Complexity and Emergence
Re 2004 Edition-
See Bryan Wynn Re Social Theory (2004) etc
http://www.research.lancs.ac.uk/portal/en/people/brian-wynne(daa91ef4-399e-4a48-b02d-cf9b1c9f5ea0)/publications.html
also
http://eprints.lancs.ac.uk/69997/1/23299460_2E2014_2E922249.pdf
"Even more, there is no general definition of complexity, since the concept achieves different meanings in different contexts (Edmonds, 1999). Still, we can say that a system is complex if it consists of several interacting elements (Simon, 1996), so that the behavior of the system will be difficult to deduce from the behavior of the parts. This occurs when there are many parts, and/or when there are many interactions between the parts. For example, a cell is considered a living system, but the elements that conform it are not alive. The properties of life arise from the complex dynamical interactions of the components. The properties of a system that are not present at the lower level (such as life), but are a product of the interactions of elements, are sometimes called emergent (Anderson, 1972). "
Gershenson 2007 (Excellent References)
ANDERSON, P. W. (1972). More is different. Science 177: 393–396.
EDMONDS, B. (1999). What is complexity?: the philosophy of complexity per se with application to some examples in evolution. In The Evolution of Complexity, F. Heylighen, J. Bollen, and A. Riegler, (Eds.). Kluwer, Dordrecht, 1–18. URL http://bruce.edmonds.name/evolcomp/. 12
SIMON, H. A. (1996). The Sciences of the Artificial, 3rd ed. MIT Press.
History of the idea. The idea that the dynamics of a system can tend, of themselves, to make it more orderly, is very old. The first statement of it (naturally, a clear and distinct one) that I can find is by Descartes, in the fifth part of his Discourse on Method, where he presents it hypothetically, as something God could have arranged to have happen, if He hadn't wanted to create everything Himself. Descartes elaborated on the idea at great length in a book called Le Monde, which he never published during his life, for obvious reasons. (I strongly suspect the hypothetical form of his discussion was simply to keep himself out of trouble with the churches, but I'm not enough of a scholar of his life and thought to show that.) Of course, the ancient atomists (among others) had argued that a designing intelligence was unnecessary, but their arguments were all of the "worlds enough and time" variety: given enough time and space and matter, organization is bounded to happen somewhere, sometime, by sheer chance. (Lucretius gives this the interesting twist that stable forms, produced by chance, will last longer than unstable ones, but doesn't take it anyplace.) What Descartes introduced was the idea that the ordinary laws of nature tend to produce organization. --- Since there are people, taken seriously by fellow scholars, who say that self-organization u.s.w. represents a break with the Cartesian, mechanistic, reductionist, etc. tradition of science, I find this more amusing and significant than it probably is. (For related history, see Avram Vartanian,From Descartes to Diderot.)
More modernly, the term "self-organizing" seems to have been introduced in 1947 byW. Ross Ashby, and not (as some references claim) by a pair of computer scientists in 1954; the paper of theirs which is generally cited in support of this claim in fact refers to Ashby!
http://cscs.umich.edu/~crshalizi/notabene/self-organization.html
C.f Genreral Systems Theory and Complexity
See Bryan Wynn Re Social Theory (2004)
Thompson D.W.
Heylighen re Complexity and GST
1) Almost by definition, the study of complex systems involves recognition that reality isn't necessarily simple (or amenable to representation with simple models). In this regard, on a philosophical level, there's the question of whether perceived complexity is ontologic (objectively real) or merely epistemic (and thus contingent on our models). Personally, I'm not sure that this question is answerable even in principle (relates to the philosophical question of scientific realism), and maybe it doesn't need to be answered from a pragmatic standpoint.
(2) At least epistemically, complexity is ubiquitous, perhaps increasingly so, and thus the study of complex systems is practical, if not essential (especially in biological and social realms). In this regard, it's debatable whether current systems biology adequately deals with complexity versus being just another reductionistic approach.
(3) Complex systems have sets of interacting (and possibly interdependent) elements, and thus tend to form networks. Often, the specific characteristics of the elements have only limited effect on the overall system behavior.
(4) Complex systems tend to behave nonlinearly rather than linearly (in terms of response to inputs), and tend to have feedback loops.
(5) Complex systems are usually self-organizing, with no central control.
(6) Complex systems usually have emergent properties (evident at the system level, but not element level).
(7) Systems usually have multiple hierarchical levels which are typically physically distinct and thus readily discernable, and complexity can be found at one or more of these levels. A challenge is choosing the level(s) at which to model a complex system.
