The key idea here is the difference between “local” vs “nonlocal” changes in a multistable system—moving around within one basin vs jumping to another one. The prototypical picture:
For your finger example, one basin would be with-finger, one basin without-finger. For small changes (including normal cell turnover) the system returns to its with-finger equilibrium state, without any permanent changes. In order to knock it into the other state, some large external “shock” has to push it—e.g. cutting off a finger. Once in the other state, it’s there permanently (as long as there aren’t more large shocks); the new state is stable.
In the absence of large external shocks, the system hangs around in a stable basin. In terms of information in the high-level structures, this means that any information is either (a) degraded quickly, on roughly the same timescale as component turnover, or (b) maintained indefinitely. Picture an actual ball being gently shaken around in a bowl: information about the ball’s exact position at any given time will be lost quickly; its position a minute or two later won’t tell us much about its position now. However, the fact that it’s in the bowl will be maintained indefinitely (more technically, maintained for an exponentially long time, assuming the average shaking energy is substantially lower than needed for the ball to jump out). Any information which isn’t lost quickly, will likely stick around for a very long time.
The key idea here is the difference between “local” vs “nonlocal” changes in a multistable system—moving around within one basin vs jumping to another one. The prototypical picture:
For your finger example, one basin would be with-finger, one basin without-finger. For small changes (including normal cell turnover) the system returns to its with-finger equilibrium state, without any permanent changes. In order to knock it into the other state, some large external “shock” has to push it—e.g. cutting off a finger. Once in the other state, it’s there permanently (as long as there aren’t more large shocks); the new state is stable.
In the absence of large external shocks, the system hangs around in a stable basin. In terms of information in the high-level structures, this means that any information is either (a) degraded quickly, on roughly the same timescale as component turnover, or (b) maintained indefinitely. Picture an actual ball being gently shaken around in a bowl: information about the ball’s exact position at any given time will be lost quickly; its position a minute or two later won’t tell us much about its position now. However, the fact that it’s in the bowl will be maintained indefinitely (more technically, maintained for an exponentially long time, assuming the average shaking energy is substantially lower than needed for the ball to jump out). Any information which isn’t lost quickly, will likely stick around for a very long time.