On the reincarnation page we state that the improbability of the discoveries made is rather beyond belief. We still 'feel' this to be the case, but had never sat down to work anything out on paper, mainly because the task appeared beyond our limited abilities as mathematicians.
Not so faint hearted our readers!
From a reader of the site:
From my (basic and rather poor) knowledge of probability:
If we consider the historical names to be random number generators then we may state the following:
The chance that a random number should match the day and month for an individual = 1:365
The chance that a random number should match the short form year for an individual = 1:100
Therefore, the chance that two numbers generated from a historical name should match the day, month and year of an individual = 1: 36 500.
This implies that the chances that two numbers generated form the names of an historical couple should match the day, month and year of a contemporary couple = 1: 1 332 250 000
This further implies that the chances that seven people (as in your reincarnation document) should be able to extract their dates of birth from seven historical character's names = 1: 86 307 800 930 445 312 500 000 000 000 000, which I am sure you would agree is rather remote.
We were rather impressed by the above. Using OUR limited knowledge of probability, we thought we'd check it out.
Unfortunately, we believe that the initial assumption to be in error. That is, that the numbers generated from the historical names are not really random in the sense used in the above calculations.
They are in fact related, in that they are generated from a single value. (eg 100 could become 51+49 = 5th Jan 1949, or 52+48 = 5th Feb 1948, etc).
By accepting this proposition, the odds are cut drastically.
The chance that one of the numbers extracted are going to match a birth day is also reduced to 1: 304, since the coding method used for November and December allows one number to be represented as two values (eg. 21 could be read as 2nd January or 1st November).
The chance that the other number extracted is going to match the short form version of a year remains 1:100.
Thus, the chance that any number generated from the name of a historical character may be split in a manner which matches the birthdate of a contemporary individual becomes 1: 404 (That is 1 in every 404 people will be able to extract their date of birth from any given historical character).
This implies that the chances that two numbers generated from the names of an historical couple could be split in a manner which matches the birthdates of a contemporary couple = 1: 163 216
This further implies that the chances that seven people who know each other (as in the reincarnation document) should be able to extract their dates of birth from seven associated historical character's names = 1: 1 756 586 560 892 125 184
Which is still rather remote, but slightly more manageable.
So we thought we'd throw down the gauntlet. What we really need is a mathematician (or a bookie) to work out the odds for us!
I feel certain that we have missed something pretty basic as well.
eg. is it correct to assume the 1:304 / 1:100 split at all?
What effect has the method used to generate the number from the historical name? These are not the same in each case, so can we assume that each has the same probability of generating a positive result?
Since all numbers generated from the historical characters names are reduced to a value less than 365, how does this affect the possible outcomes?
Since there is a finite number of possible dates from a given number, how does this affect the odds?
Our problem is simple, since only 23 people are required to be in a room to provide odds of 1:2 that two of them will share a birthday, it seems that the odds which we have come up with are rather extreme! Of course, the birthday problem does not include years. Nevertheless, the variance appears too much for our calculations to be correct.
We are not in the business of pulling wool over eyes, and so would be grateful indeed if anyone could come up with the 'correct' odds.
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