

4.3 Spanning Codes |

4.4 Reverse Codes |

4.5 Linked Codes |

4.6 First Occurrence |

5. Back to Eden |

5.1 Wheat from Chaff |

5.2 All in "Garden in Eden" |

5.3 A Mandala |

5.4 Contextual Crosses |

5.5 Overall Probability |

5.6 Adam Centered in Eden |

6. Conclusion |

Notes |

*Tarnished "Bible codes" may yet shine under new light.*

Nearly a decade ago, controversial "Bible codes" were widely publicized, which supposedly proved
the existence of God by the discovery of secret coded messages in the Hebrew text of the Torah
(the five books of Moses).^{[1]} Then the hype fizzled when critics unveiled similar messages in
English in secular texts such as *Moby Dick*, which were obviously due to random chance.^{[2]} The
final nail in the coffin seemed to be a scientific refutation in 1999 to the professional paper which
had given it credence in the first place.^{[3]} Now, like the phoenix rising from its own ashes, the Bible
code phenomenon may be returning as a renewed wave of interest is growing, based on new
discoveries which claim to overcome the objections. After reading one of the latest books
attempting to revive the subject, *Bible Code Bombshell* by Edwin Sherman,^{[4]} I felt that some of his claims were true but that others were not. To me, what is needed is a new approach which can separate the wheat from the chaff.

After a brief historical summary, this article enumerates my specific objections to the way the current research is being conducted, proposes what seems to be a better approach, and then tries it out on a few verses of Genesis. Preliminary results seem encouraging enough to share, even though the new theory is currently only in the prototype stage.

Is it possible to determine with virtual certainty whether or not an author intentionally used the proposed Bible code method to encrypt secret messages into any text? That may be an important question for those who have studied Bible codes because debunking methods have left disillusioned believers with the impression that any message whatever can be found in any sufficiently large text, so it seems to follow that one could never know with confidence whether a given message was indeed really encoded intentionally by the author.

Before discussing the actual Bible codes, let us attempt to answer that question by considering an example in English I wrote to illustrate the proposed encoding method: the allegory of "Dizzy Bear".

"Dizzy Bear" Brent: neater, no, nuttiest

Brent; rambling,

Big and ageless.

Brent wondered what it meant. He knew he might look like a big, rambling bear, and that he had been called "nutty" at times, but never "Dizzy Bear" nor "ageless."

His father liked puzzles, and Brent had received cards from him before with acrostics hidden in the verse. Sure enough, his initials D.B.B. were the first three letters of each line and also of each of the first three words of the first line. That explained at least the first letters of the nickname "Dizzy Bear", but he suspected there must be more. The words "neater, no" stuck out like a sore thumb.

He took it to one friend for help, but the reply was, "I do not believe in poetry puzzles, so it would be pointless for me to look for signs of intelligent design in poetry. That just isn't scientific, because even if I found something, it could never be proven that it was not the product of random chance."

So Brent gave the card to his mathematician friend JoAnn. She agreed to be open-minded enough
to look for hidden codes. She started her investigation with the word "neater" which just didn't
seem to fit, and soon discovered that starting with the "B" in "Bear" and counting every third letter,
it spelled out "Brent." She calculated that there is only about a 1/5,000 chance that a 5-letter
word that described the subject would appear encoded by chance with equal letter spacing in such a short text, and such that it formed a perfect cross (See Figure 1).^{[5]} So she felt she had discovered an encoded word which the author must have had in mind.

She found another encoding of "Brent" crossing through his name in the text, this time counting every fifth letter, and again beginning on the "B" in "Bear". Her hypothesis had correctly predicted a future discovery, which is the whole point of the scientific method. She estimated that there is only a 1/1,000,000 chance that an average topic word of 5 or more letters would be found crossing itself twice in so short a text.^{[6]}

When she tried extending the second discovery, it spelled out "DBrentBriggs," even including the capital letters. She knew his surname was Briggs, so this put it so far beyond chance that she didn't bother calculating the odds. She now knew that the code was real.

But what about the "D" in "DBrent Briggs"? It is capitalized, just like the other two names, and those letters exactly span the entire text, as if by design. Was "Brent" really his middle name? Suddenly the double acrostic jumped out at her, and there was no doubt in her mind that his initials were indeed D.B.B.

If his surname "Briggs" was encoded, then perhaps his first name was also. She started counting letters from the only capital "D", following the example that "Briggs" was capitalized. Sure enough, in no time she discovered the name "Dan" by counting every seventh letter. What are the chances of another name just appearing like that, starting on the capital letter indicated by the acrostic? She felt it just had to be right.

JoAnn reported back to Brent that she had cracked the code. She proudly announced that she had discovered that his full name was "Dan Brent Briggs." To her dismay, Brent told her she was wrong! She begged for another chance, which of course he granted.

When she reconsidered her reasoning, everything looked perfect up to actually discovering his first
name. There was no question that the names Brent and Briggs had been coded according to her
hypothesis. And "D" just had to be his first initial because of the acrostic. The mistake must have
been to accept "Dan" as the first name found. She realized that it was not improbable to find a 3-letter name there just by chance, even in a short verse. All she would have to do is find the next
vowel and then count that same number of letters and land on a likely consonant. Maybe his name
was "Don". Wishing that she had done so before embarassing herself, she now calculated that there is nearly a perfect chance of finding at least one 3-letter name starting on that very "D."^{[7]} She had allowed her enthusiasm to cause her to announce results prematurely.

