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Biology shows existing entropy gradient allows for indefinitely (for billions of years) sustainable systems. However our current technology and especially its scale degrades the entropy of its environment (depletes fossil energy and ore concentrates which need geological time spans to recover). We need a traversable path to a technology capable of sustainability and that path might well not exist. Edo era Japan technology might be borderline sustainable at a low population density but is a progress trap.
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The relevant constraint is the carrying capacity of the ecosystem beyond the short run, i.e. without fossil fuels, depleted resource base and the ecosystem services due the overshoot, at some level of technology sustainable under the circumstances. We’re over an order of magnitude beyond these limits, by most estimates.
This argument applies to current technology at its scale. It’s not a fundamental physical limitation. However we do not have time to leap to the next level.
Yeah. Entropy increases in a closed system, but we keep receiving low-entropy energy from the sun.
By this argument, sustainable energy is solar powered.
Yes, but current sustainable energy sources arguably can’t sustain even themselves and their support base. We can do better, but not soon and only by continuing the R&D process.