Fermi and SETI
Brilliant physicist and mathematician, Enrico Fermi, brought up more than one paradox in his published articles and many more in discussions and letters, but this question is probably referring to one for which an overview is given in
Our Galaxy Should Be Teeming With Civilizations, But Where Are They?, By Seth Shostak, Senior Astronomer, 2018, SETI Institute.
Astronomer Sara Seager's proposed equation (building on the work of Frank Drake) is one of the favored equations today. It estimates the number of planets with detectable signs of intelligent life as the product of six factors.
- Stars observed
- Proportion of observed stars that are quiet
- Average number of planets orbiting in habitable zones per star
- Reciprocal proportion of planets that can be observed
- Proportion of observable planets that have life
- Proportion of planets with life that produce a detectable spectrum of gases indicative of technological evolution
Since there is no indication that artificial life, if it were to dominate earth, would stop industrial processes, there is no need to adjust Seager's equation.
Multiplicity or Singularity
The Singularity is conjecture without any logical proof. Conversely, there is no need for a proof that artificial creations will out compete humans in some respects. The proof is that some tasks that could once be accomplished by humans alone, such as mail sorting and chess, are now accomplished faster and with greater accuracy by artificial creations.
The trend has been that the number of things done better with software, control systems, and robotics increases and the number of things done better by humans has been decreased by that amount. Because of the vision of robots permeating science fiction and the actual long-term objectives of some contemporary corporations in this field of artificial workers and beings, this is now easy for most to accept.
The Singularity is an imagined point in time when computer software and hardware will, in tandem, attain the ability to reproduce itself in a way that produces improved reproductions. Even if only some of the attempts at improvement prove to be superior in intelligence, strength, intuition, or some other feature, artificial evolution may have been created.
The idea that such will happen
- In exactly one way,
- At exactly one point in time, and
- Without any opposition or constraint
is part of the unproven conjecture. What has been offered as proof lacks mathematical rigor in a way that would have made Fermi frown, along with his contemporaries like John von Neumann and Oppenheimer. In fact, they would have wanted proof of completeness, that all human activity would be preempted by artificial equivalents, before any proof that it was to be singular in nature.
It May Have Already Occurred
Jaques Ellul, in his book Technological Society, proposes that what people today are trained to call The Singularity actually occurred hundreds of years ago, when the techniques applied by humans began to drive the behavior of society more strongly than the intentions of humans drove the direction of technology. His book is filled with a few hundred pages of examples where this tipping point has already been reached. It's remarkably convincing.
Back to Fermi and SETI
Whether the transition of control was in the past, in the future, or will never entirely complete, the impact on the Fermi paradox referenced is not significant, because the paradox is why no other intelligent life has radioed us in response to our SETI broadcasts.
Exponential Functions in the Real Universe
The most important question is whether the primary trait of intelligence is self-destruction, as some, like author of Sixth Extinction, Richard Leaky, believes. If this is the case, intelligent life is a pulse, not an ever increasing exponential curve. Ever increasing exponential curves don't actually ever occur in nature. In every other known phenomena that has an exponential growth period, it is ALWAYS followed by a decrease in acceleration ending in either a flat line or some form of chaotic vacillation.
Alternative Views of Origins
It is the work of Vladimir Vernadski that has the appearance of the higher wisdom than that of the media hound CEOs of Tesla, Google, and other large and powerful technology companies today. Buried in his book The Biosphere, he stated the possibility that evidence in star dust indicates that life may have always existed. Just as the big bang is a conjecture based on a long list of un-provable assumptions, so is the idea that life began.