Get your Portable ID!

Monday, January 12, 2009

File System Stupidity

In the interest of creating a filesystem which is more versatile than the default ones packed in with OS X Server, I spent some time looking at ZFS and was amused at the absurdity of the whole thing.

Some observations:

[stolen from]

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 litre of space can perform at most 1051 operations per second on at most 1031 bits of information.

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 1.2x1028 J.

The mass of the oceans is about 1.4x1021 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 2.4x106 J/kg * 1.4x1021 kg = 3.4x1027 J. Thus, fully populating a 128-bit storage pool would, literally, require more energy than boiling the oceans.

So they've created the first storage system which is impossible to house, let alone fill. Great. An interesting corollary to this is that therefore something with half that capacity would be impossible to back up.

Moreover, the controlling hardware for something that large would require at least an order of magnitude more circuitry to do lookups, so let's assume filling anything with a hundredth of that capacity is possible, anything with a hundred thousandth of that capacity might be considered usable, anything with a millionth of that capacity might actually be affordable and backing up half of that is conceivable.

So 87 trillion yottabytes might be considered a sane upper limit for the foreseeable future? I can live with that.