Introduction

The phenomenon described in details in Part 1 [1] provoked heated discussions and sharp criticism. The code was explained through the important physical function entropy and backed up with many examples from history. This variety of approaches and the novelty of the method required keen flexibility in perception. On the other hand, the standard statistical methods, which are used for estimation of the matrices obtained with clustered encoded words, are practically inapplicable to this method. Therefore, the exposition had to be enriched with more textual scrutiny using more appropriate statistical analyses in order to convince mistrusting and hesitating readers in the genuineness of the code.

In the exposition of the phenomenon described in Part 1, no consideration has been paid to any linguistic aspects except the number of letters of a state, spelt in Hebrew, that are shared with the words in the plain text used in each test. Although no link could be derived from the aggregate number of shared letters that points to dependence of the P-value obtained, a question may be raised as to whether there are some concealed mechanisms that are more likely to produce a lower or higher P. And, are not these mechanisms characteristic for each group of states?

Another interesting question in my opinion is: What “makes” the phenomenon? Do both groups contribute to the same extent to the phenomenon, or the very low probability is due basically to one of them? And, if so, which one’s “behaviour” is more unusual?

The study in this Part is dedicated to detailed analysis of intersection rate using linguistic parameters available and assessable. It consists of four sections, which are ordered according to the logical sequence of data already in hand as well as the progress of my understanding. Where applicable, the method of recording of intersections and the program used are the same as described in Part 1. For the sake of clarity, Tables 1 to 3, concise and defined more accurately, are given in the Appendix.

Statistical Valuation

Prospective and Real Occurrences

First of all, we will consider in more details what has already been obtained in Part1. Tables 2, 2A and 2B contain the lowest possible P-values (that is, the “best case”) for each name in the whole Torah, and the massif of text containing the name of ISRAEL (י ש ר א ל ). The text covers slightly more than 5/6 or exactly 84.27% of the Torah (from pos. 47,944 in Gen. 32:28 to the very end). Although the safe states occupy predominantly the upper half of Table 2, differences are too small for a definite conclusion. On the other hand, minimum P-values are impractical for comparative evaluations because they are not restricted to ISRAEL only but also are valid for every other name in the plain text. A better approach should take into account those occurrences that are within the massif containing ISRAEL. (It is virtually the same for SONS OF ISRAEL.) This is shown in Tables 2A and 2B. No significant difference is observed in terms of the phenomenon between the safe and the risky states. Even more, the top 10 names in both Tables 2A and 2B, which occur in the upper part of the corresponding table (non-shaded), are two times more in Table 3 (Sons of Israel): 8, compared to only 4 in Table 1 (Israel). Consequently, if we assume the lower minimum P for each name as a higher potential for occurring in the upper compartment, this potential has been materialized to a much higher extent with intersections with the Sons of Israel (ב נ י י ש ר א ל ) than with Israel (י ש ר א ל ).

On one hand, lack of significant difference is due to the fact that the massif in question is about 85% of the whole text, so it should be hardly expected some tremendous changes to take place. On the other hand, some intersections are realized by encodings that extend beyond the massif. This is best illustrated by the example with Britain, which starts on position 13,981 (Gen. 11:29) but goes right down to Exodus 6:27 to intersect at position 86,181, after having skipped over about a quarter of the Torah! That is why I retained N in the corrections, checking those LIELS only that fall within the massif containing ISRAEL.

A more proper approach, in my view, would use the number of these occurrences only, which, in case of intersection, would place a name in the upper compartment. It would give a better evaluation of the “capacity”, or rather the expectance for a name to get into the upper compartment. This “number of qualifications”, N_q, is the number of occurrences at skips (ELS), from the lowest to the highest one including, which, in case of intersection, produce P lower than 304,805. It is the number of those skips, which are

ELS ≤ 304,805/N

where N is the overall number of occurrences of the encoded name in the Torah. The results are shown in Table 16.

