Chapter 57: Mathematical Rhapsody IV
The ratio of different individuals in the group is volatile, and the minority strategy has an advantage in the majority to make it the majority, and so on. Pen × fun × Pavilion www. biquge。 Eventually, the INFO reaches a certain stable ratio, which satisfies the principle of diversity and is conducive to responding to changes in the external environment
Wave-particle duality acts like a hybrid strategy to maximize benefits
Logistic maps not only have iterative operations, but also embody a coupling system in which x represents its previous state (1-x) represents differentiation, and there is self-similarity in the operation
Chaos and large-scale behavior of populations are mutually causal, and genetic variation is a kind of chaotic behavior
Spin quantum numbers are also a role in selectivity
For a certain field, the application of least squares can establish a "local and temporary unified theory" of that field
Suppose that for a regional Ω, the following general equations have been established
(1)
The boundary condition that is satisfied on the boundary v is (2)
Applying the method of least squares, the "unified theory of local and temporary (so far)" in this field can be expressed in the form of "unified variational principle of local and temporary (so far)".
The Evolution of Physical Thought -- "From Certainty to Uncertainty, from Continuity to Discreteness, from Composition Theory to Generativeism, from Unity to Unity, from Detail to Whole, from Simplicity to Complexity, from Existence to Evolution, and from Continuity to Discreteness, from Unity to Unification." Then there is the principle of certainty of uncertainty
Different definitions of the historical period of a concept can be used to calculate the occurrence probability of different derivations, interpretations, processes, etc., so as to construct an equation model
Boundaries, the universality of context, mobility as a measure of everything, active dynamics, relativity, social connections
The absoluteness of the speed of light
The observer is also discontinuous, discrete, and its spacing is related to the speed of light
The product of the error in measuring a pair of conjugate quantities must be greater than one constant
|pxz-pzy|≤1+pxy
Novel silica gel extraction method
Communication, the transfer of information, the handling of specific rules and the decipherment of common background knowledge
1 and 0, fractals of information, first-order correspondence of letters, and second-order Morse ciphers establish multi-dimensional closed rules
Coding is communication
eiθ=cosθ+isinθ
zn=rn(cosnθ+isinnθ)
(cosθ+isinθ)n=cosnθ+isinnθ。
pv/t=c, pv=nrt, the proportion of the set
The hierarchy of atomic structures derives similarities, and electrons circulate as money as equivalents in redox reactions
Dependent, crossover proportions predict vertical relations, and the bias x and y of high dimensional derivatives
The form of interaction I tend to be in the form of Maxwell's equations, which have vertical relations
The ratio of heat to temperature, the ratio of the amount of change to the background. Entropy, a measure of chaos, a high-dimensional structure
Microscopic molecular organisms are sensitive to concentrations
The positive and negative controls for the test are the upper and lower interval limits for the more basic cells.
The second law of thermodynamics, entropy maximization is an irreversible process, do we want to find the irreversible law that describes the fundamental interactions? This depends on probability, statistical evolution
Time is a structure and even an object that participates in the process of movement and is constantly informed
The impact and convergence of multiple concepts, methods and incompatibility of structures have prompted people to come up with more perfect structures, and now there is one of the most perfect methodologies that have been proposed first, and in the process of their development, they are constantly compatible and internally upgraded, that is, to imitate the evolution of life in our nature.
Nonlinearity and non-equilibrium make the organism highly sensitive, because the essence of life is a system of its own iterative calculations, and I think this process is not infinitely incremental, on the contrary, it constitutes a cyclical structure, but at which point it stops, it is a matter of shutdown. And diversity is both the foundation and the result.
I believe that everything is manifest, just as an iceberg is our observable entity, then this is the result of a larger part of the water below, the emergence of any model is the result of the exclusion of other models that cannot be formed, there are always some unique individuals in a group of people, and manifestation is inseparable from big data. This is the emergence of a new level
The world is not complicated, but if we want to get close to reality, we have to go far enough in this cycle, the world is the form, we are the object, and we can be computable by the former. Objects large enough also have their own form of manifestation, and philosophically it can be thought of as the mind, which breathes with the world through adjustment. The form is deterministic and reversible, while the object is irreversible and random.
The harmony of the whole and the fierce confrontation of the parts are coupled.
Feynman's path integral is an operation of individual probabilities.
Away from the equilibrium molecule, there can be information transfer, which is the conversion of entropy
Complexity is related to the number of objects and their relationships, while periods can be broken down into various combinations.
Energy level transitions are a feature of dimensional change
The stratification of the whole implies the breaking of a continuous symmetrical group.
