A case for lattice schemes in fundamental physics

Philosophy

A synthesis of trending topics in pancomputationalism.  I introduce the notion that "strange loops" engender the most atomic levels of physical reality, and introduce a mechanism for global non-locality.  Writen in a simple and accesssible style, it seeks to draw research in fundamental physics back to realism, and have a bit of fun in the process.

A case for pursuing Lattice Schemes in Fundamental Physics, by Rowan Grigg Research has shown that many of us hold intuitive beliefs about the way physical systems behave, which turn out to be contrary to reality.i For example, subjects are given a depiction of a billiard ball being drawn in an arc across a table. Asked what happens when the ball is released, some have the ball continuing along the arc, while others have the ball proceeding in a straight line tangential from the arc. From as early as Zeno in the 5th century BCE, we have known intuitively that for any division of one, 1 , there will always be a fraction, 1 ( + 1) , that is smaller. This general idea has been rigorously formalized in the Continuum Hypothesis, a proposal that the real number line is infinitely divisible.1 Yet since Leucippus, a contemporary of Zeno, we have intuitively recognised that any division of matter should eventually arrive at fundamental particles which cannot be divided any further. Mathematics has been routinely and effectively used to model physical systems, yet unreasonably so, for since Zeno and Leucippus, our most primitive assumptions about mathematics have been in fundamental disagreement with our most basic assumptions about matter. General Relativity (GR) is a so called 'classical' theorem, for it assumes a direct correlation between mathematics and the physical world. GR suggests that both space and time, like the real number line, are infinitely divisible, and just as in division of real numbers by zero, GR too breaks down when the dimensions of space and time fall to zero at the 'singularity', predicted by GR to have been the starting point of the universe. In an attempt to incorporate GR within Quantum theory, many researchers are considering the possibility that time and space are not continuous, but rather arise in discrete 'quanta'.ii We have long known the scales at which GR and Quantum theory should theoretically merge. Max Planck simply substituted his equations within those of Einstein, from which emerged fundamental units, among them the Planck length and the Planck time. The Planck length (~10-35 metres) is the distance light travels in a vacuum in one interval of Planck time (~10-43 seconds), so that in 1043 Planck intervals (1 second), light travels 10-35.1043 metres or 108 metres. In the theory of Quantum Loop Gravityiii, space itself is thought to consist of 'atomic' spheres of space each having a diameter of one Planck length. The GR model is now being thought of as having been a useful approximation to what is a fundamentally quantized reality. Our ancient intuition of reality's discrete quantization is thus winning favour over our equally ancient intuition of a mathematical continuum. Yet we have known since its inception that the Quantum model is also incomplete, for it can only predict the probabilities, rather than the actuality, of matter's behaviour, and it is unable to decouple the 'observer' from objective external reality. At the time Quantum theory was introduced, physicists still held great hope for discovering what the philosopher Emanuel Kant called "the thing in itself" – discovering what physical reality actually is, rather than merely learning how to effectively model its behaviour. This hope has however been 1 Formally, the hypothesis states that there is no intermediate cardinality between the set of rational numbers and the set of real numbers. consistently dashed by experiments which have unequivocally demonstrated non-locality.iv Entangled particles, separated from each other in space and time, influence each other faster than a signal travelling at the speed of light could be passed between them. Quantum theory, in its most commonly followed guise, implies that objects at the farthest reaches of space can (somehow) exchange information with each other instantaneously, in apparent violation of Special Relativity. The prospect of returning to realism emerged in the late 1960s with the publication of Calculating Spacev by computing pioneer Konrad Zuse. Zuse proposed that reality was comprised of machines which he called 'cellular automata'. He envisaged all material reality to be a cubic lattice of these cellular automata, each one connected to its neighbours on all sides. Displays such as those seen at the opening of the Beijing Olympics provide a useful illustration of his idea. Participants are arrayed across an arena, each holding a selection of coloured cards, one of which they raise above their heads at any given time. Each person is responsible for just one element of the two-dimensional composite picture that emerges above them. For the purpose of the display, each person assumes the role of a cellular automaton. The music playing in the arena provides a universal 'clock' that precisely synchronizes the ongoing changes in the display. If, for example, a blue 'dot' needs to move across the picture from left to right, a simple rule would be for each automaton to get its cue for the next pixel from its current neighbour to the left. Then with each beat of the music, the dot would proceed smoothly across the display. One can imagine providing each automaton with a simple set of rules to follow on each beat, also taking into account its neighbours to the front, back and right, such that intricate and unique patterns emerge. If such a system is extrapolated out into three dimensions, Zuse suggested that cellular automata could generate complex and unique realities, such as that which we now inhabit, rather than merely their representations. We must ask however, what are these 'cellular automata' themselves made of, where are they, and where did their rules of engagement come from, just as we might ask what atoms are made of, or where the laws of Nature come from. Ed Fredkin, long time champion of 'computational physics', argues that the 'automata' are constructed out of an abstract substance he calls 'pure information'.vi Stephen Wolfram avoids the issue of a substrate altogether, for he does not see cellular automata and their interactions as an actuality, somehow lurking behind our perceived reality. Rather, in his "New Kind of Science", he employs the theory of cellular automata as an analytical tool for merely modelling reality, just as mathematics is employed for more conventional modelling of physical systems.vii Max Tegmark however, like Fredkin, wants to know what Kant claimed we can never know – what we are ultimately made of. In his "Ultimate Ensemble", he argues that physical reality is not merely modelled by mathematics, but that physical structures and mathematical structures are one and the same thing – reality is made of mathematics, just as Fredkin's world is made of information.viii This is an attractive idea, for we can easily see what mathematics is (an abstract series of relationships), and just as easily see that all of mathematics in itself has no material substance. Thus in Tegmark's scheme, we have something (physics) which is constructed out of nothing (mathematics). Tegmark argues further that the universe is composed entirely of mathematical structures which are computationally decidable. The concept of computability arose out of Alan Turing's work on a scheme for algorithmically generating mathematical relationships, and then deciding if those relationships were valid.ix His imaginary 'machines' could compute each candidate function for as long as it took to decide its validity. Functions which are both computable and decidable are vital to a quantized model of reality, because like quanta themselves, these functions are finite. The entire computation of such functions, as well as the Turing machines that compute them, can be represented by a finite string of binary digits, and ultimately by a single integer – a Turing machine is fundamentally an abstraction. Turing discovered that a particular class of his machines were 'universal' – a Universal Turing machine could simulate any other Turing machine including itself.2 Such machines have since become a practical reality – today's general purpose computers. Nick Bostrom has argued that the substrate of our reality, for example the 'cellular automata' of Zuse's lattice scheme, is in fact a much larger computer that lies outside our perceived reality.x The drawback of this idea, a darling of science fiction, is that it merely shifts the substrate of existence back one step. We