Saturday, November 25, 2006

More Songs About Elephants and Food

The other day, having my own peculiar interest in elephants, while researching the subject, I stumbled across an interesting page of elephant jokes. Among these were the following:

How do you get three elephants into a taxi?
One in the front, next to the driver, and two in the back.

How do you know there's an elephant in your house?
There's a taxi outside with two impatient elephants.

How do you know if there's an elephant in your refrigerator?
There's a taxi outside it with two impatient elephants.

These excellent elephant jokes were reminiscent of one I had heard and remembered from my youth:

How do you fit six elephants in a Volkswagen?
Three in the front, and three in the back.

Upon reflection, I realized that there is a lesson buried in this seemingly illogical humor, a lesson in problem-solving. Problems often seem, at first blush, impossible to solve. Elephants are very, very large animals. At the time I had heard the joke initially, about 40 years ago, Volkswagens came in two distinct and distinctive types: The original Beetle, and the Bus. Neither of these was large enough to accomodate a single elephant. The Beetle had a time holding more than two people due to the smallness of the back seat area.

Of course, it wouldn't be an elephant joke if it made sense. An elephant joke, like a David Lynch film, doesn't seem to make any sense initially. However, to quote from one of my favorite films by David Lynch, "Lost Highway," "There's no such thing as a bad coincidence." Elephant jokes have an internal set of rules, unlike almost any other joke form. They do not follow the rules of ordinary jokes, but there is an internal logic, and a logical consistency in their illogic.

Okay, where am I going with this? Oh yes, something about problem-solving, and putting six elephants into a Volkswagen. Is it impossible to fit six elephants into a Volkswagen? No, not at all.

Do I see your eyebrows raising? Is this some kind of trick? No, it is not. If we apply the logic of analysis to the problem, we see that the first step is to accurately define the problem. The human brain is a remarkable device, capable of feats of perception and calculation that dwarf the capabilities of the most powerful of computers we have yet to create, and possessing intelligence that artifical intelligence can only mimic in clumsy and minscule ways. In fact, it is so vast and complex that it is somewhat unreliable. We have the capacity (by necessity) of being able to perceive only a portion of something, and construct an intelligent model of the whole, with more or less accuracy, depending on the circumstances.

In fact, it is not the thing itself that we perceive, but the model that we create in our brain. For example, driving down a "Lost Highway" late at night, we may see a small pair of bright lights at a distance, which move only a little, and yet relative to one another, they seem to remain in the same configuration. As we observe the shape and configuration of these lights, and their subtle left, right, up, and down movement, we begin to buid a model of a vehicle in our brains. Depending upon the visiblity and distance, combined with our experience in driving, and our knowledge of automobiles and similar human vehicle constructions, we may begin to fill in some of the details. We "see" a car, estimate its' size, speed and distance, perhaps even something about its' make and model.

As the lights begin to grow in size, we presume that the vehicle is approaching us. We estimate the time it will take before we will be in close proximity to the vehicle, and develop a navigation plan that takes the vehicle, its size, distance, and so on, and includes instructions for avoiding a collision.

The crux of the problem here is, when we get close enough, we realize that we have not been looking at the headlights of a vehicle at all, but a pair of reflectors on the rail along the side of the road. In fact, our model was flawed. Of course, we immediately revise the model and continue with the plan, taking into account the new parameters of the model.

The point I'm making is that, when analyzing a problem, we are presented with limited information, no matter how well the problem is explained to us. Because of the nature of the way we think, we are prone to make assumptions about the missing information. In the case of the elephant joke we are discussing, we envision in our minds a Vokswagen Beetle (old or new, depending on our life experience), and taking into account the context of the "problem" (an elephant joke), we also model six full-grown elephants, crammed into a tiny car.

The image/model we have created is undeniably humorous; it is ludicrous. And, with the proper sense of humor operating, most of us laugh at the silliness of the idea. Of course, some of us lack an appreciation for that sort of humor, and may grimace, look crestfallen, or respond in some other less-than-positive manner. But that is the exception, not the general rule.

However, looking at the joke as a problem to solve, while it may seem at first glance to be a ridiculous impossibility, that is only because of the assumptions we have made, due to the intent of the joke. Good analysis tends to minimize assumptions, a skill which is not easily acquired, because we are trained from birth to make assumptions, and for good reason. Our perception is, after all, limited. Our ability to make assumptions, to build working models that provide intelligent guesses about missing data, constitutes an important aspect of our ability to survive and prosper in life.

In fact, breaking down the "problem" into its' actual consituent components, with nothing added, no assumptions made, we are left with the following:

  • The goal is to fit six elephants into a Volkswagen.
  • There is nothing specific regarding the elephants in the requirement.
  • There is nothing specific about the Volkswagen in the requirement.
  • There is no specification that the vehicle may not be altered.
  • There is no time limit regarding the achievement of the goal.

Obviously, fitting six fully-grown average elephants into a Volkswagen Beetle is an impossibility. However, elephants, when they are born, are only 2 1/2 - 3 feet tall, and weigh in the neighborhood of 250 pounds. One could easily imagine fitting three of them into a Volkswagen Beetle.

However, the type of Volkswagen is not specified. One could almost certainly fit six infant elephants into a Volkswagen bus. I would not be surprised if, in fact, this has never been done.

But let's imagine that a Volkswagen bus is just a little too small for six infant elephants. Today, there are even larger Volkswagen vehicles made. And a Volkswagen bus could certainly be modified to accomodate six infant elephants.

In conclusion, while I have certainly spoiled the original joke, I hope that I have demonstrated some important skills necessary to successful problem-solving. First, don't walk away from a problem simply because it gives a first impression of being impossible to solve. Second, make as few assumptions as possible. Third, use your imagination to conceive of unusual solutions to the problem. Don't limit your thought, but take advantage of your ability to constuct imaginary models of a huge variety of types to choose from. There is no such thing as a bad idea. There are only ideas which are superior to other ideas. Even a seemingly ridiculous idea may spark thought that leads to a reasonable or achievable one.

Finally, be persistent. Persistence is a virtue that, along with patience, is often responsible for solving many apparently impossible problems. In fact, patience is possibly more important than persistence. Some, perhaps even most problems eventually solve themselves. And sometimes, perhaps most often, the best action to take in solving a problem is to do nothing, at least as a first step.

There's something about nothing...

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