Ask “okay, why is this intractably hard?”. This might be multiple reasons.
Do those reasons seem intractably hard to fix? If so, recurse and ask “why” again.
Does one of them not seem intractably hard? Then, make a plan for fixing it. Then, if that plan seems cost-effective, do the plan.
Your intractably hard problem is now solved!
This doesn’t seem very novel (“break a problem down into simpler problems” is a pretty canonical tool). But I felt like I got a more visceral understanding of the skill, and how to notice its relevance.
One concrete skill I gained from my 2 weeks of Thinking Physics problems was:
Notice something feels intractably hard
Ask “okay, why is this intractably hard?”. This might be multiple reasons.
Do those reasons seem intractably hard to fix? If so, recurse and ask “why” again.
Does one of them not seem intractably hard? Then, make a plan for fixing it. Then, if that plan seems cost-effective, do the plan.
Your intractably hard problem is now solved!
This doesn’t seem very novel (“break a problem down into simpler problems” is a pretty canonical tool). But I felt like I got a more visceral understanding of the skill, and how to notice its relevance.