To solve the important problems we face, we cannot stay at the level of thinking that created them in the first place. ——Einstein

From the outside, the system has behavior. From the inside, the system has structure. The system is the unity of behavior and structure.

We can only hope to estimate how the computational effort will grow as the size of the problem grows. Experience shows that unless some simplification can be made, the increase in the number of calculations is at least the square of the increase in the number of equations. This is the "square law of calculation".

People always simplify complex mechanical systems through informal methods before starting to apply formal methods.

Newton's research went even further. He noticed that because of the Sun's unique mass, each planet and Sun could be viewed as a system, separate from other systems. In this separated system, only two objects remain. The technique of decomposing a system into several non-interacting subsystems is very important for all mature disciplines, and is certainly equally important for system theorists. To understand the importance of this decomposition, just think of the "square law of calculation."

Among these simplifications, Newton and his contemporaries were generally more aware of and more concerned about simplifying assumptions. Physics professors who teach Newtonian calculations today do not. Therefore, it is difficult for today's students to understand why Newton's calculations of planetary orbits rank among mankind's greatest achievements.

Newton was a genius, not because his brain had super computing power, but because he could simplify and idealize so that ordinary people's brains could understand the world to a certain extent. By studying simplified methods of past successes and failures, we hope that the progress of human knowledge will not rely too much on genius.

These physicists include Gibbs, Boltzmann and Maxwell. They inherited a set of observational laws (such as Wave-Eyer's law) that describe the behavior of gases with certain measurable properties (such as pressure, temperature, and volume). They believed that gases were made of molecules, but needed to explain how this belief related to the observed properties of gases. What they do is to assume that these interesting observed properties are some average properties of molecules, rather than properties of one of the molecules.

We see again that in order to obtain relatively accurate laws about the interaction within an organism and with the external environment, we must require that the organism has a considerable structure and quantity. Otherwise, the number of interacting particles will be too small, and the "law" will be very inaccurate.

What is the scope of application of statistical methods? What is its relationship with the scope of application of mechanical mechanics? There is a saying that statistical mechanics faces "disordered complexity", that is, the system itself is very complex, but its behavior shows enough randomness, and therefore has enough regularity to allow statistical research.

In today's society, mechanical technology benefits from the inspiration of mechanical mechanics, reducing complexity by reducing interrelated components. On the other hand, management techniques benefit from the achievements of statistical mechanics, which regard the crowd as merely interchangeable units in an unstructured group and simplify it by taking the average.

For systems between small numbers and large numbers, both classic methods have fatal flaws. On the one hand, the square law of calculation points out that middle number systems cannot be solved analytically; on the other hand, the square root law of N warns us not to expect too much from the average value.

Like most laws of general systems, we also find a form of the law of numbers in folklore. Converted into our daily experience (we are both familiar with such systems and helpless with their performance), the law of middle numbers becomes Murphy's law: Whatever can happen, will happen.

When analyzing the parts or characteristics of things, we tend to exaggerate the obvious independence and ignore (at least for a period of time) the essential integrity and individuality of the combination. We decompose the body into organs and the skeleton into bones. Psychology is taught in a similar way, subjectively breaking down the mind into its component parts, but we know very well that judgment or knowledge, courage or tenderness, love or fear do not exist independently but are part of the most complex whole. a performance or imaginary coefficient.

Biology and social sciences are not as "successful" as physics. They cannot arbitrarily cut the world in front of them into small pieces, because what they get is indivisible. Anatomists have had some success, but we're not interested in what someone does when they're broken down. Sociologists have had even less success, because their main interest is in "humanity" with the properties of a numerical system, properties that cease to exist if the system is decomposed, abstracted, or averaged. If behavioral scientists try to understand "individuals" through averaging, the individual's characteristics will be spread out. If they try to isolate individuals for research, they also cut off the connection between the research object and other people or other parts of the world. The individual becomes only an artifact of the laboratory and no longer a human being.

