31 of December 2009
This text deals with mathematics from a common sense point of view, to understand it you need to know
certain parts of Senior High School mathematics. I have used a discussion on probabilities to judge
whether Bible Code findings are reliable to be encoded (no code key has been found).
Numerous predictions are believed to be encoded in Bible Code matrixes, through a (much) better proximity
between related terms than expected by chance. But is it real?
It is the Torah (the five Books of Moses in Hebrew) that is believed to be coded this way.
I am a skeptic and I have pondered Bible Code probabilities for six years, I have built and bettered this text
gradually and a number of additional notes now form a fifth main section. I hope my text is now finished.
My first section is about the most well-known proof for the code, The Great Rabbis Experiment. Then I
have a description of what a matrix is in a Bible Code program. My third section is mainly on matrix
probabilities, and my fourth section deals with other factors of importance and misleading ways to research.
If you don't like theory you can skip the section about matrix and text probabilities, and the appendix.
Some consider this Bible Code religion, I consider it defective mathematics (and defective linguistics).
As far as I know, most mathematicians and linguists acquainted with this Bible Code don't believe in it.
This experiment was published in Statistical Science in 1994, offered by the paper as a challenging puzzle.
The experiment seemed to prove a proximity code for some related terms in Genesis. Term pairs of Rabbi
names (appellations) and corresponding dates of birth or death were examined. For the term pairs chosen
(two selections), the probability to get the final result by chance was told to be 0.0016 percent.
The term occurrences examined had an equal number of steps between their letters in the text (a skip),
and the distances were measured with the text arranged in matrixes according to certain rules.
In my opinion the experiment has some big and simple flaws, I consider three of them the most important.
First the experiment is (a kind of) a sample test. In my opinion the method used is not likely to detect
the possible code. Genesis contains less than seven percent of the skip term occurrences in the Torah,
and normally most occurrences of the term pairs used were left out or given a reduced weight in the
experiment (according to disputable rules). Most occurrences are expected to be chance occurrences,
but the result diagram indicated that a lot of encodings were found. In my opinion not reasonable
with the method used.
Second the experiment was successful only in Genesis. It did not work in the other four books of the Torah,
and they are believed to be coded too.
Third the full list of terms used was not indisputable, for the Rabbis chosen many appellations (totally) and
some ways to write the dates were left out. Both the full list of terms used and a smaller selection were used.
In Statistical Science in 1999 it was proven that the result did not hold generally, in the investigation
made it was valid only with a good choice of terms and spelling variations (but both sides question each
others results). In this case the result was achieved in "War and Peace", but of course a good selection
works in any book. Also the second and the third point above were told in the text from 1999.
A normal way to check a scientific result is to make full-scale control experiments. A few such experiments
to check The Great Rabbis Experiment in Genesis were described, they gave no considerable result. But also
these experiments were sample tests (of the same kind as the original), where many appellations (totally)
and some ways to write the dates were left out. These experiments could in my opinion not disprove the code
theory, but they were maybe good to test the research methods.
I can add that The Great Rabbis Experiment had results that were roughly 100 times diverging for
both of the two lists used, two of four results were much worse than the claimed final result.
A matrix is formed by the letters of a freely chosen first term and an area of surrounding letters in a right angle array. If the letters of the first term are found one thousand letters apart in the Torah, we say that the term is found at the skip 1 000. The program normally displays the letters of the first term vertically, so with the skip 1 000 we get text rows that are 1 000 letters long. Around every skip occurrence of the first term, the program can search for freely chosen related terms (I mean related to the first term). Related terms can be vertical, diagonal or horizontal. They can also be formed by every second or third letter and so on. We only search for terms having a skip in the plain text. When we search within the full text at all possible skips, the program tries every possible skip from every possible starting point. If we use rowsplitting we divide the rows 2 or 3 times or more. Then we get the letters of the first term at every second or third row and so on, displayed diagonal if the rows are not evenly divided. The program searches both forwards and backwards in the text, so the terms can be displayed in both directions. The plain text is called the skip one and skips backwards are denoted with a minus sign. When the program frames the terms of a matrix in a tight rectangle, that area is called a cropped matrix. There may be exceptions from this description.
If there are encodings we risk to miss some of them if we don't search in the full text at all possible skips.
