Vision is worth the while
Hamming has a great quote on the importance of vision.
It is well known the drunken sailor who staggers to the left or right with n independent random steps will, on the average, end up about _ān _ steps from the origin. But if there is a pretty girl in one direction, then his steps will tend to go in that direction and he will go a distance proportional to n . In a lifetime of many, many independent choices, small and large, a career with a vision will get you a distance proportional to n, while no vision will get you only the distance ān . In a sense, the main difference between those who go far and those who do not is some people have a vision and the others do not and therefore can only react to the current events as they happen.
I did a little experiment to visualize it https://vision-visualized.vercel.app/
There are two grids, and the goal is to go from (0, 0) to (10, 10). Which is 10 steps in total.
In one grid I generate a path by going 20 steps in complete random directions. It gets nowhere, all the time. At best maybe it gets halfway towards the vision. Some times it get close to the border (there's and insight here!). Most of the time it's just a clump of steps going around.
In the other grid, I generate a path but this time only 50% is random, the other 50% is towards the goal. In this case, most of the time it gets to the destination, sometimes even in less than 20 steps. And even if it doesn't, it is rarely the case that it gets too far off.
Even if only half of our decisions are oriented towards a vision, it is better than having no vision at all.
But there's another insight I got from these visualizations, that I hadn't thought about before. š¤Æ
In the random case, as I pointed out, it rarely even gets close to some of the borders (11 straight steps).
If we accept that anything worthwhile in life takes effort and time to get there, then what's worth chasing is at the edges of the grid.
Going about our lives with no vision, not only gets you nowhere in particular, it also rarely gets you to a meaningful and rewarding destination, those edges of the grid.