Glad you like my pictures.
Illustrative chart of the logistic, don't take at face value numerically. Shows how the linear chart typically squashes data in the lower orders of magnitude. You can barely see the price data in red. And you can see how unreliable an extrapolation that extends orders of magnitude beyond the data.
This curve-fitting exercise comparing the logistic and polynomial models does have some value if you don't take it too far, or too literally. At least, it directs one's attention at the long term.
I didn't curve-fit the stock to flow model, which paints an unrealistic picture in the long run. And I don't bother with models that put time on a log scale, which is nonsensical.
Of course, time is logarithmic, but it doesn't start on January 3, 2009.
It started 14 billion years ago, which means that for all practical purposes time is linear in our lives and for millions of years before and after.
http://www.turbulence-online.com/Publications/log_time_cosmology_final_printed.pdfEven though you are asserting a 14 billion year timeline, any kind of specific new invention that has paradigm shifting attributes is going to see a curve that is a lot more tightly packed, including the fact that some inventions might have births and deaths that are on very short time horizons, and for the sake of us mere mortal humans, we can live, and prosper, before we die by picking the right horses during our short time here.
We are going to lose some of the picture, even when we talk about time periods that are longer than 20 years, even if we might make some investment decisions for longer time periods, we can also change our investment allotments during shorter time horizons, even make substantial changes every few years, even if we might have some assets that kind of end up being killer all life performers that we might not have expected to be so in the beginning of our investment lives, whether we start investing when we are teenagers or in our twenties or thirties, but even with that if we did not have parents to really guide us with those kinds of choices, we might be stuck with some of our investment choices, too in terms of longer (lifelong) implications that we did not realize when we started down the road of investing our time and/or money in such direction.
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