I agree with the use of expected occurrences as probabilities in at least two leading Bible Code programs. But (except for in the plain text) always calculated for the skip range we research in and with a proper skip compensation. The R-value in these two programs is used as a probability, and it is used to express expected occurrences (figures of expected occurrences are expressed as their base 10 logarithms, but with plus and minus reversed so improbability becomes positive). For small values expected occurrences and the ordinary probability for one occurrence are almost the same. I consider expected occurrences typical values, but I find it hard to strictly define them. Expected occurrences have been very useful in my analyse of basic Bible Code matrix probabilities, and they have given me a relatively simple discussion in this text. It is considered improper to call them probabilities, but I consider them a kind of probabilities in this context.
The first term probability that should be used in the final matrix is (at least basically) equal to
the number of expected occurrences in the text, compensated for the skip of the final occurrence. Not
the small probability for the term to occur in one single matrix. To show it with an example I will
simplify the discussion somewhat, and leave out the influence of the skip. Start with 100 text occurrences
of the first term forming 100 matrixes, then a cropped matrix probability of one chance in 50 for the
second and one chance in 20 for the third term. The total probability for the final matrix (with all
three terms) becomes one chance in 10, that is 100 divided with 50 and 20. This corresponds to a
probability of 10 000 percent for the first term. The single cropped matrix probability for the first
term is very much smaller, since a single matrix is a much shorter text. The first term probability
holds without rowsplitting. Rowsplitting normally (almost) multiplies the number of search matrixes,
and thus the first term probability (when we try both with and without rowsplitting or try more than
one rowsplitting). We can to some extent automatically get occurrences of subsequent terms (but when
some lines are the same it is more difficult to find new occurrences in the same search area).
A deviation between the number found and the figure of expected first term occurrences, can not alter the
first term probability. I suggest the figure of expected text occurrences for the first term to be generally
used as the first term probability, compensated for the skip and when necessary for rowsplitting. This although
we may not use all first term occurrences, we can not expect to always get the search area chosen for all.
At least one leading program (the version I have checked) uses a single matrix probability for
the first term, it is not the real probability and it should not be used. If you research in that
program and use that matrix probability for the first term, you will sometimes get an exaggerated
significance that seemingly proves related terms to be encoded (the significance is the
improbability to get something by chance).
If we get the total probability through a comparison to for example one million chance matrixes (with the first term), then we must compensate for the probability for the first term. A matrix with a less good total significance can otherwise be the best. We can also compare to what we find in a number of equally long chance texts, and then compensate for the text skip only of the first term in the original matrix. Since our finding starts with the first term included, also the chance matrixes we compare to should have the first term included. We should also compensate for the matrix skips of subsequent occurrences in the original matrix. Comparison to chance matrixes doesn't compensate for the sometimes big free significance when we research with our eyes (discussed in the next main section), so the result can be very incorrect.
The text formula:
Petext = Etext x C (Pe for the use of expected occurrences as probabilities, but with my skip compensation)
Petext = The probability for the term in the text, at a skip where it occurs.
Etext = The number of expected occurrences for the term in the entire text (searching both directions).
C = The compensation for the text skip (discussed later), not a constant.
A formula for the number of expected text occurrences is given in the appendix.
If we when necessary compensate for rowsplitting, the text formula gives the first term probability that I
have suggested to be generally used.
For a one term finding in the form of a sentence the cropped matrix is not relevant, there is no proximity
to estimate. In this case we should use the text probability.
The cropped matrix formula for subsequent terms:
Pecm = Ecm x C (Pe for the use of expected occurrences as probabilities, but with my skip compensation)
Pecm = The probability for the term in the cropped matrix, at the matrix skip where it occurs.
Ecm = Expected occurrences of the term in the cropped matrix.
C = The compensation for the matrix skip (discussed later), not a constant.
Since short skip occurrences are more common, there is a compensation for the skip. The probability for a term to occur at a skip in a text or matrix text can normally be approximated as linearly falling with an increasing text or matrix skip, from twice the average to almost zero. The number of text occurrences per interval of 5 000 skips can verify it very well in the text, when we have many occurrences. At least two leading Bible Code programs (the versions I have checked) have opposite probabilities at short text skips (also in the matrix), we can therefore get text probabilities that are tenths of thousands of times too small. At least one leading program (the version I have checked) has increasing probabilities also at higher text skips (you can try matrixes with many occurrences of one subsequent term to see if a program has increasing probabilities). I have one leading program, and I have checked a similar program through internet examples.
Ecm = ( Lcm / 304805 )2 x Etext
Ecm = Expected occurrences of the term in the cropped matrix.
Lcm = The number of letters in the cropped matrix.
