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Have you ever wondered how itamp;#39;s possible to scratch a CD or a DVD and still have it play back whatever itamp;#39;s storing? The scratch really does affect the 1s and 0s on the disk, so it reads off different data from what was stored, but unless itamp;#39;s really scratched up, the bits it reads off are decoded into precisely the same file that was encoded onto it, a bit for bit copy, despite all those errors. There is a whole pile of mathematical cleverness that allows us to store data, and just as importantly to transmit data, in a way thatamp;#39;s resilient to errors. Well, okay, actually it doesnamp;#39;t take that much cleverness to come up with a way to do this. Any file, whether itamp;#39;s a video or sound or text, some code, an image, whatever, is ultimately some sequence of 1s and 0s. And a simple strategy to correct any bit that gets flipped would be to store three copies of each bit. Then the machine reading this file could compare these three copies and alway
