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Computers are literally magic.
No, really. There's a few power crystals feeding energy into an array of memory crystals, which transfer information to and from a control crystal, which uses a limited sort of intelligence to tell all the other crystals what to do. There's one physically large array of crystals that show the user what the apparatus is doing, and a few crystals that send and receive information from other assemblages of crystals that act as a way for a user to control the system.
Most of these crystals send their information and power down specially-designed conduits, but some of them, especially the ones for connecting the device to other devices, simply send information through the aether instead.