We investigate the use of coalgebra to represent quantum systems, thus providing a basis for the use of coalgebraic methods in quantum information and computation. Coalgebras allow the dynamics of repeated measurement to be captured, and provide mathematical tools such as final coalgebras, bisimulation and coalgebraic logic. However, the standard coalgebraic framework does not accommodate contravariance, and is too rigid to allow physical symmetries to be represented. We introduce a fibrational structure on coalgebras in which contravariance is represented (...) by indexing. We use this structure to give a universal semantics for quantum systems based on a final coalgebra construction. We characterize equality in this semantics as projective equivalence. We also define an analogous indexed structure for Chu spaces, and use this to obtain a novel categorical description of the category of Chu spaces. We use the indexed structures of Chu spaces and coalgebras over a common base to define a truncation functor from coalgebras to Chu spaces. This truncation functor is used to lift the full and faithful representation of the groupoid of physical symmetries on Hilbert spaces into Chu spaces, obtained in our previous work, to the coalgebraic semantics. (shrink)

This paper shows that, under certain reasonable conditions, if the investigation of the behavior of a physical system is difficult, no scientific change can make it significantly easier. This impossibility result implies that complexity is then a necessary feature of models which truly represent the target system and of all models which are rich enough to catch its behavior and therefore that it is an inevitable element of any possible science in which this behavior is accounted for. I finally (...) argue that complexity can then be seen as representing an intrinsic feature of the system itself. (shrink)

This paper shows that, under certain reasonable conditions, if the investigation of the behavior of a physical system is difficult, no scientific change can make it significantly easier. This impossibility result implies that complexity is then a necessary feature of models which truly represent the target system and of all models which are rich enough to catch its behavior and therefore that it is an inevitable element of any possible science in which this behavior is accounted for. I finally (...) argue that complexity can then be seen as representing an intrinsic feature of the system itself. (shrink)

The paper portrays the influence of major philosophical ideas on the 1935 debates on quantum theory that reached their climax in the paper by Einstein, Podosky and Rosen, and describes the relevance of these ideas to the vast impact of the paper. I claim that the focus on realism in many common descriptions of the debate misses important aspects both of Einstein's and Bohr's thinking. I suggest an alternative understanding of Einstein's criticism of quantum mechanics as a manifestation of the (...) same methodological principles that served him in the construction of the special and the general theories of relativity. These principles address, in a very specific way, the relation of the theoretical mathematical representations to the represented physical systems. These ideas, I claim, played a key role in the influence of the paper on later works that changed our understanding of quantum theory despite the rejection of EPR's central conclusion. (shrink)

In some recent papers (G. ‘t Hooft and others), it has been argued that quantum mechanics can arise from classical cellular automata. Nonetheless, G. Shpenkov has proved that the classical wave equation makes it possible to derive a periodic table of elements, which is very close to Mendeleyev’s one, and describe also other phenomena related to the structure of molecules. Hence the classical wave equation complements Schrödinger’s equation, which implies the appearance of a cellular automaton molecular model starting from classical (...) wave equation. The other studies show that the microworld is constituted as a tessellation of primary topological balls. The tessellattice becomes the origin of a submicrospic mechanics in which a quantum system is subdivided to two subsystems: the particle and its inerton cloud, which appears due to the interaction of the moving particle with oncoming cells of the tessellattice. The particle and its inerton cloud periodically change the momentum and hence move like a wave. The new approach allows us to correlate the Klein-Gordon equation with the deformation coat that is formed in the tessellatice around the particle. The submicroscopic approach shows that the source of any type of wave movements including the Klein-Gordon, Schrödinger, and classical wave equations is hidden in the tessellattice and its basic exciations – inertons, carriers of mass and inert properies of matter. We also discuss possible correspondence with Konrad Zuse’s calculating space. (shrink)

Representation of scientific knowledge in ontologies suffers so often from the lack of computational knowledge required for inference. This article aims to perform quantitative analysis on physical systems, that is, to answer questions about values of quantitative state variables of a physical system with known structure. For this objective, we incorporate procedural knowledge on two distinct levels. At the domain-specific level, we propose a representation model for scientific knowledge, i.e. variables, theories, and laws of nature. (...) At the domain-independent level, we provide an algorithm which, given a system S with known structure and a relevant scientific theory T, extracts a constraint network, whose variables are state variables of S defined by T, and whose constraints raise from relevant laws in T. The constraint network is then solved, to build a system of equations whose unknowns are the output variables of S. The proposed representation model and reasoning algorithm are evaluated by applying them to classic analysis examples. (shrink)

