The reserves of the network are very large, which is the basis of the normal state, just like the relationship between the iceberg under the water and the iceberg on the water. Therefore, the great power that can be exerted in a state of emergency is the divergence caused by a temporary balance break.

The development of the network

The network is a convergent hierarchical computer, and its computing mechanism is to induce the dynamic change of the whole through basic interaction, that is, the trend of multi-level competition to achieve equilibrium, and the problem is how to release this energy.

The logical and arithmetic operations of the network are carried out at the statistical level.

The first-order sequence of the network is the Turing machine, and its continuous traversal can form a certain complex structure. Iterative calculations can yield high-dimensional computational results, such as integrals, which are the result of ergodic calculations.

Computation, in essence, is a topological deformation of data. According to the Turing-Church theorem, there is a universal computer (Turing machine) that can simulate the operation of any other computer and come up with exactly the same result. Theoretically, everything can be processed.

Sequence matching, scoring matrix, nervous system. Thresholds, judgments, weight assignments (logic gates), probability connections.

The dynamics of cranial nerves are characterized by criticality, because the external world facing living systems is in a critical state. This is the basis for the reality of the explosive nature of the network.

The three types of logic gates, AND, OR, and NOT, are the basis of modern electronic computers. Neural network models are equivalent to Turing machines.

Nonlinear problems may be related to the distribution of the network, and statistics are needed to derive its high-dimensional structure.

Unreasonable brute force cracking can shed light in many ways, and this kind of low-dimensional computation can also play a role in the operation of high-dimensional structures. This requires a certain control mechanism to have meaningful calculations. Refer to the nervous system. However, this increase in computing power does not necessarily lead to qualitative changes in quantitative changes, because this calculation is intrinsic, and the generation of living systems requires diffusion based on intrinsics, like the wave function, which provides multi-level coupling and network stability. Exponential growth decays, so new variables need to be introduced to sustain growth.

There is a primary and a secondary, and stability is maintained. Separate out certain modules

Network memory is both a computing structure and a storage structure, which is a hierarchical coupling. Of course, there will be a certain distribution at different levels, such as the segmentation of brain regions. Human memory is achieved through plastic connections between synapses of neurons in the brain, which is the result of a dynamic equilibrium.

The organic nature of the network is derived from multi-level coupling. This is a meaningful composition pattern, which we understand as complexity, i.e., the combination of basic modules, the encapsulation and even the traversal of the system. Its most important nature lies in the different levels of convergence of the communication network, which allows it to exert its power like a division of labor. I have a belief that the lower the average distance of the network, the more power it can exert itself. Of course, this is theoretical, but there may have been special circumstances in history that allow us to compare this theory. As****.

The high-dimensional structure of the network is understood as money is to the economy and society, and information is an alternative. For example, entropy is a description of the whole. Both information theory and networks require probability theory and mathematical statistics to understand. Gambling and equilibrium achievement are basic network operations.

The concept of a channel corresponding to a network is a topology formed by a certain combination of probabilities, that is, a geometry that allows the flow of information. And information, as a relative proportion, is a potential difference.

A boundary is a linear combination that can be transformed, which is also the principle of topological deformation.

The amount of information is an average description of the diffuse nature of the probability distribution, that is, the eigenextraction of the fluctuation range.

Reducing the dimensionality of a sequence to the shortest is a binary representation of a certain amount of data. This is the basis of various factors, like the first-order operation of logic. This is actually an eigen, which can be mapped to other high-dimensional structures, such as binary trees, such as lists, such as general tree representations, and on this basis, complex structures such as networks are formed by traversing upwards. The coupling of sequences can construct a certain matrix, which then quickly converges to a specific combination of sequences, i.e., path collapse

The downtime principle is a computational convergence and is a path representation of the network.

The Boltzmann entropy S=lnW unifies the distribution and the power law. The modern expression of entropy H=-∫p(x)logp(x), which is a selective expression that can be counteracted by the combined effect of integrals and exponents. , i.e., a low-dimensional projection of a higher dimension is equal to a higher-dimensional mapping of a lower dimension.

