Matrix: the body as a source of energy
In the article The Matrix: Villains and Saviors by one of the commentators ( original commentary ), Morpheus and Neo talked about using people as an energy source. I wondered if it is possible to create a logically consistent model of a population that feeds on its own dead individuals for various reasons and is able to maintain its existence for a long time.
It is based on the classic predator-prey model with the introduction of specific corrections.
We have:
')
N is the number of living people.
M - the number of dead, suitable for processing and use.
X - the need for live food, per day.
R - production capacity of machines, cloning speed.
D - the rate of death of members of the population. We believe that at any moment in time the distribution of age is even, and the members of the population live on average 80 years with an abundance of food.
We introduce the auxiliary formula:
int FEX (double M) {
int r = int (M> 0.001);
return r;
}
Define constants:
X = 0.04 (one corpse is enough to maintain one body for 25 days)
R = 2.74 (about 1000 clones per year)
N0 = 365 (initial population)
M0 = 365000 (initial stock of the dead)
We formulate a system of equations:
dN / dt = R * FEX (M) * FEX (N0 - N) - N * (1 - FEX (M)) - D * FEX (N);
The first component of the equation is the cloning of people to preserve the population size;
The second is the death of the population in the absence of food;
The third - death due to age reasons;
dM / dt = D * FEX (N) + N * (1 - FEX (M)) - X * N * FEX (M) - R * FEX (M) * FEX (N0 - N);
The first component of the equation is the bodies of the dead due to age reasons;
The second - the bodies of the victims of hunger;
The third is the expenditure of food to maintain the population;
Fourth - the consumption of matter for the creation of clones;
Variable D is calculated each iteration using the formula D = N / (80 * 365) = N / 29200;
The results of the experiment:
The number has fallen by half in 68.5 years.
The population stabilized when the number dropped to 12-14 people.
Change the input parameters. The production of food is directly affected by the initial population size. Double her:
X0 = 730;
The results of the experiment:
The number dropped by half in 34.3 years.
The population stabilized when the number dropped to 12-14 people.
The decrease in the population size to 162 people was no surprise:
The number decreased by half in 154.2 years.
The population stabilized when the number dropped to 12-14 people.
Thus, the initial population size in this model does not have a fundamental effect. Obviously, the same situation will be with the amount of biomass.
We considered the ideal system in which the population feeds on the corpses of their relatives, and with 100% of the biomass transfer from the dead to the living.
However, Morpheus argues that the machines receive some of the energy for their activities from people from the population we are considering.
Let the technology is so good that they can take up to 10% of the energy produced by human bodies. Accordingly, we will increase the consumption of matter for each person in the population by 10%. Change in accordance with this constant in the system:
X = 1.1 * 0.04 = 0.044;
As a result of the rising costs of maintaining the population, the number of 12–13 people has become stable, which is a minor change.
Perhaps it is time to find out why the model demonstrates the viability of the population.
The second equation was built on the assumption that people who died of starvation were as edible as those who died because of age. However, it is not. We remove from the second equation the component responsible for the hungry dead:
dN / dt = R * FEX (M) * FEX (N0 - N) - N * (1 - FEX (M)) - D * FEX (N);
dM / dt = D * FEX (N) - X * N * FEX (M) - R * FEX (M) * FEX (N0 - N);
X0 = 365;
The result of the experiment: the population has halved in 62.24 years and completely died a week later.
Thus, one of the conditions for the survival of the population was the suitability of the bodies of those who died of starvation for human consumption, and the story of Morpheus from the point of view of the above model makes sense, provided that the machines from the Matrix were able to convert the hungry dead into relatively cheap food biomass.
MORPHEUS: For a long time I could not believe it. But I saw these fields with my own eyes. I saw how they process dead bodies to intravenously feed the living ...
NEO (politely): Excuse me, please.
MORPHEUS: Yes, Neo?
NEO: I tried to hold back for a long time, but on this occasion I consider it necessary to speak out. The human body is the most inefficient source of energy that one can think of. The efficiency of a thermal power plant decreases when turbines operate at low temperatures. Any food suitable for people is much more efficient to burn in the furnace. And now you say that the bodies of the dead are used to feed the living. Have you ever heard of the laws of thermodynamics?
