> Forgot to add in communication networks between the isolated I/O bound "supercomputers".
Nope. This model makes no assumptions about the actual computations being performed at each particle. The particles could be communicating or not, it doesn't matter. The total number of potentially physically computable states is still the same.
Forgot to add in communication networks between the isolated I/O bound "supercomputers". Given one set of massively parallel computers of ID number 0 to somethingbig then changing the wiring such that the peristaltic array is reversed would result in a dramatically different output.
Its kind of like a hashing function, feeding in different data (by changing the "wiring") results in different outputs.
That also leads to some interesting caching delay type problems if processor 42 halts till it gets data from processor 7 but due to cosmic inflation they're out of each other's light cones, forever. So Chaitin's constant would vary based on how fast the universe expands and what fraction lives outside of any given part's light cone.
Fun stuff to do with the constant, assuming it actually exists (as opposed to a mere concept) and can be calculated:
Given a NSA level of network spying as a resource, if you know 5% of raw (presumably non-executable) data should halt when executed and 100% or 0% of virus payloads halts (uh, yeah whatever) then periodic random sampling of supposed non-executable highly compressed video data halts at a 5% rate its probably legit and if it halts at a 100% rate then you can set off the alarm bell that something funky is happening right now online, a worm is trying to spread using buffer overflows in video codec data or something like that. Virus writers could defend against this, if they knew the constant, by making sure their virus payload halted exactly 5% of the time to mimic real raw compressed data. Cool as this hollywood movie plot sounds it would probably get simplified into CSI style "lets just enhance the pixels, ok?"
Also the SETI people could probably do something interesting with it, although I'm not clear exactly what. IF it were calculated to be exactly 7/22 (LOL) then an alien civilization repeatedly squirting 7/22 out to the world would imply that civilization has aged beyond the "must be this tall to enter" bar on the first contact ride, or they're just really big fans of the reciprocal of pi. The analogy is if you really want to impress a pre-computer civilization, give them the result of some ridiculous factoring problem that would take Andorian-centuries or whatever to calculate by hand but can be verified in minutes if you know what you're doing.