are left wondering what the "big" computer itself is made out of. This notion does however provide a useful framework for thinking about computer simulation, as does its practical application in the virtual 'realities' that now pervade the Internet.3 Putting aside the simulation of the entire universe, consider just one of Zuse's cellular automata. If the automaton is a Turing machine, then it is a 'computer' capable of simulating all the properties – vacuum energy, gravitational potential, and so on – of a single atom of space, a sphere with a diameter of 10-35 metres. The machine is not 'contained' inside this sphere, nor does it occupy any other volume of space, because space itself does not come into existence until the automaton simulates it. What then is the automaton? The automaton is itself a virtual machine that is being simulated by another automaton. And what then is this automaton? It too is being simulated by an automaton, but none other than the original automaton. The idea of this self-referential loop (known as a "strange loop") is superbly illustrated in the famous M.C. Escher woodcut "Drawing Hands". In the physical world, of course, such a scheme would represent perpetual motion and be thermodynamically outlawed. However, these machines are not part of the physical world, but rather belong to the abstract world of mathematics, which is removed from physical law – these machines are initiating the very existence of physical law itself. Each machine is processing a string of binary digits in a "desultory manner" (as Turing originally described it), and in so doing is simulating the other machine, which is an (identical) string of binary digits. Because the strings are finite in length, the process of stepping through each computation represents a cycle which returns to its starting point in a finite period. This then is the automaton's internal 'clock', the fundamental quantum of time, or 10-43 second in absolute terms. Constructed from pure mathematics, we have then generated both a fundamental quantum of space, AND a fundamental quantum of time. If we return to our stadium in Beijing, we can see that the clock signal (the beat of the music) is delivered to each participant at the speed of sound, practically at the same time. It is not practical however to deliver a simultaneous master clock signal throughout the universe, due to the limiting speed of light. So instead, each element of space 2 These can be extremely simple, for example the recently discovered 2-state 3-colour Turing machine described at http://www.wolframscience.com/prizes/tm23/ 3 eg. http://secondlife.com/ (automaton) references its own internal clock, running at a frequency of 1043 Hz. The much coarser 'atomic' clocks that are routinely used in navigation and communication are based upon physical phenomena, and are subject to significant frequency 'drift'. The internal clock of the 'space' automaton however arises from a non-physical computation, and is immune from drift. Thus all space automata across the breadth of the universe remain precisely and indefinitely synchronised with each other. We can see from this model why the speed of light should be a limiting speed. Let us suppose that a photon of light is likewise a simulated phenomenon, and that its simulation is enacted through a modified computational state in one of these 'space' automata, like the blue dot moving across a sea of white in the Olympic stadium. We presume that the automaton has an input/output interface that can communicate the system state "photon" over to its neighbour, and then change its own state back to "vacuum", within each clock cycle. If we were to line up 1043 of these automata circumference-to-circumference in a straight line, we can see how a photon "state" could be passed along this 108 metre long "bucket brigade" of automata over the course of one second. In this model, the photon is not a wave/particle "object" that makes its way through empty space. Instead, the photon is a computational state that gets passed along a 'solid' pathway of simulated space atoms. A photon, or any other simulated phenomenon, cannot propagate from one space atom to the next in any less than one fundamental clock cycle at a time. However one can consider computational states that take more than one clock cycle to be translated across space, and hence propagate at speeds below the speed of light. A macroscopic object, such as a proton coupled to an electron, might be enacted through the altered computational states of an agglomerated network of space atoms.4 This agglomeration of states could likewise propagate (as a whole) through a fixed lattice of space atoms, but at a speed fundamentally limited by the diameter and internal clock frequency of the space atoms that are hosting it. Let's suppose that this hydrogen atom 'state' is translating through the lattice of space atoms at some (necessarily sub-luminal) speed. If the energy state of the electron sub-system changes and a photon state is exported, we can see that the photon state will intrinsically propagate away from the hydrogen atom state, along the frame of the lattice, at precisely the speed of light, despite any existing vector of the hydrogen atom state it was sourced from. However, the existing vector of the hydrogen atom state may very well alter the registered energy (colour) of the exported photon state. The lattice in such proposals returns us to the Newtonian perspective of an absolute frame. Relativistic effects then emerge from the interactions between the various computational states of the automata that comprise the fixed space-time lattice. Clearly (experimentally) a state such as that representing a photon will routinely be diverted from a straight path, following on from the exchange of information with gravitational states (gravitons) that it encounters during its translation through the lattice. Inertia is explained simply as the endless and desultory processing, in the absence of any intervening input, of an object's computational states, as they are transferred between the individual automata of the lattice. With astonishing prescience, Newton tried (albeit unsuccessfully) to develop a theory of gravity avoiding non-locality in which "tiny invisible jiggling particles fill all of seemingly empty space"xi 4 The computational equivalent of the Wave Equation Where then does the lattice come from? In the 1940s John von Neumann proposed a 'universal replicator', a type of cellular automaton that can replicate itself.xii The code of the space automaton is modified so that in each computational cycle, it produces a new automaton. In this scheme, there is an exponential expansion in the number of extant automata once the replication code is enacted. Indeed, some 2 such automata would be produced in the first second of the universe's existence. If these atoms of space are close packed, like stacked oranges at a fruit market, then the universe we currently observe (with a radius of ~45 billion light years) would contain a mere 10185 such atoms – our visible neighbourhood would be a very small speck indeed, of the totality. Because each and every new atom of simulated space replicates itself in each clock cycle, the nascent universe inflates uniformly in all directions from every point within it. The initial creation of space 'atoms' would be a turbulent process, so that space itself would behave like a gas, and have a 'temperature'. The emerging space atoms would behave like ping-pong balls bouncing around in a lottery number generator. The surrealist Salvador Dali perhaps anticipated such an atomic lattice of spheres in his famous painting "Galatea of the Spheres". Through the seeding of code that acts to halt this replication, regions then form where the 'temperature' of space drops to an absolute minimum, an equilibrium that will later encompass super clusters of galaxies. In these regions, additional space is no longer being produced, so that the quanta of space bind to become the smooth, flat and rigid foam that we encounter in our local region. The regions between the galactic super clusters may however continue to produce new space automata, acting to push the super clusters apart. If the automata that encode the lattice, and encode the realities that emerge from it, are merely strings of binary digits, where did the initial arrangement of the digits come from? It is manifest that the code responsible for the laws of physics, and the evolution of the universe as we now experience it, is not trivial code. However, Jürgen Schmidhuberxiii, following on from work on algorithmic compressibility by Andrey Kolmogorov and Gregory Chaitin, has shown that the code to generate all possible automata is simpler than the code which generates one specific automaton such as the type which