We probably ought to enumerate these types of idea morphs from the past 1/2 century; I've been involved with the development of computational techniques using mathematics and modeling for a long time and will start getting together a list if I don't find that it has already been done; development meaning, of course, the evolution of our artificially oriented prowess.
Now, concepts found in abstract mathematics can relate to the 'avatar' theme. Mainly, the lift and the projection. We'll go on about that, to boot. Sufficient for now is this: many times what seems like a lift is actually a projection. And the confusion arises from a 'virtual' vertigo, so to speak.
Take the avatar, for instance. It can be embedded in a space that 'lifts' (no, not a change of usage, let me explain - at some point). However, what we see is that its usage is involved with a projection (implying into a lower-order affair - again, will explain) many times. Let this slogan suffice, for now: lifts can trample while projections squish 'being' (unfortunately, we'll have to pause to consider some t-issues - but, as said before, PTIME may apply).
And, folks, that type of thing (see Remarks 05/28/2011, below, on vertigo) is behind a whole bunch of 'oops' that we see in life. Mind you, this discussion, in no way, is meant to imply that 'gaming' is never the 'lift' that it appears to be. Rather, we want 'computational being-ness' to be more uplifting than it has been to date.
Aside: the avatar concept may have more applicability than not; in fact, it allows another way to look at several problems that might be effective; too, why limit 'avatar' to being a glorified icon (even if it exhibits behavior -- hint: think duck test against an embodiment)?
09/16/2012 -- Avatar (movie's tale) as parable.
05/01/2012 -- We'll need to talk singularity in the context of Alan. The computer has as many holes as do we; however, we can cut out of the fog.
06/22/2011 -- IEEE has a nice overview of social media and related issues.
05/28/2011 -- In what situations will an 'avatar' be confused (as in befuddled)? What? Yes, in the traditional sense, one would think never (except for those whose role might include the possibility). Because we have the quasi-empirical issues to resolve since we like to push the envelope, there is a 'vertigo' state that is possible computationally (or cyber-ally). The recent re-look at the Air France event (of 2009) that was made possible with the recovery of the flight data recorder can allow us an analog. One commenter talked about how the bucking of the plane, and it being night, did not allow any basis to determine appropriate action. That state has many more possible occurrences than we have admitted (for many reasons) to be likely in computational frameworks. We'll continue to try to explain why. The article on the Lemons problem touched on one possible avenue of expression of this phenomenon - implying, yes, that the cyber-based (without confusing map-territory) is what we know as the reality (think sensors and their increasingly electronic basis) many, many times. Aside: what the heck is money except for bits within the FED's (and its cohorts worldwide) cyber-realm, though all sorts of first-world expectations fill in its 'avatar' (if I'm allowed that stretch)?