Protocol of a Statistical Evaluation of Some Items in the AD 2006 Code Matrix

An attempt for a statistical analysis of some of the results obtained for the code about AD 2006 has been carried out.

Although it is clear intuitively that the odds for the items in Figures 1 - 4 to be there due to a pure chance are extremely small, some questions have been asked about the estimation of probabilities. These questions are provoked, as far as I am aware, because the items are short words in their majority.

The purpose of this protocol is to demonstrate that the occurrences even of the shortest words have been designed by The Great Encoder. To this end, special attention has been paid not so much to the overall number of occurrences, but to the pattern of the latter.

Statistical data obtained with salvation (ישע) and interpreted

A good example, in my view, is the word salvation (ישע). Consider the matrix shown on Figure 4. It is 51 columns long and 21 rows wide. I decided to leave it 51 columns long in order to illustrate better the contents. It is absolutely symmetrical in relation to the year 2006 (תשרקתשרקו), which occupies a considerable part of the central column. The actual meaningful contents end 1 column short both on the left and the right side. In my view, it is significant that the number of the columns that contain the information appears to be 49 – this is the number of the years between two jubilee years. This fact adds to the idea of timing that the code implies throughout.

However, in order to prevent any suspicions about data manipulation, I decided to examine a number of 51×21 or 51×20 matrices. Matrices have been built as follows. All of them had a central column containing a certain number of letters shin (ש), two of which have always been at a skip interval of 59860 – the skip dividing the two letters in the encoded 2000/6. There are 680 pairs of shin (ש) at this skip in the Torah, so the diversity required for a statistical examination is thus ensured. The other letters shin, if any, were at various places within the column. All matrices were built at skip 14965.

The matrices have been checked for all occurrences of salvation (ישע) at positive skips 2 to 25. The overall number of occurrences of ישע at + 2 to + 25 in the Torah is 1441. The count of the occurrences that are symmetrical in relation to the central column (that is, the shin in the word is among those in the central column) are reported independently.

All matrices have been examined also for salvation (ישע) appearing at any skips entirely within the rectangle formed of the central column and its two adjacent ones. Such occurrence will be called “central” from now on. The central occurrences are also reported in a separate column. The purpose of this examination was to check the odds for random occurrence of the words “winding about the trunk of a tree” shown in Figure 1. Notice that there are three occurrences in accordance with this condition in Figure 1.

Results

Data obtained with matrices containing 3 letters shin (ש) in their central column

Initially, 57 randomly sampled matrices containing exactly 3 letters shin in their central column have been prepared, printed and examined for the items as described above.

The results obtained are presented in the Table and figure below.

Table 1P. Results obtained for salvation (ישע) with 3-ש matrices.

Number of occurrences of ישע at skips +2 to 25 in a matrix	Number of matrices with these occurrences	Total number of occurrences in matrices	Number of symmetrical occurrences	Number of the occurrences in the central 3-column rectangle.
0	6	-	-	0
1	17	17	4	*6
2	13	26	0	§4
3	9	27	*4	2
4	9	36	*7	3
5	1	5	0	1
6	2	12	**4	1
Total	57	123	19	17

Note: An asterisk (*) indicates a matrix containing 2 items, while a section sign (§) indicates a matrix containing 3 items of the respective quantities.

Data obtained with matrices containing 2 letters shin (ש) in their central column

In order to confirm these results, matrices containing 2 letters shin and more than 3 letters shin have been prepared. The results obtained are summarized in the tables and figures below.

Table 2P. Results obtained for salvation (ישע) with 2-ש matrices.

Number of occurrences of ישע at skips +2 to 25 in a matrix	Number of matrices with these occurrences	Total number of occurrences in matrices	Number of symmetrical occurrences	Number of the occurrences in the central 3-column rectangle.
0	3	-	-	*3
1	3	3	1	0
2	7	14	*3	0
3	6	18	0	0
4	4	16	1	0
5	0	-	-	0
6	1	6	0	0
Total	24	57	5	3

Note: An asterisk (*) indicates a matrix containing 2 items of the respective quantities.

Data obtained with matrices containing more than 3 letters shin (ש) in their central column

Table 3P. Results obtained for salvation (ישע) with more than 3-ש matrices.

Number of occurrences of ישע at skips +2 to 25 in a matrix	Number of matrices with these occurrences	Total number of occurrences in matrices	Number of symmetrical occurrences	Number of the occurrences in the central 3-column rectangle.
1	5	5	2	3
2	4	8	0	**¶8
3	3	9	2	1
4	2	8	**4	1
Total	14	30	8	13

Note: An asterisk (*) indicates a matrix containing 2 items, while a paragraph sign (¶) indicates a matrix containing 4 items of the respective quantities.

