The paradigm of complex probability and Claude Shannon’s information theory
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...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2017-01-01
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| Series: | Systems Science & Control Engineering |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/21642583.2017.1367970 |
| _version_ | 1818265513346727936 |
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| author | Abdo Abou Jaoude |
| author_facet | Abdo Abou Jaoude |
| author_sort | Abdo Abou Jaoude |
| collection | DOAJ |
| description | 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 $ {\sc{R}} $ the contributions of the imaginary set of probabilities $ \sc{M} $ will make the event in $ \sc{C}= \sc{R} + \sc{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 $ \sc{R} $ and $ \sc{{M}} $ and $ \sc{C} $ and which are all functions of the message real probability subject to chaos and random effects. |
| first_indexed | 2024-12-12T19:52:00Z |
| format | Article |
| id | doaj.art-01a6a1dfbd5f457592fd8b5a1e44351f |
| institution | Directory Open Access Journal |
| issn | 2164-2583 |
| language | English |
| last_indexed | 2024-12-12T19:52:00Z |
| publishDate | 2017-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Systems Science & Control Engineering |
| spelling | doaj.art-01a6a1dfbd5f457592fd8b5a1e44351f2022-12-22T00:13:57ZengTaylor & Francis GroupSystems Science & Control Engineering2164-25832017-01-015138042510.1080/21642583.2017.13679701367970The paradigm of complex probability and Claude Shannon’s information theoryAbdo Abou Jaoude0Notre Dame University-LouaizeAndrey 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 $ {\sc{R}} $ the contributions of the imaginary set of probabilities $ \sc{M} $ will make the event in $ \sc{C}= \sc{R} + \sc{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 $ \sc{R} $ and $ \sc{{M}} $ and $ \sc{C} $ and which are all functions of the message real probability subject to chaos and random effects.http://dx.doi.org/10.1080/21642583.2017.1367970Complex setcomplex probabilityprobability normdegree of our knowledgechaotic factorself-informationmessage entropychannel capacity |
| spellingShingle | Abdo Abou Jaoude The paradigm of complex probability and Claude Shannon’s information theory Systems Science & Control Engineering Complex set complex probability probability norm degree of our knowledge chaotic factor self-information message entropy channel capacity |
| title | The paradigm of complex probability and Claude Shannon’s information theory |
| title_full | The paradigm of complex probability and Claude Shannon’s information theory |
| title_fullStr | The paradigm of complex probability and Claude Shannon’s information theory |
| title_full_unstemmed | The paradigm of complex probability and Claude Shannon’s information theory |
| title_short | The paradigm of complex probability and Claude Shannon’s information theory |
| title_sort | paradigm of complex probability and claude shannon s information theory |
| topic | Complex set complex probability probability norm degree of our knowledge chaotic factor self-information message entropy channel capacity |
| url | http://dx.doi.org/10.1080/21642583.2017.1367970 |
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