In other words, science is essentially about simplification. However, it must be pointed out that reductionists have not yet succeeded in reducing all phenomena to physical and chemical primitives. Whether they can succeed or not is a purely philosophical question, not a scientific question.

If the actual situation requires us to move forward, we must not stop at a simple and crude analogy, but polish it into a model that is precise, clear, and predictive.

To become a "participant-observer", you must first become a participant, which requires at least learning some local language. In fact, it mainly involves learning various non-verbal communication methods. Similarly, to integrate into a certain work subculture, you first need to learn the way of thinking and communication of this subculture.

The most dangerous mistake when developing a system of thought types is to assume that one thought pattern is more "real" than another.

Some scientists can also manage to fit into the thinking patterns of several disciplines. How did they do it? Whenever asked about this, they expressed their belief that there is an inherent unity in science. They also have only one mode of thinking, but their starting point is very high. People with this thinking mode believe that thinking modes in different fields are very similar, although their expression forms are often different.

The power of reasoning does not lie in how reasoning uses rules to guide our imagination, but in liberating us from the constraints of experience and traditional rules.

The power of generalization through induction is that we can use general rules to draw certain conclusions about unobserved situations. This is also the reason why generals can transfer from one subject to another. Every success will increase people's trust in the second-order sequence.

Of course, faith is necessary, because not every jump between disciplines can be successful. Why? Because induction cannot always be effective. But why aren't we more cautious? Why not wait for more evidence? The reason is that knowledge is growing explosively, and our brains are limited by the square law of calculation.

But it's like the eternal paradox that teachers face: teach facts and charts, or teach truth. To teach a model, the teacher must use concrete diagrams and clearly illustrate something that cannot be seen at all. Students must "learn" something so that they later realize that it is not quite what they learned it to be. But by that time, he had grasped the essence of things and began to get closer to the truth. They will spend their lives constantly revising and getting closer to the truth.

If a law contains many conditions, it can be difficult to remember when to use it, because each condition limits the scope of the law. The fewer conditions there are in a law, the more general it is. Add conditions or change term definitions? When we face such a problem, we usually choose to redefine the term.

Many general system laws are expressed in a variety of ways: as definitions, as methods of measurement, as exploratory tools, especially in negative forms that are easier to remember.

Any general law must apply to at least two specific situations.

There should be at least two exceptions to any general law.

Law of combination: The whole is greater than the sum of its parts.

The law of decomposition, that is: the part is greater than the part of the whole.

Systems theory (originally an attempt to overcome the current problem of overspecialization) became one of hundreds of academic specialties. Moreover, systems science is centered on computer technology, cybernetics, automation and systems engineering, which seems to make systems thinking become another technology (actually the ultimate technology), making human beings and society more like a "huge machine" "...

The contribution of general systems methods to thinking may be fully reflected in the methods of general systems scholars to deal with new courses.

What is the system? Poets all know that a system is a view of the world.

That's the "banana principle": heuristic thinking methods don't tell you when to stop.

People can say or write statements that are perfectly acceptable but don't make any sense. If we study some meaningless sentences, we can better understand how to say them meaningfully, because exceptions do not prove the rule, but teach us how to understand the rule.

Much of people's dissatisfaction with man-made systems stems from a disagreement with the "purpose" of these systems' design: that is, what the system "exactly" is. Of course, the answer is that the system has no "purpose", because "purpose" is a relationship, not something that can "have".

Both sides are right, but because everyone uses absolute statements, there is a problem. It seems that the "emergent" property is some "thing" possessed by the system, rather than a relationship between the system and its observer. These properties "emerge" when observers cannot or do not make correct predictions. We often find examples of things that appear "emergent" to one observer and "predictable" to another.

overall. In fact, it's hard to find an arbitrary system because once we think of one, it becomes somewhat non-arbitrary.

The most popular method of ignoring the observer is to jump directly into the mathematical description of the system (the so-called "mathematical system"), without saying a word about how to choose this description method.

As long as the members of a set are "not nothing," our reasoning is strictly content-independent, that is, it is a purely mathematical description.

Mathematicians generally assume that no matter what connections are made, unsound arguments can never be established.