The distribution of the number of letters shin in the central column of the matrices of this group was as follows:

4 letters ש	5 letters ש	6 letters ש	7 letters ש
9	3	1	1

Discussion

The average number of occurrences of the three-letter word salvation (ישע) in Hebrew appeared to be relatively constant, independent on the number of the letters shin in the central column:

2 letters shin in the central column (Table 2P): 57/24 = 2.38 occurrences per matrix;

3 letters shin in the central column (Table 1P): 123/57 = 2.16 occurrences per matrix;

>3 letters shin in the central column (Table 3P): 30/14 = 2.14 occurrences per matrix.

On the other hand, the occurrences in the central 3-column rectangle show a high dependence on the number of shins in the central column:

2 letters shin in the central column (Table 2P): 3/24 = 0.125 occurrences per matrix;

3 letters shin in the central column (Table 1P): 17/57 = 0.298 occurrences per matrix;

>3 letters shin in the central column (Table 3P): 13/14 = 0.929 occurrences per matrix.

These results could be expected – the higher number of shins leads to higher probabilities for occurrence of a word with a shin in its centre. The same is valid for the rate of symmetrical occurrences:

2 letters shin in the central column (Table 2P): 5/24 = 0.208 occurrences per matrix;

3 letters shin in the central column (Table 1P): 19/57 = 0.333 occurrences per matrix;

>3 letters shin in the central column (Table 3P): 8/14 = 0.571 occurrences per matrix.

It is evident from the above data that the rate of occurrence of both symmetrical and central ישע in all three cases is lower than 1. This is especially valid in the cases of 2- and 3-letter shin in the central column. Therefore, it seems that the most appropriate method for evaluation of the probabilities for symmetrical and central occurrences is the Poisson Distribution.

Poisson distribution is described by the general formula

λⁿ

P(n) = ——— e^-λ

n!

P(n) is the probability for n items to be found in a matrix if the probability follows the Poisson distribution. λ is called distribution parameter and it corresponds to the overall number of occurrences of a quantity spread among the total number of matrices. e is the base of the natural logarithms.

In order to use this formula for the estimation of probabilities for n = 4 (symmetrical occurrences) and n = 3 (central occurrences) in first place we must check whether the data obtained agree with the formula.

According to the Poisson distribution, the expected number of matrices that do not contain an item (that is, n = 0) will be e^-λ; the expected number of those containing one item will be λe^-λ, etc.

Let us explore the data obtained for symmetrical appearances in the matrices containing 3 letters shin in their central column. λ, as calculated above, is 19/57 = 0.3333. It is evident from the fourth column (coloured in plum) in Table 1P that the number of matrices with two symmetrical occurrences of salvation (ישע) is 4. Hence the number of matrices with one occurrence is 19 – 4×2 = 11. The number of those, which do not contain this item, is 42. The results are summarized in Table 4P. Deviation in terms of (Expected – Observed)²/Expected is given for the purpose of calculation the chi-squared (χ²) criterion.

Table 4P. Expected values according to Poisson distribution and actual data obtained with matrices with 3 letters shin (ש) in their central column containing symmetrical occurrences of salvation (ישע) at skips +2 to 25.

Number of occurrences in a matrix	Expected		Observed (O)	Deviation
	Proportion	Number (E)		O - E	(O – E)^2/E
0	0.7165	40.8	42	+1.2	0.03529
1	0.2388	13.6	11	-2.6	0.49706
2	0.0399	2.3	4	+1.7	1.25652

The calculations with the central occurrences in the matrices containing 3 letters shin in their central column are summarized in Table 5P.

Table 5P. Expected values according to Poisson distribution and actual data obtained with matrices with 3 letters shin (ש) in their central column containing central occurrences of salvation (ישע) at any skips. λ = 17/57 = 0.2982.

Number of occurrences in a matrix	Expected		Observed (O)	Deviation
	Proportion	Number (E)		O - E	(O – E)^2/E
0	0.7422	42.3	43	+0.7	0.01158
1	0.2213	12.6	12	-0.6	0.02857
2	0.0330	1.9	1	-0.1	0.00476
3	0.0033	0.2	1

The same type of calculations for the matrices containing 2 letters shin in their central column are presented in Tables 6P and 7P.

Table 6P. Expected values according to Poisson distribution and actual data obtained with matrices with 2 letters shin (ש) in their central column containing symmetrical occurrences of salvation (ישע) at skips +2 to 25. λ = 5/24 = 0.2083.

Number of occurrences in a matrix

Expected

Observed (O)