Dividing By Zero With The ‘Facit ESA-01’

The mathematics of the ‘Facit ESA-01 mechanical calculator’; don’t divide by zero.


Infinity is not a real number. It’s a concept. In Calculus class I learned about upper bounds and lower bounds; limits. Infinity is a big deal in Maths because it’s a big deal in reality – Sort of.

Anyway, I came across one cool machine not too long ago, and it used a simple math principle to divide numbers: division is a mega-system of subtraction. A whole value, x that is the result of a number, a divided by b is the number of times that b can be subtracted from a to give 0. Sometimes it gets really close to zero but it never gets there. in other words,

(a/b) = x = [#t ] (10 - 5) ~ 0

It is this principle that the Facit ESA-01 uses to divide. And unlike modern calculators that display an error message when you try to divide a number by zero, ESA tries to commit suicide.

The name of the mechanical calculator is Facit ESA-01 and you can see how it crashes in the video below:

Remembering that division is in simple terms, sequential subtraction, dividing 10 by 2 will be:

step 1: 10-2=8
step 2: 8-2=6
step 3: 6-2=4
step 4: 4-2=2
step 5: 2-2=0

10 2 is 5. It took 5 steps to arrive at 0. Dividing 20 by 0 on the other hand:

step 1: 20-0=20
step 2: 20-0=20
step 3: 20-0=20
step 4: 20-0=20
step 5: 20-0=20
step 6: 20-0=20
step 7: 20-0=20
step... I'm sure you get the idea

The calculator goes on forever and so would you calculator if programmers didn’t handle exceptions.practice

I wonder what will happen if the machine tries to divide 0 by 0: someone said that computers will eventually kill all of life after the machine must have run for 100 million years and found out the answer is 42 (lol – silly).

So, if you didn’t know why division and subtraction are on the long term the same thing, now you do. And if you learned nothing new then just remember that the next time you get  a calculator, don’t get a mechanical one — unless it’s for the collection 😉

Further Reading

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