Solving complex problems is challenging in various ways: first you have to frame the problem correctly. Next you have to understand its root causes. Then you have to identify various ways to solve it, and chose the right one. Finally, you have to implement your solution. This four-step process is challenging because it requires you to think in both convergent and divergent ways. That, in turn, requires you to be both proficient in the subject matter and  innovative. For most of us, it is the innovation part that’s the most difficult. Fortunately, by recognizing isomorphic problems you can improve your innovation.

Think of it this way, problems typically have two layers: a superficial one made of the various quantities involved (the surface features) and a deeper one that has the principles governing the relationships between these quantities—the structural features. The key to recognize isomorphic problems is to look past the superficial level to uncover those principles. Indeed, a recent report by the National Academy of Sciences points out that expert problem solvers focus on major principles, whereas novices focus on superficial aspects.

When you do look past the surface, you might realize that two problems that appear different have, in fact, the same underlying structure and may be solved in a similar way—a practice known as analogical transfer. So it is important to be able to recognize isomorphic problems. Here is one concrete way to do it.To leverage isomorphisms, start with a clear description of your problem

Start by stating your key question—the one that encompasses all the others that you want to answer. In our examples, the key questions might be, How can we increase our profitability? How can we solve the saturation of the parking lot? How can we ensure that our team’s workload remains below our work capacity?

Next, build an issue tree: a graphical breakdown of your key question that lays out in an insightful way  its dimensions in independent and collectively exhaustive branches. For instance the initial breakdown of a profitability issue tree might look like the one below. Profits are the difference between revenues and costs; therefore to increase my profits, I can increase my revenues or reduce my costs (or both, which is already considered in these two branches, so, omitted). Moving to the right, revenues might be generated by new clients and returning ones. And moving to the right still, revenue from new clients is the product of the number of clients by the unitary revenue. Etc.

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A profitability issue tree is useful to breakdown revenues and costs into their driversThe tree allows you to identify exactly once all the possible ways in which you can solve your problem, irrespective of how feasible or desirable these potential solutions are. That is, you are just mapping the solution space. At this stage, you aren’t advocating for pursuing any of these potential solutions, you are just acknowledging their existence. Just as a map shows all the roads that you can use to go from point A to point B, an issue tree lays out graphically all the ways that you can answer your key question.Building an issue tree takes time. All the more because, up to a point, to be insightful, trees might need to be custom made for your problem. The good news is that you can use existing trees to jumpstart your analysis.Next, establish equivalencies between the target problem and the reference oneAnd this is key: by using analogies, you can use an issue tree about profitability to help you solve the saturation of your parking lot. All you have to do is find the equivalency between the components: for instance, revenues become your parking capacity while {costs + margin} become your parking demand. Continuing, a client is an entity that generates revenue (i.e. parking capacity), so maybe that becomes parking space. So, to increase your revenue (parking capacity), you can either use new clients (new space) or returning clients (existing space). So far, nothing ground breaking, but the value of analogical transfer is more apparent when you move to the right in the tree. ‘”Stealing” clients from competitors’ becomes ‘using parking capacity from other organizations’. Do you have a neighbor with unused parking capacity when you need it most? For instance, if you are a restaurant whose issue is to find parking space for people that come for diner, maybe there is a bank, school, or church nearby who has unused parking space at diner time? Maybe they have a similar problem: they might need more space than they have in the mornings, when you don’t use yours. Maybe, by pooling your parking capacity, you can help each other out.This is even more apparent when you think about ‘decreasing costs’ branch (decreasing parking demand). Indeed, when thinking about fixing the parking lot saturation, only a few people think about reducing the demand, and yet this also belongs to the solution space. For a real-life analogous example, look at how IBM solved the Stockholm’s traffic issue: not by building more road (increasing capacity) but by installing a ‘tax and drive’ system with transponders that charge a variable fee depending on the time of the day (reducing demand).While these ideas might not be revolutionary, they aren’t trivial either. I have used this parking lot example with over two hundred students and professionals over the years, and no-one to date has been able to think of a comprehensive solution space that includes both partnering with another organization to increase capacity and decreasing demand.Being able to think about these types of innovative solutions is all the more challenging if you are familiar with your problem, as you lack the distance to step back, see the big picture and ask ‘silly’ questions—a result of habituation. Analogical transfer is a good way to get some artificial distance between you and your problem, which will help you consider non-trivial solutions.