The Information (59 page)

Heavy on ones, light on zeroes, this might be emitted by the flip of a biased coin. Huffman coding and other such algorithms exploit statistical regularities to compress the data. Photographs are compressible because of their subjects’ natural structure: light pixels and dark pixels come in clusters; statistically, nearby pixels are likely to be similar; distant pixels are not. Video is even more compressible, because the differences between one frame and the next are relatively slight, except when the subject is in fast and turbulent motion. Natural language is compressible because of redundancies and regularities of the kind Shannon analyzed. Only a wholly random sequence remains incompressible: nothing but one surprise after another.

Random sequences are “normal”—a term of art meaning that on average, in the long run, each digit appears exactly as often as the others, one time in ten; and each pair of digits, from 00 to 99, appears one time in a hundred; and each triplet likewise, and so on. No string of any particular length is more likely to appear than any other string of that length. Normality is one of those simple-seeming ideas that, when mathematicians look closely, turn out to be covered with thorns. Even though a truly random sequence must be normal, the reverse is not necessarily the case. A number can be statistically normal yet not random at all. David Champernowne, a young Cambridge friend of Turing’s, invented (or discovered) such a creature in 1933—a construction made of all the integers, chained together in order: