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The purpose of this paper is to apply a new idea and scientific method to evaluate the enterprise's independent innovation capability accurately.

The matter‐element, extension set and independent function in extension theory are introduced briefly. Based on extension theory, the matter‐element model on comprehensive evaluation of the enterprise's independent innovation capability is established. Then, an instance which makes structural analysis on the enterprise's independent innovation capability with extension evaluation method is given.

The matter‐element model on comprehensive evaluation of the enterprise's independent innovation capability is established. Extension evaluation method can combine qualitative analysis and quantitative analysis to reflect the changing process of the objective appropriately. By means of the matter‐element model, the evaluation result shows which the grade does the enterprise's independent innovation capability belong to.

Extension evaluation method resorting to extension theory, cannot only reveal the evaluation grade and competitive advantage of an enterprise within the industry or within the scope of the evaluation, but also show comprehensive index level of the enterprise's independent innovation capability.

It is significant to monitor the enterprise's development and changes effectively, find the key factors influencing the enterprise's independent innovation capability and take effective measures in time.

New idea and scientific method are introduced into the enterprise's independent innovation activity, and it can integrate both qualitative and quantitative analysis to solve contradictory problems.

A basic pansystems scientific view about the physical world is presented. The principle and methodology of pansystems GuanKong technology are introduced. Simple metrics for the quantization of information, risk and gain by comparison (GBC) are established and discussed, and the practical and simple membership function which realizes the transformation from qualitative to quantitative order are given, and an example showing the pansystems GuanKong in detail is also given.

In this paper, we consider the fundamental characteristics of motion in the universe in terms of the whole and local evolutionary forms of fluids, based on the theory of blown‐ups and the experiment of spinning disc of currents. It is pointed out that the practical meaning of “the invisible Tao”, see Lao Tsu for more details, is that of currents, and the central theory of fluid dynamics is the vortex flow dynamics, and the practicability of the nonlinear evolutions of mathematical models is getting away from the assumption of continuity.

The paper aims to show the existence of the systemic yoyo structure in human thoughts so that the human way of thinking is proven to have the same structure as that of the material world.

Parallel comparison is used to reveal the underlying structure existing in human thoughts.

After highlighting all the relevant ideas and concepts, which are behind each and every crisis in the foundations of mathematics, it becomes clear that some difficulties in the authors' understanding of nature are originated from confusing actual infinities with potential infinities, and vice versa. By pointing out the similarities and differences between these two kinds of infinities, then some hidden contradictions existing in the system of modern mathematics are handily picked out. Then, theoretically, using the authors' yoyo model, it is predicted that the fourth crisis in the foundations of mathematics has appeared. And, a plan of resolution of this new crisis is provided.

This paper shows the first time in history that human thought, the material world, and each economic entity, share a common structure – the systemic yoyo structure. And it proves the arrival of the fourth crisis in mathematics by using systems modeling and listing several; contradictions hidden deeply in the foundations of mathematics.

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.