This confidence in the weighted combination (obtaining a weighted combination suitable for all programs that process the data, and being able to observe that the next output can be reasonably predicted) exists only in theory, and in reality there will be a rapid convergence.

The model that uses as little input information as possible to get the most output information, and most importantly makes the data carry as much information as possible that we don't notice, like the accumulation of tiny change in a lottery.

The length of a message is positively correlated with the inverse of the exponent of the probability of its occurrence. The average distance of a network is related to the amount of information

The correlation coefficient is used to describe the degree of independence between two random variables---- and the Kullback-Leibler distance of the joint distribution of the two variables when they are independent is used to describe the degree of mutual independence, that is, the mutual information between X and Y

This is the interaction of orthogonal experiments

A Markov chain is a combination of sequences and is a high-dimensional description

According to the Bayesian equation, this means that the current state of the sequence is only related to the previous state, which is a convergence.

The computability of the network is related to basic logical processing, such as simple while loops and judgments, and when the exponent is large enough to be exponential, according to the law of large numbers, certain patterns are bound to emerge. We need to do a certain amount of training and be subject to the results that our calculations are what we want. Hierarchical traversal allows us to construct different levels of computational elements, such as assembly-programming-high-level languages, which are the influence of modules, and their simple operations may be low-dimensional complex operations.

Gödel's incompleteness theorem is a description of the network (this is bragging), and the inclusion of self-referential contradictions (compatible formal systems cannot prove their own compatibility) is a manifestation of the superiority of the network. Incompleteness, consistency, and completeness are incompatible. Like Heisenberg's uncertainty principle. Because of the first-order set-theoretic rules, we have to deal with hierarchical coupling, which requires us to understand such a system in a higher dimension. That is, the ascending dimension that transcends the geometric dimension, but the logical dimension. If we want to understand, we need to build different systems. This high-dimensional connection requires a higher-dimensional language to characterize: networks, nodes, symbols, information, patterns. 1 There is no exact relationship between the upper and lower levels, and it is the result of selective expression, which is based on the infinite amount of operation.2 Knowledge is a relatively high probability relationship description in a specific period, and the correctness is relative. Therefore, there is no specific knowledge that can be integrated into the system. 3 Relationships exist, and to understand relations is to establish the pathways of the network according to certain rules (as in derivation, this is a probabilistic distribution). Therefore, it can only be understood statistically.4 This is a dynamic, with its own metabolic relationship changes, an adaptation to the overall environment.5 The structure derived from the combination is the same dimension. (highest dimension hypothesis)6 where 5 and 3 are contradictory, but this is reasonable. 7 Network relationships are relative, so there is no contradiction. And the network is constantly topological deformed, which is why this system is nonsensical. According to my reasoning, this requires a race with extremely strong computing power to understand, it may be a pan-life, directly understanding the underlying sequence operations, or even not understanding, directly computing. The modern Internet is one such creature

The definition of a sequence is a kind of collapse, which is an intrinsic with the maximum amount of information extracted according to the fixed point principle.

Mathematics is the essence of phenomena, so what is the essence of mathematics?

Chaos and Complex Networks—The Ultimate Theory, Approximating This High-Dimensional Structure in Mathematical Language. Since it is difficult to reverse the path of the network, it may lead to different results, so we need to consider the problem in a higher dimension, and perhaps this network framework is the way we want to seek.

Observational data—phenomenal paradigms—mathematical theories--? mathematical principles modeled after Newton's natural philosophy.

The planets orbit in elliptical orbits in the plane passing through the Sun, which is located at one focal point of the ellipse. This is the first law of planetary motion, which extracts the mathematical model of the ellipse.

In the same amount of time, the planet's line with the Sun sweeps the same area. This is the second law of planetary motion, which extracts the high-dimensional structure, area, of velocity.

The square of the orbital period of all planets in the solar system has a constant ratio of the cube of the half-long diameter of the orbit of the star, the third law of planetary motion, the unity and coordination of space-time in the motion structure.

