There are 2^64 atoms in a pinhead. Therefore, a volcano has about 2^128 atoms in it. Here is the calculation:
A Pinhead of 2^64 Atoms
1/16/2011 acf
n = atoms = 2^64 ~= 10^19 = 1 e19
1 mole = 6 e23
w= silver atomic weight 108 g/mole
d = density 10g/cc
t= number of moles = n/6e23 =1.6e-5
b = mass = tw = .0017 g
v= b/d = .0002 cc = 1mm x 1mm x .2mm
a pinhead has 2^64 atoms
Cryptographic blocks use 64 bits or 128 and 256 bit quantities, so this example demonstrates the magnitudes being used for information transformations that are hard or easy, depending on the protocol design.
next: 2^128 atoms
multiply xyz by 4 million since 4 million = 2^22 ~= cube root of 2^64
4km x 4km x .8km for 128 bit
6500ft x 6500ft x 8000ft for 2^64 pinheads, for 2^128 atoms: Haleakela Volcano size
In summary, to try all 64 bit keys is like looking at each of the atoms in a pinhead. Trying all 128 bit keys is like looking at each of the atoms in a volcano. There is no planet big enough to have 2^256 atoms. It would have a volume of more than a cubic light-year, I think.