is simulating our local milieu. This 'optimally compact' code produces all possible universes (including those like our own universe that have the property of actually "working"). Raw binary states (strings of binary digits independent of any substrate hardware) could randomly assemble into this seminal configuration from which all other possible configurations then emerge. There is a finite probability that this initial combination will obtain, for time itself does not come into being until the basic clock of a self-simulating string pair first ensues. Each automaton does not 'occupy' the space lattice; each merely defines one cell within the lattice. The strings of binary digits that comprise the automata do not have any dimension in space. Likewise, the starting point of this universe, and any universe which has extent in space, is a singularity which has no extent in space. Thus the automata that define our universe, and any other universe, all 'exist' at one and the same 'place', the singularity. We usually think of effects being translated across the lattice of space, as we have seen experimentally, at speeds up to the limiting speed of light. However, if these automata can interface with each other, then they can presumably do so directly 'across' the point of the singularity. Any element in the universal space lattice can therefore instantaneously communicate with any other element. We thus have a mechanism for effects to be non-local in the context of space (simulated length), but local (to within one clock cycle of simulated time) in the context of the singularity. This prospective space-time lattice, and its implications, remains highly speculative. The challenge before us is to develop a method of interfacing directly with the code of the automata, so that we can 'read' the code, interpret the code, and potentially (carefully) 'write' back modified code. The obvious candidate programme for developing such an interface is our research into quantum computing – the ultimate "superposition" of quantum states, as we have just seen, is that of all automata at the universe's singularity. Obviously no other civilization in our universe has yet written back code that causes the universe to evaporate – the code we are currently running on probably prevents such an event. Any candidate universes whose code was not well protected would have long since halted and thus been discounted from the pool of viable universes, for it is certain that any such exposure in the code would be exploited. If we were to learn how to access the singularity, then the prospect emerges for us to visit not just the solar system or the galaxy, but any corner of this universe, or any other universe, without ever getting up from our living room, as all these realities share that singularity in common. We should view emerging relationships between mathematics and physics, such as the 'E8 Lie group' correspondences recently discovered by Garrett Lisi, as guiding us to the underlying operational codexiv. It is inevitable that the mathematics to which we have access are a subset of the computable functions that gave rise to our universe. It is possible that the mathematics itself has been produced by computing automata. It is of course also possible that more advanced civilizations than ours have already learnt how to access the data at the singularity, and have long since been monitoring our progress towards the same. For Carl, 1934-1996 i McCloskey, M (1983) "Intuitive Physics", Scientific American, April, pp114–123 ii Bojowald, M (2008) "Follow the Bouncing Universe", Scientific American, October, pp28-33 iii Ibid. iv Albert, D Z and Galchen, R (2009) "A Quantum Threat to Special Relativity", Scientific American, March, pp2633 v Zuse, K (1969) "Calculating Space", MIT Technical Translation AZT-70-164-GEMIT, MIT (Proj. MAC), Cambridge, Mass. 02139, Feb. 1970. vi Wright, R (1988) "Did the Universe just happen?", The Atlantic Monthly, April. vii Wolfram, S (2002), "A New Kind of Science", Wolfram Media, Inc. viii Tegmark, M (2007) "The Mathematical Universe", http://arxiv.org/pdf/0704.0646 ix Turing, A M (1936), "On Computable Numbers, with an Application to the Entscheidungsproblem", Proc. London Math. Soc. (2) 42, pp230-65 x Bostrom, N (2003), "Are you living in a Computer Simulation?", Philosophical Quarterly, Vol. 53, No. 211, pp243-255. xi Albert, D Z and Galchen, R (2009) "A Quantum Threat to Special Relativity", Scientific American, March, pp2633 xii Burks, A W (1966), "Theory of Self-Reproducing Automata" xiii Schmidhuber, J (2007), "All Computable Universes", Spektrum der Wissenschaft, March Special "Is the Universe a Computer?", pp75-79. xiv Lisi, A G (2008), "An Exceptionally Simple Theory of Everything", http://arxiv.org/abs/0711.0770v


A Morphology of Theories of Emergence

Philosophy

âEmergenceâ â the notion of novel, unpredictable and irreducible properties developing out of complex organisational entities â is itself a complex, multi-dimensional concept. To date there is no single, generally agreed upon âtheory of emergenceâ, but instead a number of different approaches and perspectives. Neither is there a common conceptual or meta-theoretical framework by which to systematically identify, exemplify and compare different âtheoriesâ. Building upon earlier work done by sociologist Kenneth Bailey, this article presents a method for creating such a framework, and outlines the conditions for a collaborative effort in order to carry out such a task. A brief historical and theoretical background is given both to the concept of âemergenceâ and to the non-quantified modelling method General Morphological Analysis (GMA).

Acta Morphologica Generalis AMG Vol.3 No.3 (2014) © Swedish Morphological Society ISSN 2001-2241 On a Morphology of Theories of Emergence Tom Ritchey Swedish Morphological Society Abstract: "Emergence" – the notion of novel, unpredictable and irreducible properties developing out of complex organisational entities – is itself a complex, multi-dimensional concept. To date there is no single, generally agreed upon "theory of emergence", but instead a number of different approaches and perspectives. Neither is there a common conceptual or meta-theoretical framework by which to systematically identify, exemplify and compare different "theories". Building upon earlier work done by sociologist Kenneth Bailey, this article presents a method for creating such a framework, and outlines the conditions for a collaborative effort in order to carry out such a task. A brief historical and theoretical background is given both to the concept of "emergence" and to the non-quantified modelling method General Morphological Analysis (GMA). Keywords: Emergence, general morphological analysis; theories of emergence, typology of emergence, modelling theory. "...a perpetual and unrestricted progress of the universe as a whole must be recognized, such that it continually advances to a higher state of being." G. W. Leibniz, De rerum originatione radicali, 1697 "...the universe is a process for breeding novel phenomena and states of organization, which will forever renew itself as it evolves to states of ever higher complexity and organization." Lee Smolin, Time Reborn, 2013. 1. Introduction The doctrine of emergence states that new properties, in the form of new types of behaviour, new entities and even new forms of lawfulness, can "emerge" out of complex organisational systems; and that these properties cannot be predicted from, nor reduced to, the properties of the components making up the system. This is expressed in the well-known (and well-worn) aphorism: "The whole is more than the sum of its parts". The general idea of emergence is as old as rational science itself. Its basic concept was acknowledged by both Plato and Aristotle, and it was one of the principles of neo-Platonism, both in its earlier versions (e.g. Plotinus) and its later Renaissance versions. It lay at the foundations of the German ("Eastern") Enlightenment and was "naturalised" by the British in the 1920's. The latest round of scientific and philosophical discussions concerning emergence came to life (or re-emerged, as many enjoy putting it) in the 1980's with developments in the areas of complex adaptive systems, computational modelling, theoretical biology (anticipatory systems), sociocybernetics and theories of mind and consciousness. Along with this came a new interest in the philosophical (and ontological) issues involved. T. Ritchey / Acta Morphologica Generalis Vol. 3. No. 3 (2014) _________________________________________________________________________________________ 2 The current literature on emergence theory is extensive and there is no need here to present more than a short summary explanation of the concept itself. Except for the deplorable state of Anglocentric histories of the development of the concept of emergence * , interested readers can find excellent presentations in two anthologies: Clayton & Davies (2006) is a set of 14 articles written by contemporary researchers; and Bedau & Humphreys (2008) is a sourcebook of some 25 "historical" articles written between 1970 and early 2000. Besides covering the central scientific and philosophical issues involved, these articles give a good picture of the diverse views concerning what the notion of emergence actually represents: from nothing more than a "new animist fantasy" to being a central issue for the next scientific revolution. Of course, the cliché "the whole is more than the sum of its parts" will not do; it tells us nothing about what is actually going on. A more in-depth definition of emergence is required. Several have been proposed. Generally, three interconnected issues have been identified (see e.g. Kim, 1999; ElHani & Pihlström, 2002): 1. Property emergence: When systems of objects attain an appropriate level of organizational complexity, genuinely novel (unpredictable) properties can appear at the level of the system as a whole. 