Divide by Zero on the Friden STW10 Mechanical Calculator

Please, try a divide by zero! Pleeeeeease! What would happen? What if Katherine Johnson did that in the movie Hidden Figures (this is the Friden that sits on her desk)? Would it catch fire? Would the rocket trajectory go to infinity? Now you are finally going to find out. Stick to the end for a little extra, a scene from another great movie that stars the Friden. This is a Friden STW 10 from 1956.

More about the Friden STW10 on my website:

Calculator plays the Friden March and does 0/0

Friden SWT-10 full demo video including square roots:

Restoration of this machine:

00:00 Intro
00:53 Machine setup
01:37 Division by zero
02:19 How division works: calculating pi
03:47 Division slo-mo
04:33 Redo div by 0 with explanation
05:27 Scene from the Apartment movie with hundreds of Fridens

[CuriousMarc]

Folks, no need to argue about colorful alternative mathematical theories - the thorny problem of division by zero was solved for good over 100 years ago by the rigorous development of infinitesimal calculus. Which says: division of a positive non-zero constant by something that tends to zero, tends to infinity [added note: dividing "zero by zero", or more exactly, two things that tend towards zero, is more complicated: it can give zero, infinity, or anything in-between, but that's for another time...]. So the calculator sort of gives the right answer, using almost the correct method: trying to fit an infinitesimally small number into a big one, and finding it fits so many times it goes to infinity. I would put it in the category of happy mechanical accidents.

[SolApathy]

The Div /0 command allows you to oil the mechanicals and then you can cancel the command once oiling is complete.

[chrisquick]

Teacher, "You are allowed a basic 4 function calculator for this exam."
*Walks in with this.

[RalphDratman]

There was another "dangerous" phenomenon on this or a very similar Friden machine:
The instructions warned against holding down the multiply button.
At age 12 or so, around 1963, I could not resist the temptation to challenge this rule.
The machine would make terrible noises and then jam up so badly that the service person had to come fix it!

[absurdengineering]

My mother had (likely still has) a cell counting “calculator” that was used to manually count blood cells in the field while staring into a microscope, touch-type-style. It didn’t have a motor, but it sure did clink-clunk, and it even had a bell. There was a little crank on the side used to reset counts to zero. It was “portable” – it’d fit into an oversized purse, turning into a first-class bludgeoning weapon. The case was made from bent heavy sheet steel.

[krisztiannemeth]

What really fascinates me is that they implemented this division algorithm *fully mechanically*. It would be just a couple of lines in any programming language, but with springs and rods... Wow. Hats off to the designers!

[gabrielathero]

So the inventors added an extra Anti-Idiot-Button. Clever XD

[lwilton]

There were several ways you could get those machines into an infinite or else very long calculation; the div stop button was handy for aborting most any calculation if you realized that you had fat-fingered the inputs before it was finished thinking.

This is also what happened with early computers that didn't have a check for divide by zero. They would just "lock up" in an infinite loop until someone hit the reset key. They didn't blow up, or go insane, or any of those things that newspapermen and authors and Hollywood screen writers claimed they did.

[jimshaw]

When I was an intern, we got a new one of these in the engineering department. I hesitate to disclose the year. I was young and now I am old.

Who else but a college intern would try dividing by zero on the first day of its use? Off the Friden went to the unstoppable quotient races. After a couple of minutes, I realized there was no way provided to stop it. No "div-stop' key on our early model. I had to pull the plug. No one else could stop it, despite repeated attempts. It had cost so much, all were afraid to break it.

We had to call for Friden service to reset the machine. He explained that it was a good thing I unplugged it because the internal motor was only rated for 'intermittant duty.' No, it probably would not have caught fire, but it would have overheated, likely damaging the motor windings. Expect smoke!

Epilogue: We later got the first Friden model that could do square route. I swear you could have sold tickets to watch that machine work. Basically, it did square route the same way we would do it on paper, a sort of trial-by-square. The carriage did this amusing dance, but sure enough, it worked.

Square route was rather "like a dog walking on its hind legs; it didn't do it well, but was amazing it did it at all." And it achieved the correct answer.

[ProvingDemons]

You genius you have cracked perpetual motion!

[gokartbuyer]

Is it me or does anyone else find this incredibly satisfying to listen to?

[Rich-onfe]

That's incredible that they foresaw the whole information revolution and popularity of youtube etc.

[HazeAnderson]

355 / 113 = PIE? And this whole time I have been using an oven ...

[celsojr]

When I was a 10 years old child, my father gave me a strange old digital calculator, wich had that strange function to hide the floating point until you press a button to show the fractions. When I divided some number by zero, it did not showed "E" or something like that.. just stucked on zero...but imagine what I discovered that when you pressed the floating point option. It was just like you evidenced in this mechanical calculator. Amazing! It took to me 35 years to find another machine that explained to me what was really happening, since not even my math professors could do it. Thanks a lot!!!!

[denisethasder]

A wonder of technology, even in this day

[hifijohn]

now people know when electronic calculators came out in the early 70's they were considered so amazing.

[jayglenn]

Because Division by 0 approaches infinity. What a beautiful mechanical way of expressing that.


Note: dividing by 0 does not =infinity because infinity is not a number. Dividing by 0 _approaches_ infinity. If this was not so all math would be broken.

[gregory]

Nice to see one in action, we had one in my parents’ office when I was a kid. The sound of it working and the decimal slider brings back memories.

[berkeleygang]

My father had one of these at work. I did this same experiment. I freaked out when the calculator started smoking. I don't remember what I did to make it stop. I was sure I was going to get in trouble.

[SpaceCowboy]

This would make a sick drum track for a black metal song.