There have been countless millions of bizarre coincidences reported and there is nothing worth being investigated?
Rodney,
Do the following examples help?
(A)
Suppose you watch a Bridge player being dealt his hand of thirteen cards. How long would you have to wait till he is dealt thirteen hearts? Answer: several million years. But, instead of thirteen hearts suppose you were looking out for the following hand:
2s, 6h, Qh, 7d, Jd, 5c, Ks, 2d, 8c, 8s, 10d, 4s, 6s
How long would you have to wait? Again, several million years. However, if the Bridge player is dealt the hand shown above, there will be absolutely no reaction. On the other hand, if he is dealt thirteen hearts, he will think it was nothing short of a miracle.
Every hand has the same probability of being dealt (about 1 in 600 million), but it is only the ones with a
pattern that provoke a reaction.
In other words, very improbable events occur all the time but it's only when we perceive a pattern, that we take notice and think something amazing has happened.
(B)
You walk around the streets of your local town and take down the birthdates of randomly selected individuals you meet on your journey. How many people would you have to meet before there is a 50/50 chance that two will have the same birthdate. The answer is 23 people (and, if you can be out by one day, the number is 14 people!). Doesn't sound right does it? You would think that it would be something more like 600 people. In fact, if you go out specifically looking for two people born on the 4th July, you WILL need more than 600 people before there is a 50/50 chance.
Coincidences can seem "amazing" because we apply the wrong probabilities. We are "amazed" only because we apply the probabilities of obtaining a specific match (requiring 600 people, in this case) to a situation which is really only a random match (requiring only 23 people).
(C)
When we trawl for patterns in random data, it is easy to think we find them much more frequently than we would expect to by chance. Again, this is because we are looking for ANY pattern, not a SPECIFIC pattern, but we apply the probabilities of the specific pattern that we just happen to find. Also, we stop when we find it, not realizing how long it could take before we would find it again.
For example, the decimal expansion of Pi is a well known set of random numbers. If we trawl it for patterns, we find, for example, a sequence of 10 even digits by the time we get to the 78th digit. That is equivalent to getting a sequence of ten heads in 78 flips of a coin. The probability of a sequence of 10 heads is actually once in 1024 flips of a coin. So we have an amazing coincidence here don't we? Well, not really. The sequence doesn't occur again in the first 1000 digits of Pi.
BillyJoe