Derivatives

The more math I do, the more I try to apply the decisions I make and analyze the rate of change in my actions. I believe that if life is a function itself, then the first derivative of life would represent the motivation behind the decisions you make. If plotted as a line, the changes in your actions throughout your life must stem from the motivations that drive these nested changes.

I find it interesting to think of life as a function and the first derivative as motivation because it adds clarity to changes that might otherwise remain hidden. For example, consider a complex set of numbers—such as the outputs from a particular algorithm: -1, -2, 3, 14. Attempting to draw a pattern between them might involve arbitrary steps like starting at -1, subtracting 1, adding 5, and then adding 11. This approach seems handwavy and makes it difficult to identify a clear pattern. However, viewing these numbers as derivatives of a function provides a more structured understanding. Derivatives represent the rate of change of a function, allowing for the recognition of more complex behaviors. By applying the first derivative to the people around you and yourself, you can observe simpler, emergent behaviors instead of dealing with a complex series of seemingly random additions and subtractions.

I believe this is only the first step. When you take the second derivative of your life as a function, you gain insight into your value system—something more concrete than motivations, which can change with new insights. A value system reflects who you are, and while it is difficult to see this in others compared to the first derivative, it is easier to observe in yourself. Large changes in your motivations and how they are applied can reveal shifts in your value system.

Finally, the integral of your life as a function represents the net change of your life. It is the accumulation of all the decisions you have made and the actions you have taken—the sum of all the first derivatives of your life. This integral reflects the total change and the net effect of your life as a function. It is the most important aspect, as it encompasses the overall trajectory of your life based on your accumulated choices and actions.

There are derivatives higher than just your value system, and you can even attempt to assign meaning to integrating the net changes in your life. While these higher-order derivatives may hold meaning, it diminishes as the order increases. If you can identify your own second derivative and observe the first derivatives of the people around you, you begin to remove the layers of abstraction that previously existed.