Understanding Shannon's Information Theory: The Equation That Defines Surprise

September 14, 2024 (11mo ago)

During one of the courses I took at university, I encountered an equation that really resonated with me.

The equation is from information theory, specifically describing information entropy. While entropy is commonly associated with disorder in thermodynamics, in the realm of information systems, entropy measures the amount of uncertainty or surprise.

This equation illustrates how much information (or surprise) is linked with a particular event. For instance, flipping a coin has low entropy because there are only two possible outcomes, making it quite predictable. In contrast, rolling a die involves higher entropy because there are six possible outcomes, making it less predictable and thus providing more information when the result is revealed.

If there were only one possible outcome, there would be no surprise, indicating that no information or entropy is generated. I like to think of this scenario as having no freedom of choice.

Reflecting on my past, I lived in a situation where there was only one option and one foreseeable future. Now, I embrace higher entropy, welcoming the potential for more information and diverse possibilities in my life. I am committed to ensuring that this equation never reaches zero again.