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Information entropy (Foundations of information theory: Part 2) - Matthew N. Bernstein

mbernste.github.io · 1,359 words · saved by 1 readers

The mathematical field of information theory attempts to mathematically describe the concept of “information”. In this series of posts, I will attempt to describe my understanding of how, both philosophically and mathematically, information theory defines the polymorphic, and often amorphous, concept of information. In the first post, we discussed the concept of self-information. In this second post, we will build on this foundation to discuss the concept of information entropy. In the first post of this series, we discussed how Shannon’s Information Theory defines the information content of an event as the degree of surprise that an agent experiences when the event occurs. We discussed how surprise intuitively should correspond to probability in that an event with low probability elicits more surprise because it is unlikely to occur. Thus, in information theory, information is a function, I 𝐼 , called self-information, that operates on probability values p∈[0,1] 𝑝 ∈ [ 0 , 1 ] : On

The mathematical field of information theory attempts to mathematically describe the concept of “information”. In this series of posts, I will attempt to describe my understanding of how, both philosophically and mathematically, information theory defines the polymorphic, and often amorphous, concept of information. In the first post, we discussed the concept of self-information. In this second post, we will build on this foundation to discuss the concept of information entropy. Introduction In the first post of this series, we discussed how Shannon’s Information Theory defines the information

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