It’s so easy to imagine the wrong kind of computer history museum. I imagine a warehouse of old computers, each with a label giving its technical specifications and production date, where aged computer users can gather to reminisce about that time when they got the Gablergle 23-19 and they had to learn how to program with those crazy punchcards.

The Computer History Museum in Mountain View, Calif., is not that museum. It manages to be fascinating both for people who’ve been intimately acquainted with computers for decades (one of the friends I visited with) and people who know how to use them but know basically nothing else (me). I came out of there with new knowledge, which is what I’m going for at a museum. So, two thumbs enthusiastically up.

As far as I’m concerned, computers are magic. You type, you move the mouse, you install programs, and things happen. A few weeks ago I had to explain what a computer chip was, in a feature story for kids–so you can’t just fudge it, you really have to explain the concept–and I did a weak job, frankly. These darn things have grown and changed and spread so much just in my lifetime and I don’t really know what they are or how they work. It’s depressing.

Well, now I know a little more. The museum moves in chronological order, starting with early calculators. When I first saw the calculators, I thought, oh, yeah, calculators, they’re kind of like computers. But gradually I realized–it’s the other way around. Computers do calculations. Lots of calculations. Fast. They’re calculators that do the math required to display pictures and play videos and run climate models.

In the first gallery, you can try out some of the old-timey calculators, like an abacus–I played around with one, and I can see how one could get really fast at doing calculations that way.

An abacus does the kind of math I understand–adding, subtracting, multiplying, dividing. Within a few rooms, the math these computers were doing surpassed anything I learned. (Or remember. It probably all came up in calculus classes.) In the 1930s, people started building differential analyzers, computers that can do differential equations and can therefore be used for physics, economics, and rocketry.

Here’s an integrator. It’s part of the 1945-or-so Rockefeller Differential Analyzer. It’s a set of gears that mesh together and, well, do integrals, I guess.

The idea that something I struggled to understand in calculus class can be done by little metal gears is kind of mind-blowing to me.

Soon, computers got bigger and people figured out how to store programs on them. Then the whole computer thing took off. The museum got all the way up to the modern day, with the internet and various amusing pieces of ephemera from the dot-com bubble era.

The museum also goes into a past, with a totally cool computer built from a Victorian design…but I’ll save that for another day. UPDATE, 11/28: It’s another day now. Read about the Babbage machine.