(8) The behavior of complex systems appears to involve an interplay between randomness and order, and thus predictions regarding the behavior of complex systems may unavoidably have to be probabilistic (at least in some cases).
(9) Complex systems tend to be dynamic, adaptive, and evolving (sometimes in surprising ways), rather than moving towards an equilibrium steady state. This evolution can include variation and selection at multiple hierarchical levels (individual elements, groups of elements, network topology, etc.).
(10) Complexity suggests that the future may be relatively open, which gives freedom but also limits prediction and control.
(11) Study of complex systems fosters development of new kinds of observables.
(12) As a tool for studying complex systems, computer simulation allows handling of huge amounts of information and solution of problems far beyond analytical (paper and pencil) limits, even though the underlying models may be complicated and thus difficult to understand intuitively.
(13) Complexity may be the borderline between simple problems and unsolvable problems.
(14) Whether "complexity science" exists or ever will exist as a coherent field is a matter of debate. There's likewise no consensus on a definition of complexity (it may be more a matter of "family resemblance" rather than necessary or sufficient conditions) or whether we will ever discover universal laws of complexity. Nevertheless, there's still real and steady progress in this (proto)field, and studying complex systems both benefits from and fosters interdisciplinary efforts, including philosophical reflection.
"New" Paper: Facing Complexity: Prediction vs. Adaptation
One of the presuppositions of science since the times of Galileo, Newton, Laplace, and Descartes has been the predictability of the world. This idea has strongly influenced scientific and technological models. However, in recent decades, chaos and complexity have shown that not every phenomenon is predictable, even if it is deterministic. If a problem space is predictable, in theory we can find a solution via optimization. Nevertheless, if a problem space is not predictable, or it changes too fast, very probably optimization will offer obsolete solutions. This occurs often when the immediate solution affects the problem itself. An alternative is found in adaptation. An adaptive system will be able to find by itself new solutions for unforeseen situations.
- Gershenson, C. (In Press). Facing Complexity: Prediction vs. Adaptation. To be published in Martorell, X. & Massip, A. (Eds.) Complexity and Language.
- Full paper at http://arxiv.org/abs/1112.3843
- Versión en español en http://arxiv.org/abs/0905.4908
- Gershenson, C. (In Press). Facing Complexity: Prediction vs. Adaptation. To be published in Martorell, X. & Massip, A. (Eds.) Complexity and Language.
- Full paper at http://arxiv.org/abs/1112.3843
- Versión en español en http://arxiv.org/abs/0905.4908
http://complexes.blogspot.co.uk/2008/11/new-book-complexity-5-questions.html
CARLOS GERSHENSON :COMPLEXITY: DESIGNING COMPLEX SYSTEMS
Language
One of the main obstacles to adopt a novel scientific paradigm is our language. The way in which we speak, write, and describe things determines how we understand them. Newtonian dogmas find their roots in Platonic and Aristotelian language.
In the Greco-Latin worldview, which has dominated “western” cultures, one absolute truth is assumed. From this perspective, the mission of science is to “discover” the truths of the world. This presupposition becomes evident in classical logic, which includes the principle of the excluded middle (something is true or false, but not something else) and the principle of non-contradiction (something cannot be true and false at the same time). Classical logic, as well as traditional science, has been very useful, especially in closed systems.
Nevertheless, the truth of any proposition depends on its context (Gershenson, 2002b). This fact can be generalized from Gödel’s (1931) incompleteness theorem. Gödel proved that in any formal system, such as mathematics, there are statements that cannot be proven. The root of this “problem” lies in the fact that axioms of a formal system cannot be proven from within that system, precisely because axioms are presupposed. This is relevant, because if axioms change, statements can change their truth value. For example, the statement “parallel lines never intersect” is true within Euclidean geometry. In fact, this is one of its axioms. However, there are other geometries, which do not consider this axiom, in which the statement is false, since parallel lines do intersect at the infinite. This can be visualized projecting the plane on a (Riemann’s) sphere: if two parallel lines are projected on a sphere, these intersect on the opposite side of the sphere. This condition of formal systems leads to the “silly theorem problem”: for any silly theorem (e.g. 1+1=10), there are infinite sets of axioms for which the silly theorem is true (e.g. use base 2). However, in practice this problem is trivial, because experience tells us which axioms are useful. Nonetheless, it should be noted that there is no set of “true” axioms. There are axiom sets over which formal theories can be based. Depending on the uses of the formal theory, others can be chosen. For example, Boolean algebra can be based on a single axiom (Wolfram, 2002). Still, proving theorems based on a single axiom can be more complicated that with other axiomatic systems.
