Picture = 1000 Words

Imagine a jet airplane with four large engines. Do you have the picture in your mind? Keep your mental image of this aircraft, because we are going to need it…

This is a story about pictures. (You are still picturing that airplane, right?)

300x300 aero chartThe picture here is a clipping from an aeronautical chart known as a sectional. Let’s take a closer look at some of its characteristics.

1. The image is 300 pixels by 300 pixels. That’s 90,000 pixels.

2. Suppose that each pixel can contain either a red, a green, or a blue color. That’s at least 3 x 90,000 = 270,000 different combinations that we could make on the chart. (The number is actually much larger.)

This quick and dirty estimate is just that, an estimate, and you can easily see how much larger the number can be. The number is important, because it gives us an idea of how much information a picture can contain.

As the old saying goes, Picture = 1000 Words.

Now let’s get back to the mental image I asked you to conjure up at the beginning…

Take a look at the pictures below. Did you imagine either of these airplanes? Or did you imagine something along the lines of a traditional passenger jet?

720 engine test bedThe two airplanes are very different. Yes, both of them have (at least) four large engines. But the photos contain a thousand more subtle differences, very important ones.
C-17 Shackle 1

When we summarize a characteristic in words–when we try to describe what we see in the picture–we lose some of the information. The same is true in statistics. It’s time to adapt twenty-first century graphics capabilities along with our nineteenth century statistical tools.

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Where Do We Go From Here

How do we find our way then, when we are exploring the unknown, blazing a trail into uncharted territory? How do we apply elementary statistical principles to transform uncertainty into decisive action? What is to prevent us from making a preposterous application of ATOMs when we deal with very complex situations, those in which our intuition fails?

These questions are not much different from those faced by Chuck Yeager before he ever broke the sound barrier or Neil Armstrong as he took that first step on the moon. Neither of these men, nor anyone around them–with hundreds or thousands of highly educated, very scientific people on these teams–knew what to expect. Or did they…?

ATOMs is a monthly column that introduces analytical tools of mathematics and statistics and illustrates their application. To read more about ATOMs, you can read Where Do We Go From Here, or view the online workbook here.

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