How Not to Be Wrong: The Power of Mathematical Thinking

by Jordan Ellenberg

The Mars orbiter Mariner 9 sent pictures of the Martian surface back to Earth using one such code, the Hadamard code. Compact discs are encoded with the Reed-Solomon code, which is why you can scratch them and they still sound perfect. (Readers born after, say, 1990 who are unfamiliar with compact discs can just think of flash drives, which use among other things the similar Bose-Chaudhuri-Hocquenghem codes to avoid data corruption.) Your bank’s routing number is encoded using a simple code called a checksum. This one is not quite an error-correcting code, but merely an error-detecting code like the “repeat each bit twice” protocol; if you type one digit wrong, the computer executing the transfer may not be able to puzzle out what number you actually meant, but it can at least figure out something’s wrong and avoid sending your money to the wrong bank.