The very first computers existed long, long before the microchip-powered devices we use every day here in the future. And over the centuries, there have been various different kinds of mechanical calculators and other computing devices that use physical means—unalterable cogs and gears—to turn one number into a different one. That this is possible is obvious, but how is it possible, exactly?

This 1953 training film has you covered. Forty minutes long (all of them good, I promise), it provides a slow, coherent, and exhaustive explanation of exactly how gears can do math, all framed in the context of the Navy's now-ancient but still mind-blowingly impressive fire control computers. These geared behemoths carefully computed the angles needed to hit moving targets from other moving targets with arcing shells fired from giant naval cannons. No small feat.

The tutorial starts simple, with how just two gears can do multiplication. From there it's just a few more steps to calculus. It makes more, elegant sense than you would think. Just watch:

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This isn't the only old video out there that's proven to be as instructive as any new-fangled YouTubery ever could be. You may recall this lovely 1937 lesson on the operation of a car differential, which is every bit as useful today. Or this 1942 Disney-animated film about how to fire a Boys Anti-tank rifle, which has maybe outlived its usefulness a little bit. And while they heyday of the giant, sophisticated mechanical computer may be long gone, the logic behind its many interlocking gears and pegs and cams is as mesmerizing as ever.

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