The birth of the computer
1946 ENIAC, the first modern electronic computer, was created at the University of Pennsylvania in the United States. Although today the ENIAC’s computing power is no match for a cell phone or even a $10 calculator, it was powerful. The ENIAC is so bulky that it takes several large rooms to fit in, and it uses so much power that lights dim in every house across the city.
ENIAC was the first modern computer because the founders of modern computer theory were Alan Turing and Von Neumann. Alan proposed the theoretical model of the Turing machine, and Von Neumann designed the basic structure of the modern computer. He formulated the computer model in mathematical language, storing programs and data in memory.
Thinking into code
In fact, the development of computers did not happen overnight. Modern electronic computers belong to the narrow sense of the computer, and the broad sense of the computer actually includes all human-made computing equipment, such as the ancient abacus is also a computer, but it is driven by human, and mechanical computers, using mechanical gears to calculate.
In a broader sense, computers should be understood more as ideas. In fact, computer is to help human thought into code simulation, which requires us to decode the thought first. In ancient times, there were philosophers who studied logic and mathematics, and the greatest of them were Plato and Aristotle, who were teachers and students to each other.
Aristotle separated philosophy from science for the first time and studied logic. He believed that logic was the foundation of all science and was the founder of formal logic. He relates human thought to existence and then illustrates logic in light of reality. Aristotle proposed a syllogism in the logic of inference:
All animals die all people are animals so all people die
Heterogeneous lenovo
Logic and mathematics have developed separately since Aristotle. It was only later that the German philosopher Leibniz tried to combine them, by combining the two existing ideas in order to form a third innovative idea, the alien association. Later, mathematical logic was developed, and computational science based on mathematical logic was also developing. For these people, the goal was to express abstract logic in precise mathematical notation,
With computers, most people think that computing and logic are inseparable, and some even think that the essence of computing is logic. The relationship between logic and mathematics is that logic does not equal mathematics, but someone once tried to construct mathematics based on logic. How do logic, computation and mathematics fit together?
Harmonic algebra and geometry
Before Descartes, algebra and geometry were independent subjects. However, geometry’s over-dependence on figures and forms and algebra’s over-dependence on formulas have restricted their development. At this time, the French mathematician Descartes connected the two through different associations and established analytic geometry, so he is also known as the father of analytic geometry.
Descartes invented the now familiar cartesian coordinate system, the X and y axes, which successfully reconciled geometry and algebra. From this point a circle can be described by an equation or by a coordinate system. In addition, analytic geometry also laid the foundation for the creation of calculus.
A fusion of logic and algebra
Most people have probably never heard of Booleans, and programmers are at best aware of booleans, but Boolean logic is the core theory of computers. Leibniz’s dream was to fuse logic and mathematics, a dream pushed forward by The British mathematician George Bull, who combined Aristotle’s syllogism with algebra through strange associations and invented binary.
Arithmetic can be used for addition and multiplication, while logic is mainly or, and, etc. Can they be combined? Logic or something like addition, where two intersecting sets have elements that belong to only one of them. The logical and is the elements that two intersecting sets have in common, which is similar to multiplication. And it only works in the case of zeros and ones, which connects arithmetic and logic through binary operations.
Shannon’s binary
It was Claude Shannon who brought Boole’s logical operations into computers. Shannon was an engineer at Bell LABS. Shannon is not as well known as a famous scientist. He is probably only known by computer science majors, and he is probably also known for information theory. In fact, One of Shannon’s great achievements was his integration of logic into the computer, thus successfully separating the logical layer from the physical layer. Thanks to Shannon’s mapping of logic to the physical world, computers have evolved like never before.
In fact, it was he who combined binary operation with electronic devices to realize the logical function, which laid the foundation of today’s computing mechanism. He designed additive circuits to construct complex arithmetic operations, and these circuits are the components of modern computers. Even as smaller and more advanced transistors were built, they were based on Shannon’s circuitry.
Turing’s Turing machine
Turing machine (Turing Computer) is an abstract computing model proposed by mathematician Alan Matheson Turing (1912 ~ 1954). Alan tried to design computers in the language of mathematical logic, abstracting the process of people using pen and paper to perform mathematical operations, and replacing them with a virtual machine.
The Turing machine had an infinite strip of paper divided into small squares, each with a different color. A machine head moves on a tape, and the machine head has an internal set of states and some fixed programs. At each moment, the machine head will read a grid information from the current paper tape, and then search the program table in combination with its own internal state, output information to the paper tape grid according to the program, and transform its own internal state, and then move.
Every decision-making and thinking person can be abstractly regarded as a Turing machine, which has four main elements: input set, output set, internal state and fixed program. If the person is abstracted, the input set is everything that is seen, heard, smelled and felt in the environment. The output set is every word and every action of a person, as well as facial expressions and movements; The set of internal states can be thought of as an internal set of states, and the set of all possible states will be astronomical.
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