According to the Wikipedia article on the Analytical Engine, some other chap called Ludgate designed a streamlined version which could do a 20-digit decimal mul

According to the Wikipedia article on the Analytical Engine, some other chap called Ludgate designed a streamlined version which could do a 20-digit decimal multiply in about 6 seconds; its volume was about 230 litres. (He made detailed plans but never actually built it.) 20 decimal places is about 64 bits. One design for a 64x64->128 multiplier is described in http://www.patentstorm.us/patents/5912832/description.html http://www.patentstorm.us/patents/5912832/description.html and takes about 33k gates to achieve a propagation delay of about 200 gates. I'm not sure what propagation delays are like on modern CPUs; let's suppose it's 20ps per gate, so that a modern-silicon multiplier can do a 4ns multiply in 33k gates. How much space should we think of that as taking up? Not just the volume of the gates themselves; we need some volume for circuit boards, cooling, power supply, etc., etc., etc. A small modern PC might be a litre in volume and contains maybe the equivalent of 200M gates (CPU, memory, whatever else). So 33k gates corresponds to maybe 1/600 of a litre. So, in volume per unit power, modern technology beats Ludgate's version of the analytical engine by maybe a factor of (230 x 6) / (1/600 x 4x10^-9) or about 2x10^14. (Don't take this too seriously; there are a lot of very dubious assumptions in the above.) Now, let's say Google has 10^5 machines occupying 1 litre each. The equivalent in analytical engines would be 2x10^19 litres, or 2x10^16m^3. The radius of the earth is about 6.4 x 10^6 m, so its surface area is 4 pi r^2 ~= 5x10^14 m^2. About 1/3 of this is land, so let's say 2x10^14 m^2. So we'd need to cover the land area of the earth 100m deep in analytical engines. Dubious assumptions or not, I think I agree with your guess.