Image: http://www.thekathleenshow.com/2010/09/12/robin-t-lakoff/
"Mainstream reality theory counts among its hotter foci the interpretation of quantum theory and its reconciliation with classical physics, the study of subjective consciousness and its relationship to objective material reality, the reconciliation of science and mathematics, complexity theory, cosmology, and related branches of science, mathematics, philosophy and theology. But in an integrated sense, it is currently in an exploratory mode, being occupied with the search for a general conceptual framework in which to develop a more specific theory and model of reality capable of resolving the paradoxes and conceptual inconsistencies plaguing its various fields of interest (where a model is technically defined as a valid interpretation of a theory in its universe of reference). Because of the universal scope of reality theory, it is subject to unique if seldom-recognized demands; for example, since it is by definition a universal theory of everything that is real, it must by definition contain its rules of real-world interpretation. That is, reality theory must contain its own model and effect its own self-interpretative mapping thereto, and it must conform to the implications of this requirement. This “self-modeling” capacity is a primary criterion of the required framework.
...
According to its mandate, the true description of reality must possess two novel features not found in any dominant paradigm: (1) global structural and dynamical reflexivity or “self-excited circuitry”, with perception an integral part of the self-recognition function of reality; (2) matter-information equivalence, an identification (up to isomorphism) of concrete physical reality with information, the abstract currency of perception. Together, these features constitute a cosmological extension of cybernetics, or equivalently, a metacybernetic extension of cosmology.
...
When a set of observations is explained with a likely set of equations interpreted therein, the adhesion between explanandum and explanation might as well be provided by rubber cement. I.e., scientific explanations and interpretations glue observations and equations together in a very poorly understood way. It often works like a charm…but why? One of the main purposes of reality theory is to answer this question.
The first thing to notice about this question is that it involves the process of attribution, and that the rules of attribution are set forth in stages by mathematical logic. The first stage is called sentential logic and contains the rules for ascribing the attributes true or false, respectively denoting inclusion or non-inclusion in arbitrary cognitive-perceptual systems, to hypothetical relationships in which predicates are linked by the logical functors not, and, or, implies, and if and only if. Sentential logic defines these functors as truth functions assigning truth values to such expressions irrespective of the contents (but not the truth values) of their predicates, thus effecting a circular definition of functors on truth values and truth values on functors. The next stage of attribution, predicate logic, ascribes specific properties to objects using quantifiers. And the final stage, model theory, comprises the rules for attributing complex relations of predicates to complex relations of objects, i.e. theories to universes. In addition, the form of attribution called definition is explicated in a theory-centric branch of logic called formalized theories, and the mechanics of functional attribution is treated in recursion theory.
...
The fact that most such theories, e.g. theories of physics, point to the fundamental status of something “objective” and “independent of language”, e.g. matter and/or energy, is quite irrelevant, for the very act of pointing invokes an isomorphism between theory and objective reality…an isomorphism that is subject to the Reality Principle, and which could not exist unless reality shared the linguistic structure of the theory itself.
Perhaps the meaning of this principle can be most concisely expressed through a generalization of the aphorism “whereof one cannot speak, one must be silent”: whereof that which cannot be linguistically described, one cannot perceive or conceive. So for the observational and theoretical purposes of science and reality theory, that which is nonisomorphic to language is beyond consideration as a component of reality.
Diagram 7: In this syndiffeonic diagram, the assertion “Language differs from reality” is laid out along an extended line segment representing the supposed difference between the relands. Just as in the generic diagram above, both relands possess the attribute “inclusion in the relational syntactic medium (Language Reality)”. Because they are both manifestations of the same underlying medium, their difference cannot be absolute; on a fundamental level, reality and language share common aspects. This is consistent with the nature of the “difference” relationship, which is actually supposed to represent a semantic and model-theoretic isomorphism."
