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Obviously I don't anticipate FTL. Do you?
Yes, but exploiting resources in our solar system is already difficult and costly. Currently there is nothing in space worth the cost of going there or bringing it back, maybe in the future it will be different, but I expect progress to be relatively slow.
Interstellar colonization might be forever physically impossible or economically unfeasible. Even if it is feasible I expect it to be very very slow. I think that's the best solution to Fermi's paradox.
Tom Murphy discussed these issue here and here. He focused on proven space technology (rockets) and didn't analyze more speculative stuff like mass drivers, but it seems to me that his whole analysis is reasonable.
I'm penalizing them because they seem to be far away from what current technology allows (consider the current status of the Blue Brain Project or the Human Brain Project).
It's unclear how many hidden hurdles are there, and how long Moore's law will continue to hold. Even if the emulation of a few human brains becomes possible, it's unclear that the technology would scale to allow a population of billions, or trillions as Hanson predicts. Keep in mind that biological brains are much more energy efficient than modern computers.
Conditionally on radical life extension technology being available, brain emulation is more probable, since it seems to be an obvious avenue to radical life extension. But it's not obvious that it would be cheap and scalable.
I think the most likely scenario, at least for a few centuries, is that human will still be essentially biological and will only inhabit the Earth (except possibly for a few Earth-dependent outposts in the solar system). Realistic population sizes will be between 2 and 10 billions.
Total processing power is more difficult to estimate: it depends on how long Moore's law (and related trends such as Koomey's law) will continue to hold. Since there seem to be physical limits that would be hit in 30-40 years of continued exponential growth, I would estimate that 20 years is a realistic time frame. Then there is the question of how much energy and other resources people will invest into computation.
I'd say that a growth of total computing power to between 10,000x and 10,000,000x of the current one in 20-30 years, followed by stagnation or perhaps a slow growth, seems reasonable. Novel hardware technologies might change that, but as usual probabilities on speculative future tech should be discounted.
From Wikipedia:
It's already happening.
Current process size is ~22nm, silicon lattice size is ~0.5nm . Something around 5..10 nm is the limit for photolithography, and we don't have any other methods of bulk manufacturing in sight. The problem with individual atoms is that you can't place them in bulk because of the stochastic nature of the interactions.