accelerate until the system is in a state far from its original position. In contrast, if the ball in state (a) or (c) is displaced, the balance will merely rock a bit back and forth, and the ball will roll slightly within its cup until friction restores it to its original equilibrium.

Suppose we push down gently on the right arm of the balance causing a slight tilt, as shown in (a1). When we let go, the ball will rattle around for a bit as the balance tilts back and forth. Once things settle down, the system will return to its original state of rest, with the ball in the left cup. As noted above, this position is stable in the face of small perturbations.

If instead we push the right arm somewhat farther down, as shown in (a2), the ball will eventually roll over the fulcrum and slide down into the right cup. This is an example of a system passing a threshold. When the pressure is relieved, the system does not return to its original state. A temporary influence can have permanent effects; this is what is known as hysteresis .

This device illustrates other kinds of behavior that are common in the climate system. The equilibria illustrated in the top row are steady, in that the system sits still without moving. But suppose that the ball in state (a) or (c) is given a gentle push. If the friction is low, the ball in either case will rattle around for a long time, but will remain in its original cup. This illustrates the notion of an unsteady regime—the “left cup” regime and the “right cup” regime. A strong enough push at the right time could cause a transition between one regime and the other.

An unusual application of force could cause unexpected behavior. Hit it hard enough, and the device might do something different from anything seen before. For example, the arm of the balance might bang against the table, and the ball could bounce out of the cup and roll away.

Now imagine that you have never seen the device and that it is hidden in a box in a dark room. You have no knowledge of the hand that occasionally sets things in motion, and you are trying to figure out the system’s behavior on the basis of some old 78-rpm recordings of the muffled sounds made by the device. Plus, the recordings are badly scratched, so some of what was recorded is lost or garbled beyond recognition. If you can imagine this, you have some appreciation of the difficulties of paleoclimate research and of predicting the results of abrupt changes in the climate system.



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