http://www.ctmu.org/
COGNITION AS INTERACTION
"Many cognitive activities are irreducibly social, involving interaction between several different agents. We look at some examples of this in linguistic communication and games, and show how logical methods provide exact models for the relevant information flow and world change. Finally, we discuss possible connections in this arena between logico-computational approaches and experimental cognitive science."
http://www.illc.uva.nl/Publications/ResearchReports/PP-2005-10.text.pdf
http://staff.science.uva.nl/~johan/research.html
"Preference is a key area where analytic philosophy meets philosophical logic. I start with two related issues: reasons for preference, and changes in preference, first mentioned in von Wright’s book The Logic of Preference but not thoroughly explored there. I show how these two issues can be handled together in one dynamic logical framework, working with structured two-level models, and I investigate the resulting dynamics of reason-based preference in some detail. Next, I study the foundational issue of entanglement between preference and beliefs, and relate the resulting richer logics to belief revision theory and decision theory."
http://www.springerlink.com/content/aw4w76p772007g47/
Utility and Value of Information in Cognitive Science, Biology and Quantum Theory
A generalisation of the concepts utility and information value is given for the non-commutative case. In particular, states and utility operators are considered in dual linear spaces equipped with pre-orders, generated by a wedge of utility operators. It is shown that solutions to the information value problem give rise to an isotone Galois connection between the pre-ordered spaces. A particular form of this connection depends on the choice of a functional representing information resource. The properties of information resource are discussed from the point of information value theory, and an example is presented that generalises several known forms of classical and quantum information. Potential areas of application of information value in cognitive science, biology and quantum theory are discussed.
http://tinyurl.com/quantumbioinformaticsIII
"What is space computing, simulation, or understanding? Converging from several sources, this seems to be something more primitive than what is usually meant by computation, something that was along with us since antiquity (the word "choros", "chora", denotes "space" or "place" and is seemingly the most mysterious notion from Plato, described in Timaeus 48e - 53c) which has to do with cybernetics and with the understanding of the front end visual system. It may have some unexpected applications, also. Here, inspired by Bateson (see Supplementary Material), I explore from the mathematical side the point of view that there is no difference between the map and the territory, but instead the transformation of one into another can be understood by using a formalism of tangle diagrams."
http://arxiv.org/PS_cache/arxiv/pdf/1103/1103.6007v2.pdf
"In ref. [7], S. Majid presents the following `thesis' : ``(roughly speaking) physics polarises down the middle into two parts, one which represents the other, but that the latter equally represents the former, i.e. the two should be treated on an equal footing. The starting point is that Nature after all does not know or care what mathematics is already in textbooks. Therefore the quest for the ultimate theory may well entail, probably does entail, inventing entirely new mathematics in the process. In other words, at least at some intuitive level, a theoretical physicist also has to be a pure mathematician. Then one can phrase the question `what is the ultimate theory of physics ?' in the form `in the tableau of all mathematical concepts past present and future, is there some constrained surface or subset which is called physics ?' Is there an equation for physics itself as a subset of mathematics? I believe there is and if it were to be found it would be called the ultimate theory of physics. Moreover, I believe that it can be found and that it has a lot to do with what is different about the way a physicist looks at the world compared to a mathematician...We can then try to elevate the idea to a more general principle of representation-theoretic self-duality, that a fundamental theory of physics is incomplete unless such a role-reversal is possible. We can go further and hope to fully determine the (supposed) structure of fundamental laws of nature among all mathematical structures by this self-duality condition. Such duality considerations are certainly evident in some form in the context of quantum theory and gravity. The situation is summarised to the left in the following diagram. For example, Lie groups provide the simplest examples of Riemannian geometry, while the representations of similar Lie groups provide the quantum numbers of elementary particles in quantum theory. Thus, both quantum theory and non-Euclidean geometry are needed for a self-dual picture. Hopf algebras (quantum groups) precisely serve to unify these mutually dual structures.''