Another example can be seen with Newton’s laws, which were considered absolute truths, rulers of the universe. Still, at very small or very large scales, they do not apply. It is not that they are “wrong”. Newton’s laws apply to a certain context, and their common usage demonstrates their efficacy.
Within language, people have attempted to expel ambiguity by formalization, e. g. Tarski (1944). However, language is by nature ambiguous. It is better to understand contradictions (Priest & Tanaka, 1996; Gershenson, 1999) than ignoring them.
The limits of our descriptions can be illustrated with the following example. Assume there is a sphere, half white and half black. If the sphere can be seen only from one perspective, actually a circle will be perceived. Of which color is the circle? The answer will depend on the perspective from which the sphere is observed. The circle might be white, black, half and half, 10% white and 90% black, etc. (See Figure 3).
Of which color is the circle? The “right” answer will change depending on the perspective of the observer. Averaging answers will not be closer to the “truth”, since it is highly probable that there are more observers from certain perspectives and less from others. In this case, we know beforehand that we are describing a sphere, not a circle, and that the sphere can be rotated and examined from a multitude of perspectives. However, all phenomena that we describe can have more and more features and dimensions.
One of the main obstacles to adopt a novel scientific paradigm is our language. The way in which we speak, write, and describe things determines how we understand them. Newtonian dogmas find their roots in Platonic and Aristotelian language.
In the Greco-Latin worldview, which has dominated “western” cultures, one absolute truth is assumed. From this perspective, the mission of science is to “discover” the truths of the world. This presupposition becomes evident in classical logic, which includes the principle of the excluded middle (something is true or false, but not something else) and the principle of non-contradiction (something cannot be true and false at the same time). Classical logic, as well as traditional science, has been very useful, especially in closed systems.
Nevertheless, the truth of any proposition depends on its context (Gershenson, 2002b). This fact can be generalized from Gödel’s (1931) incompleteness theorem. Gödel proved that in any formal system, such as mathematics, there are statements that cannot be proven. The root of this “problem” lies in the fact that axioms of a formal system cannot be proven from within that system, precisely because axioms are presupposed. This is relevant, because if axioms change, statements can change their truth value. For example, the statement “parallel lines never intersect” is true within Euclidean geometry. In fact, this is one of its axioms. However, there are other geometries, which do not consider this axiom, in which the statement is false, since parallel lines do intersect at the infinite. This can be visualized projecting the plane on a (Riemann’s) sphere: if two parallel lines are projected on a sphere, these intersect on the opposite side of the sphere. This condition of formal systems leads to the “silly theorem problem”: for any silly theorem (e.g. 1+1=10), there are infinite sets of axioms for which the silly theorem is true (e.g. use base 2). However, in practice this problem is trivial, because experience tells us which axioms are useful. Nonetheless, it should be noted that there is no set of “true” axioms. There are axiom sets over which formal theories can be based. Depending on the uses of the formal theory, others can be chosen. For example, Boolean algebra can be based on a single axiom (Wolfram, 2002). Still, proving theorems based on a single axiom can be more complicated that with other axiomatic systems.
Another example can be seen with Newton’s laws, which were considered absolute truths, rulers of the universe. Still, at very small or very large scales, they do not apply. It is not that they are “wrong”. Newton’s laws apply to a certain context, and their common usage demonstrates their efficacy.
Within language, people have attempted to expel ambiguity by formalization, e. g. Tarski (1944). However, language is by nature ambiguous. It is better to understand contradictions (Priest & Tanaka, 1996; Gershenson, 1999) than ignoring them.
The limits of our descriptions can be illustrated with the following example. Assume there is a sphere, half white and half black. If the sphere can be seen only from one perspective, actually a circle will be perceived. Of which color is the circle? The answer will depend on the perspective from which the sphere is observed. The circle might be white, black, half and half, 10% white and 90% black, etc. (See Figure 3).
Of which color is the circle? The “right” answer will change depending on the perspective of the observer. Averaging answers will not be closer to the “truth”, since it is highly probable that there are more observers from certain perspectives and less from others. In this case, we know beforehand that we are describing a sphere, not a circle, and that the sphere can be rotated and examined from a multitude of perspectives. However, all phenomena that we describe can have more and more features and dimensions.