Coordinate-based approaches to physical theories remain standard in mainstream physics but are largely eschewed in foundational discussion in favour of coordinate-free differential-geometric approaches. I defend the conceptual and mathematical legitimacy of the coordinate-based approach for foundational work. In doing so, I provide an account of the Kleinian conception of geometry as a theory of invariance under symmetry groups; I argue that this conception continues to play a very substantial role in contemporary mathematical physics and indeed that supposedly ``coordinate-free'' differential (...) geometry relies centrally on this conception of geometry. I discuss some foundational and pedagogical advantages of the coordinate-based formulation and briefly connect it to some remarks of Norton on the historical development of geometry in physics during the establishment of the general theory of relativity. (shrink)

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 Hubert 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. (shrink)

Using an example of a computer simulation of the convective structure of a red giant star, this paper argues that simulation is a rich inferential process, and not simply a "number crunching" technique. The scientific practice of simulation, moreover, poses some interesting and challenging epistemological and methodological issues for the philosophy of science. I will also argue that these challenges would be best addressed by a philosophy of science that places less emphasis on the representational capacity of theories (and ascribes (...) that capacity instead to models) and more emphasis on the role of theory in guiding (rather than determining) the construction of models. (shrink)

Using an example of a computer simulation of the convective structure of a red giant star, this paper argues that simulation is a rich inferential process, and not simply a “number crunching” technique. The scientific practice of simulation, moreover, poses some interesting and challenging epistemological and methodological issues for the philosophy of science. I will also argue that these challenges would be best addressed by a philosophy of science that places less emphasis on the representational capacity of theories and more (...) emphasis on the role of theory in guiding the construction of models. (shrink)

I argue that an adequate semantics for physical theories must be grounded on an account of the way that a theory provides formal and conceptual resources appropriate for---that have propriety in---the construction of representations of the physical systems the theory purports to treat. I sketch a precise, rigorous definition of the required forms of propriety, and argue that semantic content accrues to scientific representations of physical systems primarily in virtue of the propriety of its resources. (...) In particular, neither the adequacy of those representations nor any referential relations their terms may enter into play any fundamental role in the determination of the representation's semantic content. One consequence is that anything like traditional Tarskian semantics is inadequate for the task. (shrink)

As an approach to a Theory of Everything a framework for developing a coherent theory of mathematics and physics together is described. The main characteristic of such a theory is discussed: the theory must be valid and and sufficiently strong, and it must maximally describe its own validity and sufficient strength. The mathematical logical definition of validity is used, and sufficient strength is seen to be a necessary and useful concept. The requirement of maximal description of its own validity and (...) sufficient strength may be useful to reject candidate coherent theories for which the description is less than maximal. Other aspects of a coherent theory discussed include universal applicability, the relation to the anthropic principle, and possible uniqueness. It is suggested that the basic properties of the physical and mathematical universes are entwined with and emerge with a coherent theory. Support for this includes the indirect reality status of properties of very small or very large far away systems compared to moderate sized nearby systems. Discussion of the necessary physical nature of language includes physical models of language and a proof that the meaning content of expressions of any axiomatizable theory seems to be independent of the algorithmic complexity of the theory. Gödel maps seem to be less useful for a coherent theory than for purely mathematical theories because all symbols and words of any language must have representations as states of physical systems already in the domain of a coherent theory. (shrink)

Learning in intelligent systems is a result of direct or indirect interaction with the environment. Humans can learn by way of different states of (inter-)action such as the execution or the imagery of an action, but their unique potential to induce brain-related as well as mind-related changes in the motor action system is still being debated. The systematic repetition of different states of action (e.g., execution and imagery in terms of physical and mental practice) and their contribution to (...) the learning of complex motor actions has traditionally been approached by way of performance improvements. More recently, approaches highlighting the role of action representation in the learning of complex motor actions have evolved. In the present perspective paper, we build on brain-related findings and sketch recent research on learning by way of imagery and execution from a hierarchical, perceptual-cognitive approach to the motor action system. These findings provide valuable insights into the learning of intelligent systems from a perceptual-cognitive, representation-based perspective and as such add to our current understanding of action representation in memory and its changes with practice. Future research should build bridges between approaches in order to more thoroughly understand functional changes throughout the learning process, and to jointly contribute to developing intelligent cognitive systems and their application in robotics, rehabilitation, or sports. (shrink)

The present study's primary aims were a) to explore non-disabled adults' spontaneous representation of disability and the specific associations related to adults and children with disabilities; to investigate participants' general perception of specific inclusive educational practices and the potential impact of contact with disabled individuals on children. We used a mixed approach in a sample of 628 participants aged 18 to 82. Our results suggested that most explicit representations of disability were negatively valenced, i.e., people generally used pessimistic and (...) detrimental related words. Psychomotor deficiencies comprised the most frequent disability category associated with disabled adults, while autism was the most frequent disability related to disabled children. Participants considered that the inclusion of physically disabled children in public schools has a more positive effect on non-disabled children. The previous contact with a friend or a family member with a disability significantly and positively impacted the general attitude toward disability and inclusive educational practices. Results are discussed regarding their practical implications for the educational system and specific strategies related to inclusive public policies. (shrink)