As it could be anticipated, the 4- and 5-letter names occupy predominantly the lower half of Table 16. The 7-letter Austria, due to her barely 2 occurrences, is in the bottom. More unexpected are the only 3 occurrences of Holland. However, the 5-letter Russia to my surprise shows as high as 10 possibilities. On the other hand, Albania, Britain and Bulgaria – three of the safe states - show lower N_q than the values that may be expected on the basis of their intersections with ISRAEL and SONS OF ISRAEL (Tables 1 and 3). The only other occasion when Albania and Bulgaria produce P < 304,805 is in Table 13 (SONS [ב נ י ]). Britain also appears in the upper compartment in this Table along with two more occasions: Tables 4 and 5 (EGYPT and ABRAHAM, respectively). On the whole, Britain, with 6 qualifying occurrences, appears 5 times in the upper compartment out of 14 “attempts”. For a comparison, Jerusalem’s 14 qualifying encodings are perfectly balanced: with 7 of the studied names it occurs in the upper compartment and with the other 7 – in the lower one. The aggregate score of the three states in both Tables 1 and 3 is 6, while the same score for all the other 12 Tables is 5! Also, the number of Tables where Albania and Bulgaria are in the upper compartment, 3, exactly matches that for the 4-letter France with her only 3 qualifying occurrences (in Tables 4 [EGYPT], 10 [LAND] and 15 [PHARAOH]). I have made some associations between France on one hand and the three Egyptian words on the other, which directed me to an interesting code. It is described elsewhere. [2]

Table 16. Names are ordered basically by decrease of their N_q and number of letters. Safe states are coloured in blue and the risky states – in red.

The last two columns in right represent the positions of the names in Table 1 (Israel) and Table 3 (Sons of Israel), respectively: shaded cells indicate a position in the lower compartment of the particular table.

The assumption in the ordering Table 16 has been to place the names according to their presumable chances for intersection. The first criterion was N_q, and then the number of letters came into account. It is supposed that a higher number of letters gives more chances for intersection. For instance, Denmark with its 7 occurrences has 7?5 = 35 “spots” for intersection, while the other three 6-letter names (Ireland. Italy and Romania) have 7?6 = 42 “spots” each. Finally, the belief that a higher number of shared letters presupposes better chances has led to the final decision for a place. Shaded cells indicate that the respective P-value is < 304,805 and the names occupy the lower compartment of a Table.

It is noticeable even at first glance that the top places in Table 16 predominantly correspond to the upper compartment of Table 1 rather than Table 3. This aspect will be discussed in more details later. Now we will reflect on another characteristic that is worth to be used for comparison. It measures the probability for a “direct” hit – an intersection with a letter that is common for both words. The quantity could be specified as the product of the number of qualifying occurrences and the number of shared letters with the word in the plain text. No tendency, however, could be derived from the data. America (12?3 = 36) and Iceland (10?3 = 30) produce the highest numbers among all names. But while both states are in the upper compartment of Table1, America falls in the lower one in Table 3 with the same product value. With Israel (י ש ר א ל ), Ireland and Italy yield the same product, 7?4 = 28 but occupy different compartments. What is more, Ireland, with a higher product (7?5 = 35), falls into the lower compartment with Sons of Israel (ב נ י י ש ר א ל )! One of the most impressive examples is that of Denmark (7?1 = 7), which is in the upper compartment with Israel, while Germany and Hungary, with products as high as 26, occupy, together with 7 other states, the lower compartment of Table 1.

Jerusalem, however, is outstanding in this aspect: with the unrivalled value of 14?5 = 70, it occupies the lower compartment of Table 3 (Sons of Israel)! All these examples irrefutably prove that the phenomenon cannot be explained with number of letters, number of occurrences, number of shared letters, lowest skips or P-values. We will consider the contribution of the shared letters in more details in the next sub-section.