http://planetmath.org/encyclopedia/IHESOnTheFusionOfMathematicsAndTheoreticalPhysics2.html
"In the first of three articles, we review the philosophical foundations of an approach to quantum gravity based on a principle of representation-theoretic duality and a vaguely Kantian-Buddist perspective on the nature of physical reality which I have called `relative realism'. Central to this is a novel answer to the Plato's cave problem in which both the world outside the cave and the `set of possible shadow patterns' in the cave have equal status. We explain the notion of constructions and `co'constructions in this context and how quantum groups arise naturally as a microcosm for the unification of quantum theory and gravity. More generally, reality is `created' by choices made and forgotten that constrain our thinking much as mathematical structures have a reality created by a choice of axioms, but the possible choices are not arbitary and are themselves elements of a higher-level of reality. In this way the factual `hardness' of science is not lost while at the same time the observer is an equal partner in the process. We argue that the `ultimate laws' of physics are then no more than the rules of looking at the world in a certain self-dual way, or conversely that going to deeper theories of physics is a matter of letting go of more and more assumptions. We show how this new philosophical foundation for quantum gravity leads to a self-dual and fractal like structure that informs and motivates the concrete research reviewed in parts II,III. Our position also provides a kind of explanation of why things are quantized and why there is gravity in the first place, and possibly why there is a cosmological constant.
Keywords: quantum gravity, Plato's cave, Kant, Buddism, physical reality, quantum logic, quantum group, monoidal category, T-duality, Fourier transform, child development"
http://philsci-archive.pitt.edu/3345/
"In 1993 the famous Dutch theoretical physicist G.’t Hooft put forward a bold proposal. This proposal, which is known as the Holographic Principle, consists of two basic assertions:
“Assertion 1: The first assertion of the Holographic Principle is that all of the information contained in some region of space can be represented as a `Hologram' - a theory that `lives' on the boundary of that region. For example, if the region of space in question is a Coffee shop, then the holographic principle asserts that all of the physics, which takes place in the coffee shop, can be represented by a theory, which is defined on the walls of the Tearoom.
Assertion 2: The second assertion of the Holographic Principle is that the theory on the boundary of the region of space in question should contain at most one degree of freedom per Planck area.18
Before, I have assumed that the information in space-time, in it’s entirely, is reflected and registered in singularity. To make it objective, Holographic theorists convert the whole ordeal to spatial form again but with one dimension less and present it to us. On the context of the proposed model, we can ignore the inverse Fourier transform and imagine that information remains in spectral state while in singularity. We do not have to pass to spatial phase (do not have to conjugate) and look at the shadow in the wall to realize that information is out there. Or we may do that for objectivity reasons, but at least we'd better appreciate and recognize the spectral state of the information. This is similar to mind function. According to holographic brain Theory, information remains at spectral form in the brain. That is what I am trying to convey about the singularity as well. In holography, we stay in the spatial boundaries, to demonstrate the experiment. In this model however, I surpass all spatial dimensions and introduce a geometrical point to accommodate information.
We have enough information to dare passing the spatial boundaries. Our imagination can help us building theories and present them for speculation and investigation. Meantime if we establish a sound theory for mind function, we can utilize mind activities as analogy to explore beyond finite world. Holographic theory, says that all the information can be present in space with one-dimension less. M theorist (representing different Super String theories) found out that the answer of major paradoxes could not be found in our 4-dimension space-time. To find solutions they had to look out of 4-dimensional space. My question is why did they have to travel to assumed spaces with different dimensions to create a basis to solve the paradoxes? Why couldn't we untie and free ourselves from space boundaries? We know from the Einstein’s Special Theory of Relativity that time and space are not absolute.
At this point, let me add this beautiful piece from the University of Cambridge DAMTP web page.18
Holography through the Ages
To them, I said,
the truth would be literally nothing
but the shadows of the images.
Plato, The Republic (Book VII)
Plato, the great Greek philosopher, wrote a series of ‘Dialogues’, which summarized many of the things, which he had learned from his teacher, who was the philosopher Socrates.
