Image: Phase diagram of water, Solé. Phase Transitions , 4 I've proposed to sympathise the concepts of emergence in addition ...
Image: Phase diagram of water, Solé. Phase Transitions, 4
I've proposed to sympathise the concepts of emergence in addition to generativeness as existence symmetrical (link). Generative higher-level properties are those that those that tin survive calculated or inferred based on data nearly the properties in addition to states of the micro-components. Emergent properties are properties of an ensemble that receive got substantially dissimilar dynamics in addition to characteristics from those of the components. So emergent properties may appear to survive non-generative properties. Further, I sympathise the thought of emergence inwards a weak in addition to a rigid sense: weakly emergent properties of an ensemble are properties that cannot survive derived from the characteristics of the components given the limits of observation or computation; in addition to strongly emergent properties are ones that cannot survive derived in principle from total cognition of the properties in addition to states of the components. They must survive understood inwards their ain terms.
Conversations amongst Tarun Menon at the Tata Institute for Social Sciences inwards Bombay were real helpful inwards allowing me to broaden somewhat the means I sympathise emergence inwards physical systems. So hither I'd similar to consider some additional complications for the theory of emergence coming from ane specific physical finding, the mathematics of stage transitions.
Complexity scientists receive got spent a lot of effort on agreement the properties of complex systems using a dissimilar concept, the thought of a stage transition. The transition from liquid H2O to steam as temperature increases is an example; the transition happens abruptly as the scheme approaches the critical value of the stage parameter -- 100 degrees centigrade at constant pressure level of ane atmosphere, inwards the instance of liquid-gas transition.
Richard Solé presents the electrical flow dry reason of complexity theory amongst honor to the phenomenon of stage transition in Phase Transitions. Here is how he characterizes the total idea:
In the previous sections nosotros used the term critical request to depict the presence of a real narrow transition domain separating 2 well-defined phases, which are characterized past times distinct macroscopic properties that are ultimately linked to changes inwards the nature of microscopic interactions amid the basic units. Influenza A virus subtype H5N1 critical stage transition is characterized past times some guild parameter φ( μ) that depends on some external command parameter μ (such as temperature) that tin survive continuously varied. In critical transitions, φ varies continuously at μc (where it takes a aught value) but the derivatives of φ are discontinuous at criticality. For the so-called first-order transitions (such as the water-ice stage change) at that spot is a discontinuous outpouring inwards φ at the critical point. (10)
So what is the connective betwixt "emergent phenomena" in addition to systems that undergo stage transitions? One possible connective is this: when a scheme undergoes a stage transition, its micro-components larn chop-chop reconfigured into a qualitatively dissimilar macro-structure. And silent the components themselves are unchanged. So ane mightiness survive impressed amongst the fact that the pre- in addition to post-macro states agree to real unopen to the same configurations of micro-states. The steaminess of the H2O molecules is triggered past times an external parameter -- modify inwards temperature (or peradventure pressure), in addition to their characteristics about the critical request are real similar (their hateful kinetic release energy is to a greater extent than or less equal earlier in addition to after transition). The diagram higher upwards represents the physical realities of H2O molecules inwards the 3 stage states.
Solé in addition to other complexity theorists encounter this "phase-transition" phenomenon inwards a broad attain of systems, including elementary physical systems but also biological in addition to social systems as well. Solé offers the phenomenon of flocking as an example. We mightiness consider whether the phenomenon of ethnic violence is a stage transition from a mixed but non-aggressive population of individuals to occasional precipitous outbursts of widespread conflict (link).
The disanalogy hither is the fact that "unrest" is non a novel equilibrium stage of the substrate of dispersed individuals; rather, it is an occasional abnormal dry reason of brief duration. It is as if H2O sometimes spontaneously transitioned to steam in addition to thence returned to the liquid phase. Solé treats "percolation" phenomena afterwards inwards the book, in addition to rebellion seems to a greater extent than plausibly treated as a percolation process. Solé treats woods burn downwards this way. But the representation plant as for whatsoever procedure based on contiguous contagion.
What seems to survive involved hither is a determination that is a lilliputian fleck dissimilar from touchstone ideas nearly emergent phenomena. The request seems to survive that for a certainly grade of systems, these systems receive got dynamic characteristics that are formal in addition to abstract in addition to produce non shout for that nosotros sympathise the micro mechanisms upon which they residual at all. It is plenty to know that scheme southward is formally similar to a two-dimensional array of magnetized atoms (the "Ising model"); thence nosotros tin infer that phase-transition deportment of the scheme volition receive got specific mathematical properties. This mightiness survive summarized amongst the slogan, "system properties produce non shout for derivation from micro dynamics." Or inwards other words: systems receive got properties that don't depend upon the specifics of the private components -- a contention that is strongly parallel to but distinct from the Definition of emergence mentioned above. It is distinct, because the approach leaves it exclusively opened upwards that the scheme properties are generated past times the dynamics of the components.
This thought is key to Solé's analysis, when he argues that it is possible to sympathise stage transitions without regard to the item micro-level mechanisms:
Although it mightiness appear real hard to blueprint a microscopic model able to supply insight into how stage transitions occur, it turns out that groovy insight has been achieved past times using extremely simplified models of reality. (10)
Here is how Solé treats swarm deportment as a possible instance of stage transition.
In social insects, acre colonies comport inwards complex ways, the capacities of individuals are relatively limited. But then, how produce social insects laissez passer such remarkable ends? The response comes to a large extent from self-organization: insect societies portion basic dynamic properties amongst other complex systems. (157)
Intuitively the thought is that a collection of birds, ants, or bees may survive inwards a dry reason of random motility amongst honor to each other; in addition to thence as some variable changes the ensemble snaps into a coordinated "swarm" of flying or movement. Unfortunately he does non supply a mathematical illustration illustrating swarm behavior; the closest illustration he provides has to produce amongst patterns of intense activity in addition to slack activity over fourth dimension inwards small-scale to medium colonies of ants. This periodicity is related to density. Mark Millonas attempted such an delineate concern human relationship of swarming inwards a Santa atomic release 26 Institute newspaper inwards 1993, "Swarms, Phase Transitions, in addition to Collective Intelligence; in addition to a Nonequilibrium Statistical Field Theory of Swarms in addition to Other Spatially Extended Complex Systems " (link).
This move is interesting, but I am non certainly that it sheds novel calorie-free on the topic of emergence per se. Fundamentally it demonstrates that the aggregation dynamics of complex systems are ofttimes non-linear in addition to amenable to formal mathematical modeling. As a critical variable changes a qualitatively novel macro-property "emerges" from the ensemble of micro-components from which it is composed. This approach is consistent amongst the generativity thought -- the novel holding is generated past times the interactions of the micro-components during an interval of modify inwards critical variables. But it also maintains that systems undergoing stage transitions tin survive studied using a mathematical framework that abstracts from the physical properties of those micro-components. This is the request of the serial of differential equation models that Solé provides. Once nosotros receive got determined that a item scheme has formal properties satisfying the assumptions of the DE model, nosotros tin thence effort to stair out the critical parameters in addition to derive the development of the scheme without farther data nearly item mechanisms at the micro-level.
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