Menu

Individual skill

s4h-information-entropy

0upvotes

Measures uncertainty, surprise, and information content using Shannon entropy. Use when asked 'how much information does this actually contain', 'how uncertain is this source', 'is this result surprising', 'what should I update on', 'where is the real information in this dataset', or when you need to distinguish high-information from low-information inputs.

skills/s4h-information-entropy/SKILL.md

Read pinned source

Source commit a30df8b67698ccb03ef5e35d68c2eddc5321ad3f

What was checked

Matches the observed repository HEAD
Yes
Scanner rules are current
Yes
Repository scan complete
No
Skill scan complete
No
Observed behavior
Instructions only
Last checked
Nov 11, 2026

These are observations at the recorded commit, not a guarantee of safety. Review the source before running it.

Install this skill

Choose an agent in your Stack or copy a command below. Commands fetch the pinned commit and copy only this skill directory. Existing destinations are refused. Copying a command does not install anything.

An install command is unavailable: current rules, complete repository and skill scans, an eligible behavior level and a permitted license are required.

Repository context

Repository stars (not skill ratings)
241
Repository last updated
Jul 15, 2026
License
MIT

Observed agent integration: No specific integration evidence. Standard SKILL.md installation does not imply verified compatibility.

Files and excerpt

File metadata and permitted, redacted excerpts come from the recorded scan. Source links are pinned to that commit.

Browse files
Read excerpt

# Information: Entropy

In 1948, Claude Shannon defined information in terms of surprise. The information content of a message is the degree to which it reduces your uncertainty. A message you could have predicted perfectly carries zero information — it tells you nothing you didn't already know. A completely unexpected message carries maximum information. Shannon called this quantity entropy, borrowing the term from thermodynamics: like physical entropy, it measures disorder and unpredictability.

Shannon entropy is defined as H = −∑ p(x) log₂ p(x) across all possible outcomes. The maximum entropy of a source is achieved when all outcomes are equally likely — pure unpredictability. Minimum entropy is achieved when one outcome is certain — pure predictability. Applied practically: a quarterly report that always says roughly the same thing carries low entropy. A dataset where any measurement could be anything carries high entropy. Neither extreme is ideal — maximum entropy is overwhelming, minimum entropy is uninformative.

Norbert Wiener extended this framework through cybernetics to argue that information is what distinguishes organisation from chaos in any self-regulating system. A thermostat carries information about temperature; the information is what allows the system to maintain order. Wiener's key insight: the entropic arrow runs toward decay unless information is actively used to correct it. Systems without good information channels become entropic — they drift.

Andrei Kolmogorov gave entropy a computational interpretation: the algorithmic complexity of a string is the length of the shortest program that can generate it. A truly random sequence cannot be compressed — it has maximum Kolmogorov complexity. A highly ordered sequence can be compressed to a short description — it has low complexity. The two frameworks — Shannon's probabilistic entropy and Kolmogorov's algorithmic complexity — converge: low-entropy sources are compressible; high-entropy sources are not.

The practical application is calibrating attention and weight. When a source has low entropy (high predictability), each new message from it should update you very little. When a source has high entropy (high surprise rate), each new message carries real information and deserves genuine engagement. Most people give equal attention to all messages regardless of their information content — this is the calibration error this skill corrects.

---
Back to top