If you crack open a computer, the stuff inside looks incredibly complex. It’s filled with giant capacitors and transistors that are nanometers across (and billi

If you crack open a computer, the stuff inside looks incredibly complex. It’s filled with giant capacitors and transistors that are nanometers across (and billions of them!)You might think that you need all this stuff—-or at least the giant machines of yore—-to do interesting computation, but you don’t! A Turing machine shows how you can recreate all of this with just a strip of paper and a lookup table. It is incredibly simple, and yet it can reproduce any operation your shiny new machine can (at least in theory). This formalism provides a way to study computation abstractly, without worrying about how much RAM something has, or whether it uses RISC or MIPS instructions. Since it’s so simplified, it can also be used as a yardstick to determine whether other “symbol-processing systems” (C Macros, PostScript, Magic: the Gathering) can support general-purpose computing.