Start with a 1d edge between two nodes. An abstract version of a cable between two network points. We know by Claude Shannon's results that Bitrate = Bandwidth*log10(1+S:N). Keep that one in mind.
But what if we started with a plane, instead of an edge? A wall, instead of a cable? Then we could split the plane indefinitely...oh but we can't do that! Planck distance starts becoming an issue. So ~1/1.6E-35 or 6.3E34 edges/m is the largest possible amount of cables per metre, and ~4E69 cables per square metre cross section area.
But just as information may be transmitted in waves through an approximately 1d medium, they can be sent through that cross sectional area; just each of the 4E69 cables carrying signal, that's all right? It'd be like a wave coming into a port; as long as you split the harbour into fine enough paratitions, you can transmit independently, and get data independently.
What if went a step further? And started transmitting information through volumes. Perhaps a point particle in the middle of a sphere transmitting information to or from the entire surface of that sphere. Or...backwards in time or something! Then we're talking 2.5E104/m3...but there's also planck time to consider, so the smallest resolution is pretty much defined at 2E43 Hz...and there can't really be any more than 1 bit per time in this context(a single bit is hard enough to imagine)...so we're up to 5E147 bits per cubic metre....but why would we stop there? Let's use the entire observable universe.. 8.8E26 being used this way; bingo, 4.4E174 bits per universe.
4.4E174 bits = 1 log ( 1 + S/N )
log24.4E174 = 1 + S:N
log2 4.4 + log2 10E174 -1 = S:N
2.1+578+1 ~= 581 = S:N
Or if we account for time as another spacelike dimension...the age of the universe...4.4E174*4E17 ...or 1.8E192 bits per universe
log2 1.8E192 = S:N + 1
~192log2 10 + log2(1.8) -1 = S:N
for not only the universe, but using the entire history of the universe as some kind of space-time anteanae. Assuming this were all possible, of course.
So if your S:N is over 638dB for anything, either I screwed up or you did. How could you get that certain of anything? Actually, even if I screwed up, I'm probably not off by more than a few dB!
But what about
- the curvature of the universe? Does this help direct information?
- the unobservable universe? Are we, and everything we can detect down to the big bang skin at the edge of the observable universe merely a bubble in something unimaginably larger?
- what about moral propositions?
- what about the concept of S:N? If it isn't absolutely meaningful this analysis falls suspect immediately
- certainty of your own existence? Maybe it's just information that must travel, must be communicated. This would solve math issues, too as reflexive statements and other axiomatic information might be self-provable, and hence would not be affected by S:N. Information about the material universe.
Other interesting things come from this too, you can measure how powerful a transmission medium is by how close it approximates this. my modem is what, -599dB from perfection? You can also measure how much information is stored within any given thing in terms of dB depending how large it is, too. I wonder if there's a way to put mass-energy into this somehow? Oh looks like there's a planck energy. But for how that'll fit in, I'll have to give some thought, and really, I should make sure what I have now is approximately correct first, anyway :)
Also, /., why don't you like my preformatted sections? Your treatment of <pre> makes baby dinojesus cry.