We're used to using computers to do math now. Spreadsheets, on screen calculators, and other tools that are digital. I have several rather complex calculators that I still use. Underneath the push buttons they are digital as well.
Before transistors and digital technology there where calculators of course. Mechanical ones. I'm not talking slide rules (though I have several of those as well). I'm talking mechanical calculators. With moving parts. I have several addiators, and I've used a comptometer. I've never had the chance to see or use a CURTA. They're still a bit hard to find and rather expensive.
Still even those mechanical marvels do one equation at a time and solve it for one answer at a time. There are times you need to solve multiple equations continuously. It turns out there are mechanical calculators or early mechanical computers that did exactly that. They computed several equations with constantly changing inputs automatically over time.
Why would you need such a calculation? Well you and I wouldn't but imagine that you were in the navy. Shooting is a complicated business. You have to know how fast your ship is moving and it what direction. Then you need to figure out how fast the other ship is sailing and in what direction. Then you have to figure out where to aim your guns. You have to point your guns and shoot far enough so that your shells will land where the enemy ship will be. Then add wind and currents and...
It's as complicated as it sounds.
Turns out there where mechanical computers to do the calculations. In case you wanted to know how the mechanisms inside worked... how a mechanical computer could add or subtract or multiple or do much more complicated math... there are a series of US Navy training films from the 1950s online.
I keep having to remind myself how clever people were before computers and before the latest modern technology. Not only are the mechanisms simple they work on changing inputs and give continuous output. Rather remarkable. With all the pieces put together in one computer it must have been a high tech miracle of the age. Or maybe it was nothing special. Just something you'd expect on the latest ships.
The video is in multiple segments. Here's part 1, part 2, part 3, part 4, part 5, part 6, and part 7.