me:

In the simplest model you have observer histories which are an infinite time series of ever more complex — yet finite — mental snapshots. So there is no one highest finite complexity level where you should expect to find yourself. Instead you should always expect to find yourself growing yet more complex... and it certainly seems like we will be able to continue the 100,000 year old exponential memetic growth for quite a while yet.

Let me come at it from a different angle — and yeah, time is a special overarching relationship. I think time is necessary in the formation of well-defined ASORs. OK, what am I talking about? — consider just the example of the information in pi. The are many different representations of the information in pi: you can have just the circumference of a circle divided by the diameter, there's the infinite decimal expansion: 3.141592654..., there are series expansions: 4(1-1/3+1/5-1/7+1/9-...). So there are finitely complex implicit representations and infinitely complex explicit representations. It would be much nicer to just count among the finite implicit representations — each one's ASOR can then be encoded into a simple finite integer (sort of like Godel's numbers). Working in complete, compact, implicit representations also gets rid of the 'noise' ASORs, i.e. the randomly connected graphs, which have very little representation invariant information (otherwise they would dominate the counting in the ensemble).

So we are coming around to the special status of time... We want to build ASORs which, unlike pi, or the Mandelbrot set or so on, are irreducibly infinitely complex, even in the most compact implicit representation. They will then dominate the counting. You might at first just try constructing the literal power set on top of the ensemble, but as the elements of the power set just randomly connect different ASORs, there is actually very little information in this. Observers evolving in time, however, selectively pick information from the ensemble (usually from their local environments, but not always), thus evolving novel, irreducible structures through iterative trial and error — i.e. evolution via selection. Then take the limit to infinity...

So a global time-like relationship allows for the gradual, continuous, and well-defined creation of infinitely complex ASORs. These infinite ASORs are a collection of instantaneous, finite brain states that always find themselves growing more complex. There can't be any discontinuous jumping up to 'very high' complexity states, and there isn't any final highest level where you could expect to find yourself.