In high school and prior educational experiences, I remember being taught that it is much easier to prove a negative than a positive. To prove something is false, you only need one counter-example--to prove something is true, you have to really apply yourself, and those theorems and postulates you learned in geometry. Even then sometimes it can be difficult to really believe your proof is right because you have to have an underlying faith in the postulates and theorems on which it is based.
In life, it is easier to close doors and stand still, proving to yourself that "X" will never happen, than it is to persist on the path of faith and work toward a goal. How much easier is it to guarantee you will fail a test than it is to guarantee you will get an A? How much easier is it to prove to yourself that you can isolate yourself from friendships than it is to be certain you will have a vibrant group of friends? How much easier is it to say to yourself, "life is hard" as opposed to saying, "things will improve"?
This principle--negatives being easier to prove than positives--manifests itself beyond the 9th or 10th grade student stumbling through geometric proofs. Take physics and the principle of entropy for example: all things in the universe tend toward disorder. Energy must be exerted to create, to build, to uplift.
Sometimes we want to know we are right more than we want to progress or feel peace or happiness. We prefer immediate certainty over deferred satisfaction, and thus, we limit ourselves. We prefer not to exert ourselves because we either don't want the reward badly enough, or we don't believe it really exists. We get discouraged with how we are performing at school or work and stop trying, ensuring that we will most certainly perform below our potential. We fear rejection and thereby ensure a single, friendless existence by staying home from a party instead of going to meet new people. We are proud and would rather be right about being unhappy than allow ourselves to be humble and happy.
Positive proofs in life are iterative. As we learn to trust others and ourselves, we have to exhibit faith, believe in positive outcomes, recognize positive outcomes, and then repeat the process over and over again until we develop a knowledge that good things do happen, good friendships are developed, and good accomplishments are achieved. Just like in geometry, positive proofs are still harder to solve than negative ones.