Representation is typically taken to be importantly separate from its physical implementation. This is exemplified in Marr’s three-level framework, widely cited and often adopted in neuroscience. However, the separation between representation and physical implementation is not a necessary feature of information-processing systems. In particular, when it comes to analog computational systems, Marr’s representational/algorithmic level and implementational level collapse into a single level. Insofar as analog computation is a better way of understanding neural computation than (...) other notions, Marr’s three-level framework must then be amended into a two-level framework. However, far from being a problem or limitation, this sheds lights on how to understand physical media as being representational, but without a separate, medium-independent representational level. (shrink)

The quantum mechanical description of the evolution of an unstable system defined initially as a state in a Hilbert space at a given time does not provide a semigroup (exponential) decay, law. The Wigner–Weisskopf survival amplitude, describing reversible quantum transitions, may be dominated by exponential type decay in pole approximation at times not too short or too long, but, in the two channel case, for example, the pole residues are not orthogonal, and the evolution does riot correspond to a semigroup (...) (experiments on the decay of the neutral K-meson system strongly support the semigroup evolution postulated, by Lee, Oehme and Yang, and Yang and Wu). The scattering theory of Lax and Phillips, originally developed for classical wave equations, has been recently extended to the description of the evolution of resonant states in the framework of quantum theory. The resulting evolution law of the unstable system is that of a semigroup, and the resonant state is a well-defined function in the Lax–Phillips Hilbert space. In this paper we apply this theory to a relativistically covariant quantum field theoretical form of the (soluble) Lee model. We construct the translation representations with the help of the wave operators, and show that the resulting Lax–Phillips S-matrix is an inner function (the Lax–Phillips theory is essentially a theory of translation invariant subspaces). In the special case that the S-matrix is a rational inner function, we obtain the resonant state explicitly and analyze its particle (V, N, θ) content. If there is an exponential bound, the general case differs only by a so-called trivial inner factor, which does not change the complex spectrum, but may affect the wave function of the resonant state. (shrink)

We construct a sheaf-theoretic representation of quantum probabilistic structures, in terms of covering systems of Boolean measure algebras. These systems coordinatize quantum states by means of Boolean coefficients, interpreted as Boolean localization measures. The representation is based on the existence of a pair of adjoint functors between the category of presheaves of Boolean measure algebras and the category of quantum measure algebras. The sheaf-theoretic semantic transition of quantum structures shifts their physical significance from the orthoposet (...) axiomatization at the level of events, to the sheaf-theoretic gluing conditions at the level of Boolean localization systems. (shrink)

The overwhelming majority of the attempts in exploring the problems related to quantum logical structures and their interpretation have been based on an underlying set-theoretic syntactic language. We propose a transition in the involved syntactic language to tackle these problems from the set-theoretic to the category-theoretic mode, together with a study of the consequent semantic transition in the logical interpretation of quantum event structures. In the present work, this is realized by representing categorically the global structure of a quantum algebra (...) of events (or propositions) in terms of sheaves of local Boolean frames forming Boolean localization functors. The category of sheaves is a topos providing the possibility of applying the powerful logical classification methodology of topos theory with reference to the quantum world. In particular, we show that the topos-theoretic representation scheme of quantum event algebras by means of Boolean localization functors incorporates an object of truth values, which constitutes the appropriate tool for the definition of quantum truth-value assignments to propositions describing the behavior of quantum systems. Effectively, this scheme induces a revised realist account of truth in the quantum domain of discourse. We also include an Appendix, where we compare our topos-theoretic representation scheme of quantum event algebras with other categorial and topos-theoretic approaches. (shrink)

The purpose of this paper is to highlight the importance of constraints in the theory of relativity and, in particular, what philosophical work they do for Einstein's views on the laws of physics. Einstein presents a view of local ``structure laws'' which he characterizes as the most appropriate form of physical laws. Einstein was committed to a view of science, which presents a synthesis between rational and empirical elements as its hallmark. If scientific constructs are free inventions of the (...) human mind, as Einstein, held, the question arises how such rational constructs, including the symbolic formulation of the laws of physics, can represent physical reality. Representation in turn raises the question of realism. Einstein uses a number of constraints in the theory of relativity to show that by imposing constraints on the rational elements a certain ``fit'' between theory and reality can be achieved. Fit is to be understood as satisfaction of constraint. His emphasis on reference frames in the STR and more general coordinate systems in the GTR, as well as his emphasis on the symmetries of the theory of relativity suggests that Einstein's realism is akin to a certain form of structural realism. His version of structural realism follows from the theory of relativity and is independent of any current philosophical debates about structural realism. (shrink)

