4 ms·

It makes you wonder if there would even be enough space on the surface of the earth to replace Google's or Facebook's modern day servers with the equivalent com

It makes you wonder if there would even be enough space on the surface of the earth to replace Google's or Facebook's modern day servers with the equivalent computing power of these analytics engines - my guess is no.

gjm11 16y ago
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.
- olalonde 16y ago
  Just made my guess before reading yours. Some of my assumptions are more generous than yours, but the conclusion is the same: not enough land area on earth.
olalonde 16y ago
Not even close. Google's estimated amount of servers [1]: 450 000. Let's say they each have at least a 2GHz CPU = 2 000 000 000 computations/s. That's 9 * 10^14 computations/s. Let's be overly generous and assume machine can do 1 computations/s (although it is normally much less for multiplications) as estimated by Babbage himself [2]. Let's again be generous and assume an analytical engine's surface on earth is no more than 1m^2. To attain 9 * 10^14 computations/s, one would need at least 9 * 10^14 engines. Those machines would occupy an area of 9 * 10^14 m^2. According to Wolfram Alpha [4], this is ~1.8 × land area earth. Also, consider the amount of energy this would consume! [1] http://www.datacenterknowledge.com/archives/2009/05/14/whos-got-the-most-web-servers/ http://www.datacenterknowledge.com/archives/2009/05/14/whos-... [2] http://www.fourmilab.ch/babbage/authentic.html http://www.fourmilab.ch/babbage/authentic.html, http://www.fourmilab.ch/babbage/lpae.html#SpeedOfComputation http://www.fourmilab.ch/babbage/lpae.html#SpeedOfComputation [3] http://hypertextbook.com/facts/2001/DanielChen.shtml http://hypertextbook.com/facts/2001/DanielChen.shtml [4] http://www.wolframalpha.com/input/?i=9+*+10^14+m^2 http://www.wolframalpha.com/input/?i=9+*+10^14+m^2

gjm11 16y ago

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.

olalonde 16y ago
Just made my guess before reading yours. Some of my assumptions are more generous than yours, but the conclusion is the same: not enough land area on earth.

olalonde 16y ago

Not even close. Google's estimated amount of servers [1]: 450 000. Let's say they each have at least a 2GHz CPU = 2 000 000 000 computations/s. That's 9 * 10^14 computations/s. Let's be overly generous and assume machine can do 1 computations/s (although it is normally much less for multiplications) as estimated by Babbage himself [2]. Let's again be generous and assume an analytical engine's surface on earth is no more than 1m^2. To attain 9 * 10^14 computations/s, one would need at least 9 * 10^14 engines. Those machines would occupy an area of 9 * 10^14 m^2. According to Wolfram Alpha [4], this is ~1.8 × land area earth. Also, consider the amount of energy this would consume! [1] http://www.datacenterknowledge.com/archives/2009/05/14/whos-got-the-most-web-servers/ http://www.datacenterknowledge.com/archives/2009/05/14/whos-... [2] http://www.fourmilab.ch/babbage/authentic.html http://www.fourmilab.ch/babbage/authentic.html, http://www.fourmilab.ch/babbage/lpae.html#SpeedOfComputation http://www.fourmilab.ch/babbage/lpae.html#SpeedOfComputation [3] http://hypertextbook.com/facts/2001/DanielChen.shtml http://hypertextbook.com/facts/2001/DanielChen.shtml [4] http://www.wolframalpha.com/input/?i=9+*+10^14+m^2 http://www.wolframalpha.com/input/?i=9+*+10^14+m^2