Imagine a world where it is possible to download a blueprint from the internet of whatever you wanted and have a Replicator print the object out for you, in a way where it is undistinguishable from the real thing.
This, I think we all agree, would be pretty cool. The Next Big Thing.
So, how would you do it? Well, first we need to assess how much data would be needed to form the blueprint. In order for the print to be perfect, it needs to be done with atomic-level precision. Worst-case scenario, we would have to specify the correctly ionized isotope of every single atom in the doohickey we’re duplicating. Since anything interesting will contain in the order of at least 10.000.000.000.000.000.000.000 atoms, (1E23) these are our storage demands:
For simplicity, imagine that our thingumajig is a perfect cube consisting of 1E24 atoms, i.e. 1E8 atoms on each side. Each atom would be indexed with three coordinates, each ranging from 0 to 1E8. 1E8 is roughly the same as 2^27, so any coordinate will sit comfortably within 32 bits of information, or 4 bytes. The coordinates thus require 3*4 = 12 bytes plus another 4 bytes to store information about the atom number, isotope and ionization status. So, 16 bytes per atom and 1E24 atoms gives us 1.6E25 bytes or 1.600.000.000.000 terabytes of information.
Of course, this is uncompressed, and any reasonably efficient compression algorithm looking for crystalline structures etc. would probably be able to compact the information a LOT, but even by compressing to a billionth of the uncompressed size still leaves us with 1600 TB of data, just for a doohickey containing the equivalent of about 20 grams of carbon.
At a 4 Mbit cable internet connection, this would take 3200000000 seconds or a bit more than 100 years to download.
Next thing we need is a way to rebuild from the data. If our printer is charged up with appropriate quantities of all elements, it’s just a question of nano-robots building the desired thing, following the blueprint. But this gives manufacturers a fail-safe piracy guard: build your hardware containing an abundant, but market-restricted element which costs a fortune for private people to buy, but not for the company.
To circumvent this pesky situation (and to make a replicator that doesn’t need filling up with hydrogen and silicium every other day) we need to make a cooler device: one which creates the nessecary atoms from energy. You thought 1.600 TB of data was bad? You ain’t seen nothing yet!
To return to our hypothetical object with 1E24 atoms, let’s assume an average atomic weight of 10 units. This is probably being generous (that makes the object weigh less than 2 grams), but let’s assume. A combined mass of 0.00166053886 u corresponds to an energy requirement (using Einstein’s famous E=mc^2) of 1.49E14 joules.
A barrel of oil contains 6.12E9 joules, so we’re gonna need roughly 25.000 barrels of oil to create two grams of matter. At today’s prices, we’re talking about 2 million dollars worth of oil.
100 years of download time and 2 million dollars to create a small cube? It ain’t worth it.
Then again, the internet itself was exactly as implausible 100 years ago… so who knows?
