Measurement is a Chinese word, which basically means to measure some physical properties of an object. Measuring length and volume weight are collectively referred to. Expanding the meaning of words also refers to tolerance and tolerance limits for others. "Zhou Li Shimonoseki has sex": "The same number, one quantity." Zheng Xuan's Note: "A full-scale kettle bell must have no size." Historical Records Biography of Fan Ju and Cai Ze: "Weigh, measure and adjust the weight." Song Sushi's inscription on the disappearance of Xuzhou Lotus: "If people don't measure it by hand, they must measure it."
People know mathematics by measurement. Understand mathematics through measurement, and then understand the real world. The unit of measurement is to standardize the measurement methods of different individuals and gain people's extensive knowledge.
First, the mathematical function and essential characteristics of measurement units. Without measurement, there would be no mathematics. Measurement is the basic tool and expression language for people to understand mathematics and the real world, which can vary from person to person. The establishment of measurement units is for people to express measurement uniformly and communicate clearly, so measurement units must be able to reveal the essence of measurement and get people's understanding. The essence of measurement is to express the order of some indicators of things, such as the number and size of abstract numbers; Distance; Weight; Speed.
Second, the formation process and expression form of measurement units. The formation of measurement units has generally gone through the process from pluralism to unity, from roughness to fineness, for the needs of daily life expression and scientific research. Although the unit of measurement is defined by human beings themselves, as far as the formation process is concerned, it can be roughly divided into two categories: one is obtained through abstraction and is the result of human thinking; The other is obtained by means of tools, which is the result of human practice.
Third, the innate instinct and special ability of cognitive measurement units. The reason why people can measure and have a broad understanding of the unit of measurement is based on two innate instincts, namely, the perception of quantity and the perception of distance. These two innate instincts are the thinking basis of understanding mathematics, measurement and measurement units, and because people have two special abilities of abstraction and imagination, they can be extended to the perception of some index sequences of things.
The unit of measurement is the name of the standard quantity for measuring things. The emergence and development of almost all units of measurement have gone through a long time, bearing the development process of units of measurement from pluralism to unity and from coarseness to fineness. Measurement is the essence of mathematics, a mathematical language created by human beings and a tool for people to know, understand and express the real world. As poincare said, "without tools to measure space, we can't build space."
Measurement can vary from person to person, and the unit of measurement is to standardize the measurement methods of different individuals in order to spread and exchange measurement results. Therefore, the formulation of measurement unit must be able to express the essence of measurement, scientific method, accurate expression, relative stability and be widely recognized by people.
No matter what the name of the unit of measurement is, people always use 1 to represent a unit of measurement, which is the most basic concept in mathematical research. Although the unit of measurement is stipulated by people, as far as the formation process of the unit of measurement is concerned, it can be roughly divided into two categories: one is obtained through abstraction and is the result of people's thinking; The other is obtained by means of tools, which is the result of human practice.
The object of mathematical research should be more general abstraction, which involves the essence of quantitative measurement, that is, measurement quantity. This abstract process relies on people's instinctive perception of quantity. This abstract process eventually led to the invention of decimal natural numbers. This abstract result formally abandons the title of measurement unit, but in essence it is divorced from the specific realistic background on which quantity depends. The essence of mathematical abstraction is to abandon the realistic background of things. More precisely, mathematical abstraction is to abandon all physical properties of things.
The measurement obtained by tools mainly refers to the measurement unit based on the background of things, and always contains the title of expressing the background index of things, such as describing the weight, length, energy, volume, temperature, speed and so on. Such a unit of measurement is not an abstract result, but a tool. Here, the evolution process of length units is used to analyze the essence of such units of measurement.
The essence of measuring length is to measure the distance between two points. As mentioned above, such a measurement depends on people's instinct to perceive distance, and such a measurement needs a reference object. The reference objects of people's initial distance measurement are all human organs. Such measures are still widely used in today's daily life. With the gradual deepening of scientific research, people need more and more very fine distance units, so the formulation of length units needs to move from rough to fine. Based on the formula of "distance = time× speed", the length unit can be defined by time and speed. According to Einstein's theory of relativity, the speed of light is absolute. Therefore, after people can accurately measure the time and the speed of light, the 13 International Conference on Weights and Measures in 1967 gave a strict definition of the second by using the atomic clock principle: cesium 133 radiation 9 192 63 1 770 cycle. 1983 the definition of meter length was adopted at the17th international metrology conference, that is, the distance that light travels in vacuum 1/299 792 458 seconds. In this way, people define time units and distance units in detail. Through the process of definition, we can see that no matter whether it is ancient or modern, whether it is coarse or fine, such units of measurement are formulated by means of tools, so the expression of such units of measurement has dimensions.