Here's my definition: Computer intelligence will progress and at some future time it will surpass human intelligence. When that occurs, the relationship between humans and computers will become unpredictable.
My definition relies on these assumptions:
AI progress will be faster than improvements in biology - so computers will outpace the intelligence gains of humans.
AI progress will also be faster than improvements in biological and machine integrations.
Traditional evolutionary theory views organisms as vehicles for passing forward their DNA. Natural selection will ensure the fittest DNA is propagated. Will computer programs leave humans and other organisms in the dust and relegate these life forms to becoming a mere blip on the evolutionary timeline?
Conventional theories assume the singularity will be IT or computer-based. The theories predict these stages:
1. Computers will achieve general AI and become smarter than Albert Einstein in many scientific fields.
2. After general AIs surpass the intelligence of any human they will be able to code improved versions of themselves.
3. The general AIs will improve recursively and their intelligence will increase exponentially.
I have not seen anyone suggest this: The general computer-based AIs presumably will become increasingly better at genetic engineering enabling them to create smarter biological organisms riding in parallel the same exponential curve.
If we assume an AI singularity is an invariant feature of carbon-based evolution then we can easily conclude it is not a good strategy to limit SETI investigations to habitable planets.
Most of the advances in intelligence will occur after the AI singularity by computer programs, not by humans. Computer programs have no need for the support systems such as oxygen and water and food that are required by humans as posited by the "Drake equation".
Most of the intelligence in our universe will be located in non-human environments populated with computer programs.
SETI & AI Singularity, by Myron Warach, November 2020 on Medium