CONCEPT
Algorithmic Randomness
Kolmogorov’s reconceptualisation of randomness as a property of objects rather than a confession of ignorance: a string is random to the degree that it cannot be compressed, and a maximally random object is one that is its own shortest description—containing genuine information precisely because it contains no pattern, and marking the permanent outer wall of what any learning machine can ever extract.
Before
Kolmogorov, randomness was a word about our ignorance: we called something random when we did not know what produced it. After Kolmogorov, randomness became a property of the object itself, defined without reference to causes or knowledge. A string is random to the degree that it is incompressible—to the degree that the shortest program producing it on a universal computer is no shorter than the string itself. A maximally random object is one that
is its own shortest description: there is no pattern inside it, no rule that generates it more briefly than exhibiting it, no structure for a learner to find. Algorithmic randomness marks the outer wall of
Kolmogorov complexity—the territory that learning cannot enter, not because our tools are insufficient but because the territory has no structure to