As we known, an objective thing not moves with one's volition, which implies that all contradictions, particularly, in these semiotic systems for things are artificial. In classical view, a contradictory system is meaningless, contrast to that of geometry on figures of things catched by eyes of human beings. The main objective of sciences is holding the global behavior of things, which needs one knowing both of compatible and contradictory systems on things. Usually, a mathematical system including contradictions is said to be a {\it Smarandache system}. Beginning from a famous fable, i.e., the $6$ blind men with an elephant, this report shows the geometry on contradictory systems, including non-solvable algebraic linear or homogenous equations, non-solvable ordinary differential equations and non-solvable partial differential equations, classify such systems and characterize their global behaviors by combinatorial geometry, particularly, the global stability of non-solvable differential equations. Applications of such systems to other sciences, such as those of gravitational fields, ecologically industrial systems can be also found in this report. All of these discussions show that a non-solvable system is nothing else but a system underlying a topological graph $G\not\simeq K_n$, or $\simeq K_n$ without common intersection, contrast to those of solvable systems underlying $K_n$ being with common non-empty intersections, where $n$ is the number of equations in this system. However, if we stand on a geometrical viewpoint, they are compatible and both of them are meaningful for human beings.