Think of problems as Lean does: A problem state consists of some hypotheses/assumptions, a goal, and tactics we can apply to hypotheses to infer new statements. We seek to infer a statement with the type of the goal.
Some problems only require making the right local step at each successive problem state. That’s what makes them easy in some sense. Hard problems require determining (something about) the path before useful progress can be made. I think this is intuitive, if not I can give examples.
Complication: I have variable mental clarity and energy levels.
Completing a task well first requires understanding how a task breaks down into specific actions. Then the follow through only requires executing the local steps on path. The first part is “solve a hard problem”. Requires good mental clarity. The second requires cognitive work.
Any concrete action I take ends up being just local step in the immediate context’s problem state that doesn’t have any persistent effect on my ability to assess and resolve problem states, and diminishes my reserves of energy. Feel the difference between completing a task vs practising a technique: I want persistent effects that help me respond to challenges, and the work capacity to benefit from this ability.
Challenges like “Learn to use a new mode of public transport in an unfamiliar city”, “Prove Cauchy’s theorem for finite groups”, “how to pass this exam” are all difficult for the same reasons.
How to solve problems (read: do anything substantial) when clarity and capacity are variable/limited?
Can you be more specific?
Think of problems as Lean does: A problem state consists of some hypotheses/assumptions, a goal, and tactics we can apply to hypotheses to infer new statements. We seek to infer a statement with the type of the goal.
Some problems only require making the right local step at each successive problem state. That’s what makes them easy in some sense. Hard problems require determining (something about) the path before useful progress can be made. I think this is intuitive, if not I can give examples.
Complication: I have variable mental clarity and energy levels.
Completing a task well first requires understanding how a task breaks down into specific actions. Then the follow through only requires executing the local steps on path. The first part is “solve a hard problem”. Requires good mental clarity. The second requires cognitive work.
Any concrete action I take ends up being just local step in the immediate context’s problem state that doesn’t have any persistent effect on my ability to assess and resolve problem states, and diminishes my reserves of energy. Feel the difference between completing a task vs practising a technique: I want persistent effects that help me respond to challenges, and the work capacity to benefit from this ability.
Challenges like “Learn to use a new mode of public transport in an unfamiliar city”, “Prove Cauchy’s theorem for finite groups”, “how to pass this exam” are all difficult for the same reasons.
How to solve problems (read: do anything substantial) when clarity and capacity are variable/limited?