One of the first lessons we learned is that constraints can help creativity. I know it’s not very profound by itself, and perhaps what I found to be most fascinating isn’t very profound at all, but I feel it is worth expounding upon.
We recognize that an over-constrained problem can kill creativity. The fact that there exists a notion of too little constraints for creativity is quite fascinating. I think there are 2 primary types constraints, an economic one and an artificial one.
An economic constraints is one granted by scarcity. When people say laziness is the mother of inventions, it’s where their creativity allows for them to fill a need or create value in a place where they never experienced before.
An artificial constraint is one that is not granted by scarcity. It is a constraint perhaps of one’s education or one’s available knowledge or material. This might be an arbitrary constraint but these constraints help propagate creativity.
That shouldn’t make sense to a mathematician, because a set can do anything its proper subset can do (besides being smaller). Why when given less that people can do more? Perhaps it’s the paradox of choice, that the choices makes it less worthwhile to create, but I don’t find that to be the case. I come to the grim, but really informative conclusion that the complexity of the world is too much for people to understand.
In what could be called the Curse of Dimensionality, when too many things are presented to people, their ability to wrap their minds around and create things with what they are presented diminishes greatly. It’s the combinatorial explosion combined with the curse of dimensionality. The space gets larger while the ability to jump through neighbors decrease. The space of possibilities increases O(n^n) while the Limit of the volume of the sphere from any given point reaches 0 as n gets to infinity. It’s as if the Universe expands and its weight is crushing the person from going anywhere. Anywhere it goes, it’s a needle in a haysack, so dial back the Universe and let’s just play locally. We’ll get somewhere, maybe it won’t be the global maximum, just a local one.