Solving problems in many cases requires a significant change of perspective. Drawing inspiration from the x, y and z axes of the Cartesian coordinate system, which provide an infinite number of ways of conceptualizing points in space, this article discusses three problem solving perspectives that can be useful in reconceptualizing challenges and identifying solutions: vertical thinking; horizontal thinking; and diagonal thinking.

Perspective Point Zero and Maslow’s Hammer

Whenever we face a problem, our first attempt to solve it usually involves searching for solutions in what might be called our ordinary frame of mind: our typical view of what the world is and how it works. If we imagine a graph with an x and y axis, this is the center point where the x axis and y axis cross. Let’s call this spot on the graph perspective point zero.

No two people have the same persepective point zero. This unique conceptual vantage point is a function of multiple factors: our cultural background; our family; our experiences; what we have seen, heard and read; the roles we play in life; and our personalities. These factors, which shift and combine in different ways, have a very powerful influence over our outlook, what we define as problems and how we address those problems.

Because of this, if we are psychologists, when we come across a problem our first reaction may to consider the motivations and previous life experiences of people who are involved in the problem; if we are warriors, we may think of ways that the problem can be addressed through military strategies and tactics; if we are scholars, we may look for solutions through research. These are all variants of Maslow’s insight that what we see is what we are: if you are holding a hammer, everything looks like a nail.

Hammers work very well to drive nails into wood but not into water: every problem is not a nail and if you use a hammer to fix a small crack in a porcelain vase it may not only not solve the problem but in fact make it far worse. In many cases, the hammer itself may be the problem. When this occurs, a new perspective is required to find a solution.

The Y Axis and Vertical Thinking

One way to gain a new perspective on a problem is through different types of vertical thinking. In terms of the Cartesian coordinate system, this can involve taking different vantage points along the y axis, the line on a piece of paper that runs from north to south. The essence of vertical thinking involves not fundamentally alterering the nature of one’s perspective but rather changing the level of detail that one focuses on within that perspective.

Let’s assume that we have the challenge of trying to improve sales of pizza in a pizzeria. From a vertical perspective, there are two options: one can go up or down. Going down vertically means to look for the answer to the problem by examining the problem in increasing detail. This might involve looking at the type of toppings that are used on the pizza to see if a different set of toppings would make the pizza more appealing to a wider customer base. An even more detailed vertical view would involve considering how these toppings are made to see if their quality could be improved or if they could be made or purchased at a lower cost. These are all examples of descending vertical thinking.

Ascending vertical thinking requires us to move in the opposite analytical direction. Instead of looking at additional levels of detail we take an increasingly aerial view of the problem, widening our analytical lens and trying to see new possible paths to solutions. With this approach, we not only look at the problem itself but the problem as a part of a larger business ecosystem.

In the case of the pizzeria, this might involving not only considering the pizza, but examining the pizza as a part of larger set of food offerings that the restaurant provides. If we conduct this type of analysis, it may become obvious that rather than pizza, customers in a particular area prefer other types of Italian food. It may therefore be necessary to change marketing tactics so that more people prefer pizza or include other types Italian food on the menu.

In addition to the items on a menu, the pizza could be viewed in terms of the food that is offered in a particular area or even as part of the food industry itself. From this perspective, it may be possible to identify larger facts and trends that influence dining choices, such as levels of income, demographic trends and even places of dining preference. By increasingly taking a broader perspective, it dramatically increases the types of solutions that can be identified.

The X Axis and Horizontal Thinking

The second approach to gain new problem solving perspectives is through horizontal thinking. In terms of the Cartesian coordinate system, this involves taking different perspectives along the z axis.

In horizontal thinking we move laterally to try to find solutions: this means that instead of looking at a problem with greater or lesser levels of detail within our ordinary frame of reference we try to see the problem from a completely different frame of reference.

For example, to find solutions to improve pizza sales, we might draw inspiration from culinary areas that are often not immediately associated with pizza, such as Chinese food. There could be, for example, pizza with sweet and sour chicken or for something with an Indian flair pizza with tandoori chicken: we are only limited by our imagination, the availability and cost of ingredients and consumer preferences.

Apart from ingredients we could draw on different perspectives to fundamentally alter the form in which pizza is served. In addition to circular or square pizzas, pizza could be cut into bite size pieces and served in a cup. While this “Pizza in a Cup” or “Pizza Verticale” would certainly lack the visual flair of the pizza format that we have all come to know and love and undoubtedly horrify pizza traditionalists, it would make pizza a lot easier to eat while walking in a busy urban area, it would facilitate shipping and this vertical pizza with a reduced surface area that was exposed to the colder air temperature would stay warmer longer.

Horizontal thinking is not only limited to considering alternative types of ingredients or pizza formats. It could also be applied, for example, to think of new ways that pizza could be prepared and delivered to reduce costs. The company Zume, for example, uses robots to make pizza. This is a classic example of horizontal thinking.

The Z Axis and Diagonal Thinking

A third way to identify solutions is through considering the z axis. The z axis is the axis which extends off the page and toward the person who is observing a graph. The movement of a line from two dimensional to three dimensional space is the basis for what could be called “diagonal” thinking.

The essense of diagonal thinking involves trying to integrate a thought perspective with what will happen once that thought perspective meets the reality of the world outside of that thought perspective. Any time we implement a thought, it is immediately met by other thoughts and emotions, which may be very similar or very different depending on the context; and this collision in turn creates new possibilities and thoughts.

In the context of the pizza example, if we try to change the menu we have to consider how that decision will impact not only the pizza but the larger environment in which the pizza is made and sold. Will it require new work approaches, new storage space or new employees? Will it require new marketing approaches? Each of these changes will set in motion a broader set of changes that will affect the pizzeria and the goal of building overall sales. These changes in turn will provide new ideas and potential solution paths to explore.

Conclusion

While our own outlook often holds the key to many solutions, there are times when new perspectives are helpful to see problems in a different way. Vertical, horizontal and vertical perspectives are all useful ways to broaden our problem solving view. Further, each time we try to see the world in new ways it expands our ordinary frame of mind, our perspective point zero, and this sets us up to identify increasingly innovative solution paths.