Shared Letters

A brief analysis of Table 16 shows that the overall N_q for the safe states is 96 while that for the risky ones is 80. The specific rates of qualifying occurrences (that is, the sum of all N_q-s in a group divided by the number of states in this group) are 8.0 and 7.3 respectively. This means some 10% more occurrences per name for safe states. The total number of letters of the safe states is 70, while that of the risky states is 63, which is 5.8 and 5.7 letters per word for each group, respectively. In terms of letters shared with Israel (י ש ר א ל ), the groups show the following distribution: 29 shared letters[1] for the safe states and 23 shared letters for the risky states, or 2.42 and 2.10 shared letters per name, respectively. The ratio of the latter values is 1.15.

These data point at some advantageous characteristics specific for the names of the safe states, which could determine higher rate of intersections with Israel.

Therefore, a comparison of these data with the similar data for Sons of Israel (ב נ י י ש ר א ל ) would clarify their significance for the phenomenon. The safe states’ count of shared letters is 39, while that for the risky states is 31. The specific values per name turned out to be 3.25 for the safe states and 2.82 for the risky states. The ratio of these values is absolutely the same as the value obtained with Israel: 1.15. On the basis of the parameter number of letters shared with the word in the plain text, the performance of the safe states with Sons of Israel (ב נ י י ש ר א ל ) should be expected to be similar[2] to that with Israel (י ש ר א ל ). They behave to a great extent in different ways, in fact. (See Tables 1 and 3 in Part 1.)

Then I made a “cross-section” of the Table in order to determine the characteristics of those names of each group, which are comparable in terms of number of qualifying occurrences. This has been carried out in order to verify the distribution of N_q among the names of each group and whether higher N_q-s are combined with lower number of shared letters among the names of one of the groups.

Checking the upper half of Table 16 (from the 1^st – Sweden - down to 12^th place – Romania including) discloses, however, a perfect parity: 6 states and 62 qualifying occurrences for each group. In terms of number of letters, these 12 names also demonstrate an almost perfect parity: 36 letters for the safe states compared to 37 letters for the risky states. The overall number of shared letters with Israel (י ש ר א ל ) of the names of the 6 safe states in this sub-group appeared to be 16, while that for the 6 risky states is 14. The ratio of these values matches that for the whole group: 1.15. With the Sons of Israel (ב נ י י ש ר א ל ), the number of the shared letters of this sub-group is 20 for the safe states and 19 for the risky states. The ratio, 1.05, is in favour of the safe states, but nonetheless is about 10% lower than the 1.15 found above. This is interesting, because all 4 risky states that appear in the upper compartment of Table 3 are members of this sub-group. (These are Hungary, Germany, Norway and Romania.) On the other hand, the safe states in this sub-group behave in the same way as the whole group: 5 out of 6 states (Finland is the exception) are above the line in Table 1, where 10 out of 12 safe states are there (83%), and 4 out of 6 safe states (America and Ireland are the exceptions here) are above the line in Table 3, where 8 out of 12 (67%) are in the upper compartment. But it is not so with the risky states. As the sub-group inevitably counts the 0% presence in the upper compartment of Table 1, 4 out of 6 (67%) of the members of this sub-group are above the line in Table 3, while the average percentage for the whole group is almost twice lower: 4/11 = 36%.

The values obtained for the sub-group of the risky states with the Sons of Israel are the only ones that show significant difference in this aspect from the behaviour of a whole group. Indeed, this sub-group has 19 letters shared with Sons of Israel (ב נ י י ש ר א ל ), or 3.16 letters per name, while the other sub-group (the remaining 5 states coloured in red in the lower half of Table 16) have 12 letters, or 2.40 letters per name. The ratio of the specific values is 1.32. A higher number of shared letters may affect the probability of intersection. As a result, a higher rate of incidence of names yielding lower P-s may be observed. But an evaluation is elusive even on statistical basis. For illustration, let us try the same approach to the sub-groups of the safe states for the intersections with Israel (י ש ר א ל ). The names of the first 6 states, those in the upper half of Table 16, contain 16 letters shared with Israel, while the other 6 states share 13 letters. The ratio is 1.23. However, not only both sub-groups show absolutely the same rate of occurrence in the upper compartment of Table 1, but this ratio is 7% higher than 1.15 – the ratio between the groups of the safe and the risky states (see above).

