There is a simple solution to the Fermi Paradox.
As discovered by Ilya Prigogine, open complex non-linear systems far from equilibrium statistically tend to decrease their entropy. This phenomenon is also known under other names: emergent properties, self-organizing criticality, exotropy, to name a few. This is a generalization of evolution. This is what keeps the universe from the so-called “heat death.” This is the source of complexity in the universe, from the formation of galaxies to stars in galaxies, to planets around stars, to geological processes in rocky planets, to life on at least one planet but obviously not all, to consciousness in living beings (including all mammals, as some argue), to intelligence in conscious beings, to society among intelligent beings, to economy in the societies, to technosphere (what Kevin Kelly also calls “technium”), and so on (well, something will come up, I guess, but we don’t know what).
This matryoshka spiral of rising self-organization (also known as “progress”) is potentially infinite, if the universe has infinite entropy, because the open systems far from equilibrium would them be able to continue lowering their entropy by giving it to their surroundings (so that the total entropy still rises, by the second law of thermodynamics). But to progress further up the spiral, the systems have to increase the rate of entropy exchange (just think of how much faster we exchange input and output with our environment than our planet does as a whole, relative to scale). A smaller, more complex system within a bigger, less complex system can sustain that, but not vice versa. Thus, the more complex systems become smaller and fewer between.
I don’t doubt that we will eventually find life on other planets, since this spiral of self-organization is not unique to our part of the cosmos. Life is not a fluke! But these planets would be rare. Those with intelligent life would be rarer still. So, another planet with intelligent life (I’m sure it is out somewhere, as well) is likely to be very, very far from us, in space and/or in time.
Hence, the Fermi Paradox.
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