The paradigm of complex probability and Claude Shannon’s information theory

What is it about?

Andrey Kolmogorov put forward in 1933 the five fundamental axioms of classical probability theory. The original idea in my complex probability paradigm is to add new imaginary dimensions to the experiment real dimensions which will make the work in the complex probability set totally predictable and with a probability permanently equal to one. Therefore, adding to the real set of probabilities R the contributions of the imaginary set of probabilities M will make the event in C = R + M absolutely deterministic. It is of great importance that stochastic systems become totally predictable since we will be perfectly knowledgeable to foretell the outcome of all random events that occur in nature. Hence, my purpose here is to link my complex probability paradigm to Claude Shannon’s information theory that was originally proposed in 1948. Consequently, by calculating the parameters of the new prognostic model, we will be able to determine the magnitude of the chaotic factor, the degree of our knowledge, the complex probability, the self-information functions, the message entropies, and the channel capacities in the probability sets R and M and C and which are all functions of the message real probability subject to chaos and random effects.

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Why is it important?

All our work in classical probability theory is to compute probabilities. The original idea in this research work is to add new dimensions to our random experiment, which will make the work deterministic. In fact, the probability theory is a nondeterministic theory by nature; that means that the outcome of the events is due to chance and luck. By adding new dimensions to the event in R, we make the work deterministic and hence a random experiment will have a certain outcome in the complex set of probabilities C. It is of great importance that the stochastic system, like the problem considered here, becomes totally predictable since we will be totally knowledgeable to foretell the outcome of chaotic and random events that occur in nature for example in statistical mechanics or in all stochastic processes. Therefore, the work that should be done is to add to the real set of probabilities R, the contributions of M which is the imaginary set of probabilities which will make the event in C = R +M deterministic. If this is found to be fruitful, then a new theory in statistical sciences and prognostic is elaborated and this is to understand absolutely deterministically those phenomena that used to be random phenomena in R. This is what I called ‘The Complex Probability Paradigm (CPP)’, which was initiated and elaborated in my previous papers.

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