A function in mathematics is a relationship between variables that has exactly one output for a given set of inputs. For example, if we consider the behavior: “When it might rain I carry an umbrella”, we can infer the inverse: “if I carry an umbrella, it might rain”. If you didn’t have access to a weather forecast, and wanted to guess whether it would rain, you might look to see how many people are carrying umbrellas. In this case, we are using information not from the “function” itself (raining) but rather a related representation of it (umbrellas). In mathematics it can sometimes make our lives easier to perform operations using the tools available in one space (the “inverse”) than the other (the “function”).
It is a common high school algebra problem to graphically depict the inverse of a function on a graph. A quick way to achieve this is to draw a line y = x (diagonally traversing from bottom left to top right), and draw a mirror reflection about this line. Thus emerges the pattern winding back and forth shown here.
One of the most fun games from childhood is “Opposite Day”, where everything you do and say is the inverse of what you see. It is an effective way of breaking habits and invites in new possibilities for the task at hand.
What is there to gain from intentionally deviating from a habit? The alternative may or not be better, but more importantly it can show you that our adherence to habits is not so much because the outcome serves us, but instead because it demands less effort than the alternative. Equipped with this realization, we can discover a newfound sense of empowerment in the ability to choose an alternative to what we might be unconsciously doing.
This process requires two steps: understand what the pattern is, and then work out what we can change about it. For example, we may observe a pattern of reaching for our phones before going for a morning walk. We can then consider the “inverse”: waiting until after the walk, and observing how it makes us feel.
Return home.