The Original Torah Code Hypothesis. The Torah Codes Hypothesis states that historically related words can be found at an Equidistant Letter Sequence (ELS) deliberately encoded together in Torah matrices that are smaller (more compact) than similar matrices found in non-religious texts. I have modified this hypothesis somewhat in a manner discussed at Talmud & Names to account for the fact that most names requiring more than 8 Hebrew letters will not be found in the Torah Code.
While there is a rabbinical tradition to support such encoding in the Torah (the first 5 books of the Bible), there is no such tradition for the rest of the Bible. Although many hope to use the Torah Codes as a kind of crystal ball, it’s difficult to make predictions because you can not know ahead of time which words or names will be key terms to search for. For this reason, many researchers have limited their searches to events that have already occurred. However, once an individual accepts such non-predictive search limitations, their positive findings of proven past events become clouded by the issue of what they searched for and did not find or report. If we see only their successes, it will look very impressive. If we also see their failures, then the value of the successes can be more precisely appraised. As will be seen below, with respect to Ark Code research, this site discusses statistical significance. But in the end, success is judged by very clear predictive criteria: Do the maps found encoded eventually lead to recovery of the Ark of the Covenant in the area of 31o9’ North, 33o4’ East on the Bardawil or Zuqba Peninsula of Northern Egypt?
Matrix
A matrix shows a portion of the cylinder’s surface area around the axis term which occurs at an ELS (Equidistant Letter Sequence). A matrix holds a-priori terms found near an axis term and a-posteriori terms noticed after the matrix was produced. A-priori terms are terms believed related to the axis term. They are sought before being found. Probabilities can be calculated for them. A-posteriori terms are noticed after the matrix was produced. Probabilities are usually inappropriate.
- ELS.What is really meant by ELS? Bible Code search programs like CodeFinder can be used to find words in Biblical text that have an equal number of letters between each letter of a word. So In the sentence, “The Man walkEd out thE door inTo the stAnds thaT seated 8,000 fans,” there are some people who would say that “Meet at 8” encoded at an ELS interval of 7. However, this is only true if the sentence author deliberately wrote the sentence to hide this statement. It might well be true that these words were found by a program or researcher looking for letters (and numbers) at an ELS that happened to make a phrase or sentence. In this case, we are simply looking at a random product due to chance alone. And how can we distinguish what is due to deliberate encoding from what is due to chance? Unfortunately, in the case of most Bible ELS terms, we are often left to statistical analysis and a rigorous examination of procedures used by the ELS term finder. A key point about any matrix is that the first ELS found (the axis term) is portrayed with the interval or ELS being equal to the number of letters shown on each line, unless a “row skip” (explained below) is used. Note that the spaces between words are removed. So the example of an ELS above would appear in a “matrix’ as follows:
| M | A | N | W | A | L | K |
| E | D | O | U | T | T | H |
| E | D | O | O | R | I | N |
| T | O | T | H | E | S | T |
| A | N | D | S | T | H | A |
| T | S | E | A | T | E | D |
| 8 | 0 | 0 | 0 | F | A | N |
| S | ||||||
Further, it should also be pointed out that the really proper way to display the above would be to wrap it into a cylinder with a circumference of 7 letters.
Axis Term
The first term sought is the “axis term.” The axis term appears vertically. Hebrew is normally read right to left. The code is really based on a spiraling cylinder. The ELS or “skip” of the axis term = the number of letters on each line. In general, the minimum length of an axis term should be at least 6 letters. Most often it is difficult to find axis terms longer than 8 letters unless one uses a wrapped search making more than one pass through the Torah.
Row Split
If a term like Ark of the Covenant has a skip or Equidistant Letter Sequence (ELS) of 306 letters, then the computer will place 306 letters on each line. When the second letter of the term arises, (without a row split) it will appear directly below or above the first letter. However, if a row split of 2 is used, the computer will only place half of the 306 (153) letters on each line and there will be an extra row between each of the letters of the axis term. If a row split of 3 is used, there will be two extra rows between each letter of the axis term. The larger the row split, the more terms you can match with an axis term, but it is also true that as row split increases, matrix significance generally decreases.
