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Your comment is unrelated to what I was discussing in the quoted section. I was saying you can't have growth for which f(n + k) = 2 f(n) for all k > 0 (I belie
by dllthomas 11y ago
Your comment is unrelated to what I was discussing in the quoted section.
I was saying you can't have growth for which f(n + k) = 2 f(n) for all k > 0 (I believe the only solution to that is f(n) = 0, which isn't what anyone is talking about when they talk about "exponential growth"...). This point was intended, in contrast with what I'd just said about there existing some k - to stress the notion of when the interval is picked.
- AnimalMuppet 11y agoI know. I was agreeing with you. In fact, I was giving a proof that your position was correct. Apparently, I wasn't doing it well, but that's what I was trying to do.
- dllthomas 11y agoI didn't think you were disagreeing with me - I think you were agreeing with something I didn't say. I was just speaking to definitions. Whether unbounded exponential "economic growth" is possible in a finite universe is actually a significantly more involved question. It's obviously not possible if "economic value" is bounded, but in principle could be "possible" with finite stuff in continuous space (obviously, economic value depends significantly on configurations of stuff and not just amounts). All of this is interesting, but I honestly don't expect any reasoning involving hard theoretic bounds to be of any use in determining what's likely over my lifetime, or those of my children.