Distance vs. Displacement in Research

Ever since I started digging on some very basic yet "complicated" problems on Dynamic graphs (i,e., the graphs which undergo changes in the vertex/edge set), every now and then, we get to observe some great properties underlying. That is what guides our direction for next few days. And then, with similar micro-observations, we keep building upon ideas. Eventually, looking backward, we see that the path(and hence the time) we took from start to this checkpoint, could have been exponentially smaller. This made me wondering, Research and innovations are analogous to distance and displacement.

To be continued...