Andy: "What a coincidence! I was just thinking about you both and then I ran into together you here! It must be synchronicity."
Barbara: "Hmm, I don't know... Maybe you were more likely to be thinking about us in this mothball store because you noticed last week that all our clothes are holey. And even more importantly -- how many thoughts have you had in the last fifteen minutes? And how many different components did each of those thoughts have? Maybe you were thinking about us playing baseball. Then if you saw a guy walking past with a Dodgers cap, you'd have a coincidence. Maybe you were thinking about us playing baseball in the summer. Then if you saw an advertisement for a summer getaway, you'd have a coincidence. I would bet there were probably thousands of different components in the thoughts you had in the last few minutes. And, as you walk around a public place, you see thousands of different things. So that's (roughly speaking) millions of different opportunities for a sheer coincidence to happen."
Cindy: "I agree with you, Barbara. But isn't there another interesting point there? The number of 'components' you see in the world is somewhat subjective. For example, some people have never experienced significant anxiety. If they see a stranger hiding an anxiety reaction in public, there's a good chance they won't even notice the signs. They're effectively almost blind to that phenomenon, that 'component'. Or another example. Some people don't know the first thing about computers and literally couldn't tell the difference between a MacBook and an HP. So there are no opportunities for them to notice coincidences involving MacBooks. My general point is that the more features of the world we're sensitive to, the more connections we potentially see. I think you could argue that at least some of the 'meaningful' feeling of life comes from the sheer amount of different layers and modes of organization in the world. The fact that you can look at a spoon and describe it a hundred different ways -- in terms of metallurgy, the history of its invention, the economics of production, the way reflections work on concave surfaces. And that traces of all those 'components' are dancing around in the backgrounds of our minds all the time, giving us a rich feeling of connection to the world."
Another example. 10! (10 factorial) seconds is exactly 6 weeks. What does that coincidence mean? On one hand you could say: what are the odds that any factorial would correspond to a small integer number of weeks? The factorials blow up quickly, so there are only a few possible candidates. In that sense you could say the probability is miniscule. On the other hand, a minute is 60 seconds and an hour is 60 minutes. That gives you 5, 3, 2, 2 twice as prime factors, which is great for factorials. Why do we have 60 seconds in a minute? It probably has something to do with 60 having nice divisors. Like 59 would be annoying. And so on.
You could visualize all those relationships as forming this ever deepening tree, as you probe more into it. So what does it mean that something is a coincidence?
