CFLarsen said:
If you say that these are not coincidences, and complain that people have a poor grasp of probablitities (indicating that you have a good grasp), then how did you calculate the probabilities for these events?
Can you just show us one calculation, so we can see what you mean?
Or is it merely your opinion?
It's extraordinary difficult . . . nay . . impossible to precisely calculate the probability in such cases. Certainly I am not claiming that one particular coincidence is compelling evidence for anything peculiar going on.
But let's briefly consider the plum pudding coincidence to see what tentative conclusions we might be able to come to.
The question here is out of hundreds of millions, maybe billions of people, would such an occurrence be deemed to be unusual? Well ok, let's be generous and say a pool of 2 billion. So what we're talking about here is that some person out of 2 billion by "happenstance" encounters another individual 3 times in his life, and on each of those 3 occasions there is this common factor X which was implicitly involved, and, at least in the case of one individual (Deschamps), this common factor only occurred on those 3 occasions in his life.
So we have this uncommon food called "plum pudding" on the restaurant menu and Deschamps remembers it from the one occasion he tried it as a boy, he liked it, and decides to order it. But unfortunately the very last slice had
just been ordered. This guy who ordered it turns out to be Monsieur de Fortgibu, the other guy!
Now as I say, it's impossible to really calculate how unusual this event was. We would need to have specified the chances of such an occurrence happening
prior to the event. There are so many possibilities in our lives for such unusual coincidences to happen like this. Moreover, even if in a particular individuals life we judge such an occurrence to be highly unusual, we have 2 billion people to choose from! So conclusion is that this was a coincidence. I have no problem with this whatsoever.
Then we have the third time Deschamps encounters plum pudding in his life. He was invited to a dinner party, and plum pudding was on the menu! At the dinner table M. Deschamps told his little story, remarking, 'All we need now for perfect contentment is M. de Fortgibu'. At that very moment M. de Fortgibu enters! He wasn't supposed to be there, he had got lost.
Now at this stage I think a sensible person would be thinking there's something a bit fishy going on. But still, there's still a good possibility that maybe it's just a wild coincidence. After all, we just need to consider the fantastic number of permutations out of all existing people where such an unusual coincidence could have taken place.
But the problem here is that this plum pudding episode is not an isolated one. If it were an isolated incident, then fine. It was just a wild coincidence. But these incidents are ubiquitous. To say that they are
all just wholly happenstance reveals a deep unappreciative understanding of probability.