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Availability, partition tolerance, and self-organizing maps

To construct a map, there must be an expectation of the environment. The CAP theorem lays out an abstract view of how agents can interact in an environment. The common utilization of a semantic interpretation of a response is what enables a map to be built. As an example, if the expectation of a response is that the responding entity must respond if it is non-failing, then a map can be built whereby the atomic expansion of the map happens all at once or not at all. Similarly, if the expectation of a response is that the responding entity may never reply at all, then a map can be built whereby the shrinking of the map happens partially all the time.

In a sense, the semantic interpretation that is used to construct the map depends on the probability of error. If the probability of error is very low, then it is a reasonable expectation that every entity must respond if it is non-failing. If the probability of error is very high, then it is not a reasonable expectation that every entity must response if it is non-failing. The meaning of "error" here means anything that transcends the semantic interpretation of a response.

From an engineering perspective, the probability of error is often a compound variable, and from the perspective of the CAP theorem, it is a reflection of how thin the data is spread over a computing substrate. The larger the spread of the data over a set of distinct agents, the more the probability of error compounds. Fundamentally, there is always a relationship between the atomic probability of error, the number of distinct agents, and the compound probability of error. In a sense, the CAP theorem is closer to biology than computer systems, because there is always some atomic probability of error that leads to an expectation of interpretation, which leads to an organization of a map.

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