[extropy-chat] Singularity heat waste

[Anders Sandberg]

The outermost limits are of course the Brillouin inequality saying that
the entropy dissipation cost kTln(2) per erased bit. While we can use
reversible computing, thermal nois is going to cause errors and error
correction is irreversible operation.

If bits are stored energy wells of depth E, the probability that thermal
noise  makes it jump is on the order of exp(-E/kT) per second. So if the
civilization has I bits of information at temperature T, it has to
dissipate

P = k ln(2) T I exp(-E/kT) Watts

Also note that if information grows, empty memory has to be erased by
storing new data. So we have to add a growth term

P = k ln(2) T (I exp(-E/kT) + I')

Assuming molecular bonds, E=1e-19 J, T=3K and a solar input of 1e22 W plus
k=1.38e-23 we get a limit of:

3.48477063e44 = exp(-2415.45894)*I + I'

The first term on the right is extremely small (around 1e-1000I), so
apparently the information growth is indeed the limiting factor here.
(in my old darling http://www.jetpress.org/volume5/Brains2.pdf I look at
energy dissipation limits)

An information gain of 3e44 bits/s is pretty nice. It corresponds to
filling a 1 m^3 volume with a few kilograms of matter up to the Bekenstein
limit of information every second. Assuming molecular storage and using
the solar system mass it will fill its capacity of 1e52 bits in 1e 33e6
seconds - it will fill up in little over one year. So there you have it,
given these assumptions.

-- 
Anders Sandberg,
Oxford Uehiro Centre for Practical Ethics
Philosophy Faculty of Oxford University