To make it easier to find names, she wrote out the verse in lines spaced by five, being the spacing between the letters of the second encoded "Brent" she found. Mathematics told her that encoded names with any spacing would show up in straight lines in that diagram if the lines were extended at the edges to repeat letters if necessary. She was then shocked to find "Den" (short for Dennis) spaced at both 6 and 11, "Dog" (a nickname?) spaced at 21, and "Dil" (short for Dilbert) spaced at 26.^{[8]} And there could be even other longer names. How could she know which was right? Or maybe those are all there by chance and his first name is Dumpelstilskin, too hard to encode, hence only abbreviated. How could she possibly tell which name, if any, was correct? Maybe there was no new revelation to discover.

She now realized what a huge advantage it had been to already know that his last name was Briggs.
She persevered and finally discovered the name "Dennis" by extending out the name "Den" she had found spaced every eleventh letter. She squealed with delight when she found it also ended on the very last letter of the verse, as did "DBrentBriggs" (see Figure 2). She calculated that the chance of finding a common six-letter name, which also followed the established pattern of spanning the verse, was only about 1/18,000.^{[9]} Now there was no doubt that "Dennis" was the name purposely hidden in the codes by its author, and she was right.

Afterward, Brent went to his father, the creator of that one verse (or uni-verse), and thanked him for having taken the time to write it and code it so cleverly. His father was grateful that his son had believed in him enough to study his words carefully. Brent then asked if the inclusion of the second name "Den" was there by chance or by design. His father replied that he didn't plan that name at all, but it was there only by chance, even though it also followed his coding rule of intersecting the name "Brent" in the text.

The probability of finding an example produced by chance of the full name, consisting of at least 12 letters (which could include up to 2 initials) of a person mentioned in a text by their own first, middle or last name (consisting of 5 or more letters), encoded within 100 consecutive letters which include that name, such that both the full name and one of their three names (of 6 or more letters) exactly spanned each other, and also with the contextual name again encoded in a perfect cross, is about one in 14,000,000,000,000,000,000,000.^{[10]}

To grasp the magnitude of that number, it means that if there were a biography of every person who had ever lived on earth since Adam, that mentioned one of their names a thousand times, and an equal number of novels and news stories had been written that did likewise about real or imaginary people, and then all of that literature were searched to find an example meeting those criteria, there would only be a one in a hundred million chance of finding even one success!^{[11]} And that is not even requiring that all of the encodings have the first letters of each name capitalized, nor requiring the double acrostic, as in the "Dizzy Bear" example! Thus, if the coding is structured well-enough, then it becomes clear that it didn't occur by chance.

One of the first examples found was the following. Starting with the first Hebrew "t" (*taw*) in
Genesis and counting every 50th letter, it spells out "torah."^{[14]} That by itself could be due to pure
chance and hence meaningless, but the same effect is also observed in Exodus. That is, beginning
on the first *taw* in Exodus, and counting every 50th letter, again yields "torah." The probability of that occurring by chance in a randomly selected chapter of the Torah is only about 1 in 1800, so the possibility that such codes are real seemed to merit further investigation.^{[15]}

This type of code, in which one finds a sequence of letters by skipping the same number of letters in succession, is called an "equidistant letter sequence" (ELS). The number of letters counted to the next letter is called the ELS spacing. The "Dizzy Bear" example used ELS codes of spacing 3 ("Brent"), 5 ("DBrentBriggs") and 11 ("Dennis").

Little progress was made from this point before computers could be used to easily do the counting
for us. Excellent, inexpensive programs are now available to do this laborious job.^{[16]} And when they were used, then it became almost too simple to unleash their power to find
codes everywhere. For example, "torah" is found encoded 34 times at various ELS spacings in the
first chapter of Genesis, which is about the number expected to be found just from random
chance.^{[17]} So how can we know if any of those codes were intentionally put their by the author?

When that method seemed to produce meaningful results, a paper was published by a peer-reviewed statistics journal in 1994.^{[18]} With that credibility, a best selling book was written that
brought the result to the public awareness, written by an investigative reporter who sensationalized it.^{[19]} Without appreciating the underlying statistics well enough, but knowing what people buy, he
immediately applied the techniques to predict the future. His book did much to discredit the entire
field, for it was easily refuted. But there were also serious criticisms of the original scientific paper
itself.

But even a few errors in the text will cause errors in the codes over any interval containing an error that either adds or deletes a letter. Another response to this criticism is that we are talking about God as the author, and he could know ahead what letters would be left out, and could have planned for that contingency. Thus, some researchers look at codes separated by thousands and even hundreds of thousands letters, and take them very seriously.

More serious criticisms of the work deal with what is sometimes called by statisticians "snooping" and "tuning." Snooping occurs when one peeks ahead at the data, and then proceeds to calculate the probability of that data being found using assumptions based on not having looked ahead. Tuning refers to changing ones definition of what constitutes a success to fit the data which has been snooped. Most often, these two cardinal sins in statistics are committed inadvertently rather than maliciously.

The demise of the scientific paper on which so much was based came mostly from tuning criticisms. It was pointed out that many of the rabbis whose names were found associated with their birthdates were called by appellations that worked. This is a classic example of tuning. When all names of the rabbis were included to allow for failures, the effect was found to disappear.

For me, the problem is that when I read the early chapters of the book dealing with the above, I was grateful that finally that work was progressing, and that I could rest easy that someone else was doing it just fine. But then as I read the rest of the book, I felt that the researchers have again had wandered off into Fantasy Land. So, rather than review the new work, I feel the need to vent my own criticisms of all of the work which has been done to date, and to offer a proposed solution.