Chemical equilibrium is the structure of a positive and negative process that is infinitely polynomial, weighted or the cause of change. I believe this is non-convergent. This is similar to the third law of mechanics, where forces are always reciprocal.
The holding of the phase is part of the coupling.
The uneven concentration distribution of substances in the region is a prerequisite for coupling, and the concentration difference provides a potential energy, so we should pay attention not only to the location of the matter but also to its relationship
The evolution of the state of the system over time is visualized by the movement of representative points in phase space
A coupled system of one degree-of-freedom subsystem is not integrable
Understand how the various parts of the system interact with each other
The network determines the individual nature, and its capacity determines its coupling degree, that is, the network. This is studied from the intermediate level of the individual and society
Does the path dependence of complex systems be as fixed as the atomic energy levels, and this means that the general laws of the largest systems are hidden in the smallest elements? We need to relate terms and transform them to a certain extent, such as the inversible operator transformation of time and quantum in a system
The topological space is related to the continuity of the function, and the manifold is the topological space of the calculus of the function, which can be expanded locally with a power series
The manifold is local Euclidean and satisfies certain compatibility conditions, which makes it fitting that its hierarchy participates as an entity in the coupling of the levels: it needs to rely on a whole space
Manifolds are different for different dimensions
In a space of a certain dimension, bounded functions can be mapped to constants
The manifold is like the probability space of electrons, which we know can be localized into an image, but this image is not unique, what we see is the appearance of the hidden state
Use the Riemann surface to make a non-function a function, which is the inverse dimensionality reduction
The establishment of space is the establishment of relationships, and space is seen as an algebra that can be operated between spaces
The establishment of the derivative is to find the regional variation of Euclidean space, and in the operation that determines the subsequent development with its own development, it is both a form and an object, and it is self-consistent in the process of continuous transformation. But this is single-threaded, and I think the present state has both the past and the future, that is, it does not recognize the unidirectionality of time, like a triangle-like coupling system
1=n/n=(1/n)^n;(1/n)^n+1=(1+1/n)^n=eThis is an external derivation, where n becomes infinity and is often equivalent
h*(bg)=h*(bh),h≠g
h=gl(l(g)) stacking
Group, constructing a specific operation to make a certain object relatively self-consistent, which is a regular space. The operation is ab*bc=ab^2c. The matrix is ab*bc=ac, which is not self-consistent, but the result is still an element of the group
The relationship curve between the volume mass, i.e., density, and the volume fraction, i.e., proportion, can be matched by parabolas, but these arcs are not smoothly connected---- for the quadratic polynomial p(x), if there is maxp(x)=m in the interval of 2l length, then the absolute value of the derivative of p(x) is less than or equal to 4ml
Time is perpendicular to the spatial dimension, and the projections of the vertices and edges of the four dimensions are probabilistic, and when the three-dimensional organism decides to understand the four dimensions (the dimension includes the impossible), the dimension is a collection of possibilities
How do you introduce the imaginary number i?(2+1) in a living organism. 5i)*(-1+2。 4i)=-5。 6+3。 3i and what we see is 2*-1=-5. 6, which requires complex spaces to explain the phenomenon of non-conservation. Whereas the multiplication of complex numbers is the multiplication of modulus, and the amplitude and angle are added
Complex numbers are representations of the magnitude and direction of vectors
Elementary variables, Euclidean geometry - non-Euclidean geometry, group theory - set theory, topology, abstract algebra, mathematical logic - system theory
Mass and quantity are two low-dimensional projections of entities, and mathematics studies quantity, the relationship between quantity, change and even change, and the relationship between relations. The study of quantities consists of numbers, abstract numbers, real number systems, complex number systems, and algebraic systems composed of groups, rings, and fields
Spatial forms, discrete systems, and connected phenomena are the basic mechanisms of biological four-dimensional 1 differential geometry, topology 2 number theory, modern algebra 3 differential equations, function theory, functional analysis
Space-time is a medium with etheric properties in the universe, elementary particles are the manifestation of space-time, which can be regarded as a closed coil, and the coupling of different combinations of coils is an observable entity such as chemical elements. The reason why it is a closed coil is that it is unstable if it is not closed
Each knot can be linked to a polynomial invariant, and the number of intersections can measure the complexity of a projection diagram, but the operability of the lines makes the overall intersection and the transformation of the continuum group continuous.
The topology focuses on continuity
The essence is an averaging abstraction, like the expectation of probability, and the variation of the group in turn determines the essence
Heredity is atomized and relatively solidified
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