Вычисление: Определение, Модели и Философские Аспекты

Any type of calculation
A computation is any type of arithmetic or non arithmetic calculation that is well defined. Common examples of computation are mathematical equation solving and the execution of computer algorithms. Mechanical or electronic devices (or, historically, people) that perform computations are known as computers. Computer science is a field that involves the study of computation.

The notion that mathematical statements should be 'well defined' had been argued by mathematicians since at least the 1600s, but agreement on a suitable definition proved elusive. A candidate definition was proposed independently by several mathematicians in the 1930s. The best known variant was formalised by the mathematician Alan Turing, who defined a well defined statement or calculation as any statement that could be expressed in terms of the initialisation parameters of a Turing machine. Other (mathematically equivalent) definitions include Alonzo Church's lambda definability, Herbrand Gödel Kleene's general recursiveness and Emil Post's 1 definability. Despite the widespread uptake of this definition, there are some mathematical concepts that have no well defined characterisation under this definition. This includes the halting problem and the busy beaver game. It remains an open question as to whether there exists a more powerful definition of 'well defined' that is able to capture both computable and 'non computable' statements. Some examples of mathematical statements that are computable include:
All statements characterised in modern programming languages, including C++, Python, and Java. Gualtiero Piccinini's summary of this account states that a physical system can be said to perform a specific computation when there is a mapping between the state of that system and the computation such that the "microphysical states [of the system] mirror the state transitions between the computational states."

Philosophers such as Jerry Fodor have suggested various accounts of computation with the restriction that semantic content be a necessary condition for computation (that is, what differentiates an arbitrary physical system from a computing system is that the operands of the computation represent something). This notion attempts to prevent the logical abstraction of the mapping account of pancomputationalism, the idea that everything can be said to be computing everything.

Gualtiero Piccinini proposes an account of computation based on mechanical philosophy. It states that physical computing systems are types of mechanisms that, by design, perform physical computation, or the manipulation (by a functional mechanism) of a "medium independent" vehicle according to a rule. "Medium independence" requires that the property can be instantiated by multiple realizers and multiple mechanisms, and that the inputs and outputs of the mechanism also be multiply realizable. In short, medium independence allows for the use of physical variables with properties other than voltage (as in typical digital computers); this is imperative in considering other types of computation, such as that which occurs in the brain or in a quantum computer. A rule, in this sense, provides a mapping among inputs, outputs, and internal states of the physical computing system.