I am enjoying the topic.
The more data you have, the more aspects of the world you can consider. Someone creating a mathematical model may consider 10 or 20 variables. They may have solid, written data about the historical values of those variables. In the best-case scenario, they may be quite sure that they have good, reliable data. But still, it's just 10-20 variables. What are the consequences of not considering all sorts of other variables that may have big impacts?
Someone just pondering over the problem for a little bit may consider thousands of variables based on their experience (their nervous system having recorded actions and their consequences as they propagate through the system). But that data is not reliably stored - our nervous systems change our memories over time, the memories may get recorded in problematic ways to begin with, and so on.
Maybe we can take the best of both worlds - reliability of data AND system-wide mapping. There are various models that endeavor to do this.