complexity in terms of "algorithmic compression"

"the complexity of something is the size of the smallest program which computes it or a complete description of it. Simpler things require smaller programs." - Gregory Chaitin (138-139)

"the complexity is directly proportional to the length of the shortest possible description of that object. As a corollary we can give a rather clear-cut condition for something to be random (i.e. maximally complex): a string of letters is random is there is no rules for generating it whose statement is appreciably shorter-- that is, requires fewer letters to write down-- than the string itself. So an object or pattern is random if its shortest possible description is the object itself. Another way of expressing this is to say that something is random if it is incompressible." When understood in this way, complexity and compressibility are indirectly proportional: the less compressible, the more complex, and vice versa." -John Casti (139)

qtd. in Mark C. Taylor, The Moment of Complexity (2001)