Assuming (a big assumption) continuous and uninterrupted exponential technological progress on Earth, it would seem to set up some interesting implications for interstellar colonies and each's respective technological progression. The farther away the colony in light-years, the farther away from the human technological "center of mass" the colony would lie. It would take many generations for such a colony to "catch up" if ever since the population of a colony would necessarily not be very large at first. In theory, the number of technical people would certainly be disproportionate to the ratio of workers on Earth, but still the technological progress would be slower at first which could make all the difference. As an example, if humans would establish a colony X around 30 light-years away, the colony would have to 'wait' for the signal from Earth of all the technological developments from Earth. Let's just assume there would be a powerful laser signal that would be sending news and information from Earth to colony X and vice versa at the light-speed. Thus Earth would always be 30 years ahead on the technological growth curve, of course assuming no interruptions like an end-of-days asteroid strike. And such a growth is exponential, thus in real terms, the differences would be more stark over time. Think of the differences of tech development in the year 1940, 1970, and 2000. The amount of progress between 1970 and 2000 was much more than between 1940 and 1970.
In the next post, I will further explore the implications of this progress differential across interstellar distances.
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