Tuesday, June 9, 2015

Efficiency Revisited

In "Efficiency and Completion Time," I discussed how the amount of time it takes to complete a generic task typically takes longer than the minimum possible time. I've since explored the math behind that observation, and how it might vary across the world's population using insights described in "Changing People."

It turns out that what I called the "efficiency" of performing a task is equivalent to what we commonly know as a compounding interest rate on a credit card we're not paying off, where we are exponentially depleting the remaining amount of the task. If efficiency varies randomly from zero to one across the population, then the 68% of people in the central bulge of the bell curve will have efficiencies between about 0.4 and 0.6. That is, a typical person will accomplish between 40% and 60% of the remaining part of a task during a period of time that is the best case for accomplishing the entire task, which includes preparation and perfect luck. Very skilled people working on state-of-the-art projects, in my experience, are at the high end of "typical" efficiency, which is at the low end of the top 16% of the population that includes only one person who can achieve the task in the best-case time.

Realistically there is a limit to luck, which based on my testing experience is around 95%. This means that multiple attempts at a task are unlikely to all achieve more than 95% of it. Typical people take about 3 to 6 times as long as the best case to complete 95% of a task. Only 47 people on our whole planet could accomplish 95% of a task in the best-case time or less (notably, at the beginning of civilization this number was ten – at least two breeding couples – with this efficiency).

Of course, tasks are extremely variable, which would seem to make these kinds of comparisons meaningless. That variability is, however, covered by the definition of best-case time, which includes the influence of such things as technological aids, the education available to the population, and inherent complexity. Efficiency is explicitly tied to just what humans can do, which is subject to finitely limited physical and mental capabilities that influence the performance of all tasks, so the time to complete a task must be measured as the time that humans are involved in activities that support it, which includes education, skill development, and acquisition of resources.

It is also important to note that each person may not have the same efficiency for all tasks: for example, someone with 20% efficiency for one task may have 80% efficiency for another task; the bell curve simply represents the number of people who have given efficiencies. Tasks may also have common aspects that allow people to have about the same efficiency for multiple tasks, especially those that enable them to meet their basic needs in a natural environment.

In this context, our social infrastructure, which includes education, can be seen as a means of accelerating the effective completion level of common tasks to a point where further action on specific tasks takes a reasonable amount of time, especially those that affect the goals of the society – the most critical being its survival. This also involves preparing people to cooperate (another common task) so they can collectively benefit from each other's strengths (high efficiencies), and offset each other's weaknesses (low efficiencies) under changing conditions that force adaptation through performance of modified or additional tasks. With a random distribution of efficiencies across the world's population, it would take seven times the best time to prepare 99% of the population to do a common task in the best time; that factor, and the limit of time available (perhaps 13 hours per day) would determine how many common tasks could be prepared for.

One of the most common tasks in human history is our joint effort to dominate the natural world, which materially translates into maximizing our consumption of ecological resources (our ecological footprint). Our achievement of the task on a per-person basis has accelerated, with the best-case time since the beginning of civilization shrinking through radical changes from more than 220,000 years to around one year, and the appearance that we may have already achieved the task around 2011 and are now going backwards.