You’ve got an idea of how to solve a problem. Great! How can you know if it’ll work?
The most obvious way is to test the idea. If your problem space is small enough, you might even be able to test it while controlling some variables. However, odds are good that you’re dealing with a problem space that doesn’t lend itself to a controlled environment or a quick feedback loop. In these cases, the ability to quickly gauge the efficacy of an idea is important because it helps prevent you from wasting time. But sometimes you’re not able to prove whether or not a solution is possible. That could be because of limited resources for testing (maybe you don’t have the budget for a large survey of prospective users), or it’s impractical to test (maybe you’re working on a solution for protecting earth from comet collisions).
In cases like this, it may be much easier to disprove your idea. If you’re trying to implement a solution to a problem, your plan needs to hold up against reality. If you are able to disprove all or part of your solution, you can either correct your assumptions or completely change your perspective of the problem. The sooner you can do this, the sooner you can improve your approach.
There are a few ways to go about disproving your idea. One is to identify the components and examine the connecting spaces. Are there transitions between steps or interactions between elements? If so, are there any inconsistencies that you can’t resolve? If you are designing a process, record where pieces of information are created and used. Is there a point where information is required prior to its creation? Or is there a gap where the information doesn’t have a path between its creation and use?
Another approach is to look for scenarios that should be impossible according to your mental model. As an example, if you had a solution that depends on getting a certain degree of accuracy from a piece of hardware. Start by determining whether or not our current understanding of physics allows for that level of accuracy.
Now that you’ve punched a hole in your plan, what do you do next?
Your first option is to repair the hole you just created. Was there a false assumption? Correct that assumption and see how that affects any dependent theories. Was there information you had previously missed? Add that to your view of the problem space and see what changes. Was there an edge case you hadn’t considered? Focus on solving just the edge cases and see how that handles the common case.
Your second option is to choose a fundamentally different approach. Did the issue you encountered break your entire approach? It’s time to look for a new path, not just a branch of your current path. You could use lateral thinking to find non-obvious solutions. Try to find a solution that might be simpler, more elegant, or more efficient. You can look for inspiration in an organic analogy. Identify the hardest-to-solve aspects of your problem and see what they have in common, then see if a solution can be formed from that commonality. Use the Five Whys approach to look at the problems behind the problem — you may find that the problem you’re experiencing is just a symptom of a larger (but solvable) problem.
What do you do if you’re unable to disprove your idea? What have you learned? Technically, nothing. The lack of disproving isn’t the same as proving. You may indeed be on the right path, or you may not have found the right aspect to disprove. This just means that you haven’t found the right test, which might ultimately be the actual implementation of the idea. If this is the case, proceed — but with caution.