The first joyful property of using sets is the refinement of the concept of an observer. What an observer does is observe. These observations may be some kind of feeling from physiological organs, or they may be readings from measuring instruments, or they may be a combination of the two. An observation can be expressed as selecting an element from a set that contains all possible observations of this type by this observer.

In the "observer" model, we must always remind ourselves: How much computing power does this model require? But please note that we do not require that our "observer" can make every observation "correctly" (the ragged and shabby elements), because these are our original, undefined elements, and when using them, "Correct" is meaningless.

We may not be able to tell whether an observation is correct. However, without a symbolic representation of "correctness," there cannot be an in-depth discussion of observers and their observations. Therefore, the concept of consistency is introduced here: that is, whether one set of observation results is consistent with another set. Clearly, as Lincoln pointed out, the consistency of symbols does not depend on how the observer names the observation.

Note that the concept of a super-super-observer is much like the concept of "fact" in that it encompasses "all possible" observations. In other words, what we call "fact" is very close to what some people call "God."

Queen of Hearts Music Box

As the saying goes, "seeing everything" does not mean "understanding everything", because understanding means knowing which details can be ignored. Our "learning" is just seeing the "same" situation recurring. This is what we call a "state", and if this situation is repeated, the observer can recognize it again.

Distinguishing too many states is what we mentioned earlier as insufficient generalization.

The universal observer's law, that is, the eye-brain law: To a certain extent, brainpower can make up for the lack of observation. Based on symmetry, we can immediately derive the brain-eye law: To a certain extent, observation can make up for the lack of brain power.

A distinction is made between original properties and auxiliary properties - the former is intrinsic to matter, and the latter is the product of the interaction between a subject possessing certain original properties and the sensory organs of a human or animal observer.

Likewise, the assumption that observations must be consistent with existing theory introduces conservatism into scientific research. If an observation is inconsistent with existing theory, it is likely to be discarded as an "error."

"A state is a situation that can be recognized when it recurs." But if we do not combine multiple states into one "state", no state will recur. Therefore, in order to learn, we must give up some potential differences in states and give up the possibility of learning all the details. Alternatively, we can write it as the dough-kneading law: If we want to learn something, we must not think about learning everything.

Function symbols are particularly important in general system thinking, because when we cannot accurately describe the behavioral characteristics of the system, we can use it to represent part of the knowledge of the system.

So what mistakes do scientists make when doing this kind of decomposition? There are two main answers to this question. 1. At a certain stage, he may omit something in a functional relationship, and further decomposition will cause errors because of this, although a good approximate law may be obtained. We can call it an incomplete fallacy. 2. Even if the observation is complete, the decomposition process will eventually stop, either because the observer's ability is limited (including the observer's patience is limited), or because the "actual" situation does not allow continued decomposition.

All success in physics research depends on the judicious selection of the most important objects of observation, combined with the brain's spontaneous abstraction of some features. Although these characteristics are attractive, current science is not advanced enough for research to yield useful results.

Because we are looking at the problem from the perspective of a super observer, we can let other observers expand the observation, improve the granularity of observation, or enhance the memory ability, but they do not have the information needed to make these choices.

We just saw the failure of the decomposition strategy caused by incompleteness. In fact, we can turn this idea upside down and use it as an intuitive definition of completeness. In other words, no matter how we choose from isomorphisms or how many fine perspectives we decompose into, we will not discover new essences. We also see that completeness can only be an approximation, and since it is based on a jump of inductive belief, it cannot be guaranteed to be correct. The reductionist fallacy arising from incompleteness is acceptable because we have all experienced it in some form.

However, the second reason for the failure of simplification is more difficult for some people to accept, and this is the issue of complementarity. Physicists first encountered this problem of fit and predictability because physics was more advanced in its ability to apply simplifying strategies. In addition, some scientists (or people who call themselves scientists) are usually so far away from a complete view that they are not surprised that their decompositions sometimes go wrong. If physics had not proposed "complementarity" (a peculiar model of reductionism), then probably no one would have accepted this concept.