One can never state that a phenomenon has been described completely, since our perceptions and descriptions are limited and finite. But one can always encounter in natural phenomena novel properties, interactions, relations, and dimensions. Just like with the sphere, we cannot describe completely any phenomenon, since our descriptions are limited and phenomena are not.
Figure 3. What is the color of the circle? It depends on the perspective from which the sphere is observed.
Does this imply that all hope of understanding the world should be abandoned? Certainly not. But we should be aware that our descriptions, if they are “correct”, they would be so only within a determined context. There is no risk of “wild subjectivism”, since our contexts are socially constructed. In other words, we reach agreements. What should be accepted is that there are no absolute truths, that the world changes, that our descriptions of the world also change, and that these changes have a limited predictability. We should take advantage of this dynamism instead of ignoring it or hopelessly trying to get rid of it.
Another example can be seen with colors. The color of an object can change depending on the illumination under which it is observed. In darkness, all objects are black. Behind rosy lenses, all objects are of a rose hue. Again, there is no risk of “radical relativism”, because even when there might be more than one description for the same phenomenon, we can agree on the context under which the phenomenon is described and decide over its properties under a shared context. This leads us to reflect over the difference between the model and the modeled.
The model and the modeled
Plato’s myth of the cavern illustrates the presuppositions and aspirations of classical science, which are embedded in our language as well. Plato describes a cavern, where people are chained and can only see a wall. Behind them, different objects are found, which project their shadow on the wall. People can only see shadows. Plato writes that these people fool themselves, since they do not perceive reality. Philosophy (and later science) is the method to discover the truth. Philosophers can break their chains and see the reality in full color outside the cave, not only shadows.
Before going further, a distinction between the model and the modeled should be made. Models are descriptions of modeled phenomena. As such, models depend on the observer. Since there are no observations independent of observers, nor descriptions independent of a describer, there cannot be a
Figure 3. What is the color of the circle? It depends on the perspective from which the sphere is observed.
Does this imply that all hope of understanding the world should be abandoned? Certainly not. But we should be aware that our descriptions, if they are “correct”, they would be so only within a determined context. There is no risk of “wild subjectivism”, since our contexts are socially constructed. In other words, we reach agreements. What should be accepted is that there are no absolute truths, that the world changes, that our descriptions of the world also change, and that these changes have a limited predictability. We should take advantage of this dynamism instead of ignoring it or hopelessly trying to get rid of it.
Another example can be seen with colors. The color of an object can change depending on the illumination under which it is observed. In darkness, all objects are black. Behind rosy lenses, all objects are of a rose hue. Again, there is no risk of “radical relativism”, because even when there might be more than one description for the same phenomenon, we can agree on the context under which the phenomenon is described and decide over its properties under a shared context. This leads us to reflect over the difference between the model and the modeled.
The model and the modeled
Plato’s myth of the cavern illustrates the presuppositions and aspirations of classical science, which are embedded in our language as well. Plato describes a cavern, where people are chained and can only see a wall. Behind them, different objects are found, which project their shadow on the wall. People can only see shadows. Plato writes that these people fool themselves, since they do not perceive reality. Philosophy (and later science) is the method to discover the truth. Philosophers can break their chains and see the reality in full color outside the cave, not only shadows.
Before going further, a distinction between the model and the modeled should be made. Models are descriptions of modeled phenomena. As such, models depend on the observer. Since there are no observations independent of observers, nor descriptions independent of a describer, there cannot be a
“direct” access to phenomena. Just by tagging them with a name, we are simplifying them to a description, a generalization, a model. This implies that even “breaking the chains”, what people will see outside Plato’s cave will not be the reality. It will be a different description of reality. It cannot be proven that this or any other description is the “correct” one, since the usefulness of descriptions depends on the purpose for which they are used. In other words, the only we can perceive is “shadows”.
Humanity has always aspired for perfection. In science, this translates into seeking absolute truths. In engineering, this translates into faultless systems. We should admit our limits, our lack of perfection, and that our engineered systems are also limited and imperfect. These limits are natural and inherent, not a defect, since infinite potentialities cannot be contained within our finitude.
Humanity has always aspired for perfection. In science, this translates into seeking absolute truths. In engineering, this translates into faultless systems. We should admit our limits, our lack of perfection, and that our engineered systems are also limited and imperfect. These limits are natural and inherent, not a defect, since infinite potentialities cannot be contained within our finitude.
