Alan Mathison Turing: the cradle of Computing

The computer revolution began effectively to be held in 1935, on a summer afternoon in England, when Alan Mathison Turing (1912-1954), a student of King’s College, Cambridge, during a course taught by mathematician Max Neumann, took note Entscheidungsproblem of Hilbert. Meanwhile, as was briefly mentioned in the previous item, a part of the mathematical community was seeking a new kind of logical calculus, which could, among other things, put in a sustained mathematical basis heuristic concept that is to carry out a calculation. The result of this research was fundamental to the development of mathematics: it was whether it is possible to have an efficient procedure to solve all the problems of a particular class that was well defined.

All these efforts eventually form the theoretical foundation of what came to be called “Computer Science.” The results of Gödel and Turing motivated decision problem first try to characterize exactly which functions are capable of being computed. In 1936, Turing was acclaimed as one of the greatest mathematicians of his time, when he foresee his colleagues that you can perform computational operations on the theory of numbers through a machine that has built the rules of a formal system. Turing defined a theoretical machine that has become a key concept within the Theory of Computation. He emphasized from the beginning that such mechanisms could be built, and its discovery is just opening a new perspective to the effort to formalize mathematics, and at the same time strongly marked the History of Computing. The genial perception of Turing was the replacement of the intuitive notion of an effective procedure for a formal idea, mathematics.

The result was the construction of a mathematical concept of algorithm notion, a notion that he modeled building on the steps that a human being is when performing a particular calculation or computation. It formalized the concept of algorithm.

The Turing Machine

One of the first models of the abstract machine was Turing machine. As Turing himself wrote: “Computing is written symbols on paper. Assume that the paper is a grid, the flatness can be ignored, and it is not essential. Suppose the number of symbols is finite. The computer behavior is determined by the symbols which he notes at one point, and his mental state at that time. Suppose there is a maximum number of symbols or squares that he can watch every moment. To observe more successive operations are required.

Let us assume a finite number of mental states. Let’s imagine that the actions taken by the computer will be divided into such elementary operations that are indivisible. Each action consists of changing the computer system and paper. The state of the system is given by the symbols on paper, the symbols observed by the computer and your mental state. Every operation, no more than a symbol is changed, and only the observed change. Besides changing symbols, operations must change the focus of observation, and it is reasonable that this change should be made for symbols located at a fixed distance of the above. Some of these operations involve mental state changes the computer and then determine what the next action. ”

Turing’s work was documented in On Computable Numbers with an application to the Entscheidungsproblem, published in 1936. He described in mathematically precise terms how powerful it can be an automatic formal system with very simple rules of operation. Turing determined that mental calculations consist of operations to transform numbers into a series of intermediate states progressing from one to another according to a fixed set of rules until an answer is found. Sometimes it is using paper and pencil, not to lose the status of our calculations.