popular science

Seeing the World Through Entropy

From subway queues to algorithm design and the attention economy: measure uncertainty and tame chaos with simple rules.

Author: You · ~12 min read · Updated: October 22, 2025

What entropy is — without formulas

Entropy is a handy word for “how many futures are on the table.” The more possible scenarios and the more evenly they are distributed in probability, the higher the entropy — that is, the uncertainty.

Gas molecules zip around freely — many micro‑states → high entropy. A parade line where everyone stands perfectly still — predictable → low entropy. In the information sense, entropy tells us how many “bits of surprise” an event carries: rare events surprise us and carry more information, frequent ones less.

Information is what reduces uncertainty. A good system manages entropy where it matters.
Two bar charts: on the left one tall bar (low entropy), on the right a flat distribution (high entropy). Low entropy Categories High entropy Categories
Entropy as “variety of chances”: a single favorite vs a fair lottery.

We don’t always want low entropy. Without diversity (randomness) there is no exploration, learning, or creativity. Art is controlled noise; engineering is controlled order. Life is a balance of the two.

Entropy in subway queues

Why does the same queue sometimes fly and sometimes freeze? It’s not just the average service time — it’s the variability (entropy) of arrivals and service.

Idea: the same average ≠ the same experience. Two counters at 1 minute each can yield very different queue lengths if the operators’ times fluctuate differently.
Two service lines compared: without buffers, tasks of uneven duration cause spikes; with a buffer, peaks are smoothed. No buffers With a buffer (message queue) High variance → wait spikes Buffer smooths peaks → predictable time
Consistency beats peak speed: reduce variance, add parallelism and buffers.

Another trick is cross‑training: when any staffer can handle any request type, the system is less vulnerable to spikes — you reduce the uncertainty about where the bottleneck will appear.

Practice: if you can’t speed up service, reduce its spread. Consistency often matters more than raw speed.

Queueing theory formalizes this: the variance of arrivals and service weights average waiting time almost as much as their means.

Entropy in algorithms and data

Compression: you can’t squeeze randomness

A file whose symbols are equiprobable has high entropy — there’s little to compress. A compressor “earns” bits from predictability: the more repeats and patterns, the lower the entropy, the stronger the compression.

Search & sort: paying to remove uncertainty

Sorting is a way to spend compute to reduce entropy in data. An ordered list shrinks the “space of options” during search and decision‑making.

Decision trees & information gain

A good question is the one that reduces uncertainty the most. In decision trees, a feature that best splits data into clean groups yields high information gain.

A decision tree: the root question splits the set into two cleaner groups, lowering entropy. Question A? Entropy ↓ Entropy ↓ Before After
A “good” feature is the one that makes groups most homogeneous.

Hashing & evenness

An ideal hash function makes keys look random — a uniform spread lowers the entropy of collisions and keeps access times steady.

Load tests & headroom: buying predictability with reserve

Capacity buffers and message queues are “tanks” for noise. They flatten spikes, reducing the uncertainty of user‑visible latency.

Entropy of attention

Feeds keep you engaged with measured unpredictability: interleaving expected with unexpected. Too uniform → boredom; too chaotic → fatigue. The sweet spot is where novelty exists but the risk of error is low.

An inverted‑U curve: X — unpredictability, Y — engagement. Optimum is in the middle. flow zone low unpredictability → boredom high unpredictability → overload engagement unpredictability
Dose novelty: a dash of surprise sustains attention; chaos kills it.

Six simple rules for working with entropy

  1. Make states explicit. Process maps, checklists, and status indicators turn uncertainty into observable stages.
  2. Trim the tails. Tame rare but costly failures: limits, timeouts, guardrails, quorums.
  3. Add buffers. Time and capacity headroom are cheap ways to swallow demand spikes.
  4. Calibrate randomness. Inject controlled variety where learning or creativity is needed: top‑N sampling, A/B tests.
  5. Track spread, not just averages. Put medians and percentiles in reports — they “see” chaos.
  6. Max predictability, min bureaucracy. Automate the routine, but leave room for exploration.

Mini‑experiments & metaphors

  • Kitchen queue. Split serving into “quick” vs “complex” dishes — watch the waiting‑time entropy drop.
  • Shuffled playlist. If shuffle clumps the same artist — that’s poor pseudo‑randomness: entropy too low. Try “smart shuffle.”
  • Day planning. Block quiet, notification‑free windows: predictable focus slots raise decision quality.
  • Text compression. Zip a paragraph with repetitions and one without — compare archive sizes: where entropy is lower, compression is better.

Takeaways

Seeing the world through entropy means noticing the hidden cost of uncertainty and managing it. Don’t chase perfect order; learn to regulate noise.