An Old Fashioned Mechanical Calculator Shows us Why We Don't Divide by Zero

Apr 14, 2016 | Novi

We've all been taught that you can't really divide by zero. And tradition holds that the reason for this is that the answer you get is essentially "∞" or "infinity." But that isn't the whole story. A digital calculator will often give you "0" as an answer or an error message of some sort, but a mechanical calculator has no such programing to account for such a request, so it just does what it's told. Take a look…

You see it just starts chattering away caught in a look processing away presumably forever or until it breaks down or the plug is pulled. But why is that? Well it has a bit to do with the nature of division. See division as we know it might be better described as sequential subtraction. As far as a computer is concerned twenty divided by four, for example is just:
a. 20 - 4 = 16
b. 16 - 4 = 121
c. 2 - 4 = 8
d. 8 - 4 = 4
e. 4- 4 = 0

But look what happens when you use that same method to divide by zero:
a. 20 - 0 = 20
b. 20 - 0 = 20
c. 20 - 0 = 20
d. 20 - 0 = 20
e. 20 - 0 = 20

It's the same answer over and over again… infinitely. Which is why you hear people say the answer to anything divided by zero is infinity, because while it's not exactly the case, infinity is what you end up with, as that poor mechanical calculator found out the hard way.