Saturday, December 12, 2015

The nine-dot puzzle and connecting "outlying dots"

image: Wikimedia commons, with dots added (link to original).

The "nine-dots puzzle" is often presented as an exercise in "thinking outside the box," and it most certainly is that.

But it is also an excellent metaphor for the process we undergo as we deal with the data life presents to us and as we attempt to find paradigms which help us to understand that data. 

The puzzle is a thought-exercise in which nine dots are arranged in three rows of three (or three columns of three, whichever way you choose to look at it), similar to the arrangement of a "tic-tac-toe" pattern. The illustration above shows the arrangement for the puzzle.

The goal of the game is to try to connect all nine of the dots, using only four straight lines, without picking your pencil (or pen) up off of the paper (or writing surface):

If you have never had the opportunity to wrestle with this particular puzzle, and would like to try it for yourself without reading any discussion that might give away the solution and thus spoil the fun of the game, please stop reading now and come back later!

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Readers who are familiar with the possible solutions will know that in order to connect all nine of the dots with only four straight and connected lines, you have to be able to "think outside the box" and draw the lines beyond the boundary of the implied square that the dots make by their arrangement. 

Obviously, there is nothing in the rules of the puzzle as stated which forces you to draw the lines within the borders of the square created by the outer dots. That invisible boundary is only "self-imposed" -- and yet it will prevent you from finding the solution until you can see that you don't need to stay within the "mental cage" that we unthinkingly impose on ourselves when presented with this puzzle for the first time.

So, the nine-dots puzzle is an excellent illustration of that tendency, and of the need for examining our own "self-imposed barriers" in other situations in our lives -- situations that may involve more data-points than just nine dots arranged on a page.

But I believe the nine-dots puzzle can also provide an additional, related illustration of the way we tend to impose "paradigms" or "frameworks" or "filters" through which we view the myriad data-points or "dots" which we find in the world around us during our journey through this incarnate life. In many ways, we do this out of necessity, in order to be able to make sense of things, beginning when we are very small and progressively altering our paradigm or framework as we grow up and encounter new data-points or see new ways of connecting ideas or explaining events.

The question that this puzzle illustrates very well, in my opinion, is the question of "What do you do, when you find that the paradigm you are using leaves out important dots?"

This is the question that is worked out in most of the mystery stories and "CSI television shows" that we enjoy, going back to the formula used by Arthur Conan Doyle in the Sherlock Holmes stories (or in the Scooby Doo television series from the late 1960s and early 1970s, or in the pioneering mystery stories written by Edgar Allan Poe in the first half of the nineteenth century).

In those stories, "the authorities" usually have a theory or thesis that they are using to explain the evidence or clues that they have found -- a paradigm or framework with which they are "connecting all the dots," so to speak. Then, the outsider in the story (such as Sherlock Holmes, or Scooby and the gang) comes into the picture and discovers a few more "dots" which the solution offered by the authorities leaves out. 

Above: Four lines which attempt to connect all the dots -- but Sherlock Holmes (or Shaggy and Scooby) might ask, "What about these two dots over here?"

Through the course of the investigation, a new outline or framework to connect all the dots emerges, leading to a new way of understanding the situation (and often revealing that the culprit was someone quite different from the person implicated in the original storyline accepted or promoted by the authorities). 

I think this is a very helpful metaphor which is applicable in many different situations -- from the way we choose to understand important events in history, to the way we interpret the "big questions" regarding the meaning of life and our purpose here in this material world.

By virtue of the fact that this material-spiritual universe in which we find ourselves contains far more than "nine dots" for us to try to understand, there are an almost-infinite variety of paradigms or frameworks or "shapes of the lines" which people adopt in order to try to make sense of the world around them.

When we find one that seems to work as an explanation, we can be very resistant to letting go of it, even if we start noticing some suspicious dots that our framework doesn't seem to include or connect very well. 

There is actually good reason for being somewhat resistant to casting aside a paradigm which we have adopted over the course of time and which seems to do a reasonably good job of explaining and connecting the dots we have encountered over the course of our life. Data-points which originally looked like "outliers" may turn out to have been illusory, or deceptive, or irrelevant for some other reason. New paradigms which someone offers and which seem to connect these new dots may in fact ignore other dots which our old framework did explain, but which the new framework asks us to forget about.

We don't want to be too careless about jettisoning one paradigm which seemed to explain the universe (or some historical event) and adopting one that radically re-draws the lines in a shape that was totally different from what we were using before. Because of this, people are usually very resistant to doing so, and with good reason.

But, as the stories of Sherlock Holmes or Scooby Doo or Edgar Allan Poe (and countless others, including many from real life) all illustrate, there are in fact times when the outlying dots are important enough to cause us to re-evaluate even our most cherished and tightly-held explanation or belief system. 

There are times when our paradigm-driven interpretation or understanding of the events that are going on in the world around us is actually deeply mistaken, and when continuing to use a mistaken paradigm or framework will actually lead to very serious negative consequences.

Although it takes a lot to let go of a framework or paradigm that we have held for a long time and which seemed to "connect all the dots" for us for many years, sometimes it is necessary. Most of us have probably had the experience of doing so at least once or twice already.

I have already explained in the past (in many interviews and in the introduction to my most-recent book) that the world-view or paradigm provided by a literal interpretation of the scriptures collected into what we today call the Bible seemed to "connect all the dots" very well for me for many years of my adult life.

However, the more evidence that I found which indicated that the stories in the Bible -- virtually from first to last -- can be shown to allegorize the features and motions of very specific constellations, the more I had to question whether the shape of the line I was using as a framework or paradigm was accurate. Eventually, I saw "enough outlying dots" that I was forced to alter my understanding of the way they all fit together.

The same sort of process can also be applied to the framework of history, or to specific historical events which have had a great impact on the direction of geopolitical events. I believe that the analogy of the "nine-dots puzzle" is very helpful in this regard, and that it can remind us to always be sensitive to the possibility that the way we are interpreting events or the relationship between data-points might be completely mistaken and in need of serious revision.

Of course, I also think that spending as much time as possible looking at the stars and identifying constellations will help anyone to become better and better at "connecting the dots"!