Word Frequency
Just as in English, some words are very high frequency (like THE or AND), in Hebrew two or three letter words are extremely high in frequency unless they are composed of somewhat rare letters. The higher the frequency of a word in the open text or at an ELS, the lower the significance of its match with an axis term.
Matrix Size
The bigger the matrix, the more likely it is that short or moderate length ELSs (up to 6 letters) will be found somewhere on the matrix. This is like looking in a phone book. If you rip a page out at random, and look for a single last name, it probably will not be there. But if you use the entire phone book, the chances to find it are greatly improved.
Spelling
Even within the Torah, there are multiple spellings of the same word. Code adversary Dr. Brendan McKay points out that the Rabbi Abulafia synagogue in Tiberias, Israel has the rabbi’s name spelled four different ways on the same building. The more spellings one can use to find a match, the less significant the match will be. Such multiple spellings must be factored in to any probability calculation describing the significance of a matrix.
Wrapped vs. Unwrapped Matrices
The best Torah Codes programs allow for the computer to make more than one pass through the 304,805 letters of Torah to find a term at an ELS. In general, this practice is most legitimate in search for axis terms that are 8 or more letters long because many terms this long can only be found with more than one Torah pass. The wrapped matrix mimics Jews reading the Torah. They finish reading the last word in Deuteronomy each Simchat Torah holiday, and then immediately begin reading at the first word in Genesis again. Some Codes researches do not employ software like CodeFinder that has the ability to find wrapped matrices. This is often true of Israeli Codes researchers. These people only can find unwrapped matrices where the computer is unable to make more than one pass through the Torah. Although CodeFinder software is, in my opinion, the best Codes product on the market,I have been unable to convince many of my orthodox Jewish colleagues to use it because the program also includes the files of the New Testament. Many Orthodox Jews will not allow mention of the Nazarene’s name, let alone allow any form of a New Testament into their homes. The New Testament files can be deleted, but my friends do not want to even have to undergo that requirement. I have asked Kevin Acres, CodeFinder software creator, to sell a version of his product without the New Testament on it, but more than a decade of such pleas have gone unanswered. This has greatly limited the ability of Israelis (who naturally have the best ability to understand the Hebrew on a Torah Codes matrix) to fully understand the true miracle that the Torah Code seems to be.
Torah Code Restrictions and Modification to Probability Calculations.
My basic protocol for calculating the significance of matrices is found on this site at Skip Tables. With time the value of short ELSs that were not at skips +1, -1, N or -N where N is the skip of the axis term has come into question by me and a number of other Torah Codes experts. Therefore, the following modifications have been built into my work for most if the last 10 years:
(1) Emphasize key words found at skip +1 by just using their frequency at skip +1 alone. This usually (but not always) equates to their frequency in the open text, the exception being when two sequential words make up one larger word with a different meaning.
(2) Emphasize key words found at skip -1, N and -N where N is the axis term skip by just using their frequencies at -1, N, -N and also +1.
(3) Reject any matrix with an axis term less than 6 letters in length.
(4) Reject any matrix with no axis term that is just a mix of short 3 to 5 letter ELSs.
(5) Reject any 3-letter ELS that does not have its letters within three letters of each other.
(6) While I may show them and while I often discuss them, I reject all a-posteriori finds for calculation purposes.
(7) I would never do a matrix based on a year as an axis term because it is too short and because I have seen many thousands of times that years are not statistically important, or to phrase it another way, there is no evidence seen that dating events was a purpose of the Code. This fits in with the concept that God, in His mercy, hides the date of death for most people.
(8) Axis terms that can found at a single ELS like Ark of the Covenant (in Hebrew alef resh vav nun bet resh yud tav) are never split into two spatially separated words like Ark and Covenant. The term must appear as 8 letters in sequence as it appears in Torah; or as 9 letters in sequence as it appears in the 3rd to 6th chapters of Joshua as Ark of THE Covenant (alef resh vav nun hey bet resh yud tav).
