### ARTICLE

# I, Slide Rule

##### APRIL 20, 2010 by RICHARD W. FULMER

I am a slide rule. For nearly three and a half centuries, my ancestors and I commanded the western scientific and engineering worlds. We could be found in humble shops, helping carpenters reckon areas and volumes; we fought on battlefields calculating trajectories for artillery officers; we were engineers’ constant companions, determining stresses, flow rates, velocities, and countless other things; we flew to the moon with the astronauts.

Slide rules were more than mere calculating tools; we were icons. Just as stethoscopes symbolize the medical profession, we came to symbolize engineering and science. We were works of art–precision-tooled pieces of etched wood, metal, and ivory. We helped build the modern world, yet not a single person on the face of the earth knows our worth.

Sounds impossible, doesn’t it? But for over two centuries even the world’s great economists argued over how value was to be determined. Some believed it came from the labor employed to make us. Others thought that our “absolute utility” dictated our value, while still others believed that our value was based on our cost of creation. There is nothing in such notions. But before I reveal the truth, let me tell you more about the wonder that is me.

My life was made possible through the genius of Scotland’s John Napier, baron of Merchiston. Napier invented the concept of the logarithm. A number’s logarithm is the power to which 10 must be raised in order to produce the number. For example, the logarithm of 100 is 2, because 100 is 10^{2}, where 2 is the number of 10s that must be multiplied together to get 100. Slide rules are based on a special feature of logarithms: The sum of the logarithms of two numbers is equal to the logarithm of the two numbers’ product. That is:

log x + log y = log(xy)

This feature can be used to simplify computation by converting the relatively complex calculations of multiplication and division into addition and subtraction.

Soon after Napier published his discovery, Edmund Gunter of Oxford realized that two rulers etched with logarithmic scales could be used to add or subtract two numbers’ logarithms and thereby multiply or divide the numbers. For example, adding the logarithm of 2 on the bottom scale (represented below) to the logarithm of 3 on the top scale yields the logarithm of 6:

Division is performed by reversing the process. This same slide rule setting also shows other multiples of 2:

2 x 1.5 = 3, 2 x 2 = 4, 2 x 2.5 = 5, and so on.

In addition, the setting would be used for calculations involving 2 multiplied or divided by multiples of 10, such as:

0.02, 0.2, 20, 200, and 2000.

It is my user’s job to keep track of the decimal point.

Clearly, our simple yet elegant design is the work of genius. Imagine my surprise, then, when in the early 1970s, electronic calculators appeared and my brothers and I became worthless nearly overnight. Not only that, but the machines and factories that made us also became worthless. They had value only as long as we did, and any equipment that could not be used for other things became just so much scrap metal. Worse, the knowledge needed to make us lost its value as well. Craftsmen who had spent their lives creating us became unemployed when the factories they worked in closed.

Calculators were mere boxes filled with wires, chips, and garish red lights that flashed out numbers. They took no skill or flair to operate; they were soulless lumps of plastic that worked only as long as their batteries lasted. Yet these lumps replaced us. Thousands of my brothers were discarded. I was lucky; I was merely shoved into a drawer and forgotten for nearly four decades.

I had been purchased, along with a sturdy leather case, for $20, but suddenly I had no value at all. I had not changed in any way, I could still calculate as well as ever. The labor that had gone into me had not changed, nor had my materials, nor my cost of manufacture, nor the knowledge needed to make me. I was the same as I had always been, except that now I was unneeded, unwanted, and forgotten.

As the years passed, however, a strange thing happened. People wanted us again–not as calculating devices but as “memorabilia.” Amazingly, slide rules just like me have been sold for well over a hundred dollars! Whole websites have been built extolling my virtues and selling my brothers, fathers, grandfathers, and even some of my few surviving great-grandfathers. Even more remarkable is that, in another 60 years, I will be a hundred years old, an antique, and my value will be multiplied manyfold.

How can it be that I started out life worth $20, but was worthless within a few years? How can it be that decades later, I am valued more than I had been when I was new–even though I am no longer wanted as a calculator but as an “object of art”?

Well, it’s because my value never had anything to do with inputs or objective calculations. Nor, once determined, is it established for all time. Value is, instead, subjective. It is based on the needs and desires of the moment, which vary by person and even for the same person as times and circumstances change. My worth will fluctuate through the coming years, even though I will not change. What will change is people’s perception of me, and therefore what they are willing to pay for me.