2. Irreducibility: Emergent properties are not only unpredictable from, but irreducible to, the lower-level constituents from which they emerge 3. Downward causation: Emergent properties, as higher-level entities, manifest genuinely novel causal powers which affect their lower-level constituents in ways that could not be actualised at the level of the interaction of the constituents themselves. This is also referred to as higher-level or global supervenience (see Paull & Sider, 1992 for a detailed discussion). But this "definition" is just a starter. First of all, there are two general approaches to studying emergent phenomena: the synchronic and the diachronic. The synchronic approach studies the emergent properties of a given system here and now. It does not concern itself with how these properties, or the system that embodies them, came into existence or evolved over time. For instance, the study of the already existent phenomenon of mind as an emergent property of the brain represents a synchronic approach. This was put forward, for example, by Sperry (1983). The diachronic approach studies the development of emergent properties over time, i.e. as an evolutionary process (and thus is called evolutionary emergence). For instance, how human (selfreflexive) consciousness emerged in the development of homo sapiens over the past million is an example of the diachronic approach. At this point in time, these two approaches are not (conceptually) integrated. Another issue is the question of just how much emergence is actually going on. For instance, Morowitz (2004) – in his aptly titled book The emergence of everything – sees it literally everywhere, from the large scale structure of the universe, to language and the concept of God. At the other end of the spectrum is the Australian philosopher and consciousness scientist David Chalmers (2006), who only recognizes one "real" or genuine case: the emergence of reflexive selfconsciousness from the human brain. Similarly, Vladimir Vernadsky (1986, 2007), the Ukrainian geo-biochemist working in the 1920's and 30's, concentrated on the "two great emergent events": the emergence of the biosphere from the geosphere, and the emergence of the noösphere from the biosphere. * This deserves an article in itself. While Anglo-Saxon histories make it clear that there is no room for emergence in the mechanical, clock-work world of the British Enlightenment (essentially based on the Locke-Newton program), these histories are written as though G.W. Leibniz never existed, and as though the German Aufklärung (the "Eastern Enlightenment") never took place. Not only did the German version of the Enlightenment accommodate emergence; it was essentially based upon the idea. Furthermore, there is seldom any mention of the fact that the purported British "founders" of emergence – J.S. Mills and G.H. Lewes – freely admit that they were directly influenced by the writings of the German emergentists Herder and Goethe. Indeed, what Anglo-Saxon science did with these classical German scholars fully justifies Janik & Toulmin's (1996) statement: "... one of the gravest misfortunes that can affect a writer of great intellectual seriousness and strong ethical passions is to have his ideas 'naturalized' by the English" (p.19). T. Ritchey / Acta Morphologica Generalis Vol. 3. No. 3 (2014) _________________________________________________________________________________________ 3 These different attitudes to what is, and what is not, to be considered real or genuine emergence brings us to perhaps the fundamental issue – the great divide – in modern emergence theory, i.e. the ontological status of emergence. The great divide is between what has come to be called "strong" vs. "weak" theories. Strong theories of emergence (a.k.a. ontological emergence) regard emergent properties and "downward causality" (higher-level supervenience) as ontologically real, representing genuinely new causal agents and processes. Sperry's (1983) concept of consciousness as a non-reducible property and a causal agent having downward influence over cerebral function is an example of strong emergence. Weak emergence (a.k.a. epistemological emergence) regards emergence as a methodological issue only, i.e. that all causality "really" only comes from below, i.e. from the physical substrate. Certain higher-level phenomena may be unexpected, but that is because we lack the requisite knowledge and scientific methods to rigorously account for these emergent phenomena. In principle, however, they are completely deducible from laws concerning the lower-level (material) domain from which they have emerged. One may ask if there is any practical issue involved in this theoretical divide: if both sides of the argument are willing to accept the phenomena of emergence, what does it matter? It matters immensely. Although there are certainly different shades of weak emergence, in both the early (1920's) British Emergentists (see e.g. Alexander, 1920; Morgan, 1923; Board, 1925; Whitehead, 1929) and contemporary texts (especially from the natural sciences), the essentials are clear: to the extent that such weak theories see emergence simply as a sign of our (i.e. science's) ignorance concerning how to correctly apply reductionist methods to higher levels of organisation, then it is but an updated version of the traditional empiricist-reductionist program: you accept the phenomenon of emergence, but essentially deny its "reality". As Herbert Simon (1996, p.171) points out, "... this weak form of emergence poses no problems for even the most ardent reductionist." Strong emergence, on the other hand, has profound consequences for science and the understanding of nature: "Strong emergence has much more radical consequences than weak emergence. If there are phenomena that are strongly emergent with respect to the domain of physics, then our conception of nature needs to be expanded to accommodate them. That is, if there are phenomena whose existence is not deducible from the facts about the exact distribution of particles and fields throughout space and time (along with the laws of physics), then this suggests that new fundamental laws of nature are needed to explain these phenomena. (Chalmers, 2006, p 245.) "...if we are correct about macro-determination or 'emergent determination' ... [then] the result is a vastly transformed scientific view of human and non-human nature." (Sperry, 1986, p 269, cited in McLaughlin, 2008.) Despite this basic dichotomy, the one thing that most would agree upon is that the notion of emergence itself is a complex, multi-dimensional concept; and that, to date, there is no single, generally agreed upon theory of emergence. Instead there are many variations of such theories. In addition, there seems to be no common meta-theoretical framework by which to systematically identify, exemplify and compare such different theories. This article proposes a method for initiating the development of such a meta-theoretical framework. It is built upon earlier work done by Kenneth Bailey, Professor of Sociology (retired) at the University of California at Los Angeles (U.C.L.A.). Bailey's work on the classification of theories of emergence was done in the area of social systems and sociocybernetic theory. However, we feel that the concepts he treated in this area are expressed at a level of abstraction that make them relevant, as least as a starting point, to theories of emergence generally. T. Ritchey / Acta Morphologica Generalis Vol. 3. No. 3 (2014) _________________________________________________________________________________________ 4 This article is divided up into the following sections: Section 2 presents Bailey's earlier typological analysis of emergence as concerns social systems. Section 3 gives a short background to General Morphological Analysis (GMA), for those readers who are new to this area. Section 4 presents an outline for the development of a meta-theoretical framework for theories of emergence, in the form of a morphological inference model. 