Randomness is a concept that Dawkins usually attempts to qualify and differentiate. The process of adaptation within his neo-Darwinian paradigm of selfish genes and natural selection is not random at all–it is driven by the brute physical agency of the Natural Selector. What is random are the mutations, which he apparently conceives of as happening one nucleic acid at a time in a fragmentary and fundamentally non-directed, non-vitalistic, non-holistic way. His approach is a consequence of Crick’s central dogma of a one-way flow of information from DNA to mRNA to protein, a paradigm blind to the work of the whole living cell to maintain, repair, and (re)generate the order of the crystalline molecules in the nucleus of each of our cells. I do agree with Stephen J. Gould‘s sense of the contingency of biological history; there are many other adjacently possible worlds. I don’t think contingency is the same as randomness, though. The history and development of life on earth, or of protons and electrons in space-time, can be full of adjacent possibilities and still display a clear directional tendency in its large scale dynamics. An Omega Point is not necessarily the imposition of an artificial design that determines the free play of nature, but can be an erotic lure embedded in the dynamics of nature itself (as in Teilhard de Chardin and Whitehead).
Stuart Kauffman talks about “exaptations,” when an organ used by one generation for one task begins to be used by another generation for entirely new, perhaps adaptive, behaviors (as with the first fish to use air bladders as lungs). This sort of mutation is not random, but the result of a sort of Baldwinian evolution through learned behavior.
I think Whitehead’s conception of Creativity is actually very close to the concepts of randomness and chaos. Chaos just needs a dancing partner, rather than conveniently and irrationally being imagined as the sole source of reality. It’s not “God v. not God,” “theistic creationism” v. “atheistic chaosism.” It’s the presence of God and Purpose and Order mutually conditioned by the abyss of creativity and the pure, relentless renewal of nature. Randomness is always on the verge of spilling over into order, which is to say that pure novelty–absolute randomness–cannot manifest or enter into actuality but as the head of a ouroburos eating its own tales and memories, driven by the desire for the immortality of its own experiences.
In other words, randomness is the womb and the tomb of order, its creator and its destroyer. Randomness is a compost heap made of dead ideas and decaying bodies that nourishes and provokes the ongoing adventure of life and rationality.