*weary sigh*
This is a lot like the homunculus thing, those paragraphs really don't mean what you think they do, "embodied" is not being used in some lofty metaphysical sense rather embodied cognition is the perspective that the mind is not something that can exist in of itself independent of an external reality, that doesn't sound good to your ears I bet. To make this easier to understand I'll use your parallel mirrors thing (in a use & discard way), like the classic Zen question whether the unheard falling of a tree in the forest suggests it didn't make a sound, if your parallel mirrors have no light to reflect between them how could a mind exist between them?
I still wonder how a mind could exist between them at all, but whatever, no point keeping a used condom, let's keep the focus on what embodied cognition is.
Traditionally AI researches sought to understand intelligence as a thing in of itself, as if they could simply write a sentient mind into existence with the right line of code, such inspiring hubris, this way of thinking gave rise to the procedural AI we all know well, the bad guys in every video game, behaviourally sophisticated yet fatally limited, clockwork made of ones and zeros.
Procedural AI doesn't think, it does, it does simply what its code tells it to do like a character in a book, and you can write in all sorts of instructions to have the reader flip back and forth between pages based upon external factors, and that gives it the illusion of intelligence but really that intelligence is only the will of the programmer, the writer who wrote the book, a book that will never change unless someone changes it.
Some procedural AIs have the ability to learn to some extent, philosophically this makes it very hard for me to classify them, the line between what is a person and what is not is actually a vast expanse of ambiguity, I spend much of my time here agonising over my principles, I digress.
Procedural AIs react to external factors and learn through sensors, without this input having a mind is moot, so obviously one simply can't make a thinking computer, it needs to learn to be about to grow and a reality to learn about (a simulated body still counts as embodiment) and if you want it to think in terms of self then it needs a body through which to interact with and perceive reality so that it may perceive itself through its own actions.
Having extensively studied the human neural net researchers have developed various simulations of it and there's an emerging field of people who utilise the principles of the human analog neural net to design digital equivalents, I call mine a node net
This new generation of AI is based upon the foundation of embodied cognition and as such isn't designed as something the coder tells what to do in their coder, rather the goal now is to try and distance ourselves as much as possible from the processes taking place, to have the AI learn for itself, to build vast conceptual structures of their own from the most basic parts, like we do,
You don't see it on the news but incredible progress is being made every single day, it's a very exciting time to be alive, personally I don't predict a singularity as such, but when all the factors line up the automation revolution will be upon us, things are going to happen, incredible things.