Tl;dr: I agree it’s important to learn how to navigate, but more to avoid wasted motion than to avoid hitting posts.
Polya’s recurrence theorem sheds some light here. Running forever in the infinite meadow, the blindfolded child is guaranteed to hit the post. But if the child’s moving through a higher-dimensional space, his chance of hitting the post is very small unless the post starts out nearby. A fish swimming randomly, forever, through an ocean of infinite breadth and depth, has only a 36% chance of ever returning to its starting position. Higher dimensionality helps us avoid random hazards, but also prevents us from finding random benefits.
To me, then, the biggest threat is not hitting the occasional post, but wasted motion. Moving about costs time, money, and energy, and sometimes leads to no reward and nothing learned. In the short term, (semi)-random motion can be pleasurable, and is often necessary. I’m fine with running into a few posts if I can learn or gain a lot. But I do worry about running around in the infinite meadow until I die of exhaustion.
Even “cashing in” a reward, like money, in order to realize a concrete benefit, like a delicious meal, is a complicated form of movement on its own that can go wrong in all kinds of ways. It wasn’t until I met my girlfriend, who’s a big foodie, that I realized how much work goes into finding good eats in the Portland food scene, even though there are lots of great restaurants. Sometimes, she’ll spend an hour or two looking at options before picking where we’ll go. And the payoff is absolutely worth it.
Polya’s recurrence theorem sheds some light here. Running forever in the infinite meadow, the blindfolded child is guaranteed to hit the post. But if the child’s moving through a higher-dimensional space, his chance of hitting the post is very small unless the post starts out nearby. A fish swimming randomly, forever, through an ocean of infinite breadth and depth, has only a 36% chance of ever returning to its starting position. Higher dimensionality helps us avoid random hazards, but also prevents us from finding random benefits.
It seems worth noting that, though humans do live in a very high-dimensional configuration space, the “hazards” we worry about also live in that same space, and as such may not be such easily avoidable objects as the points discussed by Polya’s recurrence theorem. (An infinite line in three-dimensional space, for example, is analogous to a point on a two-dimensional plane, and is likewise guaranteed to be hit by a sufficiently long random walk.)
Tl;dr: I agree it’s important to learn how to navigate, but more to avoid wasted motion than to avoid hitting posts.
Polya’s recurrence theorem sheds some light here. Running forever in the infinite meadow, the blindfolded child is guaranteed to hit the post. But if the child’s moving through a higher-dimensional space, his chance of hitting the post is very small unless the post starts out nearby. A fish swimming randomly, forever, through an ocean of infinite breadth and depth, has only a 36% chance of ever returning to its starting position. Higher dimensionality helps us avoid random hazards, but also prevents us from finding random benefits.
To me, then, the biggest threat is not hitting the occasional post, but wasted motion. Moving about costs time, money, and energy, and sometimes leads to no reward and nothing learned. In the short term, (semi)-random motion can be pleasurable, and is often necessary. I’m fine with running into a few posts if I can learn or gain a lot. But I do worry about running around in the infinite meadow until I die of exhaustion.
Even “cashing in” a reward, like money, in order to realize a concrete benefit, like a delicious meal, is a complicated form of movement on its own that can go wrong in all kinds of ways. It wasn’t until I met my girlfriend, who’s a big foodie, that I realized how much work goes into finding good eats in the Portland food scene, even though there are lots of great restaurants. Sometimes, she’ll spend an hour or two looking at options before picking where we’ll go. And the payoff is absolutely worth it.
It seems worth noting that, though humans do live in a very high-dimensional configuration space, the “hazards” we worry about also live in that same space, and as such may not be such easily avoidable objects as the points discussed by Polya’s recurrence theorem. (An infinite line in three-dimensional space, for example, is analogous to a point on a two-dimensional plane, and is likewise guaranteed to be hit by a sufficiently long random walk.)