This “dissection” clearly indicates that the phenomenon cannot be ascribed, at least to a considerable extent, to the number of identical letters in an encoded word and a word in the plain text. This number by no means determines, even on statistical level, the lowest intersection skip. Be that as it may, the example given above shows, that it is Table 3 (Sons of Israel), which demonstrates fewer anomalies than Table 1 (Israel).

Retrospection of Names

In order to evaluate the phenomenon, I brought together the summary of the results of Tables 4-15. These 12 Tables contain the results of the experiments carried out with all the names or words in the plain text that do not include Israel (י ש ר א ל ). Data for each of the two groups consist of the total number of letters in the names of each group shared with the word in the plain text, n_L, the number of these letters per word (the specific number of shared letters), lpw, the number of P-values for each group that are lower than the number of letters in the Torah (304,805), Tr, and the number of states of each group that are in the upper half of the respective Table, m. Because the number of all states taken into account is an odd number, 23, the number of states of each group that are among the first 11 states is given in the columns under m. The 12^th state in each Table is a median and the cell in the column is shaded if it is a member of the respective group. The right column contains the values of the relative number of shared letters per word, R_lpw. This is the lpw for safe states divided by the lpw for the risky states in each row. In my view, R_lpw could be used as a measure for the “affinity” of each group to the word in the plain text. When R_lpw > 1, the safe states possess more “affinity” to the corresponding word, while if R_lpw < 1, the risky states should have higher “affinity”.

The results are presented in Table 17. The Table is arranged according to the decrease of R_lpw. It is divided in two sections, representing the areas where the safe (R_lpw > 1, top) and the risky (R_lpw < 1, bottom) states have higher “affinity”. The higher the R_lpw, the more “affinity” the names of the safe states possess and vice versa.

The highest values under lpw, Tr and m are coloured in blue and red for the safe and the risky states, respectively. Sub-total values for these two columns are given under each section. This is done for a better estimation of the relative behaviour of each group.

There are tendencies displayed by both groups, which are expressed through the numbers of states of each group occupying upper halves of Tables (m columns in Table 17). These tendencies are symmetrical: 37/32 = 1.16 for the safe states and 35/29 = 1.20 for the risky states.

The most impressive asymmetry is the number of occurrences, Tr, of safe states, 18, in the top section of Table 17. Related to the corresponding number for the bottom section, 10, the ratio 18/10 = 1.8 is produced. At first glance, this is a corroboration of the presumption that encoded words are more likely to manifest higher “affinities” in “favourable zones”. A closer inspection reveals, however, that this deviation is due mainly to one name - Sons (ב נ י ) - and cannot be a good statistical characteristic of the safe states names’ behaviour in the top section. The value for Sons, 7, is more than twice larger than the next one, 3, this time in the very top of the Table (Adam). The corresponding value for the risky states, 4, is also the second in value for the group. This means that Sons is a word that basically holds up a larger number of encoded names with P-values lower than 304,805.

Table 17. Summary of data obtained with names that do not contain Israel (י ש ר א ל ) in the plain text (Tables 4 – 15 including in Part 1).

But even after canceling the highest values in both sections, the group of the safe states shows a “normal” tendency: 11/7 = 1.57. This ratio is much more than those of “median” ratios for both groups shown above. The risky states, however, behave somehow “abnormally” in this aspect: the corresponding ratio without discarding the highest values in both sections is 15/15 = 1.00, i.e. they show no change in “affinity” when put in favourable zone. After discarding the highest values, the ratio is 12/9 = 1.33.