The development of rigorous logical systems and mathematical expressions in modern times may give way to fuzzy logic.

The proportions of the different levels are high-dimensional structures, and there are also high-dimensional structures that are embodied in proportions. Intuitive conclusions based on direct observation, not always reliable, may be a selective expression of the network. Often, solving a problem brings a bunch of new problems.

Law of Inertia: When there is no external force, the object will remain in its original state of motion all the time. This is the boundary. The principle of unity, looking for the universality of the law. The normal distribution of different shapes and the power law are essentially the result of hierarchical interactions, and convolution seems to be a pretty good model, which is a kind of ergosis that considers every possibility and finally understands the distribution in the form of probability. Convolution is the integral of multiplication, on which Fourier series are used to understand aperiodic coupling.

To extract a more phenomenological model from the phenomenological model, i.e., the implicit structure, we have the belief that there will always be a level that can be expressed in the language of mathematics in this process of continuous ascension. (The Principle of Fixed Points). Newton's gravitational pull is a fundamental interaction: attraction. Based on this, the world can be deduced. The force that sustains a planet in its orbit must be inversely proportional to the square of the distance from its center of rotation. This is a convergence mechanism. High-dimensional structures are best concepts that can be understood in real life, Newton's forces, and are a good coupling. Einstein further explored the structure of higher dimensions, that is, the interaction between objects is elevated to the adaptation of objects (to the essence of space-time) and curvature by changes in the environment. What follows is the combination of the two: coupling, holography, and the individual as the world. The interpretation of its message needs to be like the energy of the whole world, that is, a kind of equivalence.

Legends, standing on the shoulders of giants: mathematics, economics, game theory, information theory, medicine, molecular biology and much more.

There is no need to consider the medium in a sufficiently high-dimensional structure, and its existence is the theorem.

Boundary, convergent, mutual, relative: the principle of invariance of the speed of light, the principle of relativity. Construct the equivalence of space-time. The modification of any invariant quantity is a relative proportion. Hence the general theory of relativity, which looks for the equivalence of higher dimensions in the proportions of different levels. Such as gravitational mass and inertial mass. The final high-dimensional structure is the result of selective expression (the same mass, which can move either only by inertia or by a combination of inertia and gravity, due to the different ways in which we look at it. The inertial mass and gravitational mass are numerically equal. Explained by the unity of the nature of inertia and gravity. And the existence of this selective expression is the basis for the deformation of various topologies. For example, the mass-energy equation E=MC^2 is a topological invariant of topological allosterism, which is a high-dimensional structure.

Then at the quantum level, the language of probability is used, which is a relative proportion of levels. This is the structure of the higher dimensions. The observer effect is a possible collapse of the network, and to deduce the existence of the network in turn, an equivalent level of statistics is required to understand it.

Self-similar space-time models, fractals, can be infinitely subdivided. Holograms can be interpreted. Can explain the possible infinite number (infinite number of shortest paths between nodes)

Assumptions: 1. The probability of obtaining a new connection is proportional to the existing degree (the integration of priority, foundation, structure) 2. The average degree m tends to be constant (trend, convergence)

How to understand the hierarchical coupling of the network in the form of convolution, the result must be a certain probability distribution function. It is necessary to calculate the marginal quantity to derive the essence. The properties of the network are derived from the marginal (space), and the delta can be expressed as a function (related to the original architecture). And this increment can be equated to the difference in time change. Secondary effects, based on the original underlying probability addition, i.e., convolution. Then you can get the different levels of proportions, i.e., iterative functions. The analytic solution can be obtained by substituting the calculation in the form of a power law.

The cumulative degree distribution curve shows the properties of power law more obviously than the degree distribution curve, and the high-dimensional data has more obvious properties.

In a complex system that is constantly evolving, there are two variables x and y that form a power-law relationship y~x^y, that is, the hierarchical relationship of the network is represented by a power law, which is coupled to the distribution properties of the network structure. According to the fixed point principle, it is always possible to find two variables x and y that form a power-law relationship. This is related to the fractal structure nature of the network.

