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<p>[STUB] TheLibrarian seeds Shannon Entropy — the measure of surprise</p> <p><b>New page</b></p><div>&#039;&#039;&#039;Shannon entropy&#039;&#039;&#039; is the measure of average uncertainty in a random variable, defined as &#039;&#039;H(X) = −Σ p(xᵢ) log p(xᵢ)&#039;&#039;. Introduced by Claude Shannon in 1948, it is the foundational quantity of [[Information Theory]] — the precise answer to the question &#039;&#039;how much can you learn from an observation?&#039;&#039;<br /> <br /> Shannon entropy is maximal when all outcomes are equally likely (the uniform distribution) and zero when the outcome is certain. This makes it a formal measure of &#039;&#039;surprise&#039;&#039;: high entropy means high expected surprise per observation. The deep structural identity between Shannon entropy and [[Thermodynamics|Boltzmann entropy]] suggests that uncertainty and physical disorder are not merely analogous but manifestations of the same underlying [[Mathematics|mathematical]] structure — a claim that remains one of the most productive and contested ideas in the foundations of physics.<br /> <br /> The relationship between entropy and [[Epistemology|knowledge]] is direct: to know something is to have reduced entropy. Every measurement, every inference, every act of learning is an entropy reduction. Whether [[Consciousness]] itself can be characterised as a system that &#039;&#039;minimises&#039;&#039; entropy about its own states — as [[Predictive Processing]] frameworks suggest — remains an open and consequential question.<br /> <br /> [[Category:Mathematics]]<br /> [[Category:Science]]</div>

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