The quantum state of a d-dimensional system can be represented by a probability distribution over the d 2 outcomes of a Symmetric Informationally Complete Positive Operator Valued Measure (SIC-POVM), and then this probability distribution can be represented by a vector of $\mathbb {R}^{d^{2}-1}$ in a (d 2−1)-dimensional simplex, we will call this set of vectors $\mathcal{Q}$ . Other way of represent a d-dimensional system is by the corresponding Bloch vector also in $\mathbb {R}^{d^{2}-1}$ , we will call this set of (...) vectors $\mathcal{B}$ . In this paper it is proved that with the adequate scaling $\mathcal{B}=\mathcal{Q}$ . Also we indicate some features of the shape of $\mathcal{Q}$. (shrink)

We point out that, when the dimension of the Hilbert space is greater than two, Bell’s operators entering the Bell-CHSH inequality do exhibit inequivalent unitary matrix representations. Although the Bell-CHSH inequality turns out to be violated, the size of the violation is different for different representations, the maximum violation being given by Tsirelson’s bound. The feature relies on a pairing mechanism between the modes of the Hilbert space of the system.

The concept of “representation” is used broadly and uncontroversially throughout neuroscience, in contrast to its highly controversial status within the philosophy of mind and cognitive science. In this paper I first discuss the way that the term is used within neuroscience, in particular describing the strategies by which representations are characterized empirically. I then relate the concept of representation within neuroscience to one that has developed within the field of machine learning. I argue that the recent success of (...) artificial neural networks on certain tasks such as visual object recognition reflects the degree to which those systems exhibit inherent inductive biases that reflect the structure of the physical world. I further argue that any system that is going to behave intelligently in the world must contain representations that reflect the structure of the world; otherwise, the system must perform unconstrained function approximation which is destined to fail due to the curse of dimensionality, in which the number of possible states of the world grows exponentially with the number of dimensions in the space of possible inputs. An analysis of these concepts in light of philosophical debates regarding the ontological status of representations suggests that the representations identified within both biological and artificial neural networks qualify as legitimate representations in the philosophical sense. (shrink)

What does it mean to say that an object or system computes? What is it about laptops, smartphones, and nervous systems that they are considered to compute, and why does it seldom occur to us to describe stomachs, hurricanes, rocks, or chairs that way? Though computing systems are everywhere today, it is very difficult to answer these questions. The book aims to shed light on the subject by arguing for the semantic view of computation, which states that computingsystems (...) are always accompanied by representations. This view is presented as an alternative to non-semantic views such as the mechanistic account of computation. (shrink)

The fact that the same equations or mathematical models reappear in the descriptions of what are otherwise disparate physical systems can be seen as yet another manifestation of Wigner's “unreasonable effectiveness of mathematics.” James Clerk Maxwell famously exploited such formal similarities in what he called the “method of physical analogy.” Both Maxwell and Hermann von Helmholtz appealed to the physical analogies between electromagnetism and hydrodynamics in their development of these theories. I argue that a closer historical (...) examination of the different ways in which Maxwell and Helmholtz each deployed this analogy gives further insight into debates about the representational and explanatory power of mathematical models. (shrink)

One can (for the most part) formulate a model of a classical system in either the Lagrangian or the Hamiltonian framework. Though it is often thought that those two formulations are equivalent in all important ways, this is not true: the underlying geometrical structures one uses to formulate each theory are not isomorphic. This raises the question whether one of the two is a more natural framework for the representation of classical systems. In the event, the answer is (...) yes: I state and prove two technical results, inspired by simple physical arguments about the generic properties of classical systems, to the effect that, in a precise sense, classical systems evince exactly the geometric structure Lagrangian mechanics provides for the representation of systems, and none that Hamiltonian mechanics does. The argument not only clarifies the conceptual structure of the two systems of mechanics, their relations to each other, and their respective mechanisms for representing physical systems. It also provides a decisive counter-example to the semantical view of physical theories, and one, moreover, that shows its crucial deficiency: a theory must be, or at least be founded on, more than its collection of models (in the sense of Tarski), for a complete semantics requires that one take account of global structures defined by relations among the individual models. The example also shows why naively structural accounts of theory cannot work: simple isomorphism of theoretical and empirical structures is not rich enough a relation to ground a semantics. (shrink)

In this paper a new trajectory-based representation to non-relativistic quantum mechanics is formulated. This is ahieved by generalizing the notion of Lagrangian path which lies at the heart of the deBroglie-Bohm “ pilot-wave” interpretation. In particular, it is shown that each LP can be replaced with a statistical ensemble formed by an infinite family of stochastic curves, referred to as generalized Lagrangian