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Consider a pot of soup. Its contents are static. Once you start stirring it the state of the contents changes rapidly. Once you stop stirring the state of the pot returns to something approximating the original state.

What is this property called?

Most things don't have this property. When you stop smashing your computer with a baseball bat it will not return to its original state.

Edit with a better example: On a farm, there is a certain number of cows. The number depends on the amount of grass on the farm. Once the population of cows is at that number it cannot increase beyond it because there isn't enough food. If the farmer were to kill a lot of cows one year for beef then the remaining cows will have more calves and the population would return to that number.

I guess I could say the system is self-correcting but then that would imply that one state of the system was more correct than the other. I don't want to do this.

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"Self-resetting"? –  Casey Chu May 5 '12 at 22:58
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10 Answers

up vote 13 down vote accepted

There are several words that apply here. The soup with the heavy stuff on the bottom and liquid at the top is in an equilibrium or a steady state. Sometimes, when you perturb an equilibrium, then remove the outside influence that was changing things, the system returns to its old steady state. So if you push a swing or a pendulum, just once, it will wave back and forth for a while and then eventually settle to hanging straight down as before. You stir the soup, it gets all mixed up, then you stop and it goes back to how it was.

But not all properties of a system depend only on their current state. In high school chemistry we learned that the viscosity (thickness or runniness) of, say, water, depends only on its current temperature - you can freeze and melt, freeze and melt, but 50 degree water will always have the same viscosity. Not true of an egg: if you boil it for ten minutes and return it to room temperature its viscosity is permanently changed.

And some systems return to a different equilibrium after a perturbance. Consider a piece of paper or wood. If you apply a little heat to it (say, a match) then it goes from being stable and just sitting around to burning. And it will happily continue to burn although the match is gone. In many cases when it has stopped burning the equilibrium it reaches is being a pile of ash and cinders. Or a burning piece of wood, if you blow on it to blow out the flame, won't go back to burning when you stop blowing on it.

In physics, you use the word elastic to mean that the shape changes with stress, then goes back to the old shape. (This is what an elastic band does.) The word plastic means that it changes its shape and stays changed, like plasticine or playdough. But if you want to use these metaphorically, tread carefully, because most people take elastic to mean "can be stretched indefinitely" and forget the part about going back to the old shape when the stress is removed. To use some more words from physics, resilient is popular for recovering back to the old state, and brittle for not doing so, like your smashed computer. And when you build a computer, you are removing a lot of entropy, getting it all ordered and carefully arranged. But in the absence of outside forces, entropy only increases. That's why the smashed computer won't go back to how it was.

Once you bring in the cows/grass example you are into predator-prey theory and not far from chaos theory, full of crazy words like saddles and strudels. There are stable equilibria, unstable equilibria, and all manner of words that mean a lot to practitioners but less in general conversation. I think your best bet is to describe one state of a system as a stable equilibrium while understanding that when you're being precise, an equilibrium can be stable to some perturbations (like stirring) but not to others (like being poured down the sink or being eaten.)

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+1 for 'elastic'. –  user3490 May 5 '12 at 22:02
This was very interesting! Resilient is the word I will use. It expresses a kind of strength in the system to overcome any change made to it. It's also short and sweet! Thanks. –  edwin May 6 '12 at 0:49
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The examples you've used aren't really related, but two words you could consider are equilibrium which is a state of balanced forces - such as with your cows example or steady-state which is the state of being stable, which might apply to your soup example.

The property of the soup that causes it to maintain a steady state is inertia.

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+1 for the first paragraph, but it is the interaction of the soup with the pot it is in that causes it to return to its original non-rotating state. Its rotational inertia is acting against this return to a steady state. (On the other hand, its rotational inertia also fought against it leaving its steady state when it was first being stirred.) –  Ben Hocking May 5 '12 at 14:22
@BenHocking - Agreed, friction stops the soup turning - but inertia keeps it that way until it is acted upon by another external force. –  Joel Brown May 5 '12 at 16:04
It's equilibrium, though. –  Tim Pietzcker May 5 '12 at 20:41
@TimPietzcker - Thank you. Edited accordingly. –  Joel Brown May 5 '12 at 20:45
I disagree with you about inertia. Inertia is what keeps the soup turning after you have stopped stirring it. –  Pitarou May 6 '12 at 6:11
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It's not a property of the soup but a property of the action, which is called a reversible change. In this case it is the fluid friction in the soup that returns it to its normal state, reversing your stirring action.