**Threw out Baby with Bath?**Most of the sequences used to discover the codes are now considered invalid because they do no meet artificially imposed statistical standards. Some insist that words must be found in pairs, some want to disallow all codes less than five letters long. Those are both indications of our ignorance, rather than derived coding standards used by the encoder. Then I look at what is allowed, certified as rare codes, and see very questionable results.**Separating Wheat from Chaff.**All that has been done so far is based on statistics. When a word is found more times than expected, there has been no good way to tell which are the "extra" codes, most likely to have be included by design, and which are the random finds. What good is a Bible code if we don't even know which codes are real? How can we possibly take the next step of reading them?**New Revelation?**Many artificial restrictions have been placed on the possible message content of the codes, such as that they cannot predict the future, and that no new religious truths might be contained in them. Since when is God restricted on what he might want to reveal? What is the point of a hidden message if it is vacuous? This restriction was apparently proposed only to avoid offending someone with different beliefs.**Surface Text Important.**The surface text (that is, the raw text, ignoring codes) is often ignored when searching for Bible codes, especially where large ELS spacings are involved. The best examples in all five of the new types of discoveries summarized above were in the context of the same topic in the surface text. But there is no formal requirement to have the surface text refer to anything related to the codes.**Minimum Spacing.**One type of wheat/chaff filter has been proposed. It was decided to pick ELS codes with minimum or near minimum letter spacing as the rule to determine their importance. That seems totally arbitrary to me. Each of these rules need to be proven as useful before being written in stone.**Outrageous spacings.***Bible Code Bombshell*lists an ELS code for "Saddam Hussein" in a sequence with a skip of 150,684.^{[22]}That is so long that it spans nearly the entire Hebrew Old Testament, with each letter being taken from a different book. Now, God moves in mysterious ways, but that is really pushing my credulity. Even though I believe that God could know ahead exactly what books would be written with what words and then arranged in what order, I still would have to see some very convincing evidence to believe that such a code is real. The most convincing codes I've seen span very short distances (less than a chapter), over which I could believe that no copyist errors have been made since the original revelation to Moses. The longer the sequence, the more probable the chance for error.**Close Doesn't Count.**My work in calendar dates has shown me that God's work is amazingly accurate. While other chronologies attempt to establish religious dates to within a year or a decade, my work has asserted that all of the important dates are usually known to quarter-day accuracy. Bringing that bias with me when I examine the evidence for Bible codes, I am unimpressed with the metric proposed by the researchers to have two codes "close" to each other. The only codes I'm impressed with so far are direct hits. That is, the encoded word shares a letter with either the surface text or another encoded word. I might be proven wrong on this point, even in my own calendar work, but I would need to see some very convincing examples. The problem with "close" is that it allows far too many hits and leads to confusion and spurious codes to be accepted as real. We need many ways to separate the wheat from the chaff.**Order.**One of the best indications of intelligent design is order. When I was encoding the "Dizzy Bear" example, I put as much order into the example as I could, to make it absolutely clear without any need to calculate complicated probabilities, that the encoded words truly were intended by the author. God's house is a house of order, not a house of confusion (2 Chr. 29:35). That is because order is a clear indication of intelligence. Most of the Bible code examples published show only a superficial order imposed by the researcher but not clearly intended by the author.

Thus, let's consider a new approach which addresses these weaknesses in the current theory.

What I propose is that a subset of ELS codes be considered. The requirement is so new and
different from what has been done, perhaps they should have a different name. Let us call them
*Contextual Equidistant Letter Sequences* (CELS). That is, the code must relate to the context in
which it appears, or else it is rejected as random. When the spacing is so large that a variety of subjects are discussed in the surface text, then at least one of the words intersected must clearly relate to the encoded word.

This contextual requirement is a little slippery, and opens the door to "tuning" criticisms. What one person thinks relates, another does not. But sometimes it is crystal clear. In the "Dizzy Bear" example, the encoded words "Brent", "Briggs", and "Dennis" all intersected the word "Brent" in the text. Note that such is only possible if the encoded word contains the very same letters as the contextual word ("Dennis" contains both an "e" and an "n" as does "Brent"). This is a very stringent requirement. It is an extreme case of what the original statistical paper was using as a metric. Those researchers required that the two sought terms intersect "near" each other. My proposal is that they intersect in exactly the same letter, and moreover, that at least some letters be contained in a related surface words. While that method may seem harsh because it eliminates so many codes, it also allows other codes to be accepted because no longer is there a requirement for two words, nor long words. A single short encoded word might be meaningful if it is composed of letters found in meaningfully related words. A preliminary attempt at an objective way to determine which words are related is proposed below, but first let us consider what might be a "Bible Code Tutorial".

As mentioned above, some of the first ELS codes found were of the word "torah" right at the
beginning of the Bible. If that is meaningful, why would the word "torah" be used? Because the
codes only occur in the Torah? I don't think so. Let's consider another idea. Suppose "torah,"
which means "law," was chosen to show examples of the *law which governs the Bible codes.* If
so, some encoded "torah" words may have been designed as a tutorial to show exactly which are
true codes and which are spurious. Let's try that hypothesis.

Now that we have examined this code more carefully, three new experiments suggest themselves to extend the theory:

The number 50 is a special number in the law of Moses because the holy day Pentecost is counted as the fiftieth day, and the jubilee as the fiftieth year. Perhaps all authentic Bible codes must have an ELS spacing of 50.

