Entropy, Signals, and the Turing Machine’s Limit of Change
Entropy, at its core, quantifies disorder and uncertainty—measuring not just physical chaos but the fundamental limits of information and transformation. In signal processing, entropy determines how predictable or chaotic a signal is: a highly ordered signal carries low entropy and high fidelity, while a noisy or random signal reflects high entropy, reducing information integrity. This concept extends deeply into computation, where the Turing machine—though idealized—models information transformation as discrete, state-driven steps, each updating a symbol much like a signal evolves. Crucially, no computation can generate information from nothing, mirroring thermodynamic…
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