What is coincidence? Is it something important or an annoyance about something we don't quite understand but which will be explained later on? Is coincidence a result of our engineered world, the world that man has created and can see or measure, or is there something that goes much deeper?
Some authors claim that coincidence is normal and that our world is somehow small or getting smaller, that we should be able to see coincidence a not much more than an engineering phenomenon resulting from purely physical laws. The problem with this logic is that it begs a question as well as throwing the baby out with the bathwater.
One of the great steps humans have made is to understand the nature of such phenomenon as electricity, radio and microwaves. We now have a strong body of science that shows how things work at the minutest level. Along with this growth of knowledge and technology, there is growing scepticism about unseen forces. We only have to look around us to see that humans engineer unseen forces all the time, that man has become master of a world of unseen capabilities allowing computation and control. What we cannot see, many will not believe. What their parents did not see, they can't either.
Along with realism and inherited habits is a flood of scepticism. We have not got to the point where the human mind seeks to know for the sake of knowing. We think and say that we have an inclination to understand a greater reality, but in everyday reality our scientists confine themselves to small enclaves of scepticism within which all is comfortable and tidy, even when our reality tells us that nothing is comfortable for long, nor neat and tidy for long. This blinkering of our willingness to be out of the box confines most human minds to the box.
It is normally too much effort or costs to much in one's career to try, even try, to think out of the box. It is easier to be told what to think, not have to think. We want to believe a reality in which we are with the majority. Most people, for example, cannot believe in a reality that has not be condoned by their parents. They say for example that smoking is good because Dad or Mom smoked therefore it will do me no harm. By not thinking out of the logic boxes of their parents, people lose their longevity. They die sooner than they should. They give up sooner than they should and they are less than they can be! I am reminded how hard it was to get people over forty to use microcomputers in the 1980's.
I am not saying that people should not try to see behind coincidences. I am say that the observation of inexplicable coincidences should not be reduced to mathematics. Coincidences are not mathematics they are physical events that happen for very real reasons. They point us in the direction of forces we don't believe in or which we would never have conceived.
In the practical world all this about coincidence has relevance when we cope with coincidences that are the result of strong physical forces. Think how hard it was to get economists to use non-linear modelling techniques even though the world is almost totally non-linear. Think how hard it is for ordinary people to see the work of inflation and understand its implications.
Our reality is that we see coincidences, but fail to understand them as the work of cooperative or competitive underlying forces. We see people dying from the effects of smoking cigars, but don't connect this with people dying from the smoking of cigarettes or pipe smoking. Because not so many people die from cigars relative to cigarettes, the deaths from cigars may be enormously underestimated. The reality is different and the coincidence of a relationship is of a stronger association than our minds lead us to believe.
Associations are coincidences that we observe most of the time. Factorial or canonical, geometric, indirect, and non-linear associations we don't observe and they don't appear as coincidences. Such associations can be deadly yet we ignore them because our minds do not see the coincidence.
The coincidences that we can see provide us with opportunities to understand associations between things or realities and non-things or non-realities, such as abstractions. For example, God is an abstraction to most people. What we associate with God reveals many things about how we approach our realities. If there exists a force that is an abstraction, we may or may not be aware of it because we do not understand the coincidences that this force produces. Thinkers such as Arthur Koestler and Rupert Sheldrake are controversial to those that think of the universe as being very tidily physical and a result of natural engineering.
Associations that include messy associations such as hidden unknown forces do not conform to existing physics and prevalent ways of thinking in institutions earning their bread and butter from salaries of patrons convinced that physical truths are the end of the story.
Although mathematics is used to dismiss coincidences, often the mathematics is flawed and about as good as the mathematics of hedge funds, and you know what happened there. Mathematical statistics itself has multiple schools. The improbable does occasionally happen and when it does it changes everything. Yes, California will get its massive earthquakes and Florida its great floods even though you or I may not ever live to see either.