The smaller and more sophisticated computers get, the less your average user is likely to know about what's going on inside them. Today's tablets and smartphones, for example, are basically just irreducible slabs of magic (the fact that manufacturers gleefully glue them together and seal them shut probably doesn't hurt that impression). But go back a few years, and the mystique starts to evaporate a bit. Your typical office worker in 1998 might not have known how to replace her own RAM, but she probably understood that the beige box under her desk wasn't anything more than a plastic shell for the components inside it.

Travel all the way back to 1948, and there's no ambiguity whatsoever. As we see in this delightful clip, unearthed by Gizmodo's resident paleofuturist Matt Novak, to get an idea of what was going on inside those hulking machines, you didn't have to do anything more than peer over the edge.

That, at least, was all you had to do to watch UCLA's differential analyzer in action. The video, produced by Popular Science and screened in theaters in front of Paramount Pictures movies, catches us up with the cutting-edge machine, recently relocated to the California campus after a stint helping the good guys win World War II. We hear how the "mechanical brain" can solve complex mathematical equations that would take other, dumber computers, months to complete. It adds. It subtracts. It integrates. It even draws! The narrator doesn't hedge the technology's promise: These types of machines will take us to the moon and beyond.

For us today, the clip is a rare look at what "computing" meant decades before the microprocessor. There's so much to see, it almost feels like you're watching a Rube Goldberg machine. Row upon row of spinning bars, like a great line-up of Nazi-fighting foosball tables, whirling in a mechanical ballet. Gears and buttons galore. From the look of things, you don't sit in front of the machine so much as in the middle of it, ensconced in all its kinetic glory. Now just for fun, watch that bit again and insert a mental picture-in-picture of yourself during a zombie-eyed session of Candy Crush on your glass telephone. The march of progress!

Of course, we do still use computers to make world-shaping advances in all sorts of fields. And is there anything really wrong with not knowing what's going on inside those smartphones in our pockets? Not really. But that doesn't mean people wouldn't like to know! Maybe, instead of letting users trick out their Moto X with a gaudy wooden backplate, Motorola should have served up a see-through offering. I'll bet it would be crazy popular.

[Hat tip: Gizmodo]