The four words might be an explanatory addition to the text. Let's consider the possibility of what might be called "explanatory codes." In the "Dizzy Bear" example, the codes gave Brent's full name, in case someone wanted to know it. Such codes would be like footnotes or hyperlinks to more information for those interested.

The four words nearly span the description of what occurred on the first day. Perhaps some codes are "spanning" codes, possibly indicating that the encoded word relates to everything spanned by it. In the "Dizzy Bear" example, the two principal codes exactly spanned the entire text, which was an indication that they were intended and not random.

Thus we have a second witness that the codes are real, and support two of the hypotheses proposed from Lesson 1. That is, the code was found with spacing of 50, it was found in meaningful surface text words, but it doesn't clearly span any concept.

Now let's do a spanning experiment, to see if that concept leads anywhere.

If the first "torah" code was indeed intended to suggest to us that a valid code might be used to span a text, then one possible experiment is to look for another spanning code. The concept of spanning occurred to me as I wrote my "Dizzy Bear" example. It was written before the following experiment was done. I made a point in that verse to pick an exact number of letters that would work to encode both "Dennis" and "DBrentBriggs" beginning with the very first and very last letter of the text, to indicate to the decoding person that I was purposely taking advantage of the fact that both names began and ended with the same letters. To me that would be a clear indication of order, because it required the exact number of letters to have been chosen by intelligent design before even a single word had been written.

So in preparing for this article it occurred to me that the Lord might have used the same idea. The
first experiment I thought of was so successful that I feel only to include that one example.
Chapter 1 of Genesis spans the activities of the entire six periods of creation. What if one "torah"
code spanned that entire chapter? I looked at the last word of the chapter and it begins with *heh*,
the same letter that "torah" ends with. The *taw* in the first "torah" is the last letter of the first word of the chapter. That in itself shows an ordering which is common with the Lord, that the last is
first and the first is last. Moreover, the first letter is found in the word "In the beginning" and the
last in the word "sixth" which exactly describes what section is being spanned.

Thus, the experiment was to see if the middle two letters of "torah" are found in exactly the right
positions in the text to form a spanning code with these two letters. The chance of that occurring in
a randomly selected text from the Torah is only about 1/500.^{[23]}. Most statistics studies only require a probability of 1/20 to be considered meaningful, so this seemed like a good test. Of course, if it failed, it might only mean that the Lord did not choose to encode that word in that manner.

The experiment was a success. The word "torah" is indeed found in an ELS sequence of spacing 554, the only possible spacing to join the two letters indicated. Looking at the two words containing the other two letters, they are "its" (Gen 1: 12:12) and "morning" (Gen. 1:23:4), which do not seem meaningful. If this code is real, as appears to me, then the results of this experiment indicate 1) that the ELS spacing does not always have to be 50, 2) an ELS might span an entire chapter, and 3) not all of the surface text words of a spanning ELS need be meaningful. The purpose of the code might be only to show that the encoded word applies to a particular text as a whole, rather than only a single word therein.

In Numbers, "torah" is again found encoded beginning in the first verse, but this time the word is
in the reverse order, starting with the *heh* and spelling "torah" backwards. Reverse codes are well known in Bible code research, and are indicated by a negative skip distance, -50 in this case. It can
be thought of as finding the last letter first and spelling the word backwards, or if the first letter is
found first, then one counts backwards to get the next. Because the implied tutorial led us directly
to examine this verse, to me it means that reverse codes are as real as the forward codes. Of
course, both need a lot more evidence to have a truly compelling proof of their existence. In this
case the surface text words also seem meaningful (Num. 1:1:4 "Moses," 1:1:16 "Egypt," 1:2:12 "names," and 1:3:10 "them") because the first chapters are about Moses recording their names and numbers.

A side discovery here, which was not part of the experiment, might be useful in designing future experiments. There is only a 1/16 probability of finding even one "torah" at spacing 50 in Numbers 1, but two were found. The other is a forward code ending in the very last verse. Again that indicates much more order than merely having been found at some random place in the chapter, as would be expected by chance. And again we see the first and last, with reversals. That code looks real to me.

Checking Deuteronomy 1 we find "torah" once in chapter one, ending in the next to last verse. It has meaningful surface text words (Deut. 1:42:14 "You be struck" 1:43:9 "and acted proudly," 1:44:9 "as," 1:45:4 "Jehovah"). That is very similar to the finding in Numbers of a code near the very end of the chapter, rather than at the very beginning. It cannot be counted as a success for this experiment, but it might be a clue to how the codes are used at the beginning and the end.

Thus, technically, the experiment failed for all three of the books of Leviticus, Numbers, and Deuteronomy, because I was looking only for forward ELS codes at the beginning of the first chapter. Had I been looking for reverse also, then Numbers would have been a success, but the odds would have been twice as likely to have been there by chance. In science we often learn more from the failures than the successes.

There is a principle in Hebrew writing called "chiasmus," which is that when one finds repetition at the first and last, then look to the middle for what is the most important. We have found forward codes at the beginning of Genesis and Exodus, and also at the end of the first chapters of Numbers and Deuteronomy. If the Lord is following a chiasmus pattern, then the most important code should occur in the first chapter of Leviticus, the middle of the five chapters.

