Matrix: the body as a source of energy
In the article Matrix: Villains and Savior, one of the commentators (the original commentary ) gave a conversation between Morpheus and Neo about the use of people as an energy source. I was wondering if it is possible to create a logically consistent model of a population that feeds on its own individuals who died for various reasons and is able to maintain its existence for a long time.
The classic “predator-prey” model is taken with the introduction of specific adjustments.
We have:
N - the number of living people.
M is the number of dead bodies suitable for processing and consumption.
X - the need of the living for food, per day.
R - production capacity of machines, cloning speed.
D is the death rate of members of the population. We believe that at any moment in time, the distribution of age is uniform, and the population members on average live 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 the 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 supply of the dead)
Let us formulate the 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 human cloning to maintain population size;
The second is the death of a population in the absence of food;
The third is death due to age-related 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-related reasons;
The second is the bodies of those who died of starvation;
The third is food consumption for maintaining the population;
Fourth - the consumption of matter for the creation of clones;
The variable D is calculated each iteration according to the formula D = N / (80 * 365) = N / 29200;
Experiment Results:
Numbers halved over 68.5 years.
The population stabilized when the number dropped to 12-14 people.
Change the input parameters. Food production is directly affected by the initial population size. Double it:
X0 = 730;
Experiment Results:
Number halved in 34.3 years.
The population stabilized when the number dropped to 12-14 people.
The decrease in the population to 162 people was not surprising: the
number was halved 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 situation will be the same with the amount of biomass.
We considered an ideal system in which the population feeds on the corpses of their relatives, and with 100% transfer of biomass from the dead to the living.
However, Morpheus claims that machines receive part of the energy for their activities from people from the population we are considering.
Let the technologies be 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%. In accordance with this, we change the constant in the system:
X = 1.1 * 0.04 = 0.044;
As a result of the increase in expenses for maintaining the population, the number of 12–13 people became stable, which is a minor change.
Perhaps it's time to find out why the model demonstrates the viability of the population.
The second equation was based on the assumption that people who died of hunger were as fit as food, as well as those who died due to age-related reasons. However, it is not. We remove from the second equation the component responsible for the dead 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;
Experiment result: the population 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 from starvation for 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 relatively cheaply convert the hungry dead to human-powered 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 restrain myself 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 you can think of. The efficiency of a thermal power plant decreases when the turbines operate at low temperatures. Any food suitable for people is much more efficient to burn in a firebox. 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 the laws of thermodynamics!
MORPHEUS: And where did you go to school, Neo?
(Pause)
NEO: ... in the Matrix.
MORPHEUS: The machines came up with an elegant lie.
(Pause)
NEO (timidly): Can I get a textbook on real physics somewhere?
MORPHEUS: There is no such thing, Neo. The universe does not obey mathematical laws.
The classic “predator-prey” model is taken with the introduction of specific adjustments.
We have:
N - the number of living people.
M is the number of dead bodies suitable for processing and consumption.
X - the need of the living for food, per day.
R - production capacity of machines, cloning speed.
D is the death rate of members of the population. We believe that at any moment in time, the distribution of age is uniform, and the population members on average live 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 the 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 supply of the dead)
Let us formulate the 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 human cloning to maintain population size;
The second is the death of a population in the absence of food;
The third is death due to age-related 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-related reasons;
The second is the bodies of those who died of starvation;
The third is food consumption for maintaining the population;
Fourth - the consumption of matter for the creation of clones;
The variable D is calculated each iteration according to the formula D = N / (80 * 365) = N / 29200;
Experiment Results:
Numbers halved over 68.5 years.
The population stabilized when the number dropped to 12-14 people.
Change the input parameters. Food production is directly affected by the initial population size. Double it:
X0 = 730;
Experiment Results:
Number halved in 34.3 years.
The population stabilized when the number dropped to 12-14 people.
The decrease in the population to 162 people was not surprising: the
number was halved 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 situation will be the same with the amount of biomass.
We considered an ideal system in which the population feeds on the corpses of their relatives, and with 100% transfer of biomass from the dead to the living.
However, Morpheus claims that machines receive part of the energy for their activities from people from the population we are considering.
Let the technologies be 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%. In accordance with this, we change the constant in the system:
X = 1.1 * 0.04 = 0.044;
As a result of the increase in expenses for maintaining the population, the number of 12–13 people became stable, which is a minor change.
Perhaps it's time to find out why the model demonstrates the viability of the population.
The second equation was based on the assumption that people who died of hunger were as fit as food, as well as those who died due to age-related reasons. However, it is not. We remove from the second equation the component responsible for the dead 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;
Experiment result: the population 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 from starvation for 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 relatively cheaply convert the hungry dead to human-powered biomass.