Asymptotically Speaking

“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., 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 – with 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 this 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

Quote of the Week

“While perfection may well be beyond realization in most circumstances, excellence is not.”  QM

Life is Like Parachuting

The annually updated book “What Color Is Your Parachute” by the late Richard Bolles has been a helpful life and career guide for multiple generations.  The basic thrust of the book is one of personally defining and designing … formulating and reformulating … a life path into which we can direct our main focus and energy with a high degree of resolve and purpose – thus creating our own unique “parachute” for our own Grand Leap into life.  [It’s available in most libraries, and worth at least one thorough perusal.]

Using the parachute paradigm, we have multiple choices in how we undertake the journey:

1)    Stay on the ground and never experience “lift-off”;

2)    Allow ourselves to get lofted into the air by whatever contrivances civilization offers (e.g., parents, schools, civic organizations, etc.), then take a Grand Leap into our own life journey from whatever altitude they have helped us attain;

3)    Never go above-and-beyond wherever find ourselves in the moment, with or without a “lofting lift”, never take the Grand Leap, and simply “hang on” to our comfort zone, living our lives vicariously thorough others;

NOTE: The forces that initially launch us will eventually run out and/or become redirected to other purposes, such that – at some point – we will be left either to fall or “fly under our own wind”.  This change in conditions may not be all that precipitous or obvious.  There may be no sudden “release of the reins” at the top.  That’s the way it SHOULD be … permitting a seamless transition from externally applied “lofting” power to internally generated “lofting” power ... except that the latter has to be fully engaged … and not only wishfully, wistfully, virtually or vicariously engaged!   

4)    Take the Grand Leap without a properly prepared parachute – or ANY parachute – and simply “wing it” all the way down.  [NOTE: “Winging it” rarely gains altitude!]  If you’re really lucky, you can latch onto someone else with a fully furled parachute and plenty of “wind in their sails”.  However, this is a highly perilous proposition with an uncertain outcome not necessarily targeted to optimize one’s personal preferences or potential.  Creating stabilizing “ballast” for smoother sailing is one thing, but becoming a “millstone” is quite another.  “Millstones” sometimes need to be cut loose. 

The personalized “color” of the parachute bears some relation to the preferred target upon which you’re intending to stake your future claims in life. 

It’s important to note that prevailing winds are subject to change in both force and direction without notice.  Thus, it helps not only to be able to “tack” against the wind, when necessary, but also to have significant anchoring or stabilizing ballast and to connect with significant others who can help catch the updrafts. 

Properly “Packing” your parachute and having intact, reliable panels – no matter what color they are – is really critical.  Consider the case of Charlie Plumb:

https://www.youtube.com/watch?v=JqtUlMA3Jqo

 “Packing a parachute” is no trivial undertaking.  You may get only one “JUMP” in life … or you may need to take a dozen or more.   The landscape and seascape keep changing and we need to be both flexible and agile to take best advantage of the conditions in which we find ourselves. 

And most of us don’t have the luxury of having someone ELSE pack OUR parachute.  Parents, teachers, coaches, Scout Leaders, etc., all provide some of the raw material and heaps of guidance, but it’s really up to US to pick the right colors, get the REST of the material we need (mining the universe), fabricate the final product (masterful tools and skills are really helpful here), and get it “packed” just right to carry us through whatever “eventualities” we might encounter. 

So how are you doing?  Are you prepared … or in the process of preparing … for the biggest JUMP of your life – whatever that might be?  Let’s keep MINING for essential raw materials, MASTERING key tools and skills, and PACKING for the long haul and for the highest altitude we can attain.  I’ve gotta go now and work on MY next parachute.  It’s gonna have to have heavy duty, high altitude serviceability!  Quartermaster