意识的数学模型

意识可以由数学模型表示,其本质是同构。

Second Asia International Conference on Modelling & Simulation

The Mathematic Model of Consciousness

Zhang Yinsheng 1

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Institute of Science & Technology Information of China,

No.15 Fuxing Road, Beijing 100038 nn

e-mail: zhangyinsheng@ , zhangyinshengnet@

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Abstract

The thought referring homomorphism of a group to the model of trasformatio 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 nn

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 relatios i the etities. The essece of cosciousess is certai correspodece betwee substance with some rules or laws.

1. The Summarization of the Definitions of Consciousness

The definition of consciousness has been disputed for several thousands year. Sometimes the debates result from the different regulations of definition. To avoid it, the following regulations of definition are proposed.

Regulation of definition 1. Definition of consciousness must be accorded with the everyday meaning of the word “consciousness”, that is, defining

consciousness is not voluntary, it is but the interpretation of the widely used for thousands year concept and is only the abstract of the characteristics of the matter, to the matter the widely used concept of consciousness refers.

Regulation of definition 2. Definition of consciousness must be acceptable both for philosophy and the science. The definer should be clear that the definition of the word “consciousness” is just one as both the philosophers and the scientists refer to, there should not be the separate interpretation of the word “consciousness” from another study fields.

Regulation of definition 3. The concept of consciousness must be common for any type of the matter to be tested by the definition-standard, in other word, no matter human, animal or machine it is, if it satisfies the definition-standard of consciousness, it should be regarded as being conscious.

By the understanding the thoughts of regulations of definition 1, we should be able to abstract the common meanings among the various definitions.

Norman Malcolm explained the common meanings. He pointed out that “being conscious” is used in the two different ways. The first use is called transitive, because this form of consciousness takes an object, that is, it is consciousness of something. The second use is called intransitive, because this form of consciousness has no object. [1]

From the viewpoint of Norman Malcolm, we can conclude that the primary sense of the word “consciousness” is transitive. We can define consciousness that the essence of consciousness is transitivity of a information system, and transitivity can be defined as a certain correspondence between the system of information and the outside matters. For example, the word “sun” correspond the entity sun. Correspondence, as the essence of consciousness, can be modeled in mathematic expression denoting the correspondence.

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