The key point of the idea of ​​complementarity is that they are two viewpoints that are not completely independent but are irreducible to each other.

Reduction is just one way to achieve understanding, there are many others. Once we stop looking more closely at a small part of the world and start looking more closely at science itself, we discover that reductionism is an ideal that has never been realized in reality. Reductionism is just a scientific belief. It must be belief, because no one has ever seen the final reduced state of any set of observations.

How does the handyman know that the upcoming job will be similar to the one in the past? This is just a belief that we have encountered before. Maybe we should name it Empirical axiom: The future will be like the past because in the past, the future will be like the past.

On this level, science and poetry are very similar. The poet begins with a metaphor and then goes on to explain in detail how his lover is like a rose, or how the dawn is like a goddess who can be embraced. The scientist starts with a complete view, then proceeds to revise and simplify, finally reducing the original function to a function of something else. Like the poet, the final reduction is assumed to be known and therefore does not need to be defined.

Metaphors can only work if we understand (or think we understand) certain characteristics of one thing and transfer them to another thing.

We use the metaphor of "part" or "thing", which is closely related to our experience of physical space, especially our experience of "boundaries".

Even so, we encounter difficulties in reasoning when dealing with systems with practical boundaries. Problems often arise because we choose boundaries based on past experience or the experience of our predecessors. Since these experiences are very effective in most cases, when they are invalid, it is difficult for us to get rid of their influence.

The problem here is that the "boundary" may not be infinitely thin, it just happens to belong to both the system and the environment. This kind of boundary is not a division, but a connection.

For observers with limited memory, properties have a thinking function. We may think that some properties are more "natural" than others, but this simply means that we are more accustomed to observing in that way.

As our work environment becomes increasingly unfamiliar, those inherited and learned perceptual abilities will become increasingly ineffective.

Invariance law: For any given property, there are some transformations that keep it unchanged and some transformations that change it.

If segmentation describes a property, it means that when the state is constant, this property does not change over time.

A relationship must conform to our intuitive understanding of properties, and the second attribute is symmetry.

Even if "friendship" is a symmetrical relationship in a specific system, we still cannot divide this system into "friends" subsystems due to the need for transitivity, that is, the third condition.

Just like scientists or poets, what they pursue is to approach "truth", and this approach can never be completed.

The accumulated problems include two situations. In the first case, the current science can solve it, but it has not yet been solved, either because there is no attempt or because of improper understanding. In the second case, current tools are not enough. This is what the general systems theory movement is really concerned with.

The law of forming strong connections: On average, the tightness of system connections is above the average level.

We do not intend to use this particular form to say outright that a system is a perfect system, but simply to call attention to the interdependent nature of it.

Some systems theorists view simulation as the ultimate tool because they believe that to explain an understanding of behavior, one must construct a system to exhibit that behavior. The inside of the system is no longer completely hidden, but completely exposed. This is a white box, not a black box.

System modelers must work hard to overcome their own instincts

We saw how to decompose "attributes" from the system through segmentation. The product space shows how to put them back together in a systematic way. If each decomposition is a real division, then the product space must include all the original possibilities. In this case, everything should have its place, and everyone should be in its place.

The points on the plane do not represent the state of one system at different times (the so-called "diachronic perspective"), but the states of different systems at the same time ("synchronic perspective"). This method works well for both perspectives and corresponds to the common scientific method of replacing successive observations of one system with multiple individual observations of similar systems, and vice versa.

Ordinary people who are not mathematicians often feel awe when they hear talk about n-dimensional space, and think that mathematicians have super thinking abilities. In fact, mathematicians are special only in their ability to extrapolate. They cannot "see" n-dimensional space and just continue to apply the same mathematical operations regardless of how many dimensions are involved. A point in two-dimensional space is designated by two numbers, and a point in three-dimensional space is designated by three numbers. Therefore, by extrapolation, a "point" in seven-dimensional space is designated by seven numbers. A one-dimensional object (a line segment) splits a two-dimensional object (a plane) into two parts. A two-dimensional object (a plane) splits a three-dimensional object (a solid) into two parts. Therefore, by extrapolation, a six-dimensional object splits a seven-dimensional object into two parts.

