sábado, 18 de março de 2017

Some analogies between life and mathematics

In math and physics, we often find equations which we cannot solve immediately because they are too general - we need what are called boundary conditions. These allow us to make the problem concrete and soluble - per example, if I want to find how the temperature is distributed in the room, I need to know the shape and size of the room.

In life, I might want to find the solution of how I should act. But this is too general - how you should act in what context? We have to first define what your space of action is, so that the boundary conditions are well-known. These boundary conditions can be your ethics, fears, troubles - such that they represent the limits beyond which you cannot act - and thus they define what your space of action actually is. Then a solution can be formulated - how should you act, given these conditions? Of course, in real life I would say that the boundary conditions are the real challenge to solving any problem. If I have a very clear sense of what my ethics, fears and values are, then I would have a perfect recipe to act in any given situation - unfortunately, the boundary conditions depend on the nature of the problem, so they are ever-changing.

Another example in math and physics is the concept of change of reference of frame, or let us just call it change of perspective. Some problems might not seem trivial - e.g. if we want to figure out the evolution in time of a spinning top as seen from an outside perspective. We can change our point of view, imagine that we are spinning with the top, study it from that perspective and then go back to our original outsider point of view with more information.

In life, a problem is often seen as unsolvable from the perspective of the individual. If taken from a different perspective, the problem might be trivial or even disappear at all - be it a psychological or a practical problem. At a minimum, a change of perspective often makes the problem more clear than it was before.

It is interesting to think that perhaps some strategies used in mathematics are general forms of what we learned in particular cases throughout life. I do not want to expand on this here, but just pin down a very abstract idea for the sake of later reflection.