304805 = The number of letters in the Torah (the Koren version, commonly used in Bible Code research).
Etext = The number of expected occurrences for the term in the entire text (searching both directions).
I expect all leading programs to display correct total figures for expected text occurrences, needed
in my formulas. Big faults would be very visible for frequent terms when we compare to actual occurrences.
The parenthesis shall be squared since the text length and the number of possible skips are equally
reduced in the cropped matrix. The area under the linearly falling curve is then the square (but some matrix
skips are seldom or never used). In both programs (the versions) I have checked the text length relation is used,
not the square. The conversion fault from text to matrix probability can be hundreds of times, sometimes more.
There are minor factors that can affect the result, so the formula above can give a relatively rough result.
Roughly 50-80 percent of our 4-7 letter occurrences with a matrix skip are seldom or never used, normally that
many have irregular skips in the text (so if the formula is used for the search area we normally find less).
On the other hand the cropped matrix is normally smaller than the search area. The matrix probability
can also be affected by the percentages of letters, if they are different from the percentages in the text.
I have tested 2 series of cropped matrixes, with exceptional occurrences excluded the formula worked
pretty well (the search areas were 39x38 and 78x78 with a 4 resp. 6 letter subsequent term).
C = 1.5 x ( ( |Smax| - |Sterm| + 1 ) / |Smax| )
|Smax| = The maximal matrix skip for the term, for the first term the maximal text skip (with positive sign).
|Sterm| = The matrix skip of the term, for the first term the text skip (with positive sign).
I suggest the theoretical maximal skip to be used (with positive sign).
Whatever skip we happen to get a single occurrence at, it is the probability to find the term in
the entire skip range (of skips used) that holds, although adjusted for the skip. We can not use the
probability to find the term at the actual single skip. When we expect and find one occurrence in the
full skip range (of skips used), that occurrence would get a small probability if we did (no matter
what the actual skip is). When we have many occurrences we should be consistent and still use the
probability for the entire skip range (of skips used), then we can compare probabilities.
Since the probability can normally be approximated as linearly falling with an increasing skip to almost
zero, I divide the remaining number of possible skips (plus one) with the full number. The probability to
find a term is in reality related to the number of possible text skip starting points (in the text or
matrix text), it does not matter what text skips a matrix contains. The probability is (roughly) proportional
to the number of possible text skip starting points for a term, and we can normally (roughly) approximate
them as linearly falling with an increasing skip. When the skip gets longer, more and more letter sequences
are cut by the end of the text or matrix text (in the matrix normally). I consider it simple to use pure
skip compensation instead of starting point compensation, but for various reasons pure skip compensation
can work bad for subsequent terms in the matrix. The pure skip compensation for subsequent terms should be
considered rough, a program should rather use possible text skip starting point compensation in this case
(in the matrix at the possible text skips). If we get an occurrence of a term with the average probability
for occurrences of that term (in the text or in a matrix), then the probability should in my opinion not be
affected by the skip. The average probability for a term occurs at about one third of the maximal skip, when
the linearly falling probability curve is reasonably linear. Therefore the C-factor should in my opinion be
1.5 at the shortest skip (whether we have one or more occurrences). But the optimal value for matrix skip
compensation can be altered for different kinds of matrixes, to compensate for the rough formula for expected
occurrences. If my two test series above are representative, a 50 percent rise can be considered generally
reasonable for subsequent terms. Another view is that the theoretical figure should be 1 to make the
probability never exceed expected occurrences. But then the probability will almost always be lower than
expected occurrences.
It is maybe improper to position the linearly falling curve at a level that gives us the full skip range
probability at the average skip for occurrences, as I have done. But I think it is necessary to use (about)
this basic level to compensate for the skip in a reasonable way, although the resulting probabilities
become a contradiction as told above. Imaginary numbers are improper too, and still useful. To avoid
the contradiction we must as far as I can see neglect that a single occurrence of a term is not equally
probable at different skips, and use only the figures for expected occurrences. But isn't this improper?
A single occurrence is very unlikely to occur at really long text skips. Anyway the difference is normally
not very big if we calculate the term probability without skip compensation.
Lterm = 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
|Smax| (text) = 152402, 101601, 76201, 60960, 50800, 43543, 38100, 33867, 30480, 27709
Lterm = The number of letters in the term.
|Smax| (text) = The theoretical maximal text skip for the term (with positive sign).
The cropped matrix is an estimation of proximity, so the probability value (normally) has to be an estimation.
Plain text probabilities can be special, see one of my additional notes for a discussion on this.