(9) Because many names require at wrapped search (more than 1 computer pass through the Torah’s 304,805 letters) to find, the wrapped search is the method used to find the name rather than splitting it.
(10) Where a full first and last name can not be found at an ELS even in a wrapped search, the first name initial and last name are sought. This generally occurs where a name has any of the follow letters: multiple samechs, tets, gimels and zayins. In such cases, if the name is just a transliteration, a shin/sin may be substituted for a samech, and a tav may be substituted for a tet.
I do not assign any significance to the axis term, no matter how long (although it is extremely rare that I ever find one over 10 letters in length).
A WORD ABOUT WHAT TO EXPECT – MATCHING A 7-LETTER KEY WORD WITH A 10-LETTER AXIS TERM. i was asked to match COVID-19 with the name of a man who found a meteorite that might have the source of he virus – EBRAHIMI. Here is what I wrote:
The trick is to find what is actually there. For COVID 19 it takes 7 Hebrew letters which would more likely be an axis term than an a priori key word. There are 4 transliterations that would work. They are (with frequency in Torah in unwrapped and wrapped finds) as follows:
kuf vav vet yud dalet yud tet (0/8)
caf vav vet yud dalet yud tet (7/35)
kuf vav vav yud dalet yud tet (1/15)
caf vav vav yud dalet yud tet (14/58)
So without more than 1 computer pass through Torah (an unwrapped search) there are, in 304,805 letters of Torah, 22 possible matches for an axis term. With a wrapped search there are 116 possible matches. Usually I look for an axis term to be 8 letters long. 7 is OK especially when there is a relatively low frequency letter like tet, but to find a 7-letter key term term that has a letters like tet, samech or zayin is extremely rare. Likewise, to put COVID-19 first and expect to find a 10-letter Hebrew word like EBRAHIMI is basically unheard of. Results for key words that are not axis terms are generally as follows:
3 letters – too short and easy to find. Rarely of great value unless at skip +1 and with rare letters.
4 letters – still short. Rarely of great value unless they are at a special case skip (+/- 1 or the absolute skip of the axis term).
5 letters – good but only excellent if they are at a special case skip or have rare letters.
6 letters – good to great.
7 letters – very good.
8 letters – rare.
9 or more letters – exceedingly rare. Basically not seen.
R VALUES. I generally don’t use Rotenberg R-values unless I’m dealing with a 10-letter axis term (or in a few cases with a 9-letter axis term that contains relatively rare Hebrew letters like tet, samech. gimel or zayin). R-values are available on Code Finder reports, but I always edit them out because I disagree with how they are used by that program. Normally I assign no value to an axis term that is 8 letters or less in length, and the higher the ELS rank of an axis term, the more I penalize the combined odds of a matrix. Here p is the probability that the characters of an ELS will match the characters of a text in a random placement. N is the number of placements of an ELS of the given skip. An R value is defined as 1/E where E = pN. E is the expected number of times that in a random letter permuted text a random placement of an ELS with absolute skip less than the absolute skip of the ELS found in the Torah text, will match the characters of the Torah text in the placement. See Code Finder: Scores or Probabilities by Dr. Robert Haralick.
Now, let’s simplify all this a bit and apply it to Figure 1. If you’re wondering about how likely the axis term was to be found in wrapped Torah, the answer is that this phrase occurs twice times at an ELS, but the one shown on Figure 1 is at the higher skip. It has an R value of 0.484 which means that based on letter frequency there is about a 32.8% chance to find it (Note: to change R value, found on the Code Finder report [in this case 0.484], to percent chance to find it, enter .484 into a scientific calculator like the TI30XA, hit second function, LOG, then 1/x and multiple by 100). As noted above, I normally consider including the R value in a calculation when the axis term is 10 letters or longer. Indeed here it is 10 letters. Thus although I reported above that the odds against finding BORDER FROM THE SOUTH and WALL with NATIONAL EMERGENCY were about 1,451 to 1, that statistics assumes no value assigned to the axis term. In fact, if we include the implication of the R value for NATIONAL EMERGENCY then the real odds against finding the 418-letter matrix are altered to about 4,422 to 1. Likewise the odds against the full matrix go from about 16,578,146 to 1 up to about 50,528448 to 1. Note: CRISIS was left off the spreadsheet, but this word had a 99.2% chance to be on the large matrix so it doesn’t appreciably change the odds.
