One of the stock examples of control is driving a car and using lateral pressure on the steering wheel to maintain its relationship to the margins of your lane of the road. This has been described most often in terms of driving down a highway with disturbances from cross winds. There is a memorable description in the archives of Dag driving and Bill, to make the point experientially (‘viscerally’ as we say) about the nature of control, reaching across from the passenger seat and gently but more and more strongly pulling on the steering wheel, then relaxing the pull. Dag got the point in a memorable way.
Here I introduce evidence which you each can verify in your own experience that we do not control the relationship of the right and left edges of the front of the car to the immediately adjacent margins of the road. Instead, we control the direction of motion toward a centered position some distance ahead along the road.
I still remember vividly the experience when I was first learning to drive. Trying to align the edges of the front fenders with the edges of the road did not work because when I was steering wrong the variables change too rapidly. Aside from over-steering and veering, alarmed attention on the near environment interfered with looking ahead to important things like crossroads, oncoming traffic, and curves in the road. Now, as an experienced driver, you can experimentally shift attention to the immediate relationship of front fenders to road margins. You will find that it feels alarmingly less well controlled.
This is why we cut corners: since the target direction is some distance ahead around the curve, it is natural to aim for that location, using peripheral vision to avoid the inside edge of the curve. If we purposely maintain centeredness in the lane rather than hugging the inside, then it is necessary to focus attention on the nearer margins, where the variables are changing more rapidly, and it feels alarmingly less well controlled.
When we drive around a sharp curve, e.g. on a switchback mountain road, the distance to which we can look ahead is reduced. It feels alarmingly less well controlled. Of course, the more ‘blind’ the curve (e.g. because of the rising terrain on the inside of the curve on a mountain road), the greater the concern about possible oncoming traffic or other road hazards ahead, while your attention is demanded on relationships closer to you.
I wonder if these factors apply to the more general cases in the contentious ‘power law’ discussion.