Boiling the Oceans
There have been some rumors flying that Apple’s implementation of Time Machine is going to go hand-in-hand with an implementation of Sun’s ZFS in OSX 10.5 Leopard. I was just reading about ZFS on Wikipedia and came across a very interesting quote on the physical limits of computation. In reply to a question about filling up a theoretical ZFS filesystem without boiling the oceans, ZFS Project Leader Bonwick said:
Although we’d all like Moore’s Law to continue forever, quantum mechanics imposes some fundamental limits on the computation rate and information capacity of any physical device. In particular, it has been shown that 1 kilogram of matter confined to 1 liter of space can perform at most 1051 operations per second on at most 1031 bits of information [see Seth Lloyd, “Ultimate physical limits to computation.” Nature 406, 1047-1054 (2000)]. A fully populated 128-bit storage pool would contain 2128 blocks = 2137 bytes = 2140 bits; therefore the minimum mass required to hold the bits would be (2140 bits) / (1031 bits/kg) = 136 billion kg.
To operate at the 1031 bits/kg limit, however, the entire mass of the computer must be in the form of pure energy. By E=mc2, the rest energy of 136 billion kg is 1.2×1028 J. The mass of the oceans is about 1.4×1021 kg. It takes about 4,000 J to raise the temperature of 1 kg of water by 1 degree Celsius, and thus about 400,000 J to heat 1 kg of water from freezing to boiling. The latent heat of vaporization adds another 2 million J/kg. Thus the energy required to boil the oceans is about 2.4×106 J/kg * 1.4×1021 kg = 3.4×1027 J. Thus, fully populating a 128-bit storage pool would, literally, require more energy than boiling the oceans.”
