Quote: a random, finite binary sequence is one that requires a program at least as long as for any other sequence of the same length [»chaiGJ_1966]

Quote: most binary sequences require programs of the same size; the number generated by smaller programs decreases exponentially; gives proof [»chaiGJ_1970]

Quote: only about one in a 1,000 series of digits can be computed by a program that is 10 digits smaller than the series [»chaiGJ5_1975]

Quote: something is random iff it is incompressible [»chaiGJ_2001]

Quote: protein is incompressible; prior context does not improve compression; perhaps due to random mutation or compact representation

Quote: the fastest way to calculate a infinite subset of a perfect, infinite set of numbers is to calculate the whole set; such sets exist [»chaiGJ_1970]

Quote: random sequences are those that require the longest programs; not random if generated by a short program [»chaiGJ_1970]

Quote: to prove that a particular series of digits is random must prove that there is no small program for it; probably impossible [»chaiGJ5_1975]

Quote: an object is complicated if its description is necessarily long [»raatP_1998]

Quote: the length of a sentence and its information content are unrelated; algorithmic information theory does not explain information [»raatP_1998]