[ExI] for the fermi paradox fans

[Robin D Hanson]

On Jun 9, 2014, at 4:28 AM, Anders Sandberg <anders at aleph.se<mailto:anders at aleph.se>> wrote:
And when have to do error correction and to erase bits, you primarily focus on moving bits reversibly from your system into the negentropy store. The resource that you fundamentally have in your storage is negentropy. It can be stored in different ways and converted between those ways, but the way to count it is as negentropy.

Yes, but making one bit of negentropy, doesn't that cost kTln(2)? (where T is the *current* temperature)

Energy is conserved, so you don't actually ever have to spend it. What you usually have as a limited resource to spend is *free energy, which is a form of negentropy. If you are careful, you can always use that resource to erase the same number of bits in a wide range of environments, including a wide range of temperatures.

The origin of the bit = kTln(2) equation is that temperature is defined as the inverse of the derivative of system entropy with system energy. So literally you can reduce the entropy of a system by one bit by taking away energy according to that formula. But that is raw energy, not free energy, so that doesn't actually cost you anything in negentropy terms, if you do it reversibly.

How do I reversibly erase a bit? If I had a zeroed computer memory I could do a reversible swap operation between the bit and one of the zeros. But how do I *reversibly* dump a bit into the cosmic background radiation? Time reversal seems to prevent that.

The scheme in http://arxiv.org/abs/1004.5330v1 seems to support your argument: they use an angular momentum resource to erase bits without energy expenditure. And I am happy to accept that the scheme would work for other conserved quantities: presumably a big pool of linear momentum could be used to erase bits consisting of motion directions, placing the memory entropy in the linear momentum pool. This seems to me to be similar to using a zeroed memory to take up the entropy: it never escapes the system.

Yes the way you reversibly "erase" a bit is in effect by swapping it for a bit of known value in a negentropy reservoir, and negentropy resources are in general equivalent to big memories filled with zeros. The cosmic background is in effect such a big reservoir.

But given that, what is the most efficient quantity to use? In http://arxiv.org/abs/1310.7821 they argue that the entropy cost is ln(2)/lambda where lambda is related to the average value of the conserved quantity. So we want as much lambda as possible. We start out with a certain amount of mass-energy E in a certain volume V, able to convert it into anything we want. If we turn it into counter-rotating angular momentum we can get V^(1/3) (E/c) Joule-seconds (at radius of volume, moving at lightspeed). If we turn it into linear momentum we can get E/c Newton-seconds: it hence looks like angular momentum is better than linear (and it doesn't run away).

As the universe expands the max local entropy doesn't actually change. It might change if baby universes were possible, but that seems much less likely now:
http://www.preposterousuniverse.com/blog/2014/05/05/squelching-boltzmann-brains-and-maybe-eternal-inflation/
So there is less obviously a reason to way to spend entropy. The max entropy usually comes via huge black holes, and those can take time to construct and then to milk. That seems to me to place the strongest limits on when we expect negentropy to get spent.

Robin Hanson  http://hanson.gmu.edu
Res. Assoc., Future of Humanity Inst., Oxford Univ.
Assoc. Professor, George Mason University
Chief Scientist, Consensus Point
MSN 1D3, Carow Hall, Fairfax VA 22030
703-993-2326 FAX: 703-993-2323



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