Sigmoid Evolution

Practically all simple feedback processes, such as chain reactions in a critical mass of fissible material, bacteria breeding in a nutrient solution or the development of knowledge work along the lines of 'everything increases proportionally to how much stuff there is' (decaying atoms produce a proportional number of neutrons which split more atoms, bacteria divide and the more you know the more things you can discover). This leads to exponential growth:
However, in most situations there are limiting factors too (lack of fissible material, lack of nutrients, information overload), which makes the rate of increase become lower when the system has evolved. This in turns slows progress, and the evolution becomes a sigmoid curve:


It has been argued that technology may develop in a similar way: new ideas and principles open up the possibilities further, speeding up development. Individual technologies are invented, evolve rapidly, and reach fairly stable mature phases until they are superceeded by more modern technologies, and the sum of technology grows exponentially.

However, there are apparently limits to technology set by physical law. It is very probable that we cannot travel faster than light (at least locally, wormholes may circumvent this), and we have to obey the law of conservation of energy. Advanced civilizations may find ways around seemingly impossible obstracles, but there might still be limits (albeit large) to how advanced technology could become.

This would lead to a sigmoid growth of technology; at first the civilization spends many thousands of years laboring with stone age technology, then developes metals which speeds things up a bit, then develops industry and science which speeds up things even more, passes through a brief phase of intense development (the Singularity) and slowly settles down as it reaches the limits set by natural law (and maybe the capability to handle the immense complexity or the technology and knowledge). Note that this does not necessarily mean the civilization stops evolving, just that its technology cannot be developed further.

What factors will affect the shape of the sigmoid? One obvious factor is how much there is to learn, which tells how high it will be. It could be that we are very near a Theory of Everything or that we have not understood anything important yet. Another factor is how fast knowledge can increase; if new things are discovered fast enough, nobody, not even an expert in the area, can keep track of all information. This will slow down progress as people "reinvent the wheel" and spend more time trying to reach the cutting edge than actually working on the cutting edge. Another problem could be that new designs can be designed very quickly (using super-AI and virtual reality) but actually building them in the physical world takes a finite time, which leads to an widening gap between what is theoretically and practically possible.

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Anders Sandberg /