*"If a problem seems too hard, the formulation is probably wrong." *-David Chapman

Often when working our way through a problem we become stuck. Getting unstuck can just be a matter of applying the right tool/concept/idea to it, but sometimes this gets us nowhere. In these cases it is worth examining the structure of the problem formulation itself. This often gives us more options than just trying different answer generators because our problem formulation has more degrees of freedom than our tools do.

Some common ways of permuting problem formulations:

- Ontological rotation involves changing which linkages you draw between nodes and thus which things cluster neatly.
- Metaphorical rotation involves importing intuitions about causality from another domain.
- Reductionist rotation is to separate out differing subsets of the problem for recursive rotation
- Connotation rotation involved changing the way the problem is represented in langauge/visually/emotionally
- Back chain rotation is checking whether our problem representation is making the same sorts of distinctions a useful answer would make.
- Forward chain rotation is checking all the affordances we currently have with the problem space.
- Reference class (outside view) rotation is checking what other things have happened in the world that look like our problem or expected answer and seeing what worked there.
- Gestalt rotation is to ask what things surround our problem, what things cause it, what things does it cause? Are those assumptions valid?
- Constraint rotation is pretending a part of our problem doesn't exist and rotating the rest separately.
- Key Assumption rotation asks if there are any cheap tests that would disconfirm parts of our current problem model.
- Pedagogical rotation involves explaining the problem to a child such that we notice that our own understanding of the problem is incomplete (forced frame-by-frame)
- Napkin math rotation involves finding the upper and lower bounds of constraints, even if we don't know exactly what they are.
- Inversion rotation is inducing a figure ground rotation in part of the problem. Try drawing the causal arrows the other way, or swapping content and context, or seeing if something remains true despite being reversed.

- Curiosity rotation is finding the part of the problem that seems alive. Invert to wonder why other parts seem dead.

- Coherence rotation asks how the existence of the problem is helping satisfy other needs.
- Taboo rotation involves asking which parts of the problem are off limits and why.
- Modal rotation is picking popular styles of reasoning or personalities and asking how they would approach the problem.
- Taxonomization is trying to divide the problem and seeing which natural categories arise