To be honest, I didn't want to write a few social analyses either. Originally, this was also a completely new idea, which means that this idea is particularly immature and naïve, so I put it here first. This time, I will continue to analyze society.
The last time we actually equated society with sets, so it's perfectly fine to transplant a lot of mathematical conclusions to sociology as they are. Of course, this time it is not to put the mathematical topology here, but to rely on the breadth. Of course, if you want to really set the topology, you have to start from the foundation and work up, because for example, the order structure and the algebraic structure, many of them are just opposite or even subsets, so if many mathematical conclusions are really valid in sociology, they will not be expanded to a little bit, and they may not even be able to complete it by using topology, and the premise of mathematics is really limited, so many conclusions are actually a true subset.
Material vs. spiritual
Since society is people-centered, it is indispensable to start from individual or collective thinking. Matter and spirit have been defined and analyzed before, but now let's take a look at their respective properties.
Contradictions with inertia are called matter, and contradictions without inertia are called spirits. Inertia also refers to keeping the original state unchanged, so if a contradiction is constant, then it can be regarded as matter. If the change is small, then it is similar to constancy, then this property is continuous. Mathematically continuity is similar to connectivity, which is conflated here for the moment. Thus materiality is defined: the contradictions that can be connected by us are called matter, and those that have such properties are called materiality. Then spirituality is discontinuous. Of course, if it is not communicable but still material, it is a different substance.
According to the nature, if there is a material contradiction that changes drastically, it can be considered that it does not have continuity. In functions, it can be described that the slope is too large or the angle is close to π/2, which is also discrete, i.e., spiritual.
The stillness and movement of society
Since society is a binary opposition between the material and the spiritual, it must be expressed from the perspective of the unification of the two, that is, the slope of the social level.
The correspondence between potential and event was mentioned before, so I will not talk about it here. There are three states as motion: resting, action, and steady. The resting state and the action state are well understood, and the steady state is in between, that is, it seems to be moving but not moving, and it seems to be static but not static.
Let's start by looking at the resting state. The resting state denotes the complete static state of society, i.e., there is nothing at all. If the social state is denoted by S, then the resting state is denoted as S=0.
The action state is also easy to understand, that is, the turmoil of society, the large-scale action of society, when the development threshold is exceeded and below the destruction threshold, M is used to represent the destruction threshold, and F is the development threshold. If S>M is called a destructive state, it is also called an inactive state. If F<S<M is called a developmental state, it is also called an active state. When kF < M≤(k+1)F, the threshold of S is said to be k order F. Thus, when rF<S<(r+1)F, where S is in order rF, it is denoted by P, P=⌊S⌋=⌊rF⌋=⌊r⌋F=rF, and ⌊⌋ is rounded down. Here F is not a number, so ⌊ F⌋ is a nonsense operation, the result should be 0, and the result projected here is still F itself. It should be noted here that generally speaking, the projection of 0 or ∅ in any direction is still itself, but the 0 or ∅ obtained by the zero operation of non-zero multiplication is not really 0 or ∅, so the result of the projection operation of this 0 or ∅ is generally not 0 or ∅. In the action state, any r and k are positive integers, and r≤k must be true, i.e., integers. k is also known as the stiffness coefficient of the system, and here is the stiffness coefficient of society.
Homeostasis generally refers to changes within the normal range. When S ≠ rF, or S=tF (t is a non-integer and t>0) and S is between ⌊t⌋F and ⌈t⌉F, it is called a steady state, and the steady state is ⌊ t⌋ order, and ⌈⌉ means rounding up, ⌈ t⌉ and ⌊t are constant ⌋. In fact, the ⌊t ⌋ here is actually r. In addition to being equal to r, when ⌊ t⌋=0 is called the basic steady state, and when ⌊ t⌋=r, it is called r-order steady state.
For any positive number q, it can be written as the addition of integers and decimal parts, that is, q=⌊q⌋+{q}, {} means to take the decimal part, ⌊q⌋ is r, {q} is the t of the 0th order steady state (basic steady state), which is directly represented by t.
- From above, S=qF=rF+tF. That is, a society in any state can be expressed as the sum of action and steady.
- Since S=S+0, a society in an arbitrary state can be added to a society in a resting state.
- To sum up the above two articles, R is used to represent the society in the state of action, 0 means the society in the resting state, and T represents the society in the steady state, then S=0+R+T, that is, the sum of the three.
- Off topic. In fact, all arbitrary meta-opposition systems can be written as the sum of the opposing aspects and the 0 state. Any contradiction that contains the opposition between motion and rest can be written as follows: P=0+J+S, where 0 is a constant function, J is a strictly monotonic function, S is a periodic function, and P is the total function. Each term in the equation can be thought of as a single or multiple like-like additions.
- Back to topic. The current situation of S is determined by R, T is only the basic steady state, which only plays a role in the development of the current S, if the number represents the order, if and only if 0T→1R, that is, the R order +1, it will have an impact on society. The order of S depends only on R and has nothing to do with 0 and T. Even if T is of order r, it can be thought of as order r plus the base T.
- From the formula, it can be seen that R is a total or no change, that is, the action potential. T cannot cause a change in the order of S, i.e., local potential. In other words, R is quantum and T is continuous.
Normal, variant, and abnormal
Finally, let's talk about a set of social dualities that I haven't talked about before.
Power refers to the degree of approaching a contradiction, that is, the power of a contradiction is the sum of the contradiction that a contradiction tends to be on the power, that is, pⁿ=p×n+p×n×n+... , "×" means to make pn, or n.
Since truth and falsehood are concepts established in consciousness, they are denoted by R¹, and right and wrong are concepts based on truth and falsehood, and therefore denoted by R². Normal and abnormal remain within Rⁿ. Definition:
- Normal: The nature of society is as expected.
- Anomalous: The nature of society does not meet expectations.
In the past, EX was used to represent the hope of X, but here T is used to denote the property, which can be interpreted as normal and abnormal in this way: if TS=EX, it is normal, and if TS≠EX, it is abnormal. The nature of EX mentioned earlier, that is, the relationship between EA and B, needs to be redefined here: take B as extremely good, then -B as extremely evil, 0 as non-good and non-evil, then EA∈[-B,B], EA<0 is evil, and EA>0 is good. Therefore, E is actually based on human consciousness twice, B is a subjective indicator, EX is a subjective indicator, so that EA is actually R², and furthermore, the previous EA is R³, so the normal and abnormal here can already be considered R⁶. Therefore, whether the society is normal, even a person may have a variety of views, the normal and abnormal of the society, many people will have more opinions, the reason, from the definition, it can be seen that the definition of normal and abnormal, based on the unstable contradiction of the application of consciousness many times, the primitive is unstable, the system will be more unstable, or the primitive belongs to the function, then the system also belongs to the function, and it is impossible to have a situation where the nature of the system is different from the primitive.