Since the plain text is not a chance text, I expect the linearly falling curve to often be far from precise
at our very shortest skips.
When we find all subsequent terms we search for and all occurrences are significant, we can multiply
the probabilities (including the first term probability) to (roughly) get the total probability. But when
we try many terms, it can be much easier to find a few than what the multiplication says. The probability
to find 3 subsequent terms out of 12, is higher than the multiplication says for 3 terms in this case.
There are 220 ways to get 3 terms out of 12 and we have 2.12 million ways to get 5 terms out of 50
(but these figures are not the increase in probability). In such cases multiplied probabilities will
give us a degree of free significance, but I don't have the general formula for it. The normal rise
in total matrix probability seems to be at least roughly 10 times (when we search for a few tenths of
clearly improbable subsequent terms and find a few). But the free significance can be hundreds of times
(theoretically even more), if we search for some tenths of less improbable subsequent terms. The fact that
chance occurrences are normally unevenly distributed can give us various degrees of free significance too.
Both programs (the versions) I have checked use the multiplication method, but multiplied probabilities are
not used in these programs (and are fundamentally wrong) for subsequent occurrences with a probability higher
than 100 percent. Such occurrences are rightly excluded in the probability calculation, they are normally
uninteresting but they can form significant patterns.
Remarkable chance occurrences and spelling changes:
Searching for terms at all useful skips in the Torah is similar to searching in a very long randomized text.
If the Torah this way has a million billion term combinations with reasonable numbers of related terms,
then probably a billion of them form very remarkable clusters by chance. And maybe we get a million big
clusters that seem impossible to get by chance. (My assumptions are rough but we deal with very big numbers.
For example we have a trillion trillion ways to choose 6 terms out of 30 000, but many differ by only
one term.) The same thing holds for any book of the same text length. Without a code key we can not know
if a finding is a remarkable chance occurrence or not. If we take in account all spelling changes that
reasonably have occurred in the Torah, many Bible Code findings must be considered remarkable chance
occurrences.
Bible Code programs and Bible Code researchers are very good in sorting out remarkable occurrences.
There are different versions of the Torah and there are spelling differences (Genesis alone had between
3 and 43 for a number of versions, when compared in Statistical Science in 1999 to the Koren version).
A trend in Hebrew spelling of importance here, has been to add missing vowels. If only 300 vowels are added
a skip code can be almost fully deleted in a 300 000 letter text, maybe one tenth of a percent of all
encodings can remain (normally only short skip encodings can remain). When a letter is added, it destroys
all skip encodings that pass this position in the text.
There is also a big number of skip terms (and sentences) in a normal size search area. It is probably normal
to by chance have many "significant" terms related to the first term, and an enormous total "significance".
If you for example have 400 related terms (and sentences) with one percent chance for each of them to occur
in your search area, then you can expect typically 4 to occur. But with the multiplied probability method
commonly used, the chance is one in 108 to get 4. This is a simplified example, but if you think a
bit further (ponder the free significance within ten power probability intervals) it indicates that we can get
many "significant" occurrences and a very big total free significance when we search with our eyes. Longer
related terms (and sentences) may contribute a lot to the total free significance, they are normally (much)
less probable to occur but we reasonably have (much) more of them. Comparison to chance matrixes doesn't
compensate for the free significance discussed here, it can be very improbable to fully get the same terms.
I mean American trillion and billion above, that is one million millions and one thousand millions.
Some ways to research that can lead you far astray:
These ways to research can be very misleading when we use good (in reality bad) selections of them, then they can show a mass of things seemingly encoded. They all increase the probability to find (seemingly) remarkable chance occurrences. I know most of these ways to research can be found in Bible Code books.
To choose a first term related to many things.
To choose a first term with many occurrences, the program searches around all of them to find your
subsequent terms.
To try your subsequent terms as your first term, it can sometimes give a lot of similar chances.
To search for many things and report only your successes.
If you know Hebrew: To search with your eyes among all terms and sentences that occur by chance in a
normal size matrix. Some will (normally) be related to your first term, and eventual long ones can
raise the total significance very much.
To use (every possible) rowsplitting, it can give you several extra chances.
To check the letters before and after your terms, if meaningful together with your terms they raise
the significance (subsequent occurrences should still be related to the first occurrence).
If your program probabilities are much better at short text skips: To try hard to find short text skip matrixes.
Beside the Torah: To search for clusters in some other book of the Bible.
To use short terms with many occurrences in your matrix by chance, and show a few seemingly remarkable
occurrences.
