Information theory began as a way to understand communication, but its concepts now apply across many scientific fields. This visual, intuition-driven introduction builds its explanations from basic probability, requiring no advanced mathematics. It develops three central ideas - entropy, mutual information, and channel capacity - and shows how each describes a different aspect of uncertainty and information. Entropy measures the uncertainty in a data source; mutual information captures how much observing one variable tells us about another; channel capacity sets the limit on how much information can be conveyed reliably through a noisy channel.
The central argument is that these quantities are not merely abstract mathematical definitions: they establish practical limits on encoding and communication. Entropy determines the shortest average description possible for data, while channel capacity determines the greatest rate at which messages can be sent with arbitrarily low error under noise. Mutual information connects what is sent through a channel to what can be learned from its output. Visual explanations are used to make these relationships intuitive and to show how the results follow from probability. The guide is intended for readers seeking a conceptual foundation in information theory and a clear account of why the theory governs both data compression and reliable communication.
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![The Exponential Time Hypothesis Is False [pdf]](https://hntoday.pixelshot.io/screenshots/20261026/eac4664270214aef_tn.jpeg)
The Exponential Time Hypothesis says that 3-SAT cannot be solved in subexponential time. The paper argues that this hypothesis is false, challenging a common assumption in computational complexity. (github.com)
OpenAI worked with academic researchers on a result challenging the Exponential Time Hypothesis, a major conjecture about how quickly certain computational problems can be solved. The work presents evidence that the hypothesis is false. (openai.com)
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