In the 1930's logicians and mathematicians like Turing, Church, Gödel, and Post contributed to the path-breaking exploration of the mechanical computational process. They became for computers what Watson and Crick would become for biotechnology. Subsequently philosophers like Hilary Putnam and Jerry Fodor developed what is now called the computational theory of the mind, in which information and computation reside in patterns of data and in relations of logic that are independent of the physical medium that carries them.
According to the computational viewpoint, the laws of nature are algorithms that control the development of the system in real time, just like real programs do for computers. (An algorithm is a rule for solving a particular problem. In many cases the rule consists of applying a special set of steps over and over again, as, for example, in long division.) A computational theory contains separate arguments about what is computed and why. It uniquely defines the resulting operation by the constraints it has to satisfy. Of fundamental importance is the nature of the problem being solved. (for example, visual perception.) As David Marr put it, "an algorithm is likely to be understood more readily by understanding the nature of the problem being solved than by examining the mechanism (and the hardware) in which it is embodied." (Vision, p.27) "...trying to understand bird flight by studying only feathers...cannot be done."
A computational process requires a representation for the input and output of the process and an algorithm by which the transformation may actually be accomplished. In Sciences of the Artificial, Herbert Simon describes problem solving as a representation of the problem so as to make the solution transparent. (p.153) For Simon, theorem proving is the prototypical case of problem solving by re-representation, in which the computational system is a set of axiomatic propositions and a set of rules for operating on the propositions. The rules describe operations that preserve the truth of the axioms. Thus the most straightforward way of proving a proposition is to make a sequence of rule applications that re-represent what the axioms say in such a way that they become the target proposition.
In Cognition in the Wild, Edwin Hutchins examines navigation as a form of cognitive computation that applies as much to the interaction of humans with artifacts and with other humans as it does to explicit symbol processing. For Hutchins, cognition is in a fundamental sense a cultural and social process.
In a computational sense, all systems of navigation answer the question "Where am I?" The mode in which the Western tradition of pilotage attempts to answer that question is in the establishment of the correspondence of map and territory. For Hutchins, navigational computation occurs through the propagation of representational state accross a series of representational media. (see pp 117 ff) In pilotage, the ship's situation is represented and re-represented until the answer to the navigator's question is transparent. For the navigator, the ship is where its lines of position intersect on the chart, the "common ground" of all the representations of its position.
Hutchins examines the cognitive system, or "cognitive ecology," in which these computations are implemented. The entire navigation system performs the computation by bringing a constellation of structured representational media into coordination with one another. This coordination requires simultaneity as well as cognitive accuracy and depends on accumulated social knowledge that often translates computation into simpler cognitive tasks (eg. aligning a hairline with a number on the pelorus) The tools developed for the task and the social roles of the performers are part of a distributed problem-solving system that can be seen as a computational machine.
The real strength of modern computers is their ability to simulate another machine ( writing, calculating, painting machines, etc.) Put another way, a computer is a second-order machine that -- when give a formal specification of a first-order machine, (e.g., a word processor) --itself becomes (simulates / realizes) this first-order machine.
(see virtual )
"So what is reality, one more time? An incompressible computation by a fractal cellular automaton of inconceivable dimensions. And where is this huge computation taking place? Everywhere; it's what we're made of." -- Rudy Rucker.