To use short abbreviated years with many occurrences, although they in reality denote years long before
the birth of Moses.
To try different ways to write Jewish dates, and try the corresponding western dates.
To accept bad grammar and bad translations.
To try different ways to spell your terms.
To try different ways to express your terms. If you have three terms and four ways to express each term
you get totally 64 ways to find them.
With a good selection of these ways to research we can get a considerable free significance.
The program (the version) I checked through internet examples seems to always give the probability 100 percent for plain text occurrences, and as the matrix probability for the first term. So it does not always use the text length conversion I have written about (from text probability to matrix probability).
A subsequent term with a less good proximity to the first term can get a very good significance,
if it happens to occur in a long and narrow matrix (and thereby within a relatively small area).
The well-known two term prediction of a world war in the Jewish year 5766 (that year ended in September
2006) is an example of this, and the way world is spelt it means young man in modern Hebrew.
Bible Code predictions have been presented at top level in Israel and USA. Such uncertain predictions
can be very misleading, but I have no strict proof against the code.
In spite of all probability flaws and all chance occurrences the Bible Code can theoretically have a
kernel of truth, also in the Koren version of the Torah if it is (close to) the original. But if there
is a code it probably has a pretty limited number of encodings, it is hard to retain the story and
use many letter changes to add terms (and starting with many code letters it is hard to form the
desired story).
Since I don't know Hebrew spelling and grammer I can not really discuss findings claimed to be long sentences. There is not only claimed gibberish, also the flexibility in the language may cause such findings (and of course a real code). Claimed longer sentence findings are often not (pure) Torah findings.
In my section about basic cropped matrix and text probabilities I have not considered the unusual situation when a subsequent term in a matrix has a text skip but not a matrix skip. In this situation the square conversion still roughly holds, and possible text skip starting points are still (roughly) proportional to the matrix probability. The situation can occur when the line division gives lines that are a bit longer than the matrix lines. Then an occurrence can for example extend diagonally towards the left side of the matrix and continue from the right side, after one different matrix skip.
I have not been able to find a rule for the search area to be used if we compare to chance matrixes. To have the same chance to get the same terms in the same number or numbers, it can be considered reasonable to use the original search area. But we can (normally) get the original finding with different search areas. If we can have a proper search area we should have a compensation if we get chance findings that are totally better or worse than the original finding, it is also of interest if we get enough chance findings to (if possible) make a roughly reliable comparison.
We should generally calculate an occurrence probability for the skip range (and text range) we research
in. But the program (the version) I have calculates the probability with a skip range from minus to plus the
text skip where the term occurs, whatever text skip range we research in. Also this program has special plain
text probabilities. Some can be very incorrect since the program treats unintentional occurrences as intentional
in this case, and calculates their probabilities for only the skip one whatever skip range we research in.
A long intentional plain text term (improbable at all other possible text skips together) can not have a
small plain text probability, so plain text probabilities can be special. The probability for an intentional
plain text occurrence should be 100 percent, and the plain text probability for an intentional term the number
of times it occurs in the plain text. The probability to get an intentional term in a cropped matrix (a matrix
found through a first term occurrence and a search area), should then roughly be the figure given by text
length conversion. We can not know beforehand what parts (or part) of the plain text we will get in the matrix,
so we can not have 100 percent probability for the intentional term to be in the matrix. In the Bible Code
theory also sentences and sequences of sentences are called terms.
Some may not agree on my higher Bible Code probabilities. The principle is to use 10 times more expected occurrences as a 10 times higher probability, in my opinion a reasonable way to compare probabilities. I can therefore have probabilities much higher than 100 percent. Orthodox mathematics says that since nothing can happen more than for sure, probabilities can never exceed 100 percent. But we can also choose to call all degrees of insignificance probabilities, not only higher ordinary probabilities. Does orthodox mathematics have patent on what to be called probabilities? I know that the probability to actually get one occurrence (not for example 2 or 3) is smaller than expected occurrences for less improbable terms. And the probability to actually get one occurrence is pretty much smaller than 100 percent, when we have one expected occurrence. The probability to actually get 100 occurrences is small, and (normally) of no interest in this context.
