Alex, I very strongly agree with your comment below: The diagrams are fundamental, and the words are secondary. Whenever there is any dispute -- start with the diagrams. Formalisms, such as mathematical notations, always have a more direct mapping to diagrams than to words. Euclidean geometry is the best example. But any book that uses algebraic notations can always map the algebra more clearly and precisely to a diagram than to any words in any natural language. Re engineering diagrams: Anybody who can't read the engineering diagram, can't understand a precise explanation written in their native language. Any simple explanation that they can understand is guaranteed to be an oversimplification. But if the engineering diagram is carefully explained to them then they can and do understand the subject. I know that point very well -- because I've done it. I also know that people who claim they understand a simple explanation, but cannot understand the diagram don't know what they're talking about. If you ask them some simple questions about how the thing works, their answers are hopelessly confused. I know that because I've met such people. If you doubt that point, try that exercise with people who claim that they understand the simple explanation. The mapping to diagrams is especially important for robots. Every action by a robot has a direct mapping to and from some kind of diagram. But the explanation in a natural language is more complex, more unreadable, and more prone to misreading and misunderstandings. John ---------------------------------------- From: "Alex Shkotin" <alex.shkotin(a)gmail.com> John, Very briefly about formal definitions. The formal definition should be compared with an engineering drawing. Everyone uses various devices, but few people can and should be able to read engineering drawings. The construction of formal definitions is important, for example, because they can be transferred to robots. Alex