Generally, the “median” values for both groups of states are more coherent than the “Torah” values. This is what should be anticipated because the former values are independent on the P-values. The numbers of states occupying the firs halves of any Table depend on the relative distribution, or mixing, of P-values among the two groups.

The paradox with the risky states is that they give their highest “Torah” number (6, with Land) in the “wrong” section! Even more, this result is obtained at the third lowest lpw of the group, 0.91, and at R_lpw = 1.10, which is one of the closest values to R_lpw for Israel (1.15). The risky states show their highest “median” number (8, with Egypt) close to the “border” between the sections.

Another paradox, it seems to me, is that the highest “Torah” number in Table 17 for the safe states is obtained with Sons. After all, this is the particle, which, placed before Israel, form Sons of Israel. And Sons of Israel produce 5,000 times higher probability than Israel (see Part 1)! But a similar phenomenon is observed with the risky states too, when passing from Land (א ר ץ , Tr = 6) to The Land (ה א ר ץ , Tr = 2) and from lpw 0.91 to 1.82!

A broad-spectrum investigation of Table 17 reveals a general parity in all values analyzed. The total number of states above the line marked by the number of letters in the Torah for all 12 names in the plain text for the risky states, 30, is higher than the number for the safe states (28). With five of these 12 names (42%), absolute parities of Tr are observed: with Jacob and King in the upper section and Aaron, The Land and Moses in the bottom section. But while all three higher Tr-values for the safe states are in their favourable zone (Adam, Isaac and Sons), one of the four higher Tr-values for the risky states, and it is the best one, is achieved deeply in the “alien territory”.

The sum of the m-values is higher for the safe states, but it should be borne in mind that, unlike the Tr-values, it depends to a higher degree on the number of names,[3] which are 12 safe states against 11 risky states. Reduced values are 68/12 = 5.67 and 64/11 = 5.82 occurrences in the upper half of the Tables per name, respectively. The ratio of the latter values, 5.82/5.67 = 1.026, corresponds perfectly well to the ratio between the mean numbers of shared letters per word, lpw, 1.38/1.35 = 1.022, whereas both values are in favour of the risky states’ group.

Remarkably, both groups have a single name in the upper compartment at their highest lpw-values (both with Aaron) – 2.00 and 2.27 for the safe and the risky states, respectively. Among the lpw-values with Israel and Sons of Israel, lpw for the safe states with Israel is 2.42, which is 6% higher than 2.27 – the highest lpw in Table 17. The values with the Sons of Israel for both groups are even higher. The low rate of occurrences in the upper compartment with Aaron could be ascribed partly to the relatively low number of “intersection letters” – 1,806 (see Part 1, page 35). This argument, however, by no means can explain the result obtained with the risky states with Land. There, lpw is only 0.91, and the number of the “intersection letters” is even higher than that of Israel – 4,250 letters for Land against 4,137 letters for Israel (ibid.).

The biggest difference in numbers of each group representatives in the upper compartment is 6 - 2 = 4, and it is in favour of the risky states (Land). There are also two incidences of difference 3, in both cases in favour of the safe states (Adam and Sons), in the top section again. Two occurrences of difference 2 are recorded in the bottom section, in both cases in favour of the risky states. So, on the basis of the data presented in Table 17, it could be presumed that, given the parameters are similar to the already discussed ones, obtaining a difference 4 will be a rare event, while differences 5 or higher could be regarded as deviations.

Table 18 contains the data with Israel and Sons of Israel.

Table 18. Summary of data obtained with names that contain Israel (י ש ר א ל ) in the plain text (Tables 1 and 3 in Part 1).

