Learning & search

The map has traps

You're designing something with 6 yes/no decisions.
Every decision tugs on the others. Find the best version.

Below is your search space: 64 possible designs, laid out as an 8×8 map. Every square has a hidden fitness — how much customers love that combination. Yellow squares are wins. Deep purple squares are duds. Neighbouring squares differ by exactly one flipped decision — a small step in design-space is a small step on the map.

If your six decisions worked independently, the map would be a single smooth hill: tweak one thing at a time and climb. But real decisions interact — a loud sound is great on a big fast product, obnoxious on a small quiet one. As interactions grow, the smooth hill shatters into a minefield of little peaks. Turn the K dial and watch:

Turn the ruggedness dial · K = how much decisions interact

K · interactions per decision0

Local peaks

traps in the terrain

Global max

—

best fitness possible

Drag K from 0 to 5. The single golden hill fractures into a dozen mini-peaks (the white rings). Every ring is a valid "local best" — a design where every one-flip neighbour is worse. You can't tell from your neighbours that you're not at the top. That's the whole trap.

Now you climb it

You start at a random design (the blue walker). Your six decisions are the cards below the map. Each card shows what happens if you flip that decision — green ↑ the design gets better, red ↓ it gets worse. Click any card to flip it. The walker teleports to its new home on the map.

Climb it yourself · click a card to flip that decision

K · interactions per decision2

Your fitness

—

% of global max

Global max

—

best design possible

Moves

Local peaks

—

traps on the map

Try this. Set K = 4. Take only green-card steps. Eventually every card goes red or grey — you're stuck. Now peek at the map: usually not the golden 🏆. Hit 🌪️ big jump and try again. You land on a totally different local peak. That's the story of NK: greedy climbing wins on smooth terrain, dooms you on rugged terrain, and different starts reach different tops.

Three explorers, same terrain

Same map. Same move budget. Three personalities:

H · Hill climb. Always takes the best-improving flip. Fastest to a peak — then stuck forever.
R · Restart squad. Hill-climbs; when stuck, teleports to a fresh random start. Diversity insurance.
L · Long-jumper. Mostly climbs, but every so often flips several bits at once. Costly. Escapes local peaks.

Watch them move. Each walker leaves a trail in its own colour. The bars below race best-fitness-so-far — that's what actually counts, since you'd remember your best design.

The race · three explorers, one map, one budget

K · terrain ruggedness3

🎯 Hill climb

—

greedy

🎲 Restart squad

—

random restarts

🌪️ Long-jumper

—

occasional big flips

The management-strategy translation. Kauffman & Levinthal's argument in plain English: on a smooth landscape (few interactions, low K), incremental optimisation wins — go faster than your rivals. On a rugged landscape (product features that constrain each other, policies that ripple), pure incrementalism strands you on a mid-height hilltop while a competitor starting from a wildly different design climbs a taller one. That's why radical entrants sometimes beat best-in-class incumbents — they climb a different hill entirely.

Diverse teams > homogeneous experts

Scott Page's The Difference generalises the restart squad. If smart searchers all start from the same place with the same heuristic, they all get stuck on the same local peak. Different searchers get stuck on different peaks — and can share their moves. The mathematical case for cognitive diversity, hiding inside an NK landscape.

Related models

🎮 Life & Local Majority — another "simple rules, surprisingly rich outcomes" story — complexity from local interactions.
♟️ Game theory — strategic interactions between decisions, cousin to NK's interactions between features.
🟦🟧 Schelling segregation — agent-based cousin; local decisions aggregated into a global landscape of outcomes.

← Path dependence Game theory →