NOT EVERYTHING THAT LOOKS IMPRESSIVE IS IMPRESSIVE
The ever constant question that pops up whenever a new matrix is found is (or should be), “Is this find significant, or the result of simple (often high) probability?” The more professional researchers generally turn to the Monte Carlo technique to arrive at an answer. Dr. Robert Haralick, who wrote the Foreword of Ark Code, has a discussion about probability on his site at http://www.torah-code.org/probability/probability.shtml. He also has a discussion about scrambling Torah texts to produce what are called “Monkey Texts” at http://www.torah-code.org/monkey_texts.shtml. This relates to the Monte Carlo technique. As applied to Torah Codes, ones scrambles the Torah text 10,000, 100,000 times or more, and then compares the results of key terms meeting in the real Torah text with the scrambled text. It matters greatly whether or not the Torah text that is scrambled to produce a Monkey text is scrambled at the letter level, word level, or verse letter. Because much is often made out of key words meeting certain phrases, it’s probably better to scramble at the verse level and then use comparisons between it and the original text. If one scrambles the Torah text 10,000 times, and then finds 1,000 better (tighter, smaller) meetings between key terms in the “Monkey Text,” then the chances are, that at best, the find in the Torah text had one chance in ten of being there. This is NOT significant. But if, in the 10,000 trials, there were only 100 as good or better meetings of terms in the monkey text, then the find in Torah might have had only about one chance in a hundred of being there. In this case, it begins to become interesting. A problem with the Monte Carlo technique when I began my research was that it was (a) often very slow due to the need to check such a high number of scrambled texts, each with 304,805 letters, and (b) it required computer software that was not available to the general public. As such, I developed an alternate method that focused on the number of rows and columns in a matrix, the number of ways a key term could fit in that size matrix (vertically, horizontally, diagonally, forwards, and backwards*); the frequency of this term at an ELS when limited to the number of ways it could fit in such a matrix, the percent of total Torah employed in the matrix; the chi-square value, and the combined total probability for everything found (which must then be adjusted for those things sought and NOT found). For those who are interested in examining the entire process, please buy a copy of ARK CODE and examine Appendices A and B (pages 183 to 221). Note: In the case of ELS maps, the probabilities derived must then be adjusted due to the requirement for the matrix to have items found be found at the correct course angles that correspond to what is seen on real world maps.
*ROFFMAN SKIP FORMULA.
The number of ways that a term (either forwards, backwards, or diagonal) can fit into a matrix is determined as follows:
(1) Let the number of skips possible in a forward direction on a row of length (r), where r = the number of columns in the matrix, be equal to “Sr.”
(2) Likewise, let the number of skips possible in a vertical direction on a column of length (c), where c = the number of rows in the matrix, be equal to “Sc.”
(3) The Roffman Skip Formula for total skips is as follows:
Skips = 2(Sr + Sc + 2[Sr][Sc]) = 2Sr + 2Sc + 4SrSc.
An example of skip value determined through use of the above tables and formula follows: Find the number of skips possible for a 4-letter word in a Matrix 28 columns by 11 rows.
