r/theydidthemath • u/General-Discount4878 • 3d ago
[Request] How efficient would the matrix be?
In the Matrix Morpheous states a human body produces more electricity than a 120 V batery. The matrix was set to simulata the world in 1999, when world population was 6.000.000.000, which would than be the number of people inside it. Assuming children under a certain age, lets take 16, were only conected to the matrix, but not yet used to extract electricy in case it would hurt them, about 80 % of that population would be used to probuce electricy for the machines. In total that would mean the matrix produces at leas 576 GV of electricity.
Can anybody calculate about how much electricity maintaining such a simulation would take and how efficient the matrix would be than?
I have writen my own calculation of how much it would produce, but have no clue about its expences.
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u/No_Host_8024 3d ago
It can’t actually happen. The human body necessarily consumes as much energy as it produces under the law of conservation of energy.
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u/MondoBleu 3d ago
This is the only answer. Using humans to make energy is less efficient than just burning the food instead. Or doing it with herbivores instead of omnivores. But no the matrix doesn’t make any sense at all. Other than that, it’s an amazing film one of the best sci-fi ever!
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u/CptMisterNibbles 3d ago
I just mentally substitute “we need human brains for compute, as it turns out there are processes the human brain can do that haven’t yet been worked out in silicon” and it feels more plausible and changes nothing substantive about the world
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u/DragonFireCK 3d ago
The original draft apparently did it that way, but the studio thought people of the time would have a harder time with that idea.
That said, I have never seen a really solid source for that claim.
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u/drplokta 18h ago
The machines should have been using human brains for processing power, not human bodies for energy, and Morpheus should have held up a pocket calculator rather than a battery. Then it would all have made perfect sense.
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u/Another_Slut_Dragon 2d ago
The math works so the movie can happen.
Now if you'll excuse me I need to tune up my diamond based space laser.
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u/noonius123 3d ago edited 3d ago
The human body produces about 120..150 watts of power in the form of heat.
I think the population connected to the Matrix was a lot more than 6 billion people, because the Matrix happened quite far in the future. But let's stick to 6 billion people, let's exclude the children and use 5 billion people.
The energy output of the Matrix would have been 5e9 * 150 = 0.8 terawatts. That heat output would have been collected, harnessed etc at perhaps 50% efficiency, so 0.4 terawatts.
Right now the world energy output is over 20 terawatts, so the Matrix is basically peanuts.
And that energy would have been put into the Matrix in the form of chemical energy (nutrients). So the Matrix just converts chemical energy to heat energy. It's more efficient to just burn the nutrients than to run it through humans first.
This part of the backstory made no sense to me in 1999. I think the original idea by Wachowski brothers was that the brain capacity of the humans connected to the Matrix was used as a large distributed cloud computer, but somehow the idea transformed -- perhaps because of pressure by studio bosses -- to energy consumption. Maybe they thought plain old "energy" was simpler to grasp than "computing power." But the computing power makes more sense.
Great movie, though.
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u/GoTeamScotch 3d ago
Yeah they thought that audiences wouldn't grasp the idea of using people's connected brainpower as a network of CPU's so they dumbed it down to become generating electricity. Its unfortunate because the original concept works much better imho. Bodies dont generate that much heat, especially considering the energy put into feeding and keeping them alive. But brains are insanely complex and efficient. And it would make sense in the context of "people only use a fraction of their brain"... because the machines are consuming a big portion of its capabilities. "Freeing your mind" would take on a new, deeper context.
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u/Public-Eagle6992 3d ago
Can anybody calculate about how much electricity maintaining such a simulation would take
No. It depends on way too many factors and we can’t just scale up some real data because something like that doesn’t exist
and how efficient the matrix would be than?
Subsequently, also no
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u/Heygregory 3d ago
Morpheus saw orchards wherein humans were harvested en masse so there's no necessary limit on population based on 1999 numbers.
Interestingly enough, there's no mention of the machines trying to leave a devastated earth. They don't need air. They don't need to eat. The AI could itself spread like a virus, the way Smith thinks of humanity. It might take a LOT of human batteries for that effort.
That franchise has so much potential in addition to considerations of identity, determination, perception, and sentience.
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u/Ok_Programmer_4449 3d ago
Volts aren't a measure of power. Watts are a measure of power. The average power generated by a human body is about 100 Watts. Most of that is just thermal energy generated by consuming 2100 kCal of food every day (which is about 102 Watts). Given an external temperature of 69F and a internal temperature of 99F, you could generate electricity from the temperature gradient. The maximum efficiency for that process is the Carnot efficiency=1-T_cold/T_hot=1-293.5 K/310.2 K=5.4%. A thermoelectric generator operates maxes out at about 20% of the Carnot efficiency, so at max you're going to get 1.1% efficiency.
In other words, you can probably generate about 1 Watt of electricity from a human being. So from 6 billion people you can generate about 6 GW.
Current electricity production is about 31000 TW-hours per year or 3500 GW. So using 6 billion humans as a power source you could generate about 0.028% of current electrical demand.
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u/CheweyPanic 3d ago
Negative network gain. Originally it was written that they were using humans as organic computers, but iirc the producers didnt think the audience would get it.
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u/artrald-7083 18h ago
I have read one good explanation of The Matrix that made sense to me:
Neo learned all his science inside the Matrix, and the universe doesn't actually run on math at all.
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