N * 1 = N
Identity may be defined as those inputs which statistically--directly or indirectly, correlate to the implementation of the AI available in the pattern space, any statistical information processing system which models said implementation, and any predictive modification of the pattern space which affects the implementation.
The obvious ramification of this is that the AI's modification to the pattern space may also modify its own implementation. This also implies that the AI can not only gauge how well a self-modification may have been executed, but may goal search to find the best modification available given the limited context of its senses and history.
Reification of this idea into actual practice also allows "hard coded" statistical overrides for the manipulation of the AI's implementation towards a goal. For lack of a better definition, especially one that wouldn't take up 10 pages in scientific explanation, this hard coded system dealing with the bounding of the manipulation of one's own implementation may be regarded as the modeling of pain.
The pain model starts off as a hard coded response system which would check to see if certain inputs (think of a continuous region, not discrete inputs) from the pattern space, or potential predictions of modification of the pattern space would result in pushing the parameters of the implementation out of stability. The system is initially hard coded because when the pain signal becomes intense "enough", hard coded modifications of the pattern space are mixed into the entire statistical processing algorithm of the AI forcing it to move out of the statistical context which is causing the pain. After the pattern space stimulus is removed or lessened, the usual information processing path is again allowed to control the information flow through the system.
However, the true power of the pain model becomes evident when the pain signal itself becomes a new dimension in the pattern space. This allows statistical prediction of pattern space modifications which would affect the pain intensity signal without having to actually perceive the pain. Of course, minimizing the pain signals would be part of the designer's goal in the construction of the AI and the previous experience of pain would be the guide to learning pattern space modifications to specifically avoid those experiences.
The upshot of the pain model skeleton is that arbitrary (not just pain), and non-hard coded models may be prescribed upon the implementation by the AI itself. For example, if the AI had been designed to have a sense of symmetry and to prefer symmetry over non-symmetry, then the AI may modify the pattern space in order to produce symmetry so as to rate the statistical information processor's inputs better than if those modifications had not been performed. Since the pattern space includes the implementation, it is not inconceivable that the implementation may be modified to ascribe to the model of symmetry if such modifications do not exceed the designer's limits of the pain model.
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