What is the nature of the computer? logic? mathematics?

Birth of the computer

In 1946, at the University of Pennsylvania was born the first modern computer ENIAC. Although today it seems ENIAC computing power and even cell phones, calculators and even a few dollars are not as good, but it is quite powerful at the time. ENIAC volume is very large, well a few large room to put it down, power consumption is also quite terror, a boot city every household lights must be dimmed.

The reason that the ENIAC was the first modern computer, because the founder of modern computer theory of Turing and von Neumann. The two super genius should we have heard, Turing proposed the Turing machine theoretical model, while von Neumann architecture designed to determine the basis for modern computers, he describes a computer model to mathematical language, the program and data are stored in the memory in.

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Ideas into the code

In fact, the development of computers does not happen overnight. Modern computer belonging to the computer in the narrow sense, but in fact the computer in the broad sense, including all human computing devices manufactured, such as the ancient abacus also belong to the computer, but it is driven by manpower, and then such as mechanical computer, using a mechanical gear to carry out operations.

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In a broad sense, the computer we should be understood as an idea. In fact, the computer is designed to help human beings will come out ideas into code emulation, which requires that we need to decode the ideological work. In ancient times it has been studied in logic and mathematics sages, which is the greatest thinkers Plato and Aristotle, two of them are also mutually teacher-student relationship.

Aristotle first time separated from philosophy and science, and conducted research in terms of logic, he thought logic is the basis of all science, it is the founder of the founder of formal logic. He will be thinking and being linked to human, then the actual logic according to clarify. Aristotle syllogism in logic reasoning:

所有动物都会死 所有人都是動物 所以,所有人都會死

Lenovo heterogeneous

Since Aristotle, logic and mathematics are separated from their research development. Only later did the German philosopher Leibniz try to combine them both through existing ideas combine to form a third innovative idea that heterogeneous association. Later he developed the discipline of mathematical logic to mathematical logic based on the idea of ​​computational science is constantly developing. For these people, their goal is to abstract logical precise mathematical notation,

For the computer, most people would think the calculation and logic are inextricably linked, and some even believe that in fact the essence of computing is logical. The relationship between logic and mathematics that does not mean mathematical logic, but once someone wants to build mathematical logic basis. How logical, mathematical calculations and the three should be fused?

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Reconcile Algebra and Geometry

Before Descartes, algebra and geometry independently, they are different in two separate disciplines. However, over-reliance on graphics and geometric forms, and algebraic equations by excessive restrictions, which are restricting their development. Then the French mathematician Descartes through heterogeneous associate these two are linked up, the creation of analytic geometry, so that he is also known as the father of analytical geometry.

Descartes invention now everyone is familiar Cartesian coordinates, x and y axes, the coordinate system of the geometric and algebraic successfully reconciled. Since a circle can be described by the equation may be represented by drawing a coordinate system. In addition, analytic geometry also laid the foundation for the creation of calculus.

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Integration of logic and algebra

Now estimated most people have never heard of Istanbul, most programmers also know Boolean type, but in fact it can be said Boolean logic is the core of the theory of the computer. Leibniz's dream is to have logic and mathematics fusion, British mathematician George Boole the Lenovo Aristotle's syllogism and algebra by combining heterogeneous, and invented the binary, this dream forward promote.

Multiplication addition arithmetic can be achieved, and the logic or mainly, and so on, can combine them together? Adder logic or similar, i.e. in two disjoint sets, some elements of which belongs to one set. Logic and is the intersection of two co-owners of a collection of those elements, this part is similar to multiplication. And that can only be established in the case of 0 and 1, which will be binary arithmetic and logic operations by connecting up.

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Shannon binary

It was Claude Shannon Boolean logic operation into the computer, Shannon was a Bell Labs engineer. Compared to the famous scientist, Shannon's fame is not large, it is estimated that only computer science people have to know him, and you know he is also estimated because information theory. In fact, the great achievements of Shannon also included his logic into a computer, so the success of the logical and physical layers separated. Thanks to Shannon mapping logical to the real physical world, this computer has been an unprecedented development.

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In fact, he is the binary arithmetic and electronics combined to achieve the logic function, now laid the operation mechanism of the computer. He designed a complex addition circuit constructed arithmetic operation, these circuits can also be components of modern computers. Even behind the increasingly sophisticated transistors get smaller, the circuit is based on the principle of Shannon.

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Turing Turing machine

That Turing machine Turing computer, is an abstract computational model proposed by mathematician Alan Mathison Turing (1912 - 1954). Turing attempt to mathematical logic design computer language, people will use paper and pencil mathematical operation of process abstraction, a virtual machine by the people to substitute math.

Turing machine has an infinitely long tape, a tape divided into a small squares, each square has a different color. A machine head is moved in the tape, the machine head has a set of internal states, there are a fixed program. At each instant, the first machine to be read from the tape into a square current information, and then combine their internal state table lookup procedure, in accordance with program information onto the output grid tape, and convert their internal state, and to move it.

Every decision will be, people will think of the abstract can be viewed as a Turing machine, the model has four main elements: a set of input, output set, and the internal state of a fixed program. If people were abstract, then the input is a collection of the environment as see, hear, smell, feel everything; the output of each word of each line is a collection of people, as well as face action; internal set of states can be the combined state of nerve cells as an internal state, the set of all possible states would be astronomical.

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