The proof is usually attributed to a 1973 paper by Bennett, but I particularly like the explanation of Fredkin and Toffoli and their billiard ball model of computing: http://fab.cba.mit.edu/classes/862.16/notes/computation/Fredkin-2002.pdf …
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Replying to @michael_nielsen @CTZN5 and
David Manheim Retweeted David Manheim
Yes, my bad.
@anderssandberg and@robinhanson have pointed this out to me, and I should have remembered. I definitely don't understand the physics yet, but thanks for pointing to the paper - it looks like it might be a clearer explanation than I've yet seen. But the point stands:https://twitter.com/davidmanheim/status/1083645585784299520 …David Manheim added,
David Manheim @davidmanheimReplying to @CTZN5 @stalcottsmith @cal_abelYou're gonna lecture me about Goodhart's law? 1) No, in this case the metric functions as a close causal approximation of the goal in the region we're discussing. Divergence in tails is always a problem, (see: regressional goodhart - https://arxiv.org/abs/1803.04585 ) but we aren't there.1 reply 0 retweets 3 likes -
Replying to @davidmanheim @CTZN5 and
Section 3.6 has a model which is just billiard balls rolling round a table, doing universal computing. No energy consumption at all. It's a very nice model, albeit not physically practical.
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Replying to @michael_nielsen @davidmanheim and
In general, there will be noise in models like this, and some energy dissipation is required to remove it through error-correction. But there's no in principle lower bound to that noise.
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Replying to @michael_nielsen @davidmanheim and
Horizon radiation actually gives a lower bound to temperature. Still, Robin pointed out one can cool further with absurd insulation; am still working out the total thermodynamic cost and optimizing. Would love to see time bounds too - reversible is *slow*.
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Replying to @anderssandberg @davidmanheim and
What horizon are you referring to? If you simply mean there's ambient noise due to the rest of the universe, the standard approach is to isolate the system. I'm not sure what the fundamental physical limits will be to that, but (a) they'll be incredibly low; and (b) they seem
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Replying to @michael_nielsen @davidmanheim and
I am thinking of the de Sitter radiation, ~10^-30 K - due to cosmological constant, so in a sense fundamental. Seems unavoidable, but can be isolated at the price of literal parsecs of foil insulators. (thickness due to need to avoid near field couplings)
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Replying to @anderssandberg @davidmanheim and
Even without the isolation, kT ~ 10^{-53} Joules is the scale of the energy fluctuations. The noise effects will be pretty small. I guess it's relevant and will require isolation on sufficient computational scale, but far beyond what happens on Earth today.
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Replying to @michael_nielsen @anderssandberg and
At a rough guess, all digital computations done by humanity to date are probably on the order of 10^35 operations, maybe 10^40. So you could (in principle) error-correct away all noise due to de Sitter radiation as a cost of < a picojoule.
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Replying to @michael_nielsen @anderssandberg and
I think that is incorrect as a physics calculation.
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Replying to @robinhanson @anderssandberg and
It's not intended as a calculation, just a ballpark estimate. A detailed calculation will depend on quite a few things, especially the depth of the computation and the details of any error-correction (i.e., cooling) strategy.
10:12 AM - 11 Jan 2019
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