Coincidences And Complexity

I have developed a method for measuring the complexity in very complex systems. This method is based on what we refer to as "coincidences".

We are all familiar with coincidences. Suppose that a five-dollar bill or a five-pound note caught your attention because it's serial number was exactly the same as your phone number. That would indeed be a coincidence.

Coincidences, of course, vary in magnitude. Suppose you were in a small town on the day that there was a market in the town. You happened to pass a certain person as you were shopping in the market. On your way home, you stop at a store in the town to get something that was not available in the market and you happen to encounter the same person again by random chance. This would be a coincidence.

Now suppose you were in a big city. You went to the other side of the city to shop at a market and you passed a certain person in the market. On your way home, far away from the market, you stopped at a store and encountered the same person again. This would not only be a coincidence but a far greater coincidence than the one that occurred in the small town.

The reason it would be a greater coincidence is that the chances of it happening in the big city would be much slimmer than in the small town. Of course, for this to be so, it must be a genuine coincidence and cannot be encounters between two people travelling on the same bus or where one is following another.

One reason that complexity is so tricky to measure is that we often do not see a system in it's real complexity. That is, there may be a difference between actual complexity and apparent complexity. The way that complexity is related to coincidence is that a coincidence can be defined as a random reduction in apparent complexity. When you experience the coincidence of meeting the same person in the city or town, the "system" (the city or town) is made to seem as if it were much smaller, in other words much less complex, than it really is.

Suppose you are calling for tech support or some kind of customer service to a call center that has a hundred operators, but you do not know that. If you by a one-in-a-hundred chance got the same operator twice, it would be a coincidence and would make it seem that the call center must be much smaller, less complex, than it really is. Such a coincidence would thus be described as a random reduction in apparent complexity.

This means that there is also such a thing as a "reverse coincidence". If you had a company that called the call center a hundred times and just by random chance got a different operator on each call, it would seem like there would have to be many thousands of operators there, making the call center seem much bigger, more complex, than it really is.

I have noticed something about coincidences. If we were to make a given type of system much more complex, the average number of coincidences will remain the same but will be greater in magnitude.

Suppose that the residents of a small town go out and randomly select ten names from their town and the residents of a big city do the same. The average number of people in the town and the city that selected each other will average out the same. This is because each person in the city has much less chance of being in such a coincidence than each person in the town, but this is cancelled out because there are so many more people in the city than in the town.

I should point out that not all complex systems have coincidences. For example, in a car engine there is nothing that we could easily measure that could be termed a coincidence. But in the more complex systems, such as the flow of money in an economy, there are measurable coincidences. A person could get the same bill with the same serial number twice by random chance.

Let's term those complex systems which we may wish to measure but do not manifest measurable coincidences "closed" or "integrated" complex systems. Let's term those systems which do manifest coincidences that we can measure "open" or "non-integrated" complex systems.

The good news is that closed complex systems tend to be simpler and easier to measure by other means, as I described in my other postings on this subject. Closed complex systems will tend to be man-made machines. In the world of coincidences, we could say that one is actually zero since there is no coincidence until the same unit is encountered twice.

The great thing about this coincidence method is that numbers of observed coincidences can give us a lot of information about a complex system without us knowing the size or all of the details about the overall system. In a perfectly fluid system, the size of the system can be estimated by the coincidence rate multiplied by the size of the control group.

An example of perfect fluidity would be a unit of currency in an economy flowing equally through all areas of the country. Think of all that could be discerned about a country's economic system, for example, if a given number of observers (the control group) recorded the serial numbers of all the given monetary units that passed through their possession during normal activity in the course of a year.

The total number of recordings in each geographical area would be recorded and then all the serial numbers that occurred only once would be discarded. The remaining data of coincidences, those numbers occurring two or more times, would tell us a vast amount about the complexity and operation of the economy that would be very difficult to learn any other way.

The first thing to do to measure the complexity of any given system is to find one or more types of coincidence that take place and then measure those coincidences. This will enable us to put an exact measure on the most complex of systems and can be done with incomplete knowledge of the system. Using this method, we can use the random reductions in the apparent complexity of a complex system, that we refer to as coincidences, to measure the actual complexity of the system.

You have probably heard of the Guinness Book of World Records. You can read more about it on Wikipedia if you like. It is a book of records which is revised yearly. The book contains hundreds of categories of world records such as the longest-lived person, the tallest and, who could eat the most chocolate cakes.

I have thought of a record which anyone could possibly break at any time, without even trying. Unfortunately, this record is not categorized in the book as of yet. But maybe someday it could be.

Coincidence involves the set of all potential results in comparison with those results which actually do happen. If the actual results make the set of all potential results appear to be less than it actually is, we have a coincidence. If more than it actually is, we have a reverse coincidence.

Coincidence involves a valley of odds between two hills of higher odds on either side. One hill represents coincidence, the other represents reverse coincidence. We distribute points, representing every event that happens. Odds are that each point will fall in the valley, but some happen to fall on the coincidence hill and some on the reverse coincidence hill.

An obvious example of a great coincidence would be the same person winning a lottery twice. Minor coincidences and reverse coincidences happen to us all of the time, but that is not what we are concerned with here. I think that the ultimate world record would be the greatest coincidence ever.

At this point, we are not really capable of measuring coincidences other than subjectively. We must carefully define the system involved, since all coincidences happen within some system. Two neighbors meeting, by chance, on the opposite side of the city would be considered as a coincidence. But it is much less of a coincidence if they rode there on the same bus or were there for the same reason. The scale of a coincidence is equivalent to the size of the system in which it takes place.

I define coincidence as a random reduction in apparent complexity. But this definition says that coincidences do not really exist in absolute reality. In the entire universe as a whole, there is actually no such thing as a coincidence, everything has a definite cause and effect.

"Random" and "apparent" are words associated with our perspective. There appear to be coincidences in systems that we define because we do not have complete information and our system is not as definite as we think it is. Coincidences are related to chaos, of which there is really no such thing. The occurrence of coincidences and reverse coincidences can only mean that we have incomplete understanding of the systems involved. Of course, due to our incomplete understanding, there are many "coincidences" that we are unaware of.

Coincidences are a manifestation of complexity. To be able to measure coincidences, which will reveal a lot about the operation of the reality around us, we must first be able to measure complexity. A the present time we are unable to measure complexity, except to describe it in general subjective terms, so we cannot actually measure coincidences.

This is unfortunate because the world gets more complex every day in terms of communications, interconnections and, population. Anyone could become a part of the greatest coincidence ever simply by going about their ordinary daily business.

Suppose you were at an amusement park as a child, standing in line to go on a ride. There is an odd number of people in your group and the group in front of yours also has an odd number of people, so that you end up sitting in the ride with a child you do not know.

Years later, in your twenties, you order a book to be mailed to you. Although you are both unaware of it, the person who packs your book order is the child who was once on the amusement park ride with you.

Years after that, while you are in your forties, you are driving across the country and you find yourself in a minor traffic accident. Although either of you have no way of knowing it, the driver of the other car is the neice of the child that you were on the ride with and the one who packed your book order years before.

Such is what we could call a "multiple coincidence", a random reduction in the apparent complexity of the world we live in.

Just imagine the possibilities if we could measure complexity, as I am trying to get us doing on my patterns blog, and thus coincidences. There would be a world record category for the greatest coincidence ever documented, and verified to have happened beyond the control of those involved. There could be a "Book of Coincidences".

Even if we could effectively measure coincidences, there would still likely be some subjectivity involved because some coincidences will surely be more important to us than others, regardless of the actual magnitude.