One of the most famous of these Dialogues is the ‘Allegory of the Cave.’ In this allegory, people are chained in a cave so that they can only see the shadows, which are cast on the walls of the cave by a fire. To these people, the shadows represent the totality of their existence - it is impossible for them to imagine a reality, which consists of anything other than the fuzzy shadows on the wall. However, some prisoners may escape from the cave; they may go out into the light of the sun and behold true reality. When they try to go back into the cave and tell the other captives the truth, they are mocked as madmen. Of course, to Plato this story was just meant to symbolize mankind's struggle to reach enlightenment and understanding through reasoning and open-mindedness. We are all initially prisoners and the tangible world is our cave. Just as some prisoners may escape out into the sun, so may some people amass knowledge and ascend into the light of true reality. What is equally interesting is the literal interpretation of Plato's tale: The idea that reality could be represented completely as `shadows' on the walls.18
Holonomic Brain
Numerous studies in neuro-physiology suggest that memories in the brain are not stored in a specific location; rather, they are dispersed over the entire brain. The conventional view is that the brain is a computational device. There is a growing body of literature, though, that shows there are severe limitations to computation (Penrose, 1994; Rosen, 1991; Kampis, 1991; Pattee, 1995). For instance, Dr. Jeff Paradeoux writes:
Penrose uses a variation of the "halting problem" to show that the mind cannot be an algorithmic process. Rosen argues that computation (or simulation) is an inaccurate representation of the natural causes that are in place in nature. Kampis shows that the informational content of an algorithmic process is fixed at the beginning and no "new" information can be brought forward. Pattee argues that the complete separation of initial conditions and equations of motion necessary in a computation may only be a special case in nature. Pattee argues that systems that can make their own measuring devices can affect what they see and have ‘semantic closure. 19
Experiments show that selective damage to certain area of brain tissue will not erase the specific related memories. It further suggests that memories are restored as frequency. The experiment performed by Bernstein is worth mentioning. Here is a summary of his experiment and the follow up work by Karl Pribram, Professor Emeritus at Stanford University and his associate:
“Bernstein dressed people in black leotards and had them perform simple tasks such as running or hammering nails against a black background. The leotard had been decorated with white dots over each joint. Bernstein took cinematographic films of these activities. On his films he therefore had a record of the movements of the dots, which described a series of waveforms. When he analyzed the records according to a Fourier procedure he was able to accurately predict the next movement in the sequence.What we needed was direct proof that cells in the motor cortex were responsive to wave forms. So Amad Sharafat, an engineering student, and I devised an apparatus, which moved a cat’s paw up and down at different frequencies. We recorded from motor cortical cells and found many that were tuned to the frequencies with which the paw was moved.” 57
He then explains:
“What the data suggest is that there exists in the cortex, a multidimensional holographic-like process serving as an attractor or set point toward which muscular contractions operate to achieve a specified environmental result.
The specification has to be based on prior experience (of the species or the individual) and stored in holographic-like form. Activation of the store involves patterns of muscular contractions (guided by basal ganglia, cerebellar, brain stem and spinal cord) whose sequential operations need only to satisfy the 'target' encoded in the image of achievement” 57
http://www.universaltheory.org/html/consciousness/holonomic_brain/holonomic_brain5.htm
"The basic meaning of ešrāq (Illumination) is “rising,” more precisely “rising of the sun” (Lane, Arabic English Lexicon I, pp. 1539-41). The term is used extensively in Arabic and Persian philosophical texts, signifying a special intuitive mode of cognition with no temporal extension (i.e., a-temporal), spatially coordinated “in” (fi) the knowing, self-conscious subject (Ar. al-mawżuʿ al-modrek bi’l-ḏāt; Pers.
man-e dānanda/ḵod-āgāh). In other words, it applies to the relation between the “apprehending subject” (al-mawżuʿ al-modrek) and “apprehensible object” (al-modrak). The term ešrāq is also widely used in popular discourse. In its general, non-technical usage in ordinary language, it signifies the “mystical” as well as the range of extraordinary types of knowledge, including personal inspiration (elhām)."