Looking there we find something very interesting, which has hitherto been overlooked as far as I
know. Starting in the second verse, there is a reverse code for "torah" with spacing -60, and then
beginning on its final "taw," there is a forward "torah" at spacing 40. The fact that 40 and 60
average to 50, which was what we were looking for, might be intentional. As a working
hypothesis, let's suppose that the tutorial is real, and that the lesson here is that *encoded words
with different ELS spacings can be linked by sharing a letter*.

There are two very intriguing aspects of linked codes. First, they increase the amount of order and are less probable than separate codes. To convince yourself of that, imagine that two examples of a very rare code have been found in a very long text. For example, suppose "Adam, the first man" were found at two different ELS spacings in Genesis, when one would not expect a phrase that long to occur even once. Now, out of all the places they might have occurred, suppose that they both share the same "A" as the encoded letter for "Adam." Without doing a lot of calculations, it is hopefully obvious that such would be much less likely than having two separate sequences.

The second nice feature of linked codes is that it consumes fewer letters for encoding. Why use up
eight letters for two encodings of "torah" when seven will do. In fact, we have already seen this.
The same *taw* was used in the original "torah" found with spacing 50, and in the spanning code of spacing 554.

As I thought about how far this principle of "economy of letters" could be pushed, I wondered what is the most codes per letter that is possible? This may be an important question for short words. Most Hebrew word roots contain only three letters. And yet three-letter ELS codes can happen so frequently that many Bible Code researchers reject all of them because they have no way to tell which are real or not. The name "Dan" really did appear in the "Dizzy Bear" verse, complete with the capital "D," without me having planned it. But now suppose that my friend's name had indeed been Dan? How could I have encoded the verse to make it clear that "Dan" was not there by chance?

"Make my lime, Solomon, a true treat."When written as three lines of nine letters each, the name "Tom" is found encoded seven times using only nine letters (See Figure 3). I do not see how anyone would need to calculate any probabilities after seeing the pattern to convince themselves that these seven occurrences of "Tom" in only 27 letters of text could not have been due to chance. I could have included one more "Tom" in by using "demo" instead of "lime," but chose not to because that would have decreased the ratio of codes to letters and also would have marred the pattern. After I created this illustration I recognized the pattern as one form of the "mandala" which is believed to have been used in Egyptian figures. Hence, I'll refer to this pattern as the mandala.

Thus, this important lesson from Leviticus may be a key to recognize encodings of three-letter Hebrew words.

This seemed like a good example on which to test my new theory, that if those excess codes were truly put there on purpose by the author, then 1) they should be CELS codes which explain more about either specific key words they intersect, or sections of text they span, as in the "Dizzy Bear" example, or 2) they could show patterns of maximizing the number of encodings while minimizing the number of letters, as in the mandala pattern of "Lime Treat". My current theory discards all codes which do not meet either of those criteria. Moreover, because this passage contains the first reference to Eden, it seemed qualified to test the hypothesis that the first time a major concept is introduced, there might be special codes around it to explain it better.

I checked out every occurrence of "Eden" as an ELS of any length greater than one and looked up
what word each letter occurred in, using an interlinear Hebrew English Bible. After sufficient data
snooping (which can be compensated for when calculating probabilities), I decided to focus on
Gen. 2:5-10, containing 329 Hebrew letters. In a passage of that length chosen randomly from the
Torah, one would expect to find the three-letter Hebrew word "Eden" about 5 times just by chance.
Note how prolific these codes are. If one did not calculate probabilities, it might appear amazing to
find any word encoded five times in such a short passage. But in this case, "Eden" appears in ELS
codes 15 times. The probability is less than one in 8,300 for that to occur by chance in a random
passage,^{[29]} so this looks like a fine place to see if context can help us determine which codes might be real and which are not.

By checking the surface text words, nine ELS codes were found that intersected key words in the
surface text in a meaningful way, while six did not.^{[31]} By the new theory, those nine would
qualify as CELS codes, and the other six are discarded as having been caused by chance. Thus, to
me this was encouraging, because it so closely matched what probability predicts, namely, that
there would be about five ELS codes found by chance alone. But this result is not compelling
because there is a better than an even chance that any one ELS will intersect some key word.^{[32]}
This is tricky business; nevertheless, it is hopefully a step toward separating out real codes, if there
are any, from wishful thinking. It turns out all nine of those CELS hits are impressive for other reasons, as we shall now see.

Now we shall see that those CELS codes not only all intersect the two most important words, they also form meaningful patterns. Those nine words fall into three groups. One of the nine intersected only key words. That one had an ELS spacing of 83, and comprised the letters Gen 2:5:8:1 in "herb," 2:6:9:3 "ground," and 2:8:5:4 "Eden." Four of the nine formed a nearly complete mandala figure as in the "Lime Treat" example, and the other four formed two crosses in meaningful contextual ways. Let us now consider the strength of those patterns in more detail.

Figure 4 shows the words "Garden in Eden" as they appear in Gen. 2:8. Remember that Hebrew reads from right to left. The word "Garden" has two letters, "in" has one, and "Eden" has three. This figure was included to help you recognize the word "Eden" to better appreciate these results.

Do any of the three letters which complete this figure occur in key words? The answer is that only one does, but probably two should have. The word on the top row is in "went up" where it states that "there went up a mist from the earth" (Gen. 2:6:2:2). To me that is not a key word. The word in the next row is "the ground" in Gen. 2:7:8:3, which was chosen as a key word. The word in the row between the two "Edens" is "pleasant" (Gen. 2:9:8:4) which perhaps should have been included in my list of key words. It is practically a synonym for the whole idea of the Garden of Eden. This is where the temptation arises to "tune" the definition of a "success" by going back and changing the list of key words. But "Eden" also sounds like a good place to avoid temptation, so I will resist the urge.

