Shapes: Their Clustering and Evolution

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Grouping similar objects into mutually exclusive groups is one of the most fundamental methods of knowledge discovery. Before the modern era the world was studied mostly qualitatively, and qualitative grouping was used to extract knowledge from the universe. For example, Aristotle divided living organisms into two groups, plants and animals, and divided animals into three groups according to how they moved: walking, flying, or swimming. Galileo used the similarity of movement of groups of stars and discovered that they are positioned in the same galaxy, which today is called the Milky Way. Mendeleev discovered the periodic table by grouping elements having similar chemical characteristics. Darwin studied the evolution of species by grouping biological bodies.