The following happens to me. I have a singular thought, something I haven’t thought about in the past thirty years. With 24 hours that shows up in my life, some matching event that also hasn’t occurred in the past thirty years. A few days ago it went like this. The thought passed through my brain of gorillas beating their chests. The next day I went to see and hear a barbershop quartet. In the course of a song they beat their chests like gorillas. This sort of thing has occurred hundreds of times. What’s going on?

When I sat down and did a mathematical analysis I was surprised to find out that there’s nothing terribly unusual about this. It goes as so.

Thirty years contain more than 10,000 days so the observed probability of any singular thought is less than 1/10000. Similarly the empirical probability of a given singular event is less than 1/10000.

Now let τ be the number of singular thoughts I have per day, let ε be the number of singular events that I notice per day, and let π be a pair, a pair of a singular thought τ followed within 24 hours by a matching singular event ε. The more singular thoughts τ, the more pairs observed in the course of a day. The more singular events ε, the more pairs observed. Both matter so what we are interested in is τε, the product of the number of thoughts and the number of events. Divide by 10000 to get the average number of pairs seen per day.

π < τε/10000

That’s it. That’s all the math.

Now let’s consider this for any old observer, not just me. Their τ, ε, and π will be different, but the equation still holds. The number of singular thoughts a person may generate and the number of singular experiences that register in their mind depend largely on them, but the equation still holds. and we can calculate their the average number of pairs they can be expected to see during a day. There are some obvious conclusions. If a person never has a singular thought then that person will never observe a pair. If a person never has a singular experience then that person will never observe a pair. If someone has about one singular thought and one singular experience per day then they will observe at most an average of one pair per thirty years. If someone has one singular thought and ten singular experiences per day then they will observe ten times as many pairs per day, making for one every three years. Same if they have ten singular thoughts and one singular experience. If someone has about ten singular thoughts and ten singular experiences per day then there are one hundred possible matches. They will observe an average of one pair every one hundred days. If someone has about one hundred singular thoughts and one hundred singular experiences per day then they will observe an average of one pair every day. That would be wild.

I can estimate my own personal value of π. I’ve observed such a pair roughly once a month. That makes my π about 1/30. Then my personal τε is greater than 333.3.

10000π = 10000/30 = 333.33…. < τε

While we can’t unconfound τ and ε to find my personal values of these quantities, we can draw some conclusions. Maybe my personal τ and ε are both 18. That would work. That means I have about 18 singular thoughts per day and 18 singular experiences as well. Hmmm, my mind isn’t that random. How about four singular thoughts per day. Then to observe that many pairs I would have to have maybe ninety singular experiences per day. I am very much a seeker after novelty so that could be.

Your milage may vary.