The chances of this much of the mandala pattern occurring around the two words "Eden" in a text from the Torah, and including at least one contextual keyword are less than 1/39,000.^{[34]} Note that this pattern approach is starting afresh to calculate probabilities. There is only a 1/39,000 chance of finding such a nearly complete mandala, without even considering the other 11 "Eden" encodings found in these six verses.

When the spacing between rows is changed to 59 letters, we see in Figure 6 of the type of cross meant. The two words "Garden" and "Eden" appear to be connected to the words "was not" and "to till" in the phrase "there was not a man to till the ground" (Gen. 2:5). What makes it meaningful is that the letter at the center of the cross appears in the word "the man." Even though none of those three words was on my key word list, it still forms a phrase: all the contextual words put together say "was not a man to till the Garden in Eden" which is nearly the same as the phrase "there was not a man to till the ground." This is much like what we saw in the very first "torah" example, where the contextual words formed another sentence much like the surface sentence.

The chance of finding such a connecting cross using the word "Eden" to connect the words "Garden" and "Eden" to any two others is 1/88.^{[35]} For now, we will not include any factor for the five words all forming a sentence because the other three words were not on my key word list. Perhaps future studies can take this sentence-forming feature into account.

Now we can finally compensate for the "snooping" done earlier. We started out with a set of six verses which for which we knew there was only a 1/8,300 chance of containing so many encodings of Eden, if there by chance. What is the chance of finding something with a 1/28,000,000 probability given that we started knowing it had purposely been selected because of having only a 1/8,300 of existing at all? The answer is that one divides the two probabilities, to get about 1/3,000.^{[37]} So starting from where we did, there was only a one in three thousand chance of getting these results. That is far less than the usual 1/20 confidence level required for most statistical studies.

The ELS codes allowed by this new theory are called "contextual" ELS codes (CELS) because only codes related to the surface text can be considered as having any chance of being real. This work is only in the prototype stage, and no scientific metrics have yet been devised. Indeed, an objective approach appears elusive because the whole definition of what is "related" seems subjective. Nevertheless, as a first application, with an eye toward developing a rigorous scientific method later, a study was made of only one occurrence of two words in the Hebrew Genesis: "Garden" and "Eden". The precise words in which all of the letters of the fifteen ELS sequences for "Eden" in Gen. 2:5-10 were examined, and nine were found to qualify as CELS codes, all of which intersected those two words. Then patterns they formed were examined which decreased the number of letters required for so many codes. That is precisely a technique that would be expected to be found in work truly encoded by the author as it would form less probable combinations, as well as leave more locations available to include other encoded words. A preliminary estimate of the significance level of this discovery is 1/3,000, far beyond the usual 1/20 required.

It must be emphasized that the results being reported here are entirely preliminary. Only one occurrence of two key words was studied using the new technique, and even then only intersections of the topic word with those two were considered. Statistics call for large samplings, and so there is much work left to be done. The only reason that it appeared worth publishing with such a small sample was that it proved so rich as to require several illustrations to show the many dimensions of just those two words. The other reason is that I plan to go back to calendar work, and hope that others will continue and perfect this new approach, if it continues to appear fruitful.

The conclusion at this early point in new research is that it appears that *at least some CELS codes
are real*, and the contextual analysis may prove to be the key to separating true from false
ELS findings. Indeed, it now appears that time might show that the Bible code phenomenon could
unfold much as did the miracles of Moses to Pharaoh: the skeptical magicians were able to
duplicate the first few, but then God's miracles kept multiplying until they were compelling. To
me, the hand of God is being manifest in just two words of his great revelation to Moses. It is no
wonder that we are commanded to live by every word which proceeds from the mouth of God
(Deut. 8:3).