2. A Typology of Theories of Emergence In 2006, Kenneth Bailey, Professor of Sociology (now retired) at U.C.L.A. presented a paper at the International Sociological Association XVI World Congress in Durban titled: "A Typology of Emergence in Social Systems and Sociocybernetic Theory" (Bailey, 2006). There he pointed out that although there is a general consensus within social systems theory that emergence is an important concept, there is a wide variety of descriptions of this concept in the literature. These different descriptions (or perspectives) derive from the fact that emergence is a multidimensional concept, and that researchers differ in their approach to this concept in two ways: 1) what types of dimensions they use in order to define the problem space of the concept, and 2) how they position themselves with respect to the issues implicit in those dimensions. Ken Bailey has been a leading figure in modern typology theory, in a direct line from Lazarfeld (1937, 1951) and McKinney (1969). Thus it was natural for him to approach this problem from the standpoint of typology analysis: "Perhaps the best way to adequately present and analyze all of the dimensions of emergence is through a typology. The purpose of this paper is to construct this typology. The typology will subsequently be used as a mechanism for recognizing and analyzing the various types of emergence that exist in contemporary social systems theory and socio-cybernetics, with the aim of ultimately eliminating much of the confusion that now surrounds the concept of emergence." (Bailey, 2006. p. 2) A typology (the Greek word typos originally meant a hollow mould or matrix) is a very simple (usually non-quantified) model based on the possible combinations obtained between a few (often two) variables, each containing a range of discrete values or states. A typology inter-relates a number of "simple" (one dimensional) concepts in order to create and explore the more complex (multidimensional) concepts which are compounded out of these simple concepts. In order to produce a typology of emergence, Bailey substructed a number of already existing theoretical frameworks for the notion of emergence. Substruction – advanced by Lazarfeld (1937) – is the process of examining the attributes of an existing (multidimensional) concept in order to identify and specify its underlying (conceptual) dimensions, which can then be juxtaposed in a typological field in order to find all of the other possible combinations of attributes. Bailey carried out substructions on works by Buckley (1998), Luhmann (1995), Miller (1978) and Mihata (1997), as well as his own work on emergence. Out of these substructions, twelve (binary) factors or parameters were identified for the determination of different conceptions of emergence. (Note: I am using the term parameter here not in its formal mathematical sense, but in its more general, systems science meaning: i.e. one of a number of factors that define a system and determine its behaviour, and which can be varied in an experiment, including a Gedankenexperiment.) T. Ritchey / Acta Morphologica Generalis Vol. 3. No. 3 (2014) _________________________________________________________________________________________ 5 The 12 parameters are: 1. Linear vs. nonlinear 2. Static vs. dynamic 3. Evolutionary vs. Non-evolutionary 4. Ordered vs. Non-ordered 5. Simple vs. Complex 6. Non-hierarchal (two-levels) vs. Hierarchical (>2 levels) 7. Transformational vs. New variable emergence 8. Small vs. Large 9. Old (variable transformation) vs. New (variables emergence) 10. Bottom-up vs. Top-down 11. Aggregative vs. Divisive 12. Non-nested (autonomous) vs. nested (non-autonomous) Twelve binary parameters produce 2 12 = 4096 combinations of attributes which represent possible (formal) frameworks for a theory of emergence. (This does not mean that all of these formal frameworks are logically or epistemologically possible.) However, twelve variables (even if they are only binaries) are too much to treat in a normal (paperbased) typology. "The usual procedure would be to form the 12-dimensional typology through substruction, then to use various forms of reduction to reduce the number of types below 4096. However, given the large number of cells in the full typology, and the fact that the full 12-dimensional typology cannot be presented on a two-dimensional sheet of paper, it behooves us to reduce the number of dimensions before proceeding to the reduction of types". (Bailey, 2006, p. 19.) Bailey proceeds to reduce the number of parameters by searching for collinearity. Simply put, if two parameters, taken from two different research approaches, essentially express the same concept, then they can be fused into a single parameter. Thus by a process of merging similar concepts, Bailey reduces the number of dimensions to four (which is pretty much the comfort-limit for typology construction "on paper"). 1. Non-hierarchal (2-level) vs. Hierarchical (>2 levels) 2. Non-nested (autonomous) vs. Nested (non-autonomous) 3. New variable emergence vs. Old variable transformation 4. Bottom-up emergence vs. Top-down emergence These four binary parameters create 2 4 (=16) type-cells in the typological field (Figure 1). Since the parameters defining this field were substructed from specific concepts of emergence already expressed by different researchers, it is a straight-forward process to plug them back in to their appropriate positions along the four dimensions. Here we see that Bailey has identified seven actual (i.e. currently employed) versions of emergence and hypothesised two (possible) new versions. In addition, there are seven "Not Yet Identified" (NYI) versions. (What is not made explicit here is the question of whether all of these NYIs are, in fact, possible, or, if not, which are logically or epistemologically impossible.) T. Ritchey / Acta Morphologica Generalis Vol. 3. No. 3 (2014) _________________________________________________________________________________________ 6 Figure 1. Bailey's four dimensional typology of emergence reduced from 12 binary parameters (adapted from Bailey, 2006, p.27.) Bailey was compelled to reduce the number of dimensions first, instead of utilising all of the 12 identified (substructed) dimensions and then reducing the number of types through the systematic comparison and evaluation of their attributes. In this case, the pre-reduction was justified, but has a price-tag: unless you are absolutely certain that you have only removed (or merged) dimensions that are essentially identical, then you may have discarded possible versions of theories of emergence, which might have implications for the whole notion of the concept. (I interpret Bailey's text such, that he would have preferred to type the whole 12 dimensional complex, had he had the practical methodological tools to do so.) Computer-aided morphological analysis allows us to comfortably work with 12 binaries. It also has some additional benefits. First of all, it will allow us to (explicitly) make the distinction between 1) identified actual (i.e. currently employed) theories of emergence; 2) "Not Yet Indentified" possible theories of emergence; and, 3) (logically or epistemologically) impossible theories of emergence. Secondly, GMA's Cross-Consistency Assessment (CCA) systematically identifies duplicate and even partially overlapping (non-orthogonal) parameters, thereby allowing for the reduction of dimensions in a methodical and transparent manner, after such parameters have been given their chance, so to speak. Also, with computer support it is possible to delete, merge or add new parameters at any time, without having to back-track and re-evaluate internal consistency. Finally, by identifying all possible (internally) consistent conditions for all possible theories of emergence (at least as these are defined among the attributes of the dimensions employed), the morphological field can be treated as a ("what-if") inference model. This will allow us to posit questions (initial inputs) and obtain answers (outputs) from the model. For instance: given a theory of emergence that is nested and top-down, what are the possible variations of this theory along the other dimensions, and which of these (if any) are logically or epistemologically impossible? T. Ritchey / Acta Morphologica Generalis Vol. 3. No. 3 (2014) _________________________________________________________________________________________ 7 In Section 4, we will put forward a method for accomplishing this task in more detail. First, a short background to General Morphological Analysis (GMA) is presented – for those who are not previously acquainted with this method. 