The Effects of Discontinuity of Convenience
Modern life is full of conveniences: washers, driers, dish washers, microwaves, automobiles, electricity, etc. As American's we tend to think of these as our birth right as opposed to a convenience for the privilidge. That's why we flip out when the electricity goes out. No act of God (i.e. lightning, falling trees, transformer explosions) should come between us and our right to electricity. But it does and suddenly we are unable to complete work given to us- even work that requires no electricity.
The ability of a person to do work is a function of the operation of these conveniences, which I call the Convenience Factor, C. When the dishwahser breaks, the electricity goes out, or the car dies, there is a discontinuity in C, causing an increase in the stress level (S), which can be moderate or severe depending on the human stress constant k.
kS ~ 1/C
The above equation is sort of misleading because it implies that as Convenience goes to zero, stress goes to infinity. This is not entirely the case, because there are several other factors at work. As an analogy, we use Special Relativity when speed approaches the speed of light. Otherwise we use the simpler Newtonian physics because it's easier and it works. Here, I will derive the easier method and not address Minimal Convenience Situations.
Ok, so moving on. The ability of a person to do work (A) is related to the amount of stress in life, the person's focus on the task, and the operation of Conveniences.
A_tot = A_stress + A_focus + A_convenience
A_focus is related to the task and generally amounts to a constant, which I will ignore because we are really interested in the ability as a function of time and this term cancels out when taking a time derivative.
A_stress is difficulte to generalize, but here we will break down the term into stress due to loss of convenience and other stress. I add the stress dues to loss of convenience to the A_convenience term and therefore calculate only the A_convenience+A_stress:loc.
When a convenience is lost, A_c suffers a discontinuity and A_s increases. In general, we say this derivative does not exist at time t when the convenience is lost. Because a person's efficiency is a function of their ability to do work, efficiency ceases to exist at the time of loss of the convenience.
The revealing part is what happens after the loss of the convenience (i.e. the derivative evaluated at time t+dt). Efficiency is hopelessly decreased until either adaptation occurs or the convenience is restored.
E ~ A_tot +F
Adaptation (F) is a slowly varying function that seems to take forever to rise to any reasonable level. It is a function of A_convenience, in that its magnitude will decrease whenever A_c decreases, then as time goes on, it will cause efficiency to rise. If A_c is restored, adaptation will either fail to rise or remain constant.
To give a real world example, I am a person who sets an agenda and generally manages to get things done. I am on time for 99% of the things that I do and late for 10%. It doesn't exactly add up to 100, because I am fairly overcommitted will completely miss those extra things.
Anyway, last Thursday, my poor car died. Not completely dead, but enough to need to be examined by a car doctor. By God's grace, I have been able to get to and from school via my chauffers (a.k.a. parents). Despite this, the loss of convenience has increased mental stress and I have been unable to complete homeworks and tasks that have no dependence on use of a car. In this instance, loss of convenience has caused a decrease in efficiency, and efficiency will remain low until either the convenience is restored or adaptation occurs. (Q.E.D.)
