Most of us are inattentive to the concept of the Working Range” that pertains to virtually everything we do, measure, observe, etc. For instance, we may employ a 100 feet tape measure to measure and (provisionally) assume that it is good for "essentially anything.” But it is useless to measure distances to nearby planets and stars, nor even measure across a wide river. Similarly it cannot measure microscopic and sub-atomic distances. A throttle (gas pedal) on a vehicle supplies fuel that increases vehicle speed and there is a near “one to one” relationship between the depression of the pedal with fuel fed to the engine and to subsequent acceleration, but only until the vehicle reaches its top speed e.g. from perhaps 5-100 mph. When a somewhat dense object enters free falls, in is “working range” of acceleration, absent air friction, it accelerates at 32 feet per second per second but only until reaching terminal velocity, dependent upon the density, air friction, etc.
There is a often a distinct proportionality, sometimes deemed one to one ratio (1:1), between input and output or between so called “cause and effect” but that relationship only exists within the working range.” A strongman, like Charles Atlas, for instance, could coax and inch a 100 ton locomotive forward for perhaps up 30-50 meters, but it may have taken a relatively long time—a few minutes of most extraordinary effort—for the strong man to invest in and build up to the speed even to “inch along” – based upon the kinetic energy formula of 1/2 MVP. The rest of us would have been hapless against such a mass. But while from a theoretical standpoint, even a 100 pound tug would start to accelerate a 200,000 pound vehicle, there would have, however, been some additional resistance to “rip” and “steal” the locomotive from its resting state i.e. a certain kind of“stickiness” that must be overcome to dislodge the object from its resting state and the 100 pounds would hardly be sufficient.
Malcolm Gladwell spoke of his 10,000 hour rule i.e. that with 10,000 hours of practice, a dancer, pianist or other practitioner achieves mastery over his/her craft. But in almost any complex skill, initial learning and improvements occur quickly, but as one becomes better and better, 10 times the effort may afford perhaps 1% improvement so that a top performer may need to spend 4-8 hours a day in practice to “stay on top” of his/her game. But in these cases, rather than seeing “the working range,” we thus observe diminishing returns on investments i.e. needing more and more input to achieve less and less.