The Mathematic Model of Consciousness

The thought referring homomorphism of a group to the model of transformation from physical structures to the psychological originated from Jean Piaget. How ever, Jean Piaget has not given a mathematic expression by which the psychological phenomena can be represented, and he has not taking the model as the common model of consciousness. In the paper, the homomorphic model of consciousness is given in a mathematic expression, by which the some important questions relevant to the consciousness are formalized and the answer can be acquired, the questions (with the followed answer solved by the homomorphic model of consciousness) are Chinese room argument, Turing machine question, Turing Test question, and about if animals have consciousness, in what the meaning of utilizing and making tools lies, if DNA and protein system have consciousness. And finally the paper concludes that consciousness exists when : (1) the units of system certainly map the entities outside the system; (2) the system operate by some rules; and (3) the rules certainly map some laws or relations in the entities. The essence of consciousness is certain correspondence between substance with some rules or laws.