3. Background to General Morphology* The term morphology derives from ancient Greek (morphê) which means shape or form. Morphology is "the study of form or pattern", i.e. the arrangement and connectivity of parts of an object, and how these conform to represent a whole or Gestalt. The "objects" in question can be physical (e.g. an organism or an ecology), social/organizational (e.g. an institution or company), or mental (e.g. linguistic forms or any system of ideas). In Europe, morphological methods were used as early as 1290s by the theologian-logician Ramon Llull (1232-1315) in his Ars magna ("The Ultimate General Art"). Gottfried Leibniz (1646-1715) later developed it into a modern, grounded method in his Ars combinatoria. However, the first to use the term "morphology" as an explicitly defined scientific method would seem to be J.W. von Goethe (1749-1832), especially in his "comparative morphology" in botany. Today, morphology is associated with a number of scientific disciplines where formal structure is a central issue, for instance, in anatomy, linguistics, geology and zoology. In the late 1940's, Fritz Zwicky, professor of astrophysics at the California Institute of Technology (Caltech) proposed a generalized form of morphology, which today goes under the name of General Morphological Analysis (GMA) "Attention has been called to the fact that the term morphology has long been used in many fields of science to designate research on structural interrelations – for instance in anatomy, geology, botany and biology. ... I have proposed to generalize and systematize the concept of morphological research and include not only the study of the shapes of geometrical, geological, biological, and generally material structures, but also to study the more abstract structural interrelations among phenomena, concepts, and ideas, whatever their character might be." (Zwicky, 1969, p. 34) Zwicky developed GMA as a method for structuring and investigating the total set of relationships contained in multi-dimensional, non-quantifiable, problem complexes. He applied the method to such diverse fields as the classification of astrophysical objects, the development of jet and rocket propulsion systems, and the legal aspects of space travel and colonization. He founded the Society for Morphological Research and championed the "morphological approach" from the 1940's until his death in 1974. Morphological analysis was subsequently applied by a number of researchers in the USA and Europe in the fields of policy analysis and futures studies. In1995, advanced computer support for GMA was developed at the Swedish Defence Research Agency (FOI) in Stockholm. This has made it possible to create non-quantified inference models, which significantly extends GMA's functionality and areas of application. Since then, some 100 projects have been carried out using GMA, for structuring complex policy and planning issues, developing scenario and strategy laboratories, and analyzing organizational and stakeholder structures † . Essentially, GMA is a method for identifying and investigating the total set of possible relationships contained in a given problem complex. This is accomplished by going through a number of iterative phases which represent cycles of analysis and synthesis – the basic method for developing (scientific) models (Ritchey, 1991). * For a more detailed presentation, see the JORS article:" Problem Structuring with Computer-Aided Morphological Analysis" at: http://www.swemorph.com/pdf/psm-gma.pdf. † For a list of projects see: http://www.swemorph.com/projects.html T. Ritchey / Acta Morphologica Generalis Vol. 3. No. 3 (2014) _________________________________________________________________________________________ 8 The method begins by identifying and defining the most important parameters of the problem complex to be investigated, and assigning each parameter a range of relevant values or conditions. This is done mainly in natural language, although abstract labels and scales can be utilized to specify the set of elements defining the discrete value range of a parameter. A morphological field is constructed by setting the parameters against each other in order to create an n-dimensional configuration space (Figure 2). A particular configuration (the black cells in the matrix) within this space contains one "value" from each of the parameters, and thus marks out a particular state of, or possible formal solution to, the problem complex. The point is, to examine all of the configurations in the field, in order to establish which of them are possible, viable, practical, interesting, etc., and which are not. In doing this, we mark out in the field a relevant solution space. The solution space of a Zwickian morphological field consists of the subset of all the possible configurations which satisfy some criteria. The primary criterion is that of internal consistency. Figure 2: A 6-parameter morphological field. The darkened cells define one of 4,800 possible (formal) configurations. Obviously, in fields containing more than a handful of variables, it would be time-consuming – if not practically impossible – to examine all of the configurations involved. For instance, a 7-parameter field with 6 conditions under each parameter contains almost 280,000 possible configurations. Thus the next step in the analysis-synthesis process is to examine the internal relationships between the field parameters and reduce the field by weeding out configurations which contain mutually contradictory conditions. In this way, we create a preliminary outcome or solution space within the morphological field without having first to consider all of the configurations as such. This "reduction" is achieved by a process of cross-consistency assessment (CCA). All of the parameter values in the morphological field are compared with one another, pair-wise, in the manner of a cross-impact matrix (Figure 3). As each pair of conditions is examined, a judgment is made as to whether – or to what extent – the pair can coexist, i.e. represent a consistent relationship. Note that there is no reference here to direction or causality, but only to mutual consistency. Using this technique, a typical morphological field can be reduced by to 90% or even 99%, depending on the problem structure. T. Ritchey / Acta Morphologica Generalis Vol. 3. No. 3 (2014) _________________________________________________________________________________________ 9 Figure 3: The Cross-Consistency matrix for the morphological field in Figure 1. The dark cells represent the 15 pair-wise relationships in the configuration given in Figure 1. There are three principal types of inconsistencies involved in the cross-consistency assessment: purely logical contradictions (i.e. contradictions in terms); empirical constraints (i.e. relationships judged to be highly improbable or implausible on practical, empirical grounds), and normative constraints (although these must be used with great care, and clearly designated as such). This technique of using pair-wise consistency assessments, in order to weed out internally inconsistent configurations, is made possible by the combinatorial relationships inherent in morphological models, or in any discrete configuration space. While the number of configurations in such a space grows factorially with each new parameter, the number of pair-wise relationships between parameter conditions grows only in proportion to the triangular number series – a quadratic polynomial. Naturally, there are also practical limits reached with quadratic growth. The point is, that a morphological field involving as many as 100,000 formal configurations can require no more than few hundred pair-wise assessments in order to create a solution space. When this solution (or outcome) space is synthesized, the resultant morphological field function as an inference model, in which any parameter (or multiple parameters) can be selected as "input", and any others as "output". Thus, with dedicated computer support, the field can be turned into a laboratory with which one can designate different initial conditions and examine alternative solutions. GMA seeks to be integrative and to help discover new relationships or configurations. Importantly, it encourages the identification and investigation of boundary conditions, i.e. the limits and extremes of different parameters within the problem space. The method also has definite advantages for scientific communication and – notably – for group work. As a process, the method demands