MORPHEUS: And where did you hear about the laws of thermodynamics, Neo?
NEO: Anyone who has studied physics at school knows about the laws of thermodynamics!
MORPHEUS: Where did you go to school, Neo?
(Pause)
NEO: ... in the Matrix.
MORPHEUS: The machines have come up with an elegant lie.
(Pause)
NEO (timidly): Can I take a textbook on real physics somewhere?
MORPHEUS: There is no such thing, Neo. The universe does not obey mathematical laws.
It is based on the classic predator-prey model with the introduction of specific corrections.
We have:
')
N is the number of living people.
M - the number of dead, suitable for processing and use.
X - the need for live food, per day.
R - production capacity of machines, cloning speed.
D - the rate of death of members of the population. We believe that at any moment in time the distribution of age is even, and the members of the population live on average 80 years with an abundance of food.
We introduce the auxiliary formula:
int FEX (double M) {
int r = int (M> 0.001);
return r;
}
Define constants:
X = 0.04 (one corpse is enough to maintain one body for 25 days)
R = 2.74 (about 1000 clones per year)
N0 = 365 (initial population)
M0 = 365000 (initial stock of the dead)
We formulate a system of equations:
dN / dt = R * FEX (M) * FEX (N0 - N) - N * (1 - FEX (M)) - D * FEX (N);
The first component of the equation is the cloning of people to preserve the population size;
The second is the death of the population in the absence of food;
The third - death due to age reasons;
dM / dt = D * FEX (N) + N * (1 - FEX (M)) - X * N * FEX (M) - R * FEX (M) * FEX (N0 - N);
The first component of the equation is the bodies of the dead due to age reasons;
The second - the bodies of the victims of hunger;
The third is the expenditure of food to maintain the population;
Fourth - the consumption of matter for the creation of clones;
Variable D is calculated each iteration using the formula D = N / (80 * 365) = N / 29200;
The results of the experiment:
The number has fallen by half in 68.5 years.
The population stabilized when the number dropped to 12-14 people.
Change the input parameters. The production of food is directly affected by the initial population size. Double her:
X0 = 730;
The results of the experiment:
The number dropped by half in 34.3 years.
The population stabilized when the number dropped to 12-14 people.
The decrease in the population size to 162 people was no surprise:
The number decreased by half in 154.2 years.
The population stabilized when the number dropped to 12-14 people.
Thus, the initial population size in this model does not have a fundamental effect. Obviously, the same situation will be with the amount of biomass.
We considered the ideal system in which the population feeds on the corpses of their relatives, and with 100% of the biomass transfer from the dead to the living.
However, Morpheus argues that the machines receive some of the energy for their activities from people from the population we are considering.
Let the technology is so good that they can take up to 10% of the energy produced by human bodies. Accordingly, we will increase the consumption of matter for each person in the population by 10%. Change in accordance with this constant in the system:
X = 1.1 * 0.04 = 0.044;
As a result of the rising costs of maintaining the population, the number of 12–13 people has become stable, which is a minor change.
Perhaps it is time to find out why the model demonstrates the viability of the population.
The second equation was built on the assumption that people who died of starvation were as edible as those who died because of age. However, it is not. We remove from the second equation the component responsible for the hungry dead:
dN / dt = R * FEX (M) * FEX (N0 - N) - N * (1 - FEX (M)) - D * FEX (N);
dM / dt = D * FEX (N) - X * N * FEX (M) - R * FEX (M) * FEX (N0 - N);
X0 = 365;
The result of the experiment: the population has halved in 62.24 years and completely died a week later.
Thus, one of the conditions for the survival of the population was the suitability of the bodies of those who died of starvation for human consumption, and the story of Morpheus from the point of view of the above model makes sense, provided that the machines from the Matrix were able to convert the hungry dead into relatively cheap food biomass.
Source: https://habr.com/ru/post/368163/
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