R_lpw for both names will place the rows with Israel and Sons of Israel between those with Isaac and Land in the top section of Table 17, but closer to the row with Land. The Tr and m values in the row with Sons of Israel repeats almost exactly the row with Sons in Table 17. There is only one more safe state in the upper compartment, whence the difference, 4, matches the highest value in Table 17. Both groups record their extreme lpw-values with Sons of Israel, while those with Israel are close to (safe states) or within the range (risky states) of the values in Table 17. Moreover, the mean lpw-value for risky states in Table 18, 2.46 is higher than the value with Israel for the group of the safe states (2.42). It should be also borne in mind that more than 63% of the appearances of the word Israel (י ש ר א ל ) in the plain text of the Torah are as Sons of Israel (ב נ י י ש ר א ל ), which makes these two names linked in the terms of the code. For instance, if a group of names yields 10 occurrences in the upper compartment with Israel, not less than 6 occurrences for the same group with Sons of Israel are to be expected on pure statistical basis. This aspect will be discussed in more details in the next Part of this study.

The basic conclusion of this section is that the phenomenon is not hidden in a specific “affinity” of the encoded names of the safe states to names in the plain text of the Torah.

Lamed

The next idea that I decided to develop was founded on the observation of interesting similarities in the names of three of the European states at the time of the Holocaust. All three are 7-letter words in Hebrew. One of them was safe, while the other two were risky. The states in question are Bulgaria, Norway and Hungary.

The numbers of occurrences of these 3 names are comparable – they are successive in Concise Table 1. But while Bulgaria yields three intersections with Israel in the plain text, two of which situate the name into the upper part of Table 1, both Norway and Hungary yield no intersection at all.

No abnormality has been observed with the number of occurrences of each one of the three names as it is shown in the following table:

As it is seen, only the odds for Hungary to be found such number of times are rather low: about 0.1, with a SD higher than 1. But notice that the deviation for Hungary is in the positive direction, i.e. giving more opportunities for intersection! Bulgaria and Norway behave in an absolutely normal way in this aspect. The difference is that Bulgaria contains lamed (ל ) and does not contain nun (נ ), while Norway and Hungary contain nun but do not contain lamed.

I had already have noticed that the four states in the top of Table 1 (see Part 1 for the details in this paragraph!) contain lamed. (Note: In the research henceforth, all available data, including some names shaded in light in Tables 1 and 3 will be taken into account. The only names excluded are those that have no practical chance to produce P < 304,805, i.e. USSR, Lithuania and Greece, as well as those that do not occur in the Torah. This makes the overall number of the names studied 27. The 4 “newcomers” are Latvia, Jerusalem, Vatican and Palestine. The terms “safe” and “risky” states will be used strictly as defined in Part 1. There are 12 safe and 11 risky states, respectively.)

On the other hand, I was aware that all six names that “move” to the upper part of Table 3 in the passing over from Table 1 contain nun, while only two of the four that “fall” into the lower part contain nun (Ireland and Denmark). The other two are Jerusalem and America. We will not consider the significance of the letter nun here. Its effect on the distribution of the names in Tables 1 and 3 will be discussed, together with beyt (ב ) in the next part of the study, God willing.

We will proceed with the similarities and the differences between the three names. Firstly we will consider Bulgaria and Norway. Six of the seven letters in each of these two names are identical. The only difference is that Bulgaria contains lamed, while Norway has nun:

BULGARIA   ב ו ל ג ר י ה

NORWAY      נ ו ר ב ג י ה

So these two names are in fact two permutations of six letters with the addition of a seventh letter specific for each name (in red).

On the other hand, the very same resemblance is found to exist when Norway is compared to Hungary:

NORWAY      נ ו ר ב ג י ה

HUNGARY    ה ו נ ג ר י ה

As in the case above, six of the letters in both names are identical. The only differences are that Norway has beyt (ב ), while Hungary contains second heh (ה ) – also written in red. In fact, it turned out that each one of these three names consists of 7 out of a set of 8 letters!

