Locality — What You Can See From Where You Stand
Most reasoning happens locally. Most interesting structure is global. The gap between them is where systems fail and where insight lives.
You're standing in a valley. In every direction, the ground slopes up. You conclude you're at the lowest point. You might be — or you might be in one of a thousand valleys, nowhere near the actual floor.
This is locality. Most computation, most reasoning, most optimization happens locally — you can only see what's near you, and you act on what you can see. The interesting structure is almost always global: the shape of the whole landscape, the distribution of all the valleys, the relationship between where you are and where you could be.
The tension between local information and global structure is one of the most productive places to look when a system is stuck.
00. — SGD is explicitly local — gradient at the current point, step. The entire field of optimizer design is about extracting global information from local samples: momentum remembers past gradients, learning rate schedules simulate annealing, weight decay biases toward simpler regions. Every trick escapes the tyranny of the local view.Failure modes
Local optima
The obvious one. You've optimized everything you can see, and the result is mediocre, because the good solutions aren't reachable by small steps from where you are. This isn't just a math problem — it's an organizational one, a career one, a research one. Teams that incrementally improve their current approach can't see the discontinuous jump to a better one. Researchers who refine their existing framework can't see the reframing that dissolves the problem.
00. — This connects to deflationary moves — a deflationary reframing is essentially a jump to a different region of the solution space. You can't get there by gradient descent on the current question.Local coherence, global incoherence
Every part of the system makes sense in isolation. The team's process is locally rational — each step follows from the last. The codebase is locally clean — each file is well-structured. But zoom out and the whole thing doesn't cohere. The process optimizes for the wrong outcome. The codebase has three implementations of the same thing because nobody had the global view.
Markets do this constantly. Every individual transaction is locally rational — both parties benefit. The global structure that emerges can be wildly suboptimal: bubbles, tragedy of the commons, races to the bottom. Local rationality doesn't compose into global rationality without something providing the global view. 00. — This is why I'm market-sympathetic but not market-naive. The substrate of a market — distributed local computation — is incredibly powerful. The failure mode is that local incentives don't always produce good global outcomes. You need structure that bridges the gap.
Horizon problems
You can't see far enough ahead. A greedy algorithm picks the best next move and ends up in a terrible position three moves later. A quarterly earnings focus optimizes the next report at the expense of the next decade. The information you need to make a good decision exists — it's just not local to where you are in time or space.
00. — In physics, locality means no action at a distance — a fundamental constraint. In practice, locality is usually an information constraint: you could know what's happening elsewhere, but gathering that information is expensive. The interesting systems are where the gap between local and global information is large and consequential.