A property of a system composed of interacting parts is emergent if it has the following characteristics. The property is
1. not present in the parts.
2. difficult to predict solely from knowledge of properties of the parts and how they interact with one another.
3. associated with a modification of the properties of and the relationships between the parts.
4. universal, i.e., it is independent of many of the details of the parts.
Different people have different views on what emergence is, particularly with regard to the second characteristic. “Difficult to predict” is sometimes replaced with “impossible”, “almost impossible”, or “extremely difficult”, or “possible in principle, but impossible in practice.” After an emergent property has been observed sometimes it can be understood in terms of the properties of the parts. An example is the BCS theory of superconductivity. This is a posteriori, rather than a priori, understanding. A key word in my statement is “solely”.
Examples of properties of a system that are not emergent are volume, mass, charge, and number of atoms. These are additive properties.
Associated with emergent properties are also unique entities, concepts, theories, and organizing principles.
Ross, like many subtle concepts it is quite slippery to give a complete definition for emergence! I wonder if parts 2 and 4 of your definition are mildly contradictory, or at least it is worth acknowledging the social parts of them.
ReplyDeleteImagine people begin to study system A, and decide they can explain its properties in some way that at the time was not possible from the individual parts (satisfying part 2 of the definition). Later people study system B, which by analogy they realize is very similar to system A (because of part 4 of the definition). It seems that we could then argue that part doesn't apply to system B because based on what we learned about system A we can now recognize the overall properties based on the individual parts of system B.
Perhaps this is just semantics, although I suppose that in a sense is the point of trying to give a definition!
The one that bothers me is number three.
ReplyDeleteThe superconductive transition or the plain solid-liquid transition does not effect propertirs of the parts, which I take to be atoms or molecules. Maybe that's not what you mean. It does effect the relationships, if, e.g. for solid-liquid you mean order versus disorder.
Of course you surely explain what you mean, but its very nonobvious from just the words.
Thanks for the helpful comment.
DeleteLet me clarify in case of the solid-liquid transition. It does effect the properties of individual parts. For example, the vibrational frequencies of a water molecule will be different in the solid, liquid, and gas states. The relationships between the parts are different, as you say, order versus disorder. More specifically, the correlations between the positions of the individual molecules are different in the solid, liquid, and gas states.
Hope this helps.
I do need to expand on this point in the text. thanks.
A very interesting topic!
ReplyDeleteAll of the 4 points seem to have sort of a "bottom-up" attitude, i.e. the emergence is viewed as something we're having hard time to build it from the parts. I think that often the situation (at least from a condensed matter researcher view) is a bit different: we already have something relatively simple (i.e. a magnet or a body in thermal equilibrium), which we can actually describe and understand on its own terms (using phenomenology, thermodynamics and so on). However, what makes one puzzled and calls for a new term is that this description appears to be incommensurable (similar to Kuhn's notion of incommensurable paradigms) with the description of the parts: it uses completely different notions (e.g. temperature and pressure instead of coordinates and velocities). I think it is precisely this incommensurability of the descriptions that calls to designate such occurrences as "emergent phenomena". For example, behavior of say, 10 billiard balls is not present in its parts (role of collisions), rather difficult to predict, indeed changes the behavior of individual parts (collisions again) and is independent of a fair amount of their properties (color, material [as long as the density is similar]; although a more thorough definition of universality may solve this issue). I wouldn't call it emergent because their description uses the same notions of coordinates and velocities, as that for a single ball. The above may sound that "emergence is in the eyes of the beholder", so one should probably emphasize the *possibility* of a compact incommensurable description for a complex system, which should be its intrinsic property.