I’m sceptical of the attempts to calculate the probability of paranormal phenomena, especially those strange or “meaningful” coincidences that psychologist C. G. Jung called ‘synchronicity’.
For example, in his book Synchronicity, Jung discussed the research of Dariex, Richet, and Flammarion who used ‘probability calculus’ to determine a probability of 1 : 4,114,545 for telepathic precognitions of death happening by random chance.
If you don’t know calculus, you don’t have to be intimidated by that. There is more involved in determining whether something happened or didn’t happen than mathematics. As someone who investigated accidents and their consequences for forty years, I know that too well.
Suppose you’re standing at the corner of a busy intersection waiting for a traffic light to change, when a bird dropping falls from the sky and lands on your head. For some reason you decide that you want to know the probability of that.
Before you do any calculating at all, you have to know exactly what happened, which means you need to know the full context in which it happened.
First of all, you need to know what species of bird it was, not only so you can know something about the behavior of the bird, but also to get a general idea of its frequency in the area. But you probably never saw the bird, so you probably will never know that.
That means, at a minimum, you have to determine (1) how many birds of all species live in the vicinity of the intersection, (2) how often other birds that don’t live in the vicinity pass by, which directions they fly in, at what hight and speed they usually fly at, etc.
Then you need to know the time of day when this happened. Hopefully you looked at your watch or phone as soon as it happened. If not, you can only estimate.
If you do know the time when it happened, and you live in a big city, you can determine how long you could have waiting there on the sidewalk by contacting the appropriate City department to determine what the timing of the lights was at that time on that specific day. The timing of intersection lights is altered more often than you think. They often change their sequence several times during the day, and switch to others on the weekend.
Once you have the timing report though, don’t be too quick to congratulate yourself on this apparently firm evidence. Trial lawyers have successfully challenged the accuracy of those reports.
You should also know something about the number of other pedestrians on the sidewalk who might have prevented you from standing in that spot. You can get an estimate of this by going back to the intersection on the same day of the week, at the same time to count pedestrians. But if you want to be reasonably accurate, you will have to go back on that same weekday several times, then average your results.
The weather may be a factor. You can get a detailed weather report from weather offices for the day and time of your incident, but weather in specific locations can be different than the overall weather in your area so you can’t be absolutely sure of anything here either.
You should also know the digestive cycle of the bird, but how you would ever find that out I can’t tell you.
The time of day changes the frequency and direction of bird flights. If there are overhead wires above the spot where you were standing, you will need to do a study of the birds to see how they use them, and whether and/or how often they release droppings from that position, especially at the time you received one. Your bird might have been sitting on a wire when it targeted you.
Did it deliberately target you? That might sound preposterous, but I’ve been watching birds since I was a boy and I’m convinced that they occasionally do this to people, house cats and probably any other animal that offends them.
Any math calculation, whether it is about a precognition of death or the activity of a bird, that is based on chance, becomes invalid if intention is involved. Precognition could involve unconscious intention.
Anyway, those are just my preliminary thoughts on the investigation needed to calculate the probability of a bird dropping landing on you.
I hope you see that the accuracy of any calculation re an event in the real world, using calculus or any other mathematics, and no matter how talented the mathematician might be, must be unreliable.
In the case of an incident like I described in my post God likes Tolstoy more than me, I suspect the improbability of that occurring by chance approaches infinity.
Of course, there are exceptions. Many will refer me to psychologist J.B. Rhine’s extensive studies of people attempting to read the face of cards hidden from them (remote viewing or clairvoyance). But this worked because Rhine understood the need for simplicity in a psychological experiment. Those were events in a laboratory. The world we live in, where paranormal phenomena occur, is more complicated than a deck of cards.
Maybe when supercomputers, vastly more intelligent than any human, arrive later in this century, or the next one, that will change, but I suspect it might take a thousand years to get to the kind of calculation the Dariex mathematicians aspired to.