Though by many standards I could be considered an environmentalist, I find the "harmony with nature" trope to be laughable. Nature is not harmonious; it is a vicious battle of killing, eating, and survival. We should absolutely preserve and protect our environment. We can never live in "harmony" with something that is far from harmonious.
I likewise find the "harmony with nature" idea to be laughable, but for a very different reason. If "nature" has any meaning at all, then we are part of it. Other animals are perfectly happy to change their situation to their benefit. Beavers, for example, can create lakes by choking off rivers. Are they living "in harmony" with nature? That feels like a strange question to me, and so I wonder why it shouldn't feel like a strange question when the beavers are replaced by humans.
Beavers, in some sense, must, because their impacts have had plenty of time to get back at the beavers if it was going to. That doesn't mean they didn't ruin it for some other species.
It's kind of the idea that the most successful parasites can't kill their hosts too efficiently or quickly, because then they run out of places to live. If you screw up your environment like that, it'll come back to haunt you.
Animals without a natural check on their population and resource consumption can also experience a population boom followed by a sharp decline and even collapse, possibly extinction.
I wonder, could you create a closed form of the final solution by allowing only a portion of the nonrenewable resources to be consumed? At least, this should remove the sudden discontinuity in the slope of the nonrenewable resources function.
> I wonder, could you create a closed form of the final solution by allowing only a portion of the nonrenewable resources to be consumed?
You may not be surprised to hear that that was my original, much desired goal, but after much thought and experiment I realized that the abrupt discontinuity caused by the exhaustion of the nonrenewables is real, for the reason that, in practice, the rate of nonrenewable use increase as their exhaustion approaches, creating an abrupt knee that resists conversion to a closed form.
> At least, this should remove the sudden discontinuity in the slope of the nonrenewable resources function.
But that abrupt end to nonrenewables is real -- it reflects the fact that the growing colony becomes increasingly reliant on them as their exhaustion approaches. So the knee can't be removed without changing the meaning of the equation.
Oh, well -- as it turns out, there are many very common differential equations that resist conversion to closed form. Orbital systems with more than two bodies are a classic example. Another one is the integral to the common exponential function that gives us the normal distribution -- very commonly used in statistics and elsewhere, but no closed form. All applications of the normal distribution use a numerical algorithm called the "error function" to produce results -- all of them approximate, and having the drawback that they cannot be symbolically differentiated or integrated.
Maybe a much more skilled mathematician that I am could find a way around this obstacle, but I doubt it.
The concept of harmony can refer to lions not chasing gazelles, which is certainly unrealistic , but it can also mean sustainable and balanced. Nature is certainly vicious and ever changing, but there is a balance in the bigger picture, and man is making (or let's say, is at risk of making) excessively disrupting changes. If that's the meaning, that's certainly not laughable.
The notion of "nature in balance" is selection bias. There are certainly places where nature is not sustainable and balanced. Look for example at what happens with the introduction of invasive species (which may happen these days because of humans, but I imagine the opening of the Bering's Strait land bridge would have lead to a similar disruption.) Pre-human nature only appeared balanced because it had had a long time to equilibrate, not because of some innate quality.
Normally, I considered "harmony with nature" to be roughly equivalent to "Nash equilibrium that won't make human extinct". In other words, human has to make way for "nature" (to a certain extend), or risk being wiped out in the long run.
Nature will always be fine, whether humanity as we know it survives is the problem.