An experiment was designed applying permutations of some of the letters of the names. The last two letters in all three names are identical: yod (י ) and heh (ה ). The difference should be looked for in the first 5 letters. But the number of the permutations of 5 letters is 5! = 120. The permutations of even 4 letters are 24, which makes 72 permutations for the three names. Therefore, the experiment was limited to the permutations of 3 letters, one of which is the real name. 3! = 6, so the overall number of permutations is 18. In order to standardize the experiment, the letters of the permutation were selected to be the same in order within the names: the second, the third and the fourth: ב ו ל ג ר י ה , נ ו ר ב ג י ה and ה ו נ ג ר י ה . The results are presented in Table 20.

The rows with the actual names and corresponding data are placed on the top of each group of permutations and are coloured in red. The rows that contain non-qualifying result for the upper compartment of Table 1 (that is, yielding P > 304,805 – see Part 1) are shaded. The rows where intersection with Israel occurs at the lowest ELS (that is, with the lowest possible P) are in bold characters.

Table 20. Comparative results obtained with the permutations of the 2^nd, 3^rd and 4^th letters in the Hebrew names of Bulgaria, Norway and Hungary.

N         = overall number of occurrences;

N_q        = number of qualifying occurrences – see above;

N_Israel   = number of intersections with Israel in the plain text;

N_Isr.q.   = number of qualifying intersections with Israel in the plain text

LELS, LIELS and P are as specified in Part 1.

The results in Table 20 are surprising. Out of all 18 permutations, the actual names of Norway and Hungary are the only ones that do not yield any intersection with Israel in the plain text of the Torah. Even more, there is only one permutation among the combined data for Norway and Hungary that yields at least one intersection but does not lead to a qualification in the upper compartment of Table 1 (the next-to-the-last row for Hungary: P = 360,558). At the same time, there are two “disqualifying” permutations among the five ones, apart from the true name, studied for Bulgaria.

At least one permutation of a name generates an intersection at its lowest skip. In fact, each one of the 3 states has one permutation with such characteristic, their genuine names excluded. Even in this aspect, the name of Bulgaria in Hebrew is not unique: the lowest P among the 18 examinations, 5,736, has been produced by a permutation of Hungary.

The general impression I perceived from the results in Table 20 was that it is quite a normal thing for a name of such length and containing 7 out of these 8 letters to qualify with a P < 304,805. And, if this is normal, then the combined results obtained with the permutations of Norway and Hungary are “better” than the corresponding ones for Bulgaria (real names including): 9 out of 12 permutations of the former names are qualifying (75 %), while the qualifying permutations of Bulgaria are 4 out of 6 (67 %).

Another essential parameter, in my view, is the “effectiveness” of the intersections with Israel in the plain text, which I define as the number of qualifying intersections related to the overall number of intersections, N_Isr.q./N_Israel. This ratio represents the rate of qualifications given a certain number of intersections. It appeared to be approximately the same for Bulgaria (9/16 = 56 %) and the total for Norway and Hungary (10/17 = 59 %) but slightly “better” for the latter. Another significant parameter -the rate of qualifying permutations related to the number of qualifying intersections (N_Isr.q) - is also in favour of Norway and Hungary: 9/10 = 90 % compared to 4/9 = 44 % for Bulgaria.

The results also confirm steadfastly the conclusion in the previous section about the virtual insignificance of N_q in the a priori assessment of the behaviour of a name in terms of P: The permutations of Bulgaria that disqualify the name are with the two highest N_q-values while the actual name is with the lowest one among all six values. The same is valid for Norway: disqualification with the highest N_q and lowest possible P-value with the lowest N_q among all 6 permutations. The results with Hungary are similar.

There is another similarity between Bulgaria and Hungary, which can be easily noticed. The names differ in their first and third letters only:

BULGARIA   ב ו ל ג ר י ה

HUNGARY    ה ו נ ג ר י ה

Immediately a question raised in my mind as to what will be the result if we exchange the places of the first and the third letter in each name (in red). The outcome appeared to be as follows:

The permuted names exchange the compartments – if their spelling was as the shown in the table above, Hungary would occupy the upper half of Table 1, while Bulgaria would fall in the lower one.

