The Matrix Machines are Idiots
I've been thinking about a problem with how the robots power themselves in the movie "The Matrix." Let me explain.
For a second, let's assume that Morpheus is right and that if the machines got enough humans they *could* use them as a source of power. This is already controversial, but assume that there's no energy loss from the little pods they're grown in to the turbines or whatever that provide enough electricity for the machines. Even so, we know that the power they provide is power they get from the humans being kept alive in a vegetative state in those pods.
We know this because the way they get Neo out is by making the machine think that he's dead and spitting him out (he's no longer any good as a battery!) Obviously, to keep a human being alive--even in such a state--you need to feed them something. Morpheus confirms this: the live humans are intravenously fed the liquefied dead. (Ignore, for a moment why the machine spits Neo out when it thinks he's dead rather than just liquefying him right there)
Let's also assume that the humans that are being liquefied are not humans that die of old age. A quick google search establishes that the average human male body is around 125,000 calories. We also know that the average person in a coma needs about 2000 calories a day to keep living. What that means is that one liquid human body gives another person about 62 days of nutrition (and, of course, 62 human bodies about 1 day).
The average life of a singe human is about 72 years or about 26,000 days. If raised from birth (ignoring differences in caloric needs through different stages of life), a human being would need roughly 52 million calories. That would amount to about 412 dead human beings needed to keep one person alive for 72 years. Though, to stick with our average assumptions, let's say that the machines only keep people alive until middle age.
So, let's can say that we have a ratio of 206 dead needed to keep one alive. Currently, there are 7.7 billion people on the planet. Supposing they liquefy all of us, they would be able to maintain ~34 million people through middle age. If those people don't reproduce they can sustain ~165,000 people, then ~800, then a little less than 4. In short, the reign of the machines can only last about 175 years.
Now, I know what you're thinking: duh, of course they would reproduce us! Fine. Suppose that there is reproduction involved. This means that at in the limiting case we have a starting population of something like 1.16 billion women between 15-35. Assuming each one gives birth every 9 months (it's a nightmare scenario in the post-apocalypse hell-world!) we have roughly 26 births per person (i.e. 20 years by 12 months divided by 9).
This gives us 28 billion more people from our initial cycle; factor in a .078 child death rate and you have roughly 26 billion people, 14 billion of whom would be able to give birth again. So maybe it's not so bad for the machines!
However, this would only be possible after 15 years and those babies gotta eat during that time. Which means that the machines would need to reserve ~11 million calories per person for those 15 years, or, roughly 1.533e+17 calories (for the 14 billion born; double that for both male and female babies), which translates to about 1.2264e+12 people just to get to the next iteration. Now, obviously, that number is much greater than the 7.7 billion people available! So, this ain't gonna cut it!
But suppose they just want to break even. Well, that won't work either. We know that 7.7 billion people can, at max, sustain 34 million people. Which means that ~12 million will be able to reproduce, resulting in ~312 million births, half, of whom, again, would need a reserve of ~11 million calories each, which, obviously is still much, much more than the initial starting population. Suppose they just want 34 million people born--that would require 3.74e+14 calories or ~3 billion people. Which, of course, is apparent when we consider that 206 people are required to keep 1 person alive for 62 days and human beings can't make 206 people 62 days after birth.
And this is all ignoring the fact that this is the amount of energy that's just needed just to keep other people alive and that these human bodies are supposed to then produce extra energy that runs the machines themselves.
In short, this is a bad plan and the machines are idiots.
Thank you for coming to my Ted Talk.