Assuming no faster-than-light travel and no exotic matter, a civilization which survives the Great Filter will always be contained in its future light cone, which is a sphere expanding outward with constant speed c. So the total volume available to the civilization at time t will be V(t) ~ t^3. As it gets larger, the total resources available to it will scale in the same way, R(t) ~ V(t) ~ t^3.
Suppose the civilization has intrinsic growth rate r, so that the civilization's population grows as P(t) ~ r^t.
Since resources grow polynomially and population grows exponentially in t, as t goes to infinity the resources per person R(t) / P(t) ~ t^3 / r^t goes to zero. And since there is presumably a lower limit on the resources required to support one member of the civilization, r must approach 1 as t goes to infinity. This could mean, for instance, that each person has only one child before dying, or that everybody is immortal and never has children.
Of course these conclusions are pretty well-known round here, but I thought the scaling argument was neat and I haven't seen it before.
This seems likely to be a problem even if we get FAI, since certainly some people's CEVs include having children, and even with a starting population of a single person with such values, we'll run up against resource limits, if the premises hold. (I suppose those future people lucky enough to live under FAI will just have to dry their tears with million-utilon bills.)
Another thought: Perhaps we could use relativity to get around this. If we expand outward at the speed of light, subjective time for people close to the edge will be greatly reduced, so each person could grow up, travel to the frontier at near lightspeed, and have their 2 children or whatever. To the rest of us I think this'll look like increasingly many people crammed at the edge of the sphere, through length contraction. (I haven't studied relativity, so this might be wrong.)
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I just got a Kindle Paperwhite. I'm still in the process of learning how to interact with the device. In case you have a Kindle, can you give me a few pointers?
1) How do you organize the relationship between the Kindle and Evernote?
2) How easily is a Kindle damaged by falling to the ground? Is it important to use a case to prevent damage?
3) Do you have tips for good PDF conversion. Especially for textbooks?
4) Anything useful to know as a new Kindle user?
I have accidentally dropped Kindle in a case a couple of times; there was no perceptible damage.
K2pdfopt is God's gift to Kindle readers. Compare a processed version of the latest paper I read with its original version.