http://www.iranica.com/articles/illuminationism
"The Sun of Reality is one Sun but it has different dawning-places, just as the phenomenal sun is one although it appears at various points of the horizon. During the time of spring the luminary of the physical world rises far to the north of the equinoctial; in summer it dawns midway and in winter it appears in the most southerly point of its zodiacal journey. These day springs or dawning-points differ widely but the sun is ever the same sun whether it be the phenomenal or spiritual luminary. Souls who focus their vision upon the Sun of Reality will be the recipients of light no matter from what point it rises, but those who are fettered by adoration of the dawning-point are deprived when it appears in a different station upon the spiritual horizon."
http://bcca.org/bahaivision/BWF/0612thesunofreality.html
"Model theory studies structures (which are usually models of some formal language): their construction, classification, and relations between them. Given that databases, graphs, and mathematical constructs studied in theoretical computer science (categories, domains, Chu spaces) can all be seen as (relational) structures, model theory provides a set of tools potentially useful for any computer scientist.
...
Below is the preliminary schedule of lectures:
Lecture 1: Introduction. Language and models of first order logic, definition of truth and entailment. Handout for the first lecture. Answers to the exercises.
Lecture 2: Maps and formulas they preserve (isomorphism, homomorphism, embeddings, substructures, direct products).
Lecture 3: Ehrenfeucht-Fraisse games.
Lecture 4: Language and models of modal logic.
Lecture 5: Bisimulation."
http://www.cs.nott.ac.uk/~nza/MGS/MGS99/index.html
"In the mathematical discipline of model theory, the Ehrenfeucht–Fraïssé game (also called back-and-forth games) is a technique for determining whether two structures are elementarily equivalent.
...
The main idea behind the game is that we have two structures, and two players (defined below). One of the players wants to show that the two structures are different, whereas the other player wants to show that they are somewhat similar (according to first-order logic). The game is played in turns and rounds; A round proceeds as follows: First the first player (Spoiler) chooses any element from one of the structure, and the other player chooses an element from the other structure. The other player's task is to always pick an element that is "similar" to the one that Spoiler chose. The second player (Duplicator) wins if there exists an isomorphism between the elements chosen in the two different structures.
The game lasts for a fixed amount of steps (γ) (an ordinal, but usually a finite number or ω)."
http://en.wikipedia.org/wiki/Ehrenfeucht–Fraïssé_game
"Notions of bisimulation play a central role in the theory of transition systems. As
different kinds of system are encountered, different notions of bisimulation arise,
but the same questions are posed: Is there a fixed-point characterization for the
maximal bisimulation, bisimilarity? Is there a minimal system, where bisimilar
states are equated? And is there a procedure for constructing a minimal system,
or for verifying bisimilarity?
The theory of coalgebras provides a setting in which different notions of transition
system can be understood at a general level. In this paper we investigate
notions of bisimulation at this general level, and determine how and when these
questions can be answered."
http://www.cl.cam.ac.uk/~ss368/calco09.pdf
Symmetry of subject and predicate
http://chu.stanford.edu/
Furthering the idea of the use of Chu Spaces for consciousness problems and especially the binding problem
http://ttjohn.blogspot.com/2005/11/use-of-chu-spaces-for-consciousness.html
Big Toy Models: Representing Physical Systems As Chu Spaces
"We pursue a model-oriented rather than axiomatic approach to the foundations of Quantum Mechanics, with the idea that new models can often suggest new axioms. This approach has often been fruitful in Logic and Theoretical Computer Science. Rather than seeking to construct a simplified toy model, we aim for a `big toy model', in which both quantum and classical systems can be faithfully represented - as well as, possibly, more exotic kinds of systems.
