Omega - LeFreq/Singularity GitHub Wiki
Big Omega is the systems-equivalent to Big O notation for algorithmic analysis. "Systems", here, means a high-level meta view of a problem, be it economics, sociology, biology, or ecosystems. These are all "systems": groups of dynamic, inter-connected agents creating higher levels of emergent behaviors.
So, instead of BigO of a bubble sort where you'll check around n2 values, a BigOmega of a computer's theoretical power might be 2n where n is your number of words (the base is probably actually wordsize(in bits)/2). Since you can form groups of words, arbitrarily, this amounts to 2n value: the value that created the personal computing revolution. (It still takes human ingenuity and imagination to get up to that value...). From where does this power come from? The pow3r of transformation inputs along with creating input data, allows new information/knowledge to be made.
Adding networking to the computer adds yet another level of value. M computers, each with 2N = M*(2N), but if they're networked, the value of the network adds M2, but my analysis (see wiki.hackerspaces.org) when combined, this becomes big omega MN, if you add in voting (explicit and implicit) to the system. Implicit voting is when human naturally select what to create in the computer. Explicit voting is somewhat like money in an economic system: everything is streamlined and accelerated. Together, these create another dimension of value all t
The transitions from differing levels of value represent the addition of another layer of dimensionality. Functions for example to a simple turing machine, add a whole new dimension to the power of the machine -- either in expressivity or computational ability. Objects are another. When you have such a shift, there should be hardware support for them, like hardware call stacks.