Powers of 10 are sexy


Would you like to nerd out with me? Good, let’s do it. And we start by officially recognizing we have completed an order of magnitude with today’s blog post! Yep, today's topic deals with powers of 10, also called orders of magnitude, and we think they are sexy.

An order of magnitude helps deal with size or scale. Let’s take an example. Think of an ant. Now think of an average adult. We can quickly conclude based on powers of 10 that the adult is three orders of magnitude taller than the ant - a huge difference you can instantly grasp!

For my fellow nerds who love math, let’s see how the numbers work. We place average height of an adult about at 1.7 meters (5 feet 7 inches). When we round 1.7 to the nearest power of 10, we round to 1 or 10^0 (1.7 is closer to 1 than 10 so we round to 1). Recall 10^0 doesn’t mean 10 x 0 = 0. Rather, the exponent tells us how many zeros we need to add to 1. So for 10^1 (or 10 multiplied 1 time) we add one zero to 1 and have 10. And 10^2 gives us 100 (we add two zeros to 1 or 10 multiplied 2 times, 10 x 10), 10^3 equals 1,000 (add three zero to 1). But if we have 10^0 we add zero zeros to 1 and just have 1.

Now back to our little friend the ant. The size of an ant works out to about 3.4 millimeters. If we convert millimeters to meters, like our 1.7 meter human, 3.5 millimeters = .0034 meters. If we round .0034 to the nearest power of 10 we get 10^-3 or 10 to the negative 3.

So now we can easily compare our ant to our human.

Ant height = 10^-3
Human height =10^0

From -3 to 0 we move forward by three exponents. In other words, the human has three powers of 10, or three orders of magnitude of height, on the ant.

The power of powers of 10

Chartlytics deals with behavior change, so do you. Chartlytics places behavior on the Standard Celeration (and we hope you do too). Because of its special scaling, we can see the orders of magnitude or powers of 10 up along the vertical axis. Below see the vertical axis for the count only chart and the daily per minute chart.


Figure 1. Two vertical axes from two varieties of daily charts: the daily count only Standard Celeration Chart and the daily per minute Standard Celeration Chart.

Notice how each order of magnitude changes by moving up one power of 10. Viewing behavior on such a scale allows us to easily analyze and compare different data very quickly. Therefore, we can make decisions about data just as fast.

Let’s put the last statement to the test. You can visualize the difference between the height of an ant and human and quickly come to appreciate a three order of magnitude change. In behavior, think about a child who can only speak 1 word a day. Then compare that behavior with a child who can speak 1,000 words a day! Literally the difference of speaking vocabulary between an infant (12 months old) and a toddler (3 years old).

And what about behaviors we would like to eliminate? A smoker takes approximately 10 puffs of smoke from a cigarette (American Cancer Society, 2014). A pack contains 20 cigarettes. So a pack a day habit = 200 puffs of smoke. Let’s say in a week a smoker consumes 5 packs of cigarettes and takes 1,000 puffs per week. Compare that to a person that takes one drag off a friend Friday night (only one puff of a cigarette per week).

Examine the two people and see what a three order of magnitude change reveals. The difference between a heavily addicted smoker and one who we might call a casual smoker at best. Furthermore, imagine what type of intervention we would need to apply to the 1,000 puff a week smoker and the 1 puff a week smoker to get either one to quit smoking?

As soon as people start charting and comparing behavior on a true scale, they discern the orders of magnitude difference between behavior. The amount of transformative power necessary to grow or decay a behavior immediately jumps out at the chart reader. Furthermore, once we place behavior on a scale we share an important trait with other mature sciences. I leave you with Ogden Lindsley's words and his thoughts on the powers of 10:

“When we looked at light qualities we accomplished little, but when we looked at light merely as differences on a frequency spectrum, we accomplished wonders of radiance. When we listened to sound qualities, we accomplished little, but when we placed sounds on a frequency spectrum we developed instruments and amplifiers far purer than the best ever crafted by quality artisans. When we puzzled over differences in the qualities of electricity, we accomplished little, but when we sprinkled electrical events over a frequency spectrum, we made great strides in electrical control and discovery” (Lindsley , 1991, p. 254).


American Cancer Society (2014). Questions About Smoking, Tobacco, and Health. Retrieved at http://www.cancer.org/acs/groups/cid/documents/webcontent/002974-pdf.pdf

Lindsley, O. R., (1991b). Precision teaching’s unique legacy from B. F. Skinner. Journal of Behavioral Education, 1(2), 253-266.

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