1. From the point of view of computational complexity, polynomial means equivalence, and exponent means difference; from the point of view of number, polynomial is an equivalence class, and exponent brings about the difference of rank. So, with a high probability, P!=NP . But why are indices so special? Can it be analyzed from an information theory perspective? In addition, from the perspective of differentiation, it means dimensionality reduction for polynomials; exponents maintain invariance, is it related to this?
2. Financial activity is like water, flowing in the direction of potential decline. The amount of water in the process does not change, but it will affect the environment on the path. Without path control, water flow can cause bad results. If there is demand, and there is no path, the flow may spontaneously rush out a new path.
3. The basic principles of the natural sciences have been studied relatively clearly, but the basic principles of the social sciences seem to be unclear, and in many places contradict the laws of the natural sciences. But living things themselves should obey the laws of nature. Unless it’s because of the introduction of a new variable through some spontaneous or other behavior.
4. The meaning of mathematics is to grasp the essence of the problem. Consistency in a system can be seen through different forms. For example, high dimensions look at low dimensions, and complex numbers look at simple numbers. Conversely, generalization from general concrete operations to abstract more general operations, such as addition, subtraction, multiplication and division, reflects the law of association between things. Perhaps, to study mathematics is to study how the universe is constructed.
5. Many times, the idea of solving the problem cannot be found because the problem has not been clearly defined. So the definition is the hardest. The reason why Tao Te Ching is difficult to understand is precisely because of the lack of this premise of definition. In this sense, the range of human perception depends on the ability to express language. So, are the expressive abilities of different languages equivalent? If not equivalent, which language is more efficient?
6. Asking questions is sometimes more important than solving them, especially in cutting-edge fields. Science is to ask questions and further find solutions. Engineering is more important to achieve better.
7. Increasing entropy means eliminating difference; decreasing entropy means introducing difference. The basic form of difference expression is comparison. And sorting is undoubtedly a natural comparison. Nature doesn’t like comparisons, but humans do.
8. The traditional goal of Eastern education is basic training, which means that there will be people who cannot get enough to eat. In the information age, there are more ways to access knowledge, which means that personal learning will become more critical; it means that education will return to the elite of Western education.
9. In the past, human civilization was based on individual abilities, that is, the development of the whole depended on talented individuals. And this model has basically approached its limit. The follow-up is either to develop group intelligence cooperation; or to see if machine-assisted thinking can break through.
10. The world is smooth in most cases, which means that the laws summarized through local analysis are likely to be general. It also means that many things have prior knowledge. But once there are a few unsmooth situations, there will be more out of control than expected.
11. Learning new knowledge will go through four stages: not understanding, feeling understood but unable to speak, being able to explain clearly to people in the same field, and being able to explain clearly across fields. Therefore, being able to talk about a thing means that you have already started; talking about a complex issue in a simple way means you really understand it.
12. Transformation (compression, encryption…) does not change the dimension and does not lose information, so it is reversible; but dimensionality reduction (hash) will lose information and be irreversible.
13. If DNA is the code for software, biology is the form in which the software’s interpretation operates. But where does consciousness come from? The essence of the physical world is information, but consciousness is not information.
14. Natural evolution is between intelligent design and random evolution, but because there are external influences, it is closer to intelligent design than random selection; but civilization evolution currently cannot see where the external influence is, which may be why civilization evolves Reasons for slower evolution relative to nature?
15. There are two major directions in the evolution of civilization: one is that all individuals greatly strengthen their ability to communicate and form a community; one is the great development of science and technology, and individuals completely separate from the group and exist independently.
16. The difference between countable and uncountable is that after separately countable division, the former will be finite, while the latter will remain infinite.
17. Information → increase order → break symmetry → destroy energy → generate mass. But how does the reverse generate information from mass? If it can also be proved, then information, energy, and quality can be unified, and the world will no longer have mysteries.
18. Both absolutely ordered and absolutely disordered systems are fragile, and most sustainable systems are always somewhere in between, and can constantly adjust themselves.
19. From the point of view of the scalability and complexity of interaction, the peer-to-peer network is polynomial, the centralized network is linear, and the hierarchical network is logarithmic. This, in turn, means that as the size of the network increases, most will naturally go through such processes as peer-to-peer, centralized, and hierarchical.
20. The ultimate mystery of how the world works is so fascinating. When I was young, I naturally took physics as my research direction. However, it soon became apparent that the subjects were unable to recognize the system itself. Probably the best way to understand a system is to construct it yourself. Information science brings a glimmer of possibility.
21. A paradox of traditional economic theory is that in order to optimize the allocation of resources, it is necessary to pass the production and consumption links. This leads to crises (economic, financial, war) that inevitably come periodically. Actually the two don’t have to be tied together at all.
22. The only difference between a market and a plan is who gets most of the resources, the contestants or the referees. Most countries now participate in both.
23. The reason why organisms evolve is because they have been unable to get rid of the influence of uncertain environmental changes; the reason why human beings stopped evolution is to create a controllable external environment through technological means.
24. In the early 20th century, the reason why physicists were able to discover the theory of relativity may have something to do with the emergence of this form of film at that time. Experience, abstraction, and association are important abilities. One of the important reasons why it is difficult for humans to imagine certain inferences in science is the lack of similar experience.
25. time == space, computation == storage.
26. Energy == Matter. Matter is the property of space, and space is the representation of information. There is a deeper level of conservation behind this. Incomprehensible experiments in quantum mechanics are much more natural if the understanding of the world simulates computation.
27. Resources are generally limited, so some members are allocated more and others less, requiring more labor and preferably acknowledging labor.
28. Local optima often lead to failure to achieve global optima. The way to improve is to introduce information and trust. Trust in technology will be the key to a new level of human social organization.
29. The essence of finance is to transcend time and space; the essence of exchange is to eliminate uncertainty through information.
30. The essence of mathematics is intuition, the cognition of the laws of the world. Calculation is just a process, not a necessity.
31. The only thing that can affect the speed of space-time is the electromagnetic force, perhaps because it is the fundamental force that makes up the world.
32. Perhaps the reason why fractals are ubiquitous in nature is that they are easier to generate with a small amount of computation.
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