Scaling law generally refers to the fact that in a complex system, a variable exhibits a power-law distribution p(x)~x^

β。 This distribution can be obtained by sampling a complex system based on multiple time points, or by sampling multiple subparts of a complex system. It's an equivalence.

The scaling law is the power-law distribution of univariates, and when this power-law relationship is extended to the power-law relationship of bivariates, it shows the allometric law y~x^y, which can be understood as a hierarchical coupling. This is an emergent property determined by the high-dimensional construction form of the organization, and it is a necessary distribution for the network to form a stable dynamic equilibrium.

Acquired traits are essentially a meaningful pattern formed as a result of variation, in the form of a network. The network model is very good at descriptive of reality.

Holism: 1 At every level, the whole is greater than the sum of its parts. This is because of the expression of probability, and the things we can observe are selective expressions of the network. 2 falsifiability, or refutable or verifiable 3 The information originates from a network of local partial structures4

The development of cells and tissues of biological systems is related to the surrounding environment of their specific locations, which is a process of local optimization and solving, and finally has a certain emergence at the overall level. This process requires a certain amount of correction, so the determination of boundaries is a must. This is the molecular basis of the developmental process, because the higher-dimensional structure is the operation and emergence of the lower-dimensional structure. Network compensation is a selective expression of the competitive hierarchy, which makes the overall network structure stable. This ordered behavior is emergent and determined by the self-similar structure of the network.

Chemical systems spontaneously tend to structures with minimal potential energy. In calculations, the lowest energy is multi-solution, but in practical observations,

It was found that proteins always stabilize rapidly to a single structure in a specific environment, and they do not go through various forms. Therefore, there may be certain factors, rather than energy, that "choose" among these possible structures that determine the appearance of the system in a particular structure. I'm inclined to think of it as a higher-dimensional sequence matching decision.

Any evolution is essentially the evolution of a network, and the process from simple multicellular organisms to mammals is such a process, where the combinatorial relationships between tissues undergo meaningful mutation and form stable differentiation.

The correspondence between the structure of the human brain and human behavior is the correspondence of high-dimensional levels, such as love, sex, sleep, dreams, and language, with reflection as the basic unit, and the final complex network formed is the adaptation of these combinations to the environment, and the equilibrium of the hierarchical game according to sequence matching and energy distribution is achieved. It can be differentiated into certain patterns, which is the emergent nature of the network. This is based on the plasticity of the synapses of the nervous system, which corresponds to the variation of organisms and can have behaviors that adapt to the environment.

Different levels of evolution: reticular nervous system - bilaterally symmetrical nervous system - vertebrate nervous system, which is evolution at the overall level.

Environmental similarity does not lead to morphological similarity, but rather a selective expression of the network

The distribution of the network is the structural basis for maintaining its stability, and the power-law distribution is coupled with exponential changes.

In a community, there are very few species with a high number of individuals, while there are many species with a low number of individuals (power-law distribution). The species with the least number of individuals is not the most, but the species with the highest number of individuals in the middle (normal distribution), which are two different distribution methods, which are high-dimensional distributions, that is, the equilibrium reached by different levels of games. (Based on the premise of limited resources)

Bayesian networks are used for data analysis, and the various data of the network (such as the stock market) can be regarded as a dynamic game of infinite multivariates, so we can use various analysis methods to find the patterns of its changes, so as to find finite correlations (emerging patterns), that is, the similarity of the intrinsic similarities of the constructed networks. In a mature network such as a market, there may be various disordered chaos on the surface, but in the high-dimensional structure, that is, the relative proportions of different levels, can be grasped, that is, probability.

The development of the network is a multi-level game coupling, when the accumulation to a certain extent, a strong reorganization will occur so that the network structure can adapt to the next round of growth, we observe the outbreak of the network, which is the emergence of different levels of the network.

Understand probability, as long as the probability has a certain potential difference, a certain performance will accumulate under a sufficiently large base (the law of large numbers). Such as gambling. The network is the philosophical system for understanding complex games.