Some further suggestions for handling hard questions, gleaned from work done in mathematics:
Hard questions can often be decomposed into a number of smaller not quite as hard (or perhaps even easy) questions whose answers can be strung together to answer the original question. So often a good first step is trying to decompose the original question in various ways.
Try and find a connection between the hard question and ones that people already know how to answer. Then, see if you can figure out what it would take to bridge the gap between the hard question and what has been answered. For example, if the hard question you are trying to answer relates to human consciousness, perhaps a (not entirely ridiculous) approach would be to first examine questions that researchers have already made headway with, like the neural correlates to consciousness, and then focus on solving the problem by thinking about how one could go from a theory of correlates to a theory of consciousness (maybe this is impossible, but then again maybe it is not). This sort of approach can be a lot faster than solving a problem from scratch, both because it can avoid requiring you to reinvent the wheel, and because sometimes linking a problem to ones that are already solved is a lot easier than solving those problems to begin with.
Don’t become attached to your first ideas. If you’ve had some great ideas that have gotten you close to solving a hard problem, but after a lot of work you still aren’t where you want to be, don’t get stuck forever in what could be a dead end. From time to time, try to refresh your perspective by starting over from scratch. Often people find it painful starting over again, or are so excited by their first promising ideas that they don’t want to let them go, but when a problem is truly hard you may well need to restart the problem again and again before hitting on an approach that really will work. This is a bit like reseeding a random number generator.
Discuss the problem with other very smart people (even if they are not experts in precisely what you are doing) and listen closely to what they have to say. You never know when someone will say something that will trigger a great idea, and the process of explaining what you are working on can cause you to gain a new understanding of the subject or, at least, force you to clarify your thinking.
Some further suggestions for handling hard questions, gleaned from work done in mathematics:
Hard questions can often be decomposed into a number of smaller not quite as hard (or perhaps even easy) questions whose answers can be strung together to answer the original question. So often a good first step is trying to decompose the original question in various ways.
Try and find a connection between the hard question and ones that people already know how to answer. Then, see if you can figure out what it would take to bridge the gap between the hard question and what has been answered. For example, if the hard question you are trying to answer relates to human consciousness, perhaps a (not entirely ridiculous) approach would be to first examine questions that researchers have already made headway with, like the neural correlates to consciousness, and then focus on solving the problem by thinking about how one could go from a theory of correlates to a theory of consciousness (maybe this is impossible, but then again maybe it is not). This sort of approach can be a lot faster than solving a problem from scratch, both because it can avoid requiring you to reinvent the wheel, and because sometimes linking a problem to ones that are already solved is a lot easier than solving those problems to begin with.
Don’t become attached to your first ideas. If you’ve had some great ideas that have gotten you close to solving a hard problem, but after a lot of work you still aren’t where you want to be, don’t get stuck forever in what could be a dead end. From time to time, try to refresh your perspective by starting over from scratch. Often people find it painful starting over again, or are so excited by their first promising ideas that they don’t want to let them go, but when a problem is truly hard you may well need to restart the problem again and again before hitting on an approach that really will work. This is a bit like reseeding a random number generator.
Discuss the problem with other very smart people (even if they are not experts in precisely what you are doing) and listen closely to what they have to say. You never know when someone will say something that will trigger a great idea, and the process of explaining what you are working on can cause you to gain a new understanding of the subject or, at least, force you to clarify your thinking.