This is a pretty friendly way to imagine our consciousnesses, in my opinion. Basically, everything conscious can have its state of mind represented as a single point in a paranoidly huge metric space of all possible states of mind.
“Metric space” just means that we can measure a sort of distance between two states of mind. What, R^(10^100)?
Now, I am, at any given moment, just a physical embodiment of one of these points. However, every passing moment changes my state. If time is discrete, then the body is jumping from point to point, and usually in very small jumps as compared to the rest of space. We can imagine a “box” in the space of all states that are fairly close to being me or that I could become. The box itself is small in relation to the space, but absolutely huge compared to my body’s state-of-mind’s discrete jumps. Points! How objective!
The points exist forever. Or, they fail to exist forever, being just abstractions. Either way, the only special thing about the point that I am at some moment is that it happens to have a physical embodiment. And every chronon, that special point changes, virtually certainly never to be physically embodied again. The majority of points, though, never will be physically embodied; at least not in this universe. When I die, basically the rest of the points don’t get embodied. This is quite sad.
Go through these frivolous motions and you discover that every state-of-mind is fleeting. Time is precious. In effect, though, every chronon you die and an extremely close copy of you comes to life, so what’s the biological death in comparison to that?
If computers were to become sentient, they would also embody a state-of-mind, I guess. Just one that would be very, very far away from the narrow strip of remotely human states-of-mind. Unless it were an upload. Blah.