Solution: Skip Tables for words ranging between 3 and 8 letters are posted on this site. For a 4-letter word use Table 1B. On it find that 28 columns = 9 possible skips forward. Thus Sr = 9. Now note that 11 rows = 3 possible skips vertically. Thus Sc = 3. Now apply the formula which is Skips = 2(Sr + Sc + 2[Sr][Sc]) 2(9 + 3 + 2(9)[3]) = 2(12 + 54) = 2(66) = 132 SKIPS. Now, let us suppose that the 4-letter term occurred at skip 100. To get an idea of how likely such a term is to be found at an ELS, search a range of 132 skips, such as from skip 101 to skip 232. The number of “hits” for this term is then divided by letters in the Control (if this is scrambled Torah the number of letters in the Control is the same as in Torah, i.e., 304,805). The quotient is the Word Frequency Per Letter. This is multiplied by the number of letters on each matrix to reveal Word Expectancy Per Matrix. It is inherent in this procedure that the larger the number of letters in the matrix, the larger the number of placements possible for any given key word at any ELS. After determining Word Frequency Per Plot we apply the Poisson Equation to see the probability that they are present at least once. This is necessary to determine a true probability for each word. Just because a word is likely to appear once per plot does not imply it will always be there. Words may average out to many times per plot area without actually being in a given plot of that area. Of course, if the expected frequency is sufficiently high we eventually reach a probability like .9999999 which we simply round off as 1.0.
HOW TO FIND THE CHANCE OF A TERM APPEARING AT LEAST ONCE*
- FIND PROBABILITY IT DOES NOT OCCUR BY POISSON EQUATION.
x (-lambda)
f(x) = Lambda e x = 0; lambda = expected frequency per matrix
x! 1 ‑ f(0) = THE PROBABILITY OF OCCURRING AT LEAST ONCE.
(where f(0) = the probability it will not occur)
On an Excel or Works spreadsheet, head columns as follows: A: Whatever identifies the calculation; B: Skips Used on the Matrix, C: Number of hits (onCodeFinder or similar software) in Skip Range; D: Divide by 304,805 Letters in Torah or Control; E: The Quotient Equals Frequency Per letter; F: E Quotient Multiplied by Letters on Matrix = Word Expectancy; G: Poisson Equation = 1-EXP(-F#) where # equals the row number of the item in Column F in question on the spreadsheet. If you want to know the chance for the item to be on the matrix, head Column H accordingly. The value of Column H will be the reciprocal of the value found in Column G by Poisson Equation.
* Note: While this author (Barry S. Roffman) discovered the Roffman Skip Formula, my son (an MIT geophysics graduate), Rabbi Robert Roffman, is the author of the spreadsheets and the man who first introduced use of the Poisson Equation into my research.
ROW SPLIT AND WRAPPED MATRICES
There is some indication that when a row skip or row split function for the axis term is employed, that the true value of an open text match must be the value computed by standard means divided by the row spit. The lowest ELS of Ark of the Covenant at skip -306 (cylinder circumference 306 letters) had about one chance in 2,931 of being in a 104-letter matrix with Egyptians were burying. At skip -306 there was no row split function enabled on CodeFinder. Had it been enabled and a row split of 2 were used (with a cylinder circumference of 153 letters), if the matrix size (area) were the same, I would have divided 2,931 by 2 to arrive at a value of 1 chance in 1,465. In this case however, the matrix with circumference 153 would have been larger because the match on the matrix with circumference 306 was already about as tight as it could be with the row skip function disabled. There is also a discussion about dividing the value of a matrix by the number of passes through the Torah made by CodeFinder on a wrapped (rounded torus) search before acquiring an axis term. See the permutation experiment.
SPECIAL CASE SKIPS
Finally, when computing the value of a-priori open text terms on a matrix, it is my practice to only employ the frequency of this term at Skip +1 (in unwrapped Torah) on my spreadsheet in column C. However, if the a priori term appears at skip -1, N (parallel to, in the same direction, and at the skip of the axis term), or -N (parallel to, in the opposite direction, and at the skip of the term) in column C, I list the frequency (number of hits) as the total hits at skips +1, -1, N, and -N (with wrapped Torah allowed if that was required to find the axis term. These skips are considered special because they seem to leap out at the eye of the researcher and make the case for deliberate encoding seem more plausible.
Code Skip Formula & Tables