that parameters, conditions and the issues underlying these be clearly defined. Poorly defined concepts become immediately evident when they are cross-referenced and assessed for internal consistency. Like most methods dealing with complex social and organizational systems, GMA requires strong, experienced facilitation, an engaged group of subject specialists and a good deal of patience. T. Ritchey / Acta Morphologica Generalis Vol. 3. No. 3 (2014) _________________________________________________________________________________________ 10 4. Outline for a Morphology of Theories of Emergence The appropriate first step in realising Bailey's full 12-dimensional morphology would to reproduce his original 4-dimensional study using morphological procedures. Once this is done – whatever the results – we can go on to the full 12 dimensions. First, let us take a look at what Bailey's 4-dimensional typology looks like in morphological format (Figure 4). As explained above, while the typological format embeds the four dimensions in 2dimensional space (as in Figure 1), the morphological format represents dimension in form of a table-like field: the dimensions are given in the headings at the top of the field, and their respective attributes listed below them. The advantage of the typological format is that every "type" (i.e. every 4-attribute configuration) has a unique cell which visually shows its relation to all of the other cells, and which can contain explanatory text. Thus the typology's basic structural information can be presented all-at-once in two dimensions. This is not the case in a morphological model: a morphotype is designated by selecting one attribute from each of the dimensions of the morphological field. Thus in order to display different (morpho-) types, and compare them, the model needs to be user-interactive: i.e. one needs to be able to select and compare different type-configurations. This interactive feature cannot be adequately represented "on paper". Only specific examples of type-configurations can be displayed, as seen in Figure 4, where we have selected a configuration corresponding to the Buckley, Mihata, Luhmann (BML) "Pattern Emergence" cell in Figure 1. Figure 4. Bailey's 4-dimensional typology in GMA format with one configuration selected, representing BML "Pattern Emergence" from Figure 1. Figure 5 shows the six dyadic (pair-wise) assessments (the light blue cells) required to define the "Pattern Emergence" configuration in Figure 4. However, in order to replicate Bailey's full 4-D typology in the form of a morphological inference model we must reverse engineer his whole typology. To do this we must carry out a consistency assessment on the total cross-consistency matrix in Figure 5 (i.e. 24 attribute pairs), identifying all pairs which are deemed logically or epistemologically inconsistent. Of the remaining pairs, we differentiate between those already theoretically acknowledged and those unacknowledged (unused), but consistent. Placed into proper GMA software, this will allow us to differentiate between configurations for currently formulated "theories", new possible theories, and internally inconsistent theories. T. Ritchey / Acta Morphologica Generalis Vol. 3. No. 3 (2014) _________________________________________________________________________________________ 11 Figure 5. The Cross-Consistency pairs (marked in light blue) for the BML "Pattern emergence" configuration in figure 4. Moving from a typology of four binary parameters to one of 12 binary parameters entails moving from an outcome space of 2 4 =16 configurations to an outcome space of 2 12 = 4096 configurations. It also involves moving from 24 to 264 cross-consistency assessments. Why would we want to take on such a task if we believe that we can identify certain collinear variables at the outset? Since one of our objectives is to examine and compare a number of acknowledged possible theories of emergence, then systematically identifying and examining possible non-orthogonal dimensions derived from different theories should be seen as legitimate part of the morphological approach – i.e. it should show up in the model. Indeed, one of the advantages of GMA is that it liberates us from enslavement to orthogonality. Furthermore, we wish to include suspected collinear parameters because different areas of science – e.g. physical, biological, social and cognitive – are confronted by emergence in different ways, at different levels of organisation and with seemingly different sets of laws. Since there is presently no general, integrated trans-disciplinary theory of emergence with an accepted common terminology and common modelling framework, we are wise to honour as many concepts as possible, and treat them in a single theoretical framework where they can be analysed and compared. This does not mean that we are banned from merging parameters in different versions of emergence theory if we find them obviously expressing the exact same concepts. Also, there may be good reasons to add new dimensions, which do not seem to be explicitly represented in any present theory (see below). In any event, there are advantages to using Bailey's original 12 parameters as the starting point of a collaborative meta-modelling effort, so that we do not have to start from scratch. Figure 6 shows the initially proposed morphological field of 12 dimensions. Figure 7 is its corresponding crossconsistency matrix, made up of 264 attribute pairs. T. Ritchey / Acta Morphologica Generalis Vol. 3. No. 3 (2014) _________________________________________________________________________________________ 12 Figure 6. The morphological field for Bailey's 12-D typology of emergence, generating 4096 possible formal configurations. Figure 7. The cross-consistency matrix for Figure 6, with 264 pair-wise "assessments" in 66 parameter blocks (the white and shaded 2x2s). T. Ritchey / Acta Morphologica Generalis Vol. 3. No. 3 (2014) _________________________________________________________________________________________ 13 There are a number of issues that need to be addressed upon initiating a full morphology: 1. Firstly, this work cries out for interdisciplinary collaboration. This is best done in a facilitated workshop setting where group interaction is a central feature of the process. This is because we are not only structuring a complex problem, but creating among the participants shared concepts and a common modelling framework. What is essentially a process of collective creativity is best facilitated in dialogue between participants. For this reason, we have found it best to work with subject specialist groups of no more than 6–7 persons. And here there is a problematic trade-off: is it possible for seven persons to represent an adequate knowledge base in order to accomplish the task? 2. A re-evaluation of Bailey's 12 parameters will be needed in order to re-establish and make explicit their meanings in different disciplinary contexts and in a way acceptable to a multi/trans-disciplinary group. 3. As concerns the pre-reduction of dimensions: we can do this when clearly warranted, but this time without methodological duress. We have just cause for a specific reduction when two parameters clearly represent or express identical attributes. This often happens when complex concepts are substructed from different disciplines or sub-disciplines, in which different terms are used for one and the same attribute. In this context, one of the important outcomes of developing a common modelling framework is the development of a common terminology which will allow for better communication between disciplines later on. 4. In approaching emergence from a multi/trans-disciplinary perspective, we may not only need to adjust the original parameters, but also expand them. An example is the explicit inclusion of the dimension of "weak" vs. "strong" emergence in the parameter list. Some have argued that this is not necessary, since it is claimed that any and all theories of emergence can be expressed in either way – i.e. that the weak/strong dimension lies totally outside of the problem. However, even a cursory look at Bailey's 12 parameters gives me the feeling that not all of the attributes – or at least combinations of attributes – are equally compatible with both weak and strong theories. The main point, however, is that this should be part of the modelling experiment, i.e. by including this and other relevant variables we will be able to demonstrate their "status" in this context. 