Abstract mathematical
Today mathematics has become quite abstract esoteric, but in fact it is not born that way mathematics, mathematical development is primarily driven by the reality of abstract mathematics can make it a more universal theory. Extracted from the real problems through abstract thinking and concepts in the law, will extract more essential thing is very necessary. These laws can be extended to many other disciplines, such as physics, chemistry, computer science, astronomy and so on, almost the majority of subjects related to math-related.
Digital abstract
The earliest and most simple abstract related to count, in ancient times no so-called digital symbols, the shepherd on the prairie wants to manage his flock will not see less, how to do it? They got a pile of stones, and each put a sheep sheepfold took out a stone, until all the sheep into the ring are all keep out stones, these stones represents the number of all sheep. When you want to check the number of sheep and sheep can be compared to a stone, if the stone is much less sheep.
With the later symbols can be counted by the shepherd Videos sheep, a goat corresponding to each sheep pattern will then draw a hundred sheep sheep one hundred pattern. Similarly, if it is necessary to draw 50 chicken 50 symbols chicken, duck duck on the corresponding pattern. At this point, we do not know who put forward the idea of a revolutionary, extracted from the digital specific things. Creating a digital 1,2,3,4 ..., then any number may represent an object may be chicken sheep. So far, abstracted figures in the counting process, this is a great abstract sublimation of the human mind.
Abstract arithmetic
When the digital abstracted independent, naturally leads to the problem of digital computing. For example, two sets of stones merged together a total of how many rock stars, just picked 10 apples gave the two others left himself a few, arrested five frog legs a total number of 20 sheep divided equally among 4 people per how much can the individual points. These specific issues like countless lives, but they have inherent common law, so people abstracted addition, subtraction and other operations.
In practice it was found that the production of the property between the number and the number of, and experience base class collated, thereby forming arithmetic. It contains a different relationship between digital and digital, production practice many problems can be calculated by arithmetic.
Abstract geometry
Real-world objects full of beautiful shape, with the development of human architecture, astronomy, handicrafts and other industries, it has accumulated a lot of experience in the concrete shape of the object. For example a triangle, square, circle, sphere, cube and the like. These geometric shapes have some common properties, such as length, angle, area, and volume, etc., then some people have come up from the laws of experience.
Abstract figurative objects as geometry, and then study summarizes various properties and theorems of geometry, greatly contributed to the progress of human life and production. Many things can not be measured by actual, geometry able to provide solutions, such as the circumference of the earth, the ancient Egyptians use geometrical principles can get a very close value.
Abstract unknowns
Just after numbers, arithmetic and geometry, mathematicians brought the concept of unknowns, the amount of things can be abstracted as unknown. Combined with the actual situation of constraint condition equation to express the way, we will be able to solve the problem of reverse thinking. In fact, the equation is unknown and abstract thinking to solve the problem of reverse. Presumed the outcome of x, and then placed in the mathematical reasoning equation, was derived results. The mathematical equation of abstract thinking logic, and converted into symbolic operations, so that many problems can be solved easily and more readily appreciated.
Abstract logic
Brain hole mathematician growing, this is to be abstract logic. Since Aristotle, logic and mathematics are separated from their research development. Only later did the German philosopher Leibniz try to combine them, by combining two existing ideas combine to form a third innovative idea that heterogeneous association. Later developed the discipline of mathematical logic, their goal is to abstract logical precise mathematical notation.
Can human thought into abstract symbol table, and then provide a similar arithmetic operators to manipulate these symbols it?
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