What do you consider "significant time frames"? 10 years, 1000 years, 100,000?

If human activity is destabilizing the environment (ie, we have burned an amount of carbon which is suspiciously congruent with the amount of excess carbon in the atmosphere/oceans) why is it unreasonable to expect human activities to provide a similar amount of stabilization, even if greater amounts exceed our grasp?

I gave you point because you asked the right question about the timeframe.

Consider it 12000-28000 years. Because this is timeframe between quite regular Ice Ages. And any tech-based civilization is wiped by serious icing event. Its inevitable. Thus it is not hypothetical global warming you shold be afraid of, but global cooling. And it is right about to start. Your grand-grand-grandson must get a skill of flintcnapping from you, not server administration, or stock brokerage, if ou want him live.

Everything in nature happens along exponential growth curves, so those years are meaningless. This means that not much appears to happen for long periods (few 100k years at most though), then suddenly exponential growth changes everything. As soon as the growth factor increases I would expect to see massive, unpredictable changes 5-10 generation lengths later, assuming a growth factor of 2.

> why is it unreasonable to expect human activities to provide a similar amount of stabilization, even if greater amounts exceed our grasp?

Because of thermodynamics. Given that you start from a system that is not in thermodynamic equilibrium (the earth is not, nor would it be desirable if it was), large sudden changes are par for the course, not an exception.

There is disagreement on whether it is even possible to halt the changes. You can certainly make the change turn out differently (does not mean better, just different). Thermodynamics takes it as an assumption that it is not (you cannot stabilize (ie. "cool") a gas by adding energy, no matter how large the amount, you can only let it expand into a larger area or bring it into contact with something much more stable than it is, and you'll destabilize the large thing in the process).

The causal problem here (in mathematical terms) is that while it is certainly true that "X" caused change "Y", and that Y is large, the absence of "X" would have lead to an equally large change "Z". Take for example the "3-body" phenomenon : Take the solar system. Move one 1kg rock in the asteroid belt (or almost anywhere else) 1 meter in any direction. Wait 10000 years. Look at the effect it had. Counterintuitively, planetary orbits will differ significantly as a result of that tiny movement. It won't take long for that rock to affect the paths of rocks near it through gravity. The change will grow, and before you know it it significantly affects the paths of the thousands of huge "temporary comets" that get catapulted out of the asteroid belt on a regular basis. A few of those will come close to a moon, and "slingshot" around them, significantly affecting the orbit of said moon, which will affect the path of the planet it's orbiting. Any small difference in orbit will build up over time into the positions and orbits of those planets and before you know it, nothing looks alike anymore.