The Matrix is among the first trilogies of science fiction that has left its mark on film history for its dystopic and tragic vision of a future governed entirely by machines. It was probably the first time when the reality of Earth and of human beings was questioned. Leaving aside philosophy and the dystopian world of the Matrix, I asked myself:
Would a world that works on human thermal energy ever be possible?
The Matrix world
An image representing the Matrix, seen in its real form as the code source
In the Wachowski brothers' movie, human beings are immersed in a non-specified gelatinous substance and they are linked to a huge computer called "The Matrix" making the human being no longer in control of his own body, but keeping the body alive and bodily functions intact (such as metabolism) by fooling the mind into thinking the "Matrix Experience" is a real one. The man connected to the Matrix is constantly asleep whereby all the nerve endings no longer communicate with the rest of the body but interact directly through the machine. Similar to virtual reality applications, the person is entirely absorbed into a fictitious reality that he considers to be the true reality, while he does not realize that what he considers to be the real world is nothing but a machine simulation. The only clues are given by small "glitches", system errors caused by the computer programming of the Matrix.
But is human energy enough to make these electricity intense machines work?
The energy source of the machine
The energy needed by the machines was initially given by solar panels according to the movie. Their efficiency and their great diffusion allowed the machines to accumulate large quantities of electricity and to live and prosper. The onset of the war between machines and humans led the human faction to take the drastic decision to completely cover the sky with a thick, black curtain of smoke, so as to make the solar panels useless.
At that point, the machines started to exploit the energy they accumulated in a way they considered effective enough to make them win the war: exploiting the thermal energy produced by synthetic human beings, while studying their behavior to end the war.
Due to the second law of thermodynamics, this solution will never be sustainable and it can be discarded immediately as energy must be used to create and feed the synthesized human beings.
However, let’s suppose instead that the energy comes from naturally-born human beings that are not synthetically produced in a laboratory by the machines. This opens to brutal scenarios, but the following analysis has to be considered as a pure thought exercise.
The Matrix power plant: Neo wakes up
First of all, the human body does not produce as much electricity as eels do, for example, unless we consider the small electrical impulses necessary to make the muscles move. In terms of energy quality, this form would be the most suitable as no conversion is needed, but it falls far in magnitude from the amounts produced by the body in terms of thermal energy (source). In fact, a few milliwatts (mW) of electrical energy would be enough to cause tetanus or kill a human. Moreover, the chemical energy stored in our cells is significantly higher than both of the previous forms and this is why The Matrix also recycles synthetic people who are malfunctioning to feed the rest of the bodies.
What could they do otherwise to feed such a big machine?
The land in this dystopian future is unsuitable for agriculture or biomass harvesting since the sky is completely covered and the sun no longer transmits energy to the planet.
The chemical energy of a human body
Instead of the energy contained in a human body, it is here considered the energy generically provided by 1 kg of pork meat. The pig is chosen as a parameter for comparison because it is the animal that most resembles the human internal characteristics. Considering a generic specimen that we can find at the supermarket, we can see that 1 kg of meat provides about 2400 kcal. Considering an average person of about 75 kg, each human body can provide about 180,000 kcal. This amount is enough to feed a human being for 90 days, or a quarter of a year, at a rate of 2,000 kcal/day. The human population should therefore lose 80% of its capacity each year to allow the system to survive alone, since it takes four people to meet the energy needed for a single human being for one year. Considering an average lifespan of 70 years, well, it is necessary to sacrifice 280 people just to let one live. Unsustainable and gruesome.
The daily energy produced by a human
Each person emits a heat power of 100W in rest conditions, while during sleep the energy emitted is 90W. Considering this last situation the daily production will be 2.16 kWh. This energy is given by transmission from a body temperature of 37 degrees and the surroundings at 20°C. However, the energy produced in this way has a very low exergy and therefore is not fully exploitable. Considering in fact an ideal Carnot engine, the efficiency would be just 5.5%. With this conversion you could get just 118.5 Wh of electricity per person per day, but since the inefficiencies will still be present, we keep an overly optimistic 5% for 108Wh per day.
The maximum generable energy is 756 GWh per day for a population of 7 billion humans. In a year, around 276,000 TWh can be obtained.
To understand if this quantity can be sufficient to feed the entire faction of the machines, we consider the current consumption of electricity. According to the Wikipedia sources, 20,900 TWh were consumed in the world in 2012. The energy produced would therefore be 13 times higher than that consumed currently by the world population.
Doubts and a little fanciful hypothesis
Before stating that everything assumed until now would work and that it is all feasible, it is necessary to consider that the world of the Matrix is entirely governed by machines and entirely electrified. It is also fully functional, so there are no areas that are not used by machines. Therefore, to simplify the concept, we can consider it as a macro computer the size of the Earth. Thus, consumption is not limited to the few Data Centers existing today and the energy used is far superior. In fact, if we consider the average energy consumption of a developed and efficient region of the world like Europe, the average consumption is 6300 kWh per year. Multiplying this for the 7 billion human beings, the total consumption results to be 44100 TWh, which is 2.15 times more than currently consumed.
01: The main city of the faction of the machines
Furthermore, energy production has been overly estimated at 5% efficiency, but with the present temperatures we would have highly inefficient heat exchangers, since it is difficult to have an effective heat transfer when the temperature difference falls below 10 °C. It must also be considered that 37°C is the internal human temperature, while the skin is nearer to 34°C. To be able to have an efficient heat transfer, thermoelectric technology should be exploited, which even with future improvements would hardly reach 1% efficiency , making the energy generated from this technology almost zero.
Therefore, the world reality is very far from achieving such a dystopian world.
The CommUnity Post
 This number is made up by myself based on the current state of the technology that is way under 1%. If somebody has a theoretical knowledge and would like to provide real theoretical figures through Seeback’s coefficient, Temperature and thermal gradient is more than welcome.