“In analytic geometry, an asymptote (/ˈæsɪmptoʊt/) of a curve is a line such that the distance between the curve and the line approaches zero [but never actually GETS there] as they tend to infinity.” https://en.wikipedia.org/wiki/Asymptote
In practical terms, one can approach certain unassailable goals (e.g., such as perfection) forever WITHOUT ACTUALLY GETTING THERE. However, such can still be increasingly and progressively approached … progressively distancing oneself from GROUND ZERO!
Let’s consider the goal of owning a house with an ample front and back yard, plus a front porch, bordered by a white picket fence, on a restricted access street.
One will likely start out – first – in a one-bedroom apartment with noisy neighbors on a busy street in a crowded neighborhood.
Marriage – or collusion, with two or more people working – may bump that up to a two- or three-bedroom apartment in a more “upscale” environment.
Adding children and losing one working person, but hustling a little to get a promotion, may hold things “even”. The next promotion, combined with savings accrued along the way, may keep the momentum going. But it’s going to take increasing amounts of “hustle”.
In the end, one may not actually attain either the white picket fence or the front porch or both, but, all things considered, one may end up a lot further along with SOME SORT OF ENHANCED INDEPENDENT LIVING by diligently progressing toward the goal.
The slope of the curve early in the workings is important. A steeper slope creates momentum such that one can get closer to the goal a lot faster. As graphed in the illustration, the slope of the curve is increased more by “Working Smarter” than it is by working harder! However, if you overlay the graph with a plot showing an ACCELERATED RATE of energy expenditure, everything shifts to the left, showing a much faster approach to the goal.
Imagine what the result would be by BOTH “working smarter” and putting forth more energy!
In a competitive environment – for example, where a PROMOTION may be at stake – ENERGY OUTPUT and “Hustle” are critical.
There’s an ancient parable about two hikers accidently encountering a bear in the woods. The first hiker says, “(Groan!) There’s no way we can outrun that bear!” But the second hiker replies, “All I have to do is outrun YOU!”
Two final thoughts:
First, in politics we hear about people “moving the goal posts” … making things more difficult to achieve than originally conceived or than having any “reasonable expectation” of achievement. This might be called “Asymptotic Meddling”.
Second, in sports, the “league” you’re in sets the asymptotic limits of expectation. However, some [who probably “don’t know any better”] do not consider themselves personally constrained by the asymptote, and actually go on to exceed the asymptotic limits others are up against. These “outliers” generally go on to the next higher league and may become “elite” athletes.
The “Four Minute Mile” was one such asymptotic barrier for “middle distance runners” from the beginning of time to the early 1950s (although no one knows how fast the early Greek athletes were).
“[Breaking this barrier] was first achieved in 1954 by Roger Bannister in 3:59.4. The “four-minute barrier” has since been broken by many male athletes, and is now the standard of all male professional middle distance runners. In the last 50 years the mile record has been lowered by almost 17 seconds, and currently stands at 3:43.13.
https://en.wikipedia.org/wiki/Four-minute_mile
With or without “Bears in the Woods”, there is increased distancing from Ground Zero to be afforded and there are elite Asymptotic Heights to be approached that can make the journey extraordinarily fruitful – as opposed to “fitful” – and exhilarating. Let’s get “smarter”, ENERGIZE and HUSTLE the best we can toward those Higher Heights and enjoy the view! There are lots worse places to hang out than in the “League of Champions”! Quartermaster
