The Book of Why: The New Science of Cause and Effect (Penguin Science)

by Judea Pearl

To begin at the beginning, when you talk into a phone, it converts your beautiful voice into a string of ones and zeros (called bits) and transmits these using a radio signal. Unfortunately, no radio signal is received with perfect fidelity. As the signal makes its way to the cell tower and then to your friend’s phone, some random bits will flip from zero to one or vice versa. To correct these errors, we can add redundant information. An ultrasimple scheme for error correction is simply to repeat each information bit three times: encode a one as “111” and a zero as “000.” The valid strings “111” and “000” are called codewords. If the receiver hears an invalid string, such as “101,” it will search for the most likely valid codeword to explain it. The zero is more likely to be wrong than both ones, so the decoder will interpret this message as “111” and therefore conclude that the information bit was a one. Alas, this code is highly inefficient, because it makes all our messages three times longer. However, communication engineers have worked for seventy years on finding better and better error-correcting codes.