Hard Science Fiction? Singularity Science Fiction?

So does that mean Terminator(Skynet) and the Matrix are Singularity SF?

I think not, but that's just my opinion. Terminator is about a computer network (Skynet) becoming sapient and going off the rails; the Matrix is about a very large system. Neither addresses the issue (whether it's ever going to be real or not) about exponentially increasing computer power.

Another linked theme is transhumanism, roughly defined as humans (or in later versions, AI) becoming so intellectually powerful that they transition into a different order of being that humans are never going to understand now matter how long they try. A little like the difference between sentience and sapience, often illustrated by something like this:

Imagine having a conversation with various entities, leaving aside the issue of physical ability to speak. Make it about an abstruse subject, if you like; existentialism or quantum chemistry, perhaps. Maybe it would be possible to manage this with a dolphin, but almost certainly not with a dog. The concepts are simply beyond its ability to grasp. Ever.

Now imagine a being who thinks about things of such a high order of abstraction that no human could comprehend them. Maybe for lack of time to process them, maybe simply because humans don't have enough easily available memory storage to hold them. That's a transhuman, or sometimes a transapient.
 
I think not, but that's just my opinion. Neither addresses the issue (whether it's ever going to be real or not) about exponentially increasing computer power.

Another linked theme is transhumanism, roughly defined as humans (or in later versions, AI) becoming so intellectually powerful that they transition into a different order of being that humans are never going to understand now matter how long they try.

imagine a being who thinks about things of such a high order of abstraction that no human could comprehend them. Maybe for lack of time to process them, maybe simply because humans don't have enough easily available memory storage to hold them. That's a transhuman, or sometimes a transapient.

Hmm...
But while the issue is not directly addressed it can be inferred. Both systems had to start small and then grow into the massive AI's they are.

As to "transapient". that sounds like the sphere in Independance Day Resurgence or the aliens in Arrival or the Q in Next Generation.
 

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