- Drosnin, Michael,
*The Bible Code*(New York: Simon & Schuster, 1997). - McKay, Brendan, "Assassinations Foretold in
*Moby Dick*!" cs.anu.edu.au/~bdm/dilugim/moby.html. - The original paper was Witztum, D., Rips, E., and Rosenberg, Y., "On Equidistant Letter Sequences in the Book of Genesis,"
*Statistical Science*,**9**(1994) , no. 3, 429-438, refuted by McKay, B., Bar-Natan, D., Bar-Hillel, M., and Kalai, G., "Solving the Bible Code Puzzle,"*Statistical Science*,**13**(1999) 150-173. - Sherman, R. Edwin,
*Bible Code Bombshell*(Green Forest, AR: New Leaf Press, 2005). - JoAnn noticed that it wasn't just a random word which formed the cross, but the very word which best described the subject of the verse. For a five-letter topic word to form a cross at any given spacing between letters, all four of the five letters around the center letter must fall in exactly the right spot. She calculated that the frequency of a randomly chosen letter from English text would be 0.0655 or about 1/15. (That number is found by summing the probability of finding any one letter, times its frequency, or simply the sum of all the squares of frequencies. She got them from the first table in "Relative Frequencies of Letters in General English Plain Text". That means if you pick a letter at random from English text, it probably has a frequency of .0655 or 1/15 rather than the 1/26 you might expect. The more frequent letters like "e" increase the average.) Thus, the probability of getting the other four letters of the word exactly right is 0.0655
^{4}or 1/54,000. There are 11 possible letter spacings (3 to 13) to fit in 56 letters if the topic word were centered, which makes the probability about 11 times higher, or about 1/5,000. - When JoAnn found the second cross, it was not centered as was the first, hence, maybe it was just chance that the first one was. So she relaxed the requirment for a similiar event to be found in random text to be only that the topic word intersect itself, rather than having to be centered. So the intersection could have been through any of the five letters, and hence the probability of even the first find was about five times greater, or 1/1,000. The chance of that happening twice is roughly 1/1,000 x 1/1,000, or 1/,000,000. An important technical point that seems to have eluded some other researchers, is that latter calculation is only true in the case of independent events, such as rolling dice. But these events are dependent, meaning that once a first cross is found, there is always
*less chance*of finding a second one for two reasons. First, one of the choices is used up, and secondly, that first one also removes several more choices because of collisions. Only if the probabilities are small is the discrepancy negligible. I calculate as if the events were independent, and then compensate by saying the real probability is less than the calculation. - The chance of getting the last two letters to spell a certain name at a given spacing is (0.0655)
^{2}or 1/233. She found nine possible names in her name book: Dag, Dan, Del, Den, Dex, Dom, Don, Dow, and Dud, raising the odds to about 9/233. Any of those names could be found at any one of 26 spacings (2 to 27), which increased the expected number of finds to 26 x (9/233) = 234/233 or 1.00. Multiplying in that manner only gives probabilities when they are small. As the number approaches or even exceeds one, the technical term is "expected value." If we had allowed the name to start in other places, then the expected number of finds would far exceed one. In this case, there were actually three found, "Den" twice and "Dan", which will happen about one time in six on the average. - Note that she found two names (Dil and Dog) which were not on her list of possible names. In probability experiments, it is always tempting to relax the definition of what you were looking for to include what was actually found. But on the other hand, maybe his name really is Dilbert.
- The first and last letters were already determined by "DBrentBriggs," and the only possible spacing to span the verse was eleven, so the name had to have exactly six letters, starting with a "D" and ending in "s." In her name book, she found only the names Dallas, Darius, and Dennis as possibilities. At this point she could have looked up the actual frequencies of each of those letters, but she only wanted an estimate. The chance of getting the middle four letters correct is 0.0655
^{4}time 3 choices equals a 1/18,000 probability. Note how the imposed structure made all the difference: there was only one spacing possible instead of 26 as with the 3-letter name, and only three possible names rather than one of 10,000 male first names. - The structure greatly reduces the number of possible ELS spacings that are possible. To have a name of 6 or more letters span the same distance as the full name of 12 or more, avoiding collisions, allows only 11 possible pairs of ELS spacings, of which only one will work for 6- and 12-letter names (namely the one used in this example). For any one configuration, the chance of getting each letter in the right slot is (.0655)
^{22}, being the requirement for 12 + 6 + 4 (in the cross) = 22 letters. Note that unlike JoAnn, I am counting probabilities of the first and last letter twice, to include the chance that the short and full names both begin and end on the same letters. The number of possible configurations was taken to be 3 possible names of six or more letters (first, middle, last) x 4 possible ways to include up to two initials (none, first, middle, both) x number of places the contextual name could be found in the spanned area (52 in the case of the example of 56-letter span), x the number of ELS's for the cross (11 in the example, being 3-13). For completeness, I also included the probabilities of all longer names calculated for every one of the 11 possible pairs of possible lengths, which increased the probability by a factor of 1.18. Multiplying all of those factors yields 7.3 x 10^{-23}, or 1 in 1.4 x 10^{22}. - To estimate in round numbers, assume there have been 70 billion people who have lived, leading to 1.4 x 10
^{14}references to names to check. Multiplying that times the probability of each being a success of 1/(1.4 x 10^{22}) yields 10^{-8}, or 1 in 100 million.

