One of the cornerstones of my understanding of global population and consumption is the mathematical relationship between happiness and ecological footprint (our individual consumption of ecological resources). While trying to derive real significance from the convenient abstraction, I gained insights into how much of the natural world we can safely use, the purpose and mechanics of the global economy, and how people's values influence the survival of our species. Yet still I didn't fully appreciate why it had the form it did.
In the mean time, I grappled with the dynamics of human behavior and how to derive a means of successfully communicating the lessons I was learning so they could be used to hopefully extend the lifetime of our species, which my research showed is uncomfortably limited. One approach was to focus on complexity and how it influences both comprehension and the completion of basic tasks. I studied the implications of a general relationship I had discovered in my own experience between efficiency and the timing of progress in various activities, including the propagation of error in product development and messages as represented by my writing and that of others.
I suspected that task completion might be related to the pace and nature of global consumption and population growth. While I couldn't find a close correlation, I did discover that our species is attempting to use all of the Earth's resources that don't threaten the planet's ability to meet our basic needs, and we have historically been doing so in at least four different ways at a speed that varies with how much we consume.
A few weeks ago I had the latest of a string of epiphanies that has marked my research since the beginning. I accepted the possibility that the timing of consumption might be independent of the timing of task completion, and sought to generalize how they might fit together to describe how much resources are consumed during a task. In the process, I derived a relationship of the form found between happiness and ecological footprint. I was then able to apply the generalization, which I came to call the "happiness approximation" to how happiness has changed over human history and how it could conceivably change over a person's lifetime.
As I studied the consequences of the happiness approximation, I homed in on the special cases of completion and consumption that involve full use of resources in the completion of a task, which would be optimum where resources are limited. A simple statistical simulation showed that optimum completion averaged out to 76%, and that general completion had an average of 87%. Averaging those two values produced the 82% that the happiness relationship had identified as maximum average happiness for a population (and also happens to be close to the 80% used as a rule of thumb for realistic completion by project managers.
The timing of task completion also rang a bell of familiarity. The minimum amount of time it takes to complete a task (in the simulation) is 19, which is close to the 20 years that is the lowest life expectancy in my historical data (at the earliest year: 10,000 BC). If this correlation is correct, then it is the earliest point in a person's life that they can achieve 100% happiness, which according to the simulation only happens in 14% of cases.
I also modeled a better match to traditional expectations of task completion time, including something close to achievement of historical values of happiness and life expectancy in 2015. It never achieved total or optimum completion, and still took three units of time to reach maximum consumption, which is what I typically use for planning purposes (where one unit of time represents best possible achievement). Only 2% of a general population achieves that or better, which speaks to how selective an organization must be to realistically promise such performance; much less than 1% could be expected to achieve the perfect performance that an organization might optimistically promise in one unit of time.