bluetriangle
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- Jan 27, 2024
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Hi there. I wonder if someone could help me with an unusual probability calculation. The first 107 decimal digits of tau (2pi) contain a mirror pattern and I wanted to calculate the probability of occurrence. The decimal expansion of tau will contain infinite copies of this and other mirror patterns, and I'm aware that this apparent pattern is chimeric, but it is pinned to the first decimal digit and the numbers are structural components in a second-iteration Koch snowflake (in numerical geometry) and, incredibly, through the name 'Jesus Christ' in three languages: Biblical Hebrew and Greek and modern English. These gave been converted into the numbers 151, 115 and 205 under the ordinal value system of alphabetic numeration, where, for example in English, A = 1, B = 2, C = 3, . . . . Z = 26.
Here are the first 108 digits of tau, including the first 107 decimal digits.
6.28318530717958647692528676655900576839433879875021164194988918461563281357241799725606965068423413596429617 . . . .
Here is the pattern
Since tau cannot be altered, what I'm really wondering is what is the probability that the names have somehow been guided to achieve coincidence with this pattern. Here's what I've done so far. Let's call the three rows A,B and C (my difficulty is with C, because it's slightly different, not parsing internally like the first two numbers).
A Firstly, the probability of the 151 115 115 151 mirror pattern.
There are ten digits, 0 to 9, so there is a 1/4.5 probability of hitting any number as we sum along the string. Secondly, there are two possibilities, 115 or 151 for the first hit but thereafter the pattern is set. So I say the probability of the 151 115 115 151 pattern in the first row is
B Secondly, the parsing phenomenon in the second row.
There is a 2/4.5 probability each time of the number parsing into the ordinal value of the given name an title. So the probability of it happening each time is
Of these, eight could be regarded as ordered:
Since the parsing phenomenon is independent of the mirroring pattern, I make the overall probability, by (1) and (2)
So, taking (1) and (4) we have an overall probability of the three numbers mirroring of
So my final probability of the occurrence of this phenomenon, by (5) and (6), is
This seems extraordinary and I think it good evidence (if correct) for a teleological (goal-directed) process influencing the development of these names. Could someone offer any advice on the calculation, show me where I went wrong, or offer a better way of calculating it?
One other thing: the total sum of the 107 digits is 532 and 532/107 is 4.97. The average eventually settles down at 4.5, which is why I used that as the denominator. But would it be acceptable to use 5 as the denominator?
Thank you in advance.
Here are the first 108 digits of tau, including the first 107 decimal digits.
6.28318530717958647692528676655900576839433879875021164194988918461563281357241799725606965068423413596429617 . . . .
Here is the pattern
.
Since tau cannot be altered, what I'm really wondering is what is the probability that the names have somehow been guided to achieve coincidence with this pattern. Here's what I've done so far. Let's call the three rows A,B and C (my difficulty is with C, because it's slightly different, not parsing internally like the first two numbers).
A Firstly, the probability of the 151 115 115 151 mirror pattern.
There are ten digits, 0 to 9, so there is a 1/4.5 probability of hitting any number as we sum along the string. Secondly, there are two possibilities, 115 or 151 for the first hit but thereafter the pattern is set. So I say the probability of the 151 115 115 151 pattern in the first row is
p = 2/4.5 x 1/4.5 x 1/4.5 x 1/4.5 = 1/205 or 0.0049
The pattern could have started at the first digit (6), rather than the first decimal digit, so that doubles the probabilities, giving
p = 0.0098 (1)
B Secondly, the parsing phenomenon in the second row.
There is a 2/4.5 probability each time of the number parsing into the ordinal value of the given name an title. So the probability of it happening each time is
p = 2/4.5 x 2/4.5 x 2/4.5 x 2/4.5 = 1/26, or 0.039
However there is the order to take into account. If we take the given name as G and the title as T, there are sixteen permutations.
GGGG GGGT GGTG GTGG TGGG GGTT GTGT TGGT GTTG TGTG TTGG GTTT TGTT TTGT TTTG TTTT
Of these, eight could be regarded as ordered:
GGGG GGTT GTTG GTGT TTTT TTGG TGGT TGTG
So there is a probability p of 1⁄2, or 0.5, that one of these patterns would randomly occur. Therefore the parsing phenomenon has a probability, p, of
p = 0.020 (2)
Since the parsing phenomenon is independent of the mirroring pattern, I make the overall probability, by (1) and (2)
p = 0.0098 x 0.020 = 1/5100 or 0.00020 (3)
C Row 3, the second mirror pattern: 205 205.
This is where I'm least confident. It's a different pattern and I don't know if it's valid to include it in the overall calculation. But I'll continue anyway.
The probability of the number 205 being mirrored over the same number of digits (107) is given by
This is where I'm least confident. It's a different pattern and I don't know if it's valid to include it in the overall calculation. But I'll continue anyway.
The probability of the number 205 being mirrored over the same number of digits (107) is given by
p = 1/4.5 x 1/4.5 = 1/20 or 0.049 (4)
So, taking (1) and (4) we have an overall probability of the three numbers mirroring of
p = 0.0098 x 0.049 = 1/2082 or 0.00048 (5)
The number 205 doesn't parse into 87 (Ihsous) and 118 (Christos) so that has to be taken account of. There is a 2/4.5 probability of parsing and a 2.5/4.5 probability of not parsing, so we have
p = 2/4.5 x 2/4.5 x 2/4.5 x 2/4.5 x 2.5/4.5 x 2.5/4.5 = 1/83 or 0.012 (6)
So my final probability of the occurrence of this phenomenon, by (5) and (6), is
p = 0.00048 x 0.012 = 1 in 174,000, or 0.0000058
This seems extraordinary and I think it good evidence (if correct) for a teleological (goal-directed) process influencing the development of these names. Could someone offer any advice on the calculation, show me where I went wrong, or offer a better way of calculating it?
One other thing: the total sum of the 107 digits is 532 and 532/107 is 4.97. The average eventually settles down at 4.5, which is why I used that as the denominator. But would it be acceptable to use 5 as the denominator?
Thank you in advance.