P Problems: Computers vs Humans

For Computers: Theoretically Tractable

Maze-solving is absolutely in P. Algorithms like:

• Depth-First Search (DFS)
• Breadth-First Search (BFS)
• A* Search

can solve any maze in time proportional to the number of intersections/rooms. For a computer, a maze with 1,000,000 rooms is trivial - it might take milliseconds.

Why it's in P: The time required grows polynomially with maze size. A computer can systematically explore without getting lost or forgetting where it's been.

For Humans: Practically Intractable

Humans find large mazes extremely difficult because we struggle with:

• Working Memory Limits: We can only keep ~7 items in working memory
• Backtracking Overhead: Mentally retracing steps is slow and error-prone
• No "Systematic Search": We use heuristics that can fail
• Cognitive Load: Keeping track of dead ends exhausts mental resources

A maze with just 100 intersections might be practically unsolvable for most humans without external aids.

The Key Distinction

P vs NP is about asymptotic complexity for idealized computational models, not about human cognitive abilities.

Computers excel at: Systematic search, perfect memory, exhaustive backtracking

Humans excel at: Pattern recognition, heuristic reasoning, creative leaps

This explains why a computer can easily solve a massive maze (P problem) but struggle with recognizing a face or understanding natural language (tasks humans find easy).

Other Examples of This Phenomenon

Multiplying Large Numbers

Computer: O(n²) or better - trivial for 1000-digit numbers

Human: Practically impossible without tools

Recognizing a Friend's Face

Computer: Very difficult (until recent ML advances)

Human: Effortless, even in poor lighting or after years

Conclusion

"Tractable" in computational complexity specifically means "efficient for a Turing machine", not necessarily efficient for human cognition. The P vs NP question exists in the abstract mathematical world of computational theory, which doesn't always align with human perceptual or cognitive capabilities.