Feedback

I'm actually referring to an important mathematical and physical concept, rather than the comments you give (which I also value).

Feedback is an extremely common process. Perhaps the most common case that people know is feedback involved public address systems. You have a microphone to pick up sound, which goes to an amplifier, and then out a speaker. If you put the microphone too near the speaker, then the microphone picks up some minor sound (say the sound of someone putting papers on the stand near the microphone), it goes through the amplifier and the louder sound comes out the speaker. The microphone now picks up that sound, it gets amplified even more and comes out the speaker again. Repeat through a number of cycles and the speaker is now as loud as it can be. This is a runaway feedback. Not all feedback is runaway.

A feedback can also be limited. Consider the atmosphere in this case. It has a temperature, carbon dioxide level, and water vapor level. Both carbon dioxide and water vapor are greenhouse gases, so if there is more of them, the temperature goes up. Suppose we put enough carbon dioxide into the atmosphere that its greenhouse effect (alone) raised temperature by 1 degree. If the atmosphere is warmer, we expect it to have more water vapor. That extra water vapor, let's say, produces another 0.5 degrees of warming. But, since temperature has gone up again, there's still more warming -- another half of this, for 0.25 degrees. This feeds back through increasing the water vapor to make another 0.125 degrees warming. Keep cycling through this feedback and it turns out to add another 1 degree of warming (1 = 0.5 + 0.25 + 0.125 + ...) after you've gone through an infinite number of steps. It's pretty close after a limited number of steps (99.9% of the way there after 10 cycles). We can look at these feedbacks in terms of how much of a response (multiplier) there is to a 1 degree kick to the system. I made up the number 0.5 here (every step is 0.5 times the previous). That's actually about the right size, in addition to being simple to work with. If the response multiplier is, say, 0.75 instead, then instead of getting back a total warming of 2 degrees, we would get back 4 degrees. The formula is
total = 1 / (1 - x)
where x is this multiplier, and the multiplier has to be less than 1.

Feedbacks can also produce cycles. A common illustration of this is predators and prey -- sharks and fish, or foxes and hares. Suppose one year, there are more fish than usual. The sharks, then, have a lot to eat and give birth and raise more sharks than usual. But, now that there are more sharks, they eat up even more fish than usual. That decreases the number of fish below the usual level. With fewer than normal fish, the sharks start dying off. That eventually gives us fewer than normal sharks, so the fish population recovers. And so on. The two populations could keep cycling (if the balances are right), or one could crash (depends on whether the extra sharks eat up too many fish, or whether the time of few fish lasts too long for any sharks to survive).

In the climate system, there are definitely some amplifying feedbacks and some cycling feedbacks. There don't appear to be any runaway feedbacks. That's not terribly reassuring, however, because life can get quite unpleasant even if temperatures don't run off to boiling the oceans.