He is the first one to introduce the concept of "self-organization" ("self-replication" was introduced in parallel by John von Newmann).
He has also formulated the law of "required variety". This states that control can be maintained only if the variety of means available to the controller are not less than the variety of the system which he is trying to control.
Another formulation: a variety of results of a system can be reduced only if the variety of means available to the controller is increased.
The sphere of this law is all systems: technical, biological, natural and man-made.
In An Introduction to Cybernetics, Ashby formulated his Law of Requisite Variety stating that "variety absorbs variety, defines the minimum number of states necessary for a controller to control a system of a given number of states."
Quotes of Ashby:
"A System is a set of variables sufficiently isolated to stay constant long enough for us to discuss it."
To think is to act--inside the brain.
"The test of a brain is its achievement of a goal."
"No man knows what to do against the really new."
"An Intelligence Test measures the degree to which Tester and Subject think alike."
In an article "Principles of self-organizing systems" Ashby writes that “Organization” exists as soon as a relation between “A” and “B” becomes conditional upon the value of some variable “C”. E.g. “A” is a street light, “B” are the pedestrians, “C” is the color of the light.
The concept of “organization” depends upon observer’s point of view.
Then he asks "what is a machine?" The concept of a machine has been widened due to the study of the brain and the belief that a machine can be made that works in a similar way, i.e. "thinks". Ashby writes that a a machine is that in which its internal state, and the state of its surroundings, define uniquely the next state it will go to.
Two principal books of Ashby are: 1) "Design For a Brain", & 2) "An Introduction to Cybernetics".
In the first book, Ashby attempts to define the nature of learning. Learning causes better adaptation for the whole mechanism.
In the second book, Ashby examines "adaptation" and "equilibrium" in a system, and puts an equal sign between these two concepts.