Completely precise knowledge, only logic and mathematics. In order to study specific objects as precisely as possible, the generalization tendency directs us to attach numbers to specific objects: these are quantities, such as volume, mass, energy, temperature, time, position, velocity, acceleration, and so on. Quantity, fundamentally, comes from people's measurements of objects in the sensory world, but it can also be generalized to the properties of objects in the abstract world.

The definition of quantity depends on how we measure it. To measure, we must have a standard: for example, we measure length with a ruler, time with a clock, temperature with a thermometer, and so on.

Therefore, the essence of quantity is to use numbers to represent the properties of a certain aspect of specific objects.

We must pay attention to the difference between quantity and number: number is the conceptual structure of the brain, while quantity is to use the method of measurement to associate a certain property of an object with the number. Strictly speaking, for numbers, we can derive, but for quantities, we can only observe.

Only when a large number of observations show us that these quantities conform to a certain mathematical law, we can use this mathematical law to deduce the equation of the quantity. In particular, we cannot take it for granted that the observed quantities naturally form a Euclidean space:

for example, take it for granted that the quantity of temperature should be defined in the interval from negative infinity to positive infinity.

To quantify, we must first define a unit quantity and specify a method for verifying that other quantities are equal to it. Among the five human senses, only with the help of vision can we define equality. The other four senses are relatively lacking in precision and objectivity.

For example, it is very inaccurate to use our body senses to feel the temperature: in order to know a more accurate temperature, we will look at a thermometer, and a thermometer is an instrument that converts the temperature into a visual scale.

Our senses of taste and smell are not only unstable, but also lack objective criteria: for example, some people think a cake is sweet, but another person may not think it is sweet enough; for example, sugar water tastes sweeter with a little salt.

Human hearing is more accurate than the above three senses in many aspects. For example, adding a little stirring to a very harmonious pure octave, we will hear the feeling of "beat".

If we continue to stir, the sound will become very harsh. But it still lacks absoluteness: there are very few people in the world with an absolute pitch ability; logarithmic space, which is more natural for hearing, is more difficult to understand than straight space; directly transforming other physical quantities into hearing, that is, not first Transforming into vision and then into hearing (such as the incense clock hanging with metal balls ) was difficult to operate before the advent of electronic products.