An empirical rule for behavior in state space, that is, the diachronic rule: If the behavior line crosses from , then either: 1. The system is not determined by state Either: 2. What you see is a projection, an incomplete view.

Synchronicity law: If there are two systems at the same position in the state space at the same time, then it means that the dimension of the space is too low, that is, the view is incomplete.

We propose the Rule of Counting to Three: If you can't think of three ways to abuse a tool, you don't know how to use it. Adherence to this rule protects us from the fanaticism of optimists, exaggerators, and other perfectionists of all kinds, but primarily from ourselves.

Talking about step functions and slow rising curves without knowing the time scale is technical nonsense. Time scale has no absolute meaning, it only has meaning when compared with other time scales.

Science can be seen as a process, that is, exploring the angles from which things can be viewed to produce unchanging laws. Therefore, scientific laws describe how the world looks (I discovered it), or stipulate how to see the world (how I discovered it). We really can't tell the difference between the two.

Why do physics and chemistry laboratories need to build an ideal closed environment? The purpose is to create a system with a certain status for research. Why do they like to study systems with a certain state? Because the behavior of a system with a certain state is simple. Everything that happens in the system can be represented by disjoint lines of behavior.

However, if an observer takes all these issues into account and successfully isolates the system within the walls of perfection, lines of behavior may still tangle, at which point he will say that he sees "randomness." However, observers have no reliable way to distinguish randomness from hidden openness, the "leaky wall."

Describing a system in terms of typical behavior and describing a system in terms of unexpected but important behavior are two of the ways we are used to restoring the single line of behavior we like in closed systems.

Only then did we ask the question of evolution: "How did things develop to what they are today? Why can't they stay the same forever?"

All general systems thinking must start from one of the problems and start exploring until it is forced to switch to another problem. We can never hope to reach the end, nor will we try. Our goal is to improve thinking, not to solve the Sphinx's puzzle.

Stability not only means the limit of changes that the system can withstand, but also the degree of disturbance that the system can withstand. Therefore, when we refer to stability, we include two meanings: some acceptable behavior of the system and some expected behavior of the environment.

While this argument is sufficient for scientists to study nearly closed systems, for those who cannot avoid openness in the laboratory, it is purely misleading. Specifically, it can misdirect attention, causing us to look for stability “within” the system rather than seeing it as a relationship between the system and its environment. When nature wants to preserve an irreplaceable resource, it won't do anything until people actually destroy the ecosystem. There is no precise definition of "small disturbance" yet.

Circular Argument: The current formulation of scientific aims and methods is based on a cultural idea and this needs to be clarified. If we can isolate more important cultural institutions from their unique circumstances, classify them into categories, and practice until repeated occurrences lead to precursors or functionally related things, then it can be considered that the cultural institutions we examine are fundamental and unchanging, while those things that lead to uniqueness are secondary and changeable.

Why does the system survive? In the long term, this is because the systems that don't survive are no longer there and we don't think about them. The systems we often see are systems selected from all past systems as the best "survivors."

"Persistence" refers to the period of time that a system must exist for it to be worthy of study.

If we adopt a programmatic approach to identifying similarities and differences, we can clarify the concept of "identity". This field is also known as "pattern recognition" or, more specifically for visual images, "image processing".

"Difference is the most basic concept in cybernetics", and the same is true in general systems thinking. We must always remember that this is also the most difficult concept.

Within the computer, hardware represents the "laws of nature" and is also the stage where simulation is realized. While the simulation "relies" on this hardware, the key point is the drama, not the stage management.

Law of effect: Small changes in structure often lead to small changes in behavior. Or in our words: Small changes in the white box often lead to small changes in the black box. on the other hand: Small changes in behavior often result from small changes in structure.

Old car rule: 1. Systems that regulate well do not require adaptive changes; 2. The system can simplify its conditional work through adaptive changes.