The Drake equation demonstrates that due to the vast scope of our universe, it is highly unlikely that there is not intelligent life other than us. The Fermi paradox ponders why (considering the results from the Drake equation) we have not yet detected any other intelligent life. Singularity theory anticipates a point in time where rapid growth in intelligence and replication create a border that is like an asymptote or singularity threshold beyond which lies an undefinable area that is not comparable to what we currently know as intelligence. The Schwarzchild radius describes the limit of the ability of light to escape a black hole singularity, or the “edge” of the black hole where it becomes totally black.
The answer to the Fermi paradox may lie in the idea of a singularity-like expansion in intelligence that rapidly moves beyond our ability to understand it or detect it. Just as light eventually becomes trapped by distorted space inside the Schwarzchild radius of a black hole under gravitational collapse, it is possible that intelligence that is evolving hyperbolically may move across “terrain” that is unknown or become something we are unable to recognize. An ant might be able to detect a microscope that is being used by a higher intelligence to study it, but would not have the capacity to understand much significance of the event. An amoeba would not even be able to “detect” the microscope. As the “distance” between intelligence levels grows, the ability to communicate is limited to a lowest common denominator level.
Try on this postulate: the Drake equation shows there is likely to be a very high possibility of other intelligent life in our universe, even though it is also likely to be separated by huge gulfs in space and also (more significantly) in time. This makes it highly unlikely that two intelligent civilizations would evolve at the same rate in near proximity to each other and have a reasonable chance to communicate with each other on similar levels. Our civilization seems to be very close to a massive transition in intelligence that we call, “the singularity” and this has taken place in a relatively small time frame, only tens of thousands of years at the most, since the beginning of what we consider to be the history of our civilization. If other intelligent civilizations also experience growth curves that anywhere near this (even allowing for large variations in rate), and experience a singularity-like transition event, the likelihood of two civilizations establishing communications during this time becomes very small. This leaves us with a universe populated by many intelligent civilizations, but always finding themselves alone, only able to communicate with amoebas below them on the developmental scale and something undefinable above them. Edited from Singularity Theory May Explain Fermi Paradox.