What Is Information Entropy?
Information entropy is a measure of the average uncertainty or 'surprise' associated with a set of possible outcomes. In simple terms, it quantifies how unpredictable a piece of information is. A message or data set with high entropy is very unpredictable and contains a lot of new information, while one with low entropy is highly predictable and repetitive.
Section 2: Core Principles
The concept, developed by Claude Shannon, is typically measured in 'bits'. An event with a 50/50 probability, like a fair coin flip, has the highest possible entropy for two outcomes (1 bit) because the result is maximally uncertain. Conversely, an event with a 100% or 0% probability has an entropy of zero, as the outcome is completely predictable and carries no surprise.
Section 3: A Practical Example
Imagine two sets of weather forecasts. Forecast A always predicts 'sunny' because it's for a desert. This forecast has very low entropy; you are not surprised by the prediction. Forecast B is for a region with highly variable weather, predicting 'sunny,' 'rainy,' or 'cloudy' with equal likelihood. This forecast has high entropy because the outcome is much harder to predict.
Section 4: Importance and Applications
Information entropy is a fundamental principle in data science and communications. It forms the basis for data compression algorithms (like ZIP), which work by identifying and reducing redundancy (low entropy). It is also used in machine learning for building decision trees and in cryptography to measure the randomness and security of keys.