To this end, we show how Chu spaces can be used to represent physical systems of various kinds. In particular, we show how quantum systems can be represented as Chu spaces over the unit interval in such a way that the Chu morphisms correspond exactly to the physically meaningful symmetries of the systems - the unitaries and antiunitaries. In this way we obtain a full and faithful functor from the groupoid of Hilbert spaces and their symmetries to Chu spaces. We also consider whether it is possible to use a finite value set rather than the unit interval; we show that three values suffice, while the two standard possibilistic reductions to two values both fail to preserve fullness. "
http://arxiv.org/abs/0910.2393
"A good theory is like a good map. If we plan our itinerary with a good map it gets us to where we want to go. Why? Because the logical structure of the map parallels -- or, as we will say, is isomorphic to -- the spacial structure of the roads we are travelling.
Consider the following:
a. A theory is defined by a set of variables and the set of relations among them. A map generally indicates route intersections, the connections among them and the distances between them.
b. A program is a well-specified procedure. It is defined by a set of operations and the set of relations among them. A program like an itinerary, for example, may specify operations like, "drive north on route 363 for 4.5 miles to route 611." Such operations will generally only work if they are done in a specific sequence.
c. Informally, we can think of an isomorphism as a relationship of perfect correspondence of parts. A program Px is isomorphic to a theory Tz, if and only if for each operation in Px, there corresponds only one variable in Tz. Also, for each relation among operations in Px, there corresponds one and only one relation among variables in Tz. Our itinerary will be isomorphic with our map if and only if for each critical intersection on our trip, there corresponds an operation which takes us to it.
d. To the extent that a program is isomorphic to a theory, those who pursue the program may be said to be using that theory. Mere allusions to a theory will lack many correspondences between operations and variables, and the relationships among them. A person might well, for example, get from one place to another from habit or chance without following a map. Or a teacher may say that he is "reinforcing" student "responses" without actually following operant conditioning theory, as, for example, he writes an "A" on a report card at a time and place long removed from the presence of the student's behavior.
e. Programs pursue goals. An "adequate" theory is one whose isomorphically related program achieves its goal."
http://home.comcast.net/~erozycki/Isomorphism.html
"In computer science, confluence is a property of rewriting systems, describing that terms in this system can be rewritten in more than one way, to yield the same result. This article describes the properties in the most abstract setting of an abstract rewriting system."
...
Strong confluence is another variation on local confluence that allows us to conclude that a rewriting system is globally confluent. An element a ∈ S is said to be strongly confluent if for all b, c ∈ S with a → b and a → c there exists d ∈ S with b →* d and either c → d or c = d; if every a ∈ S is strongly confluent, we say that → is strongly confluent.
A strongly confluent element need not be confluent, but a strongly confluent rewriting system is necessarily confluent."
http://en.wikipedia.org/wiki/Confluence_(abstract_rewriting)
The Communication of Meaning in Anticipatory Systems: A Simulation Study of the Dynamics of Intentionality in Social Interactions
"Psychological and social systems provide us with a natural domain for the study of anticipations because these
systems are based on and operate in terms of intentionality. Psychological systems can be expected to contain a model of
themselves and their environments; social systems can be strongly anticipatory and therefore co-construct their
environments, for example, in techno-economic (co-)evolutions. Using Dubois’ hyper-incursive and incursive
formulations of the logistic equation, these two types of systems and their couplings can be simulated. In addition to their
structural coupling, psychological and social systems are also coupled by providing meaning reflexively to each other’s
meaning-processing. Luhmann’s distinctions among (1) interactions between intentions at the micro-level, (2)
organization at the meso-level, and (3) self-organization of the fluxes of meaningful communication at the global level
can be modeled and simulated using three hyper-incursive equations. The global level of self-organizing interactions
among fluxes of communication is retained at the meso-level of organization. In a knowledge-based economy, these two
levels of anticipatory structuration can be expected to propel each other at the supra-individual level.
