We tend to think of time and distance as linear.
The 15th of the month is halfway through. 13.2 miles is half the marathon.
In some senses and cases, that’s a valid and useful way to look at the world.
Most of the time, there’s Heartbreak Hill. Or, as Appalachian Trail thru-hikers know, halfway from Georgia to Maine might be half the mileage, but it’s waaaaaay less than half the climbing. (Most of that happens in Maine, once you’re properly tired out by the mileage.)
Nature abhors a straight line, and the real world is full of power curves, exponential curves, and normal curves. Too many people struggle to draw these, let alone understand them. (Halfway along x under a normal curve may not get you halfway up y; “past the peak” means we’re halfway done, not all the way there.)
Are we there yet? How close we are depends on how you measure — and a linear measurement might turn out to be pretty misleading.
Colin Steele 