5. It would be advantageous to re-dimension the form of the morphological field. The use of many binary dimensions is not the optimal way to apply GMA, as it creates too shallow a morphological field and makes it more difficult to visualise. Both for modelling technical reasons and, I think, for psychological reasons, it would be better to work with a 6 dimensional model consisting of 4 attributes under each parameter, than with a 12 dimensional model consisting of binary attributes. This is a purely methodological and facilitation issue and does not affect the substance of the results obtained. As in the case of Bailey's paper, our task at this point is not to attempt find the "right" theory of emergence. By proposing a full morphology based on Bailey's 12 parameters, we wish to create a framework to systematically identify, exemplify and compare already existing theories within the framework of all possible theories of emergence. Hopefully such a meta-theoretical framework would help to better clarify different theoretical perspectives and create among researcher a better understand of their differing positions. T. Ritchey / Acta Morphologica Generalis Vol. 3. No. 3 (2014) _________________________________________________________________________________________ 14 6. References and Further Reading Ablowitz, R. (1939). "The Theory of Emergence", in Philosophy of Science, Vol. 6, No. 1 (Jan., 1939), pp. 1-16. University of Chicago Press. Alexander, S. (1920). Space, Time and Deity. New York, Dover publications. Anderson, P.W. (1972), "More is Different: Broken Symmetry and the Nature of the Hierarchical Structure of Science", Science 177 (4047): 393–396. Bailey, K. (2006). "A Typology of Emergence in social Science and Sociocybernetic Theory". Presentation at the International Sociological Association XVI World Congress, Durban, South Africa, Research Committee 51, Sociocybernetics, July 29, 2006. [Available on-line at: http://www.unizar.es/sociocybernetics/congresos/DURBAN/papers/bailey.pdf Bortoft, H. (1996). The Wholeness of Nature; Goethe's Way of Science. Edinburgh: Floris Books. Bateson, W. (1896). Materials for the study of variation. Johns Hopkins University Press. Bedau, M. (1997) "Weak Emergence", Philosophical Perspectives, 11:375-99. Bedau, M. & Humphreys, P. (Eds.) (2008) Emergence: Contemporary Readings in Philosophy and Science, Bradford Books. Barnard, F. M. (1969). Herder on Social and Political Culture, Cambridge University Press. Board, C. D. (1925). The Mind and it Place in Nature. Rutledge and Kegen Paul Bunge, M.(2003). Emergence and Convergence: qualitative novelty and the unity of knowledge. University of Toronto Press Chalmars, D. J. (2006). "Strong and Weak Emergence", in Clayton & Davies (2006). Clayton, P. (2006). "Conceptual Foundations of Emergence Theory", in Clayton & Davis, (2006). Clayton P. & Davies, P (Eds.) (2006) The Re-Emergence of Emergence. The Emergentist Hypothesis from Science to Religion. Oxford University Press. el-Hani, C. N. & Pereir, A. M. (2000), "Higher-level Descriptions: Why Should We Preserve Them?" in Andersen, Emmeche, Finnemann, and Christiansen (eds.) (2000). Downward Causation: Minds, Bodies and Matter (Aarhus, Denmark: Aarhus University Press), pp. 118–42. El-Hani, C. N. and Pihlström, S. (2002) "Emergence Theories and Pragmatic Realism," Essays in Philosophy: Vol. 3: Iss. 2, Article 3. Deacon, T. W. (2012) Incomplete Nature: How Mind Emerged from Matter. W.W. Norton & company. Deavel, C.J. (2003). Unity and Primary Substance for Aristotle. Proceedings of the American Catholic Philosophical Association, Volume 77. Goldstein, J (no date). "Emergence as a Construct: History and Issues". Emergence: Complexity and Organization 1 (1): 49–72. http://www.anecdote.com/pdfs/papers/EmergenceAsAConsutructIssue1_1_3.pdf Humphreys, Paul (2008) Synchronic and Diachronic Emergence, Department of Philosophy, University of Virginia, Charlottesville. http://people.virginia.edu/~pwh2a/dynamic%20emergence%20Humphreys%20article.pdf] T. Ritchey / Acta Morphologica Generalis Vol. 3. No. 3 (2014) _________________________________________________________________________________________ 15 Janik A. & Toulmin, S (1973). Wittgenstein's Vienna. Simon & Schuster, New York. Kauffman, S.A. (1993) The origins of order. Oxford University Press, Oxford. Kauffman, S.A. (1995) At Home in the Universe, Oxford Univ. Press, New York. Kim, J., (1999) "Making sense of emergence", Philosophical Studies 95, 3-36. Lazarsfeld, Paul F. (1937). "Some Remarks on the Typological Procedures in Social Research." Zeitschrift für Sozialforschung, VI, 119-139. Lazarsfeld, Paul F. & Barton, Allen H. (1951). "Qualitative Measurement in the Social Sciences. Classification, Typologies, and Indices". In Daniel Lerner & Harold D. Lasswell (Eds.), The Policy Sciences (pp.155-192). Stanford University Press. Lewes, G. H. (1864) The Life of Goethe, Smith, Elder and Co. Lewes, G. H. (1875). Problems of Life and Mind, Vol. 2, London. Kegen Paul, Tranch, Turbner, & Co. McGhee, G.R (1999). Theoretical Morphology: the concept and its applications. Columbia University Press, New York. McKinney, John C. (1969). "Typification, Typologies, and Sociological Theory". Social Forces, 48(1), 1-12. Mihata, K. (1997). "The Persistence of 'Emergence". In Raymond Eve, Sara Horsfall, and Mary E. Lee (eds.), Chaos, Complexity, and Sociology. Thousand Oaks, CA; Sage. Mill, J.S. (1930). A System of Logic Ratiocenative and Inductive. London, Longmans, Green, and Co. Morgan, C.L. (1923) Emergent Evolution. London, Williams and Norgate. Morowitz, H.J. (2004). The Emergence of Everything: How the World Became Complex. Oxford University, Paull, R.C. & Sider, T (1992). "In Defence of Global Supervenience", Philo. Phen. Res. 52: 833-54. Pepper, S. C. (1926). "Emergence", Journal of Philosophy 23: 241-245. Ritchey, T. (1991, rev. 1996). "Analysis and Synthesis On Scientific Method based on a Study by Bernhard Riemann". Systems Research 8(4), 21-41 (1991). (Available at: http://www.swemorph.com/pdf/anaeng-r.pdf.) Ritchey, T. (2002). "General Morphological Analysis A general method for non-quantified modelling". Adapted from a paper presented at the 16th Euro Conference on Operational Analysis, Brussels, July 1998. (Available at: http://www.swemorph.com/pdf/gma.pdf. Last accessed 2012-03-09.) Ritchey, T. (2006) "Problem Structuring using Computer-Aided Morphological Analysis". Journal of the Operational Research Society, 57, 792–801. (Available at: http://www.swemorph.com/pdf/psmgma.pdf.) Ritchey, T. (2011). Wicked Problems/Social Messes: Decision support Modelling with Morphological Analysis. Springer, Berlin. T. Ritchey / Acta Morphologica Generalis Vol. 3. No. 3 (2014) _________________________________________________________________________________________ 16 Ritchey, T. (2012). "Outline for a Morphology of Modelling Methods: Contribution to a General Theory of Modelling". Acta Morphologica Generalis, Vol. 1, No. 1). (Available at: http://www.amg.swemorph.com/pdf/amg-1-1-2012.pdf.) Rosenbrock, H. (1990). Machines with a Purpose. Oxford University Press. Simon, H. (1996). The Sciences of the Artificial. Third edition. MIT Press, Cambridge. Sperry, R. W. (1983) Science and Moral Priority Columbia University Press. Sperry, R. (1986) "Discussion: Macroversus Micro-Determination." Philosophy of Science 53, 265-270. Thompson, D. W. (1917). On growth and form. Cambridge University Press, Cambridge. Vernadsky, V. I (1986). The Biosphere. Synergetic Press. Vernadsky, V. I (2007), "Geochemistry and the Biosphere". Santa Fe, NM: Synergetic Press. Wellmon, C. (2010)."Goethe's Morphology of Knowledge", Goethe Yearbook, Volume 17, pp. 153177. North American Goethe Society. Whitehead, A. N. (1929). Process and Reality. An Essay in Cosmology. New York: Macmillan Company, 1929 Zwicky, F. (1969) Discovery, Invention, Research Through the Morphological Approach, Toronto: The Macmillan Company. Zwicky, F. & Wilson A. (eds.) (1967) New Methods of Thought and Procedure: Contributions to the Symposium on Methodologies, Berlin: Springer. * * * The author: Tom Ritchey is a former Research Director for the Institution for Technology Foresight and Assessment at the Swedish National Defence Research Agency in Stockholm. He is a methodologist and facilitator who works primarily with non-quantified decision support modelling -especially with General Morphological Analysis (GMA), Bayesian Networks (BN) and Multi-Criteria Decision support. Since 1995 he has directed more than 100 projects involving computer aided GMA for Swedish government agencies, national and international NGO:s and private companies. He is the founder of the Swedish Morphological Society and Director of Ritchey Consulting LLC, Stockholm. Acta Morphologica Generalis (AMG) is the online journal of the Swedish Morphologica Society. [See: http://www.amg.swemorph.com/.] Works published by AMG are licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License, and can be distributed in unaltered form. View a copy of the license at: http://creativecommons.org/licenses/by-nc-nd/3.0/