Keywords: anticipation, social system, meaning, communication, incursion, double contingency"
http://www.leydesdorff.net/casys07/casys07.pdf
"There are two different approaches in decision theory: evidential decision theory and causal decision theory. Evidential decision theory seeks to maximize the utility of a choice, taking into account what the choice tells you about yourself, and therefore, about other parts of the world that may correlate with your own behavior. A justification for evidential decision theory is given. This first involves a scenario intended to suggest evidential decision theory as an approach. Some objections to evidential decision theory being used in Newcomb’s paradox are that it seems to imply reverse causation, but it is shown that this issue is raised by any decision anyway. Light cones are used to give a simplified view of events, in which it is shown that there is no profound transition involved in going from an event causally following from a choice to one related to it less directly. The view of an outside observer is taken to show how decisions should be approached with no assumption of them having any special status as a result of being “owned” by the decider. Making a special case of your own decisions violates the Copernican principle. It is argued that, even if we try to view our decisions causally, correlation between other parts of reality will mean that choices tend to “contaminate” much of the description of reality in non-causal, indirect ways. Evidential decision theory can be justified by considering identical players in a game, and then considering almost identical players. The term “meta-causation” is proposed. A choice meta-causes an event if it corresponds to that event irrespective of whether or not the event causally follows it. Evidential decision theory is correct, but has little practical significance in many everyday situations in which we have a lot of knowledge. The next article will discuss situations where it could be relevant."
http://www.paul-almond.com/Correlation1.pdf
Converging towards what? Pragmatic and Semantic Competence
The paper tries to build a bridge between results in commonsense reasoning and inferential theories of meaning. We focus on the problem of communication and the contrast between two views of communication, the “expressive ” view and the “convergence ” view. According to the convergence view (and local holism which supports it) the meaning of a sentence is the set of inferences to which speakers converge in a discourse context. The problem is that we have no idea about the strategy of this convergence, even if it is apparent that the convergence of inferences depends on contextual clues and pragmatic factors. We claim that in order to accept the convergence view we need to supplement the idea of meaning as inference with recent results in multi-context theories. Our solution to the problem is based on a distinction between semantic competence and contextual competence defined as rule governed pragmatic competence.
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.77.6404
"Although standard game theory assumes common knowledge of rationality, it does so in a different way. The game theoretic analysis maximizes payoffs by allowing each player to change strategies independently of the others, even though in the end, it assumes that the answer in a symmetric game will be the same for all. This is the definition of a game theoretic
Nash equilibrium, which defines a stable strategy as one where no player can improve the payoffs by unilaterally changing course. The superrational equilibrium is one which maximizes payoffs where all the players strategies are forced to be the same before the maximization step.
Some argue that superrationality implies a kind of magical thinking in which each player supposes that his decision to cooperate will cause the other player to cooperate, despite the fact that there is no communication. Hofstadter points out that the concept of "choice" doesn't apply when the player's goal is to figure something out, and that the decision does not cause the other player to cooperate, but rather same logic leads to same answer independent of communication or cause and effect. This debate is over whether it is reasonable for human beings to act in a superrational manner, not over what superrationality means."
http://en.wikipedia.org/wiki/Superrationality
"There are several variants of the “binding problem,” which asks how a massively parallel system can achieve coherence. The most striking examples involve subjective experience and therefore remain intractable to experimentation. For example, we know that visual processing involves dozens of separate brain areas, yet we perceive the world as a coherent whole. Even leaving subjective experience aside, there are still compelling technical problems in understanding how a neural network can perform crucial computational tasks, such as
those that arise in reasoning about and acting in the world.
A basic problem, and the one that we will focus on, is the “variable binding” problem. As a first example, consider your ability to pick up objects. Depending on the object, its current position, and your goals, you have a very wide range of ways of grasping and manipulating
the object, all realized by the network of neurons that is your brain. This is an instance of the variable binding problem because your choice of values for the three variables object, position, and goal has consequences throughout your brain on how the action is carried out.
In conventional computing, we assume that different program modules all have access to the values of (global) variables and can modify their behavior appropriately. Any theory of neural computation needs some mechanism for achieving this kind of global effect."
http://leon.barrettnexus.com/papers/barrett-2008-nc-binding.pdf
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