There is a claimed Judaistic tradition that roughly says that short text skip occurrences are most likely to be encoded (mathematically they are generally most probable to get by chance). I don't think that this claimed tradition has ever been clearly expressed publicly (or clearly verified publicly to exist). The claimed tradition was a background to disputable sample rules in The Great Rabbis Experiment. Mathematically that experiment became (a kind of) a sample test, but from the claimed tradition point of view the experiment was probably not at all considered a sample test (rather an investigation of the occurrences considered most likely to be encoded). Judaism has a traditional belief that the Torah is coded with predictions, but I don't think that this belief says anything about proximity between related terms in Torah matrixes (as far as I know this code theory is about 25 years old.)
After The Great Rabbis Experiment a number of other experiments have been made, but it seems that only believer experiments can give sufficient results. I don't consider the original Cities Experiment an exception.
Research within reduced text and skip ranges (not in the full text at all possible skips) causes a problem. We can (normally) get a finding within different text and skip ranges, and thereby with different probability values.
My conversion from text to matrix probability can work bad for really small matrixes.
If you still wonder if the Bible Code is false or true my answer is yes, but it takes a valid proof
to know which.
My opinion is that Bible Code findings are remarkable chance occurrences.
Written by Lars Bobeck
Appendix
An almost precise formula for expected chance occurrences of a term in the text.
Etext = |Smax| x Nfirst x Fsecond x ... x Flast
Etext = The number of expected chance occurrences of a term.
|Smax| = The maximal theoretical skip for the term with positive sign.
Nfirst = The number of occurrences of the first letter (our starting points).
Fsecond = The relative frequency of the second letter.
Flast = The relative frequency of the last letter.
A relative letter frequency is the number of one letter divided with the full number of letters.
I will also give an almost precise explanation of the formula.
To calculate expected chance occurrences of a term in the text, we can use the full number of possible
skips (positive and negative) times the average probability for a chance occurrence at the single
possible skips.
This average is the average number of possible starting points (for the term at the possible skips)
times the relative letter frequencies. And the average number of possible starting points is here the
full number divided with 2. But since the formula uses only positive skips we should also multiply with 2.
When I compared two results with the formula above to the figures in my program, the difference was a
percent of a per mille.
Second my opinion on how a less defective Rabbis Experiment could have been made (it says pretty
much about the original experiment). It could have used all readily available appellations, all common
spelling variations and all common date forms. It could have used one original list, and consistently
the ordinary average formula. It could have used not too small samples of good occurrences in the
original list (only such occurrences are believed to be encoded), compared to good occurrences in a
big number of equivalent chance pair lists (without weighing). And it could have been run in the full
Torah, to rank the lists and to estimate the overall significance (normally not really determined by
the placing of the original list).
Anyway I don't suggest this experiment to be made, although the result should be more difficult to affect.
Some well-known persons, five programs and two books
The Great Rabbis Experiment was published by Doron Witztum, Eliyahu Rips and Yoav Rosenberg.
The control experiments I have written about were published by Brendan McKay, Dror Bar-Natan, Maya Bar-Hillel
and Gil Kalai.
I can also mention Barry Simon (simple discussions), Robert M Haralick (complicated discussions) and R Edwin
Sherman (as far as I know he has a compensation for free significance).
The programs I expect to be leading are:
CodeFinder (clear structure and good capacity, I have version 1.22)
The Keys to the Bible (I checked it through internet examples)
Bible Codes Plus (also called Bible Codes 2000)
Bible Search Pro (this program and CodeFinder search very fast)
Advanced Bible Decoder (I have seen no test results for it).
The most well-known book is "The Bible Code" by Michael Drosnin, it is written in a positive way but it
contains some important incorrect statements.
The book "Who Wrote the Bible Code" by Randall Ingermanson claims to disprove the code, yet it says that
there can be a big number of encoded terms at skips (to simply conclude this, see the pages 119 and 85).
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
A correction practically of small interest, a clarification and a final note
My statement that it doesn't matter what text skips a matrix contains holds for subsequent terms when we stick to vertical, horizontal and diagonal occurrences, as we normally do (what determines the first term probability is already better discussed). I have told the exceptional form broken diagonal for matrixes where the text lines are a bit longer than the matrix lines, in such matrixes and plain text matrixes we can normally have (pretty) many other occurrences (seldom or never used). Also when the difference between text and matrix line length is a bit bigger, we can normally have other occurrences.
When CodeFinder calculates an occurrence probability with a skip range from minus to plus the text skip of the occurrence, it treats the plain text as a chance text. The program version I have makes no difference between intentional and unintentional plain text occurrences, and assigns probabilities to them based on the plain text.
Intentional plain text occurrences in a matrix should not be used in a comparison to chance matrixes, we should calculate probabilities for such occurrences.