LESSONS IN LOGIC: Occam’s Razor Requires A Data Vector

This should be something most of us learned in high school. Unfortunately, especially for the younger members of our society, it isn’t taught much. So, if you already know and understand this, please bear with me while I cover this very important principle — for the sake of those among us who don’t know, or who need a refresher course.

Occam’s Razor is a philosophical principle that states, when everything else is equal, the best explanation for a given observation is usually the simplest one. To put it in very simple terms, Occam’s Razor is better known as, ‘Keep It Simple, Stupid.’

However, the point that is assumed and which so many people seem to miss is that, before we can apply Occam’s Razor to a given observation, we need to have a data vector t which we can apply that Razor. Now, what do I mean by a data vector? OK, this may sound complicated, but it is really very simple. Stay with me and I’ll try to explain it in simple terms.

A single observation can be though of as a data point. But a person cannot really apply Occam’s Razor to a single observation. For example: let’s say that I observe that I am wet. What can I conclude from this observation aside from the factual statement that I am wet? Nothing! I could be swimming. I could be standing in the rain. I might be taking a bath. A friend may have hit me with a water balloon. I simply do not have enough information to make a conclusion about how I became wet.

OK, so, a single observation represented as a data point could be displayed this way:

Now, what if I have several observations. Let’s say I observe that I am wet, it is Tuesday; there is a bird on my window sill; my mother just called; and I want to watch TV. What can we conclude from these data points? Once again, not very much. Other than that these are all factual statements, we simply don’t have enough information to draw any conclusion that connects these things together.

These scattered data points can be represented this way:

However, what happens if we have a set of observations that all start to point in a direction, like this:

See how these things all have some tangible connection? When considered together, as a group, they form a directional vector. We can represent that vector something like this:

Now we can apply Occam’s Razor. This is because we finally have enough related data from which to draw a conclusion. So, what should we conclude. From these six data points, should we conclude that there is a dog nearby? Nope. How about a gold fish? Nope again. What about a zebra? Well, maybe — if we were in Africa. This is where the ‘all things being equal’ part of Occam’s Razor comes into the equation. We are in the United States. So, even if we were in a zoo, the most likely conclusion we would draw from these six observations is that we have a horse somewhere in our vicinity.

So, what is the moral of our lesson? It’s two-fold. First, when trying to explain a series of observations, keep your explanation as simple as possible. But before you even bother to try to explain the things you observe, make sure those observations actually have enough connection between that they create a data vector.

Or, as a friend of mine once told me: if you have to use a hammer to make the pieces fit, they don’t fit. And, if the pieces don’t fit, there is no data vector. And if there is no data vector, you don’t have anything to which you can apply Occam’s Razor.

OK, I hope I didn’t bore you or sound like I was overly condescending. I sincerely hoped to help some of us understand how this principle works — especially since it can be a powerful tool in helping to unravel much more complex situations (I’ll explain how this works in later posts).