What does it mean that formal schemas versus intuitive schemas?

You have both rigorous explicit schemas and fuzzy gut-feeling schemas — both matter.

Example: A senior engineer reviews a pull request. She can articulate the formal schema: 'functions should do one thing, names should reveal intent, error handling must be explicit.' But she also has an intuitive schema — a feeling that something is off about the code's structure — that she can't fully verbalize. The formal schema catches the naming violation. The intuitive schema catches the subtle coupling between modules that will cause pain six months from now. Ignoring either one produces worse decisions than using both.

Try this: Pick a decision you made recently on instinct — a hire, a design choice, a conversation you steered a certain way. Write down what you did and why it felt right. Now try to formalize the intuitive schema behind it: what pattern did you recognize? What prior experience generated that recognition? Can you articulate a rule that captures even 60% of what your gut was doing? Write it down. You now have a formal schema draft that you can test, share, and refine — without abandoning the intuition that produced it.