Dividing by Zero on a Mechanical Calculator

Mechanical calculators are a true testament to the skill and intelligence of the engineers and designers behind each model. Some calculators are so complex that they require several tutorials to fully master them, and in most cases YouTube comes to the rescue. But the audience also wants to know other aspects, for example, their behavior with strange operations such as division by zero…

"Division by zero error". I've seen that message in many MS-DOS-compatible programs, especially when I used unusual configurations with alternative memory managers. Division by zero also had its moment of fame in September 1997, when it left the USS Yorktown cruiser without propulsion for two and a half hours.

However, this operation is older than we think. The first attempts to understand it date back to the year 600, and its impossibility was in a way identified during the 18th century. So manufacturers of mechanical calculators have inevitably had to cross swords with division by zero. How do they avoid the problem?

Mechanical calculator dividing by zero

To tell the truth… they don't entirely avoid it. A good proof is CuriousMarc's video about the Friden STW-10, a beast from 1956 (and launched on the market in 1949). When trying to compute 355 divided by 0, the machine gets trapped in an infinite loop, sounding like a machine gun.

The solution the calculator offers to break the loop (a condition that its designers clearly took into account) is the "DIV STOP" function. Now, what happens if the calculator is mechanical but not automatic? To answer that, we have an additional video published by the NFM channel. In this case, the star is a Facit NTK from 1957:

And its reaction is… the same. The user turns the lever, but the calculator remains in a loop, doing nothing. What's the reason behind this loop? In essence, mechanical calculators divide by subtraction, that is, repeating "dividend minus divisor" until reaching zero, or alternatively, the desired decimal resolution. When the divisor is zero, the calculator can never start its division by subtraction, because there is nothing to subtract in the first place.