Abstract: WHY IS THERE EVIL? We show MATHEMATICALLY that there is evil, because in a domineering species such as humanity, SELF-PREDATION, in other words, EVIL, PROVIDES WITH A STABLE ENVIRONMENT. The only hypotheses we made which go beyond standard mathematical ecology is to replace the “prey” by the enironment itself, and introducing a self-predation term, e. The latter ough not to be controversial, as abuse of humans by humans is well-documented (all and any abuse works: unequal society, plutocracy, exploitation of workers, slavery, torture, killing, etc.) Better: we accomodate altruism by changing the sign of e. So to deny the mathematization we make below of human ethology and ecology, one would have to deny both altruism and malevolence!
We modify the classical predator-prey model of two entangled Nonlinear Ordinary Differential Equations into an environment-self-predation model more appropriate to the superpredator status of humans. Humans need the environment, but also self-predate. Self predation is introduced minimally with a quadratic term whose coefficient e corresponds to EVIL.
A striking conclusion is that such a system is stable only if e > 0… In other words, one needs e, evil, to stabilize the environment. Making e negative, namely replacing evil by altruism, makes the system unsustainable. So not only does humanity suffer from original sin, but humanity could not do without it.
These are theorems which are mathematically rigorous. Strikingly, some evil is bnecessary to make civilization stable.
Another more mathematical essay will dig deeper in the stability of the system (which can readily be modified to accommodate various genocidal scenarios).
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Predator-Prey systems have long been mathematically modelled. We present our own, the
SUPER PREDATOR ENVIRONMENT SYSTEM, SPES.
It has two variables: x, denoting the edible mass of the environment (prey, and plants in calories) and y, denoting the number of humans. Both x and y are functions of time. dx/dt and dy/dt, the differentials of x and y tell how x and y will evolve.
In the absence of human predation, dx/dt will grow proportionally to x. That means that x would be an exponential in the time t. The presence of humans will force dx to become negative (x will decrease) and that’s proportional to the human population, y… and it will decrease the faster the bigger x is so that decrease is proportional to xy. This gives the first differential equation..
For the second ODE, notice that dy/dt will grow proportionally to y but also to x, hence to the product xy, It decreases proportional to the population, that is the death rate is proportional to the population
So far so good, nothing new here, it’s called the Lotka-Volterra system.
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SELF-PREDATORY DARK SIDE:
Now, thanks to our deviant mind, we introduce and add the EVIL TERM, eyy. It characterizes the superpredator who is subjected to predation only from the superpredating species [1]. The Evil Term is proportional to yy (why?Say y is large; suppose each individual composing y decides to kill n individuals in the population; that would be a decrease of ny by unit of time dt… As n –> y, QED.)
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FINAL SYSTEM:
dx/dt = rx – axy
dy/dt = bxy – dy – eyy
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The quadratic predator mortality, eyy, can represent: cannibalism, territorial wars, disease spread at high density, resource interference, behavioral crowding costs. In fact, many real predator systems observed in the wild show stronger intraspecific regulation (eyy) than prey.
We found the value of x in a stable regime. That’s:
x = (d + er/a)/b.
So the environment gets destroyed only when e < 0. When e = 0 (thoroughly pacified society), one is in the standard L-V system, characterized by huge fluctuations, as illustrated in nature by the Canadian Lynx and Rabbit boom and collapse populations.
It goes without saying the preceding SPES model applies to all sorts of situations, for example the socioeconomic crisis in Africa: the preceding shows that pure altruism will make the situation worse. This is actually why there are evil regimes there: it’s more stable that way. But it also says that if, say, Europe, wants to deal with the Africa problem, pure altruism is counterindicated…
This also explains why pure do-gooder democracy is not stable, and rare, a fact known in antiquity (as pointed out by Aristotle and Polybius, inter alia). It also explains why both Athens and Rome used the Dark Side repeatedly, even while they were democracies, etc. It also explains why plutocracy is ubiquitous and so infuriatingly stable.
The math can be pushed considerably into nonlinear dynamics and more sophisticated models.
Patrice Ayme
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[1] Some may object that Homo Sapiens is not the only species which is its own best enemy. This is irrelevant to the EVIL THEORY (it does not affect the math and conclusions above)… But also the fact that few species predate some existing megafauna has to do with the environment being already deeply degraded by Homo Sapiens… or species of predators having already been exterminated: for example the giant social saber cats which predated giant megafauna have been eliminated; elephants, hippopotamuses, etc. do not have to fear lions as much…
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Note: Dynamical Consequences of Quadratic Predator Mortality:
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Breaks Hamiltonian structure of classical L-V.
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Removes closed orbits.
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Produces globally attracting equilibrium (in many parameter regimes).
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Can prevent paradoxical predator population explosion.
Patrice Ayme's Thoughts 