- One of the best summaries is Satinover, Jeffrey,
*Cracking the Bible Code*(New York: Morrow, 1997). - It was tough to find a fair summary, most accounts are either violently against them or religiously in favor. I recommend the Wikipedia article, "Bible Code."
- Rabbi Michael Ber Weissmandl, is usually given credit for this discovery in the 1930s (
*Bombshell*, p. 28). It is said he wrote out the entire Torah on white cards in 10x10 arrays. (*Cracking*, p. 69) - There are four letters in the word "torah" in Hebrew. The probability of finding the first letter
*taw*in Exodus is 100%, because it is a common letter. The probability from Table 1 of the other three letters*waw*(frequency of 10.0% in Torah),*resh*(5.95%) and*heh*(9.21%) all occurring in the indicated place is found by multiplying those three frequencies, yielding 0.000548, or once in 1,820, if it resulted from chance. - All Bible code results in this article were either found or verified using the program
*Bible Codes 2001*, available from Ed Sherman's website at www.biblecodedigest.com. - Sherman, in
*Bombshell*(see footnote 1) includes equations on how to calculate probabilities, which are probably the same as those included in the Bible code program he sells (see. fn 15), which were used to calculate this expected value. His equations appear correct to me to calculate the number of possible ELS locations in a given text, so I used them when needed in this article. They are first, that "the total number of possible ELSs with L skips (including both forward or backward ELSs) that can fit within a text of T letters when the interval can be any number from 1 to N is N*(2T - L - N*L)" (p. 226). To find the maximum number that can fit in, substitute N with "M = integer [ (T-1)/L ]" (p. 229). He uses the confusing definition that L is one less that the length of the ELS sequence, so that for an encoded word of 4 letters, L=3. His equations for the expected number of hits and probability of any given number of hits are based on the Poisson distribution which only applies to independent events (see my fn. 6). It is an excellent approximation for long words encoded in large texts, but breaks down in the case studied in this paper of short words encoded in short texts. But, alas, I use the same equations, knowing they over-estimate the probabilities. - The first paper mentioned in footnote 3.
- See footnote 1.
- Satinover, p. 51. Research in this article was done with what is called the Koren version, used in the
*Bible Codes 2001*program. -
*Bombshell*, pp. 57-74. -
*Bombshell*, p. 139. - The probability is the chance of having the first and last letters spaced in a multiple of three (1/3), times the frequency of the second letter
*waw*(.100), times that of the third*resh*(.0595). - I found the first occurrence by searching for ELS=1 (forward only). Apparently this code was first found by Rabbi Weissmandl, but not as related to the first occurrence of "torah" (
*Cracking*, p. 85). - The probability is that of the ELS of 50 intersecting any one of the four letters in "torah" times 2 (for forward and backward). Let me define the "combinational probability" p
_{c,r}of "n" letters as the summation of the products of each of their separate frequencies, omitting "r" terms. Thus, p_{c,1}("the") = p("t")p("h") + p("t")p("e") + p("h")p("e"), where each term omits one the probability of one letter. The letter omitted is the letter found in the surface word being intersected. Then the probability that "torah" intersects itself in any letter is 2p_{c,1}("torh") = 1/283. - Essentially the same calculation as in footnote 23.
- Arguments could also be made for the spanning ending in verses 42, 49, or 51. For spanning to be a useful concept, some objective definition would be useful.
- Jeffrey, Grant,
*The Mysterious Bible Codes*(Nashville: World Publishing, 1998), alots the discovery one sentence, "In addition, the researchers found the name Eden encoded sixteen times in the same passage." (p. 85). I am grateful that Jeffrey included many shorter codes, for which he was chastised by more statistically rigorous researchers, but for which he may well eventually be vindicated. - The expected number of occurrences is the product of the frequencies of the three letters from Table 1 times the number of possible ELS sequences greater than unit spacing from Sherman's equation in footnote 17: .0369 x .0536 x .0463 x 53,138 = 4.87. Poisson statistics approximates the chance of finding "n" values, given an expected value of "m" as p(m,n) = (m
^{n}e^{-m})/n! That equation, which overestimates the probability as discussed in footnote 17, gives a probability of finding 15 encodings as 1/8,300. - Twelve words were selected as "key" out of 49 total words. In proposed order of importance, they are: Eden (8), garden (8), tree (8), life (9), knowledge (4), good (7), evil (3), planted (4), watered (5), ground (20), herb (3), and shrub (3). The total number of letters found in all occurrences of each word is listed in parentheses following the word, with anciliary letters such as "and", "in," etc. counted as part of the word, as is done in Hebrew. They comprise 82 of the 329 letters, or 25% of the text. The probabilities of the results found in this article would have been even better if those letters had no been included; further research is needed to determine if they should be counted or not.
- The meaningful CELS codes have skips of 53, 53, 105, -51, -45, -41, 58, -60, 83. The
random ELS codes had spacings of -117, -90, -71, -47, 107, 16. Note that the 16 is detected by the
new theory as spurious, whereas former theories would have labelled it the most important.

- There is an 0.75 chance that any one letter in an ELS will not be a key word, so the probability that all three Hebrew letters in "Eden" are not in key words is .75
^{3}= 0.42. - The probability of "Eden" intersecting itself is p
_{c,1}("Edn") = .00363 per possible ELS spacing. The chance of intersecting the second most important key word is the probability of getting all three letters correct (.0369 x .0231 x .0463) times 3 (number of letters in "Edn" any of which could be in any letter of key word), times 3 (number of letters in typical key word) equals 0.00036. Adding that to the probability of Eden intersecting itself yields .00399. Then multiply that result by 164 possible ELS spacings, times 2 for forward or backward gives an expected value of 1.31 intersections of an encoded "Eden" intersecting the very words "Garden of Eden" in the text. The Poisson estimate (see footnote 29) of the probability of finding 9 is then 1.31^{9}exp(-1.31)/9! = 1/118,000. - The probability of finding the three letters in the right places to form the mandala figure equals the chance of having an even number of letters between the two "Edens" (.5) time the chance of a
*daleth*there (.0231) times the chance of finding another daleth that same number of spaces before the first or after the last "Eden" (2 x .0231) times the chance of finding either an*ahyin*or a*nun*at one of the two corners (.0369 + .0463) = .0000444 = 1/22,500. Then multiply that by the chance of hitting at least one key word (.58) yields 1/39,000. - The probability is the chance of finding a
*daleth*at the right place (0.0231) times find an*ahyin*(.0369) to complete the leg starting in "Garden" times the chance of finding either an*ahyin*or*nun*(.0369 + .0463) to complete the other leg, times 80 possible ELS spacings times 2 (forward or backward) = 1/88. - The probability is that of any cross (1/88 from footnote 35) times the chance of intersecting as word as good or better than "tree" (24/329), times "knowledge" (37/329), times "

ground" (71/329) times 6 possible permutations for those three words = 1/8,200. - This is from the definition of conditional probabilities, namely, that the probability of A given that B has occurred is the probability of both A and B occurring, divided by the probability of B happening. That is really just another way of saying that any probability is the number of successes divided by the total number of possibilities.