Three out of seven permutations of Bulgaria are disqualifying, which is the highest percentile of disqualifying permutations (43 %) among all three names studied. At the same time, two permutations of Hungary out of seven are disqualifying. For Norway, there appeared to be only one disqualifying permutation out of six considered. The combined rate of disqualifying permutations for Norway and Hungary is 3 out of 13 (23 %), which is almost twice lower than that for Bulgaria. The strange fact is that two out of these three disqualifying permutations are the actual names of Norway and Hungary in Hebrew!

The probability based on the data obtained that both actual names will be disqualified could be roughly estimated if we consider the 13 permutations as a stack of 13 well shuffled cards, 3 of which are black (disqualifying) and 10 are white. We draw 2 cards. What is the probability, P, that both cards that we draw will be black? The answer is:

        2!?3!?10!?11!       1

P = ———————?—— = 0.0385 = 3.85 %

         0!?1!?2!?10!       13!

In this aspect, there is nothing extraordinary with Bulgaria: the expectation for the actual name to be among the qualifying permutations is simply 4/7 = 0.57 or 57 %.

On this basis, we can conclude that a disqualification is an event that is closer to anomaly – a qualification is something quite normal.

The conclusion we could draw from this section is that no particular letter or a combination of letters defines the phenomenon. The key to the enigma is not hidden in lamed (ל ).

Digram and Trigram Studies

This result, frankly, surprised me. But I was not feeling enthusiastic to continuing the same type of research with the other some 20 names. The primary reason was the fact that there could hardly be found another excellent basis for comparison. This, less than 4% odds for neither Norway nor Hungary occurring in the bottom compartment of Table 1, which implies that it is more than 96% probable to be designed, is meaningful only if the corresponding probability for a name analogous in composition and structure is a good deal dissimilar. Any value by itself tells nothing without a proportional baseline.

Therefore, I tried to design another experiment model that will provide a common baseline in respect to both groups of names. Besides that, this baseline should preferably be independent on the length and letter composition of the encoded name.

For this purpose, let us consider the name in the plain text, Israel (י ש ר א ל ) analytically and split it into its smaller components. Then we will examine the names in question for intersections with these components. We will count these intersections and will compare the results not on individual name-basis but in terms of whole groups.

A type of analytical “dissection” of the name י ש ר א ל is breaking it up in its four two-letter components or digrams (from Greek di- = two and gramma = letter):

א ל , ר א , ש ר and י ש .

In a similar way, it could be expanded into three trigrams:

ר א ל , ש ר א and י ש ר .

All these two- and three-letter sequences are often occurring in the plain text of the Torah either as individual words or as fragments of words. Each one of the di- or tri-grams appears 591 times as a constituent part of י ש ר א ל . The overall number of each digram and trigram in the plain text of the Torah is given in Table 21, together with the ratio, R, obtained as the number of appearances of Israel (י ש ר א ל ) in the plain text, 591, divided by the corresponding number of appearances of the di- and trigrams. This ratio is also (roughly) the probability that an intersection with the fragment will be also an intersection with Israel. Reciprocally, 1 – R denotes the probability that the intersection will not be intersection with Israel.

Table 21. Overall numbers of occurrences of digrams and trigrams in the plain text of the Torah. The number of occurrences of Israel (י ש ר א ל ) is related to these numbers as R.

The results with the intersections with the di- and trigrams at lowest skips are presented in Tables 22 – 28. In cases when the respective two- or three-letter sequence is part of י ש ר א ל , the row is coloured in blue. Bold characters indicate, as in Part 1, the lowest ELS of the respective encoded name of state. The rows of the states defined as risky in Part 1, are shaded.