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The term singularity has many definitions, one of which is

the state of being singular, distinct, peculiar, uncommon or unusual

Also it can mean

a point where a measured variable reaches unmeasurable or infinite value

I like that those are possible definitions but THE singularity, which is meant to be an event, is like this. The Famous genius John Non Neuman said:

technological progress will become incomprehensively rapid and complicated

And I think it was that idea of the future state of machine and ai converging with humanity that lead to an odd post human ecxistence was termed the Technological Singularity by Vernor Vinge in his essay "The coming technological Singularity"

In it he states

"Within thirty years, we will have the technological means to create superhuman intelligence. Shortly after, the human era will be ended"

So, basically my Singularity world idea is that human increased themselves with AI and robotic implantations and limbs until they machines/computer world surpassed human intelligence and need and thus died out the actual humans and all that is left are these odd hybrid beings in a world still run by machine but left to go to seed a bit. And the 'characters' in my works are struggling to understand their humanity which still crops up in the processing data of their machines minds. They are neither machine nor human being, so what are they?

Not sure if that makes sense, but you have made me realize I need a post to discuss this :)

It does make sense. Thank you for the explanation!