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In this paper, a detailed historical account of the birth, development, and applications of the theory of blown‐ups is given.

In this paper, some issues about model formulation and solving methods for the Lorenz’s model are discussed, which also deals with fundamental characteristics of non‐linear models. Mainly, there existed problems that Lorenz’s model was formulated based on the weak nonlinear, and spectral expansion which changed the fundamental properties of prototype of the N‐S equations. Furthermore, its solving methods, which are based on continuously smoothing schemes, not only distorted the fundamental characteristics of non‐linear models, but also led to misunderstanding of the concept of “schaos”, which has already caused confusion to people’s way of thinking. In essence, Lorenz’s chaos is an “error volute” which is trapped into “calculation of error values”. Whether it can be named “chaos” may need to be discussed with questions.

Looks at how an undergraduate had to fill in the gaps to be a success by validating research ‐ using the big names of scientific history to relate the corresponding work. Gives anecdotes of the authors’ progress and the teachers who were most noteworthy in aiding him. Uses tables to emphasize certain points about the environment and various other mathematical and scientific ideas. Emphasizes the importance of other experts’ work in this field.

Argues that the purpose for the existence of the evolution science since the seventeenth century is how to once again understand the evolution science and its origin. Explains, on the basis of this new understanding, how some of the problems dating from the seventeenth century can now be resolved. Finally, briefly describes the method of infrastructural analysis of the second stir.

After many years’ practice and experiments, it was found that quantitative analysis systems with unequal quantitative effect cannot be extended into that with equal quantitative effect. While it is related to such epistemological viewpoints as irregularity and continuity systems, an infrastructural form comparison has shown universally scientific and methodological characteristics. In combination with evolution of weather systems, our infrastructural analysis involves applications of super low temperatures, reversed information order, rolling currents infrastructure in reversal weather change and long‐term weather forecasting.

The work presented here is based on the assumption that all non‐linear properties, appearing in the evolution of magnetic fluids, are a complex system. Then, the establishment of a relationship between the structural changes in the geomagnetic field and the occurrence of earthquakes by employing the so‐called infrastructural informational analysis is undertaken. From the authors’ previously published serial work, it was found that the “zero isotropic zone” is a “discernible characteristic indication” which can be applied to the predictions of earthquakes with great practical effect.

The reason why evolutions have been studied as a special science is that there exist reversal and transitional changes – blown‐ups – in the objective reality. However, the first‐push dynamical system has not been able to provide a mechanical explanation for these dramatic changes. Provides an exploratory explanation on how to understand “time and space” and some fundamental problems of evolutions, based on a discussion of problems existing in the first‐push system. In addition, points out the fact that the essence of the evolution science is that the concept of spinning materials is not an extrapolation or continuation of the first‐push system. What needs to be emphasized is that the presented work was originally based on first‐hand scientific practice and has been successfully evidenced by practical applications.

The nonhomogeneous information is applied to the study of sudden and severe weather processes in this paper, based on the theory of blown‐ups (OuYang, 1994). Severe weather processes, such as torrential rain and severe convection, are clarified first by using the nonhomogeneous parameters in the spring in Hubei Province, and second by combining with the severe convection forecasting criteria. We can distinguish the severe convective weather processes and forecast the short‐range severe convective weather by using this theory in the spring in Hubei province. After practical applications from March 15 to May 15 in 1995, it showed that the forecast accuracy was satisfactory.

In this article, the historical victories and shortfalls of calculus and calculus‐based methods are briefly described so that a need of developing the theory of blown‐ups is given. Listed are several challenges of the theory of blown‐ups to the traditional thinking logic of continuity and characteristics of the theory of blown‐ups.

Based on the theory of blown‐ups, as described by OuYang in 1995 and 1994, for nonlinear dynamic systems on general pansystems transformation, optimization and panderivatives, etc., in this paper, we employ the method, developed in OuYang (1994), to show that the blown‐ups of the nonlinear heat conductive equation is similar to the evolution of observable ground temperature “currents”. According to this analysis, we conduct a simulation based on the historical data of Tang Shan Earthquake in 1976. The simulation results show that: the blown‐ups of the ground temperature “currents” around the earthquake area can be applied to predict forthcoming earthquakes. As for the most disastrous Tang Shan Earthquake, the prediction time is about five months in advance. If the ground temperature “current” that embodies the earth’s crust movement satisfies the unintegrable panderivative equation, we can with enough information demonstrate blown‐up mechanism and forecast relevant earthquakes.