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Thats an interesting way of looking at it. But I am looking for a definition in terms of a system. The action is reversible but what is the name of a system that reverses naturally reverses changes made to it. I may add a better example than a pot of soup. –  edwin May 5 '12 at 11:02
@edwin You can describe such a system as stable, meaning that it will return to equilibrium after being disturbed in some way. In contrast, an unstable system may also be in equilibrium but will not return to that state if disturbed, as in the example here of a ball on top of a hill. –  z7sg Ѫ May 5 '12 at 12:13
You can have a stable system with more than one equilibrium - think of a see-saw. –  Optimal Cynic May 5 '12 at 12:29
@Optimal Cynic: See-saw is bistable, and there are multistable systems. –  Kris May 5 '12 at 16:07
if you have enough dimensions an equilibrium can be both stable and unstable at the same time. A ball on a saddle that is pushed a little way up the saddle horn will roll back down to the middle, but if it's pushed a little way to the side, it will fall off. –  Kate Gregory May 5 '12 at 21:16
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This is a monostable system. It has only one stable state, so when you perturb the system it returns to that state. Physics, electronics and logic are full of systems like that. Contrast bistable and astable.

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Perhaps you mean self-regulatory or self-restorative. A system that controls itself and returns to an equilibrium by itself could be called a self-regulatory system.

You cannot apply this word to trivial systems - like pot with soups or smashed PCs. Instead you could use it for natural processes like food chain for example, or physical and chemical systems or reactions.

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This is a good suggestion. I think the important element here is not complexity but that an autoregulatory or homeostatic system actively maintains its own state, as in an organism or a machine. –  z7sg Ѫ May 5 '12 at 12:20
This is also helpful. Thanks. Also "self-resetting" was suggested by Casey Chu. –  edwin May 6 '12 at 0:53
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Nonhysteretic works.

Dictionary provides a marginal definition of hysteresis.

Wikipedia does a much more complete job.

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This is not the word I am looking for but I might find a use for "hysteresis" in describe how long a system takes to return to its original state. –  edwin May 6 '12 at 0:56
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The word rebound seems to most closely fit the bill, "to bound or spring back from force of impact".

The word is normally used with respect to athletics and elastic balls, but I have also heard it used when referring to the ability of a system to recover after an external stimulus is removed.

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I agree with Shyam and would like to offer a close relative, self-stabilizing.

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Something which returns to the original state is resilient. Not sure if this applies to stirred soup, however. It has to do with returning to the original shape, and is also applied to human psychology: resilient people are those who bounce back from difficulty.

Steel is resilient because it is elastic. However if it is stretched beyond its elastic limit, then it doesn't recover.

Elastic is perhaps not a good word though because it is already used some disciplines in ways that have little to do with recovering to an initial state. For instance the price of some commodity may be said to be elastic. If we say that the number of cows on a farm is elastic, that may bring in connotations of how it varies with other parameters.

There is memory. Objects which can recover their shape from a ridiculous amount of deformation are said to have memory.

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Your herd of cattle is in dynamic equilibrium. I.e. if you do something to push the system out of its equilibrium state, the balance of forces (in this case, the rates of birth and death) will change in such a manner as to return it to that state.

Most things don't have this property.

I disagree. Most systems are in some kind of dynamic equilibrium. You just don't notice them because they're so commonplace and boring. You're like a fish that doesn't notice the water it's swimming in.

For example, I weigh about 80 kg. When I sit on a chair, the chair keeps me suspended above the ground by exerting an upward force that precisely balances my own weight. When I stand up, the chair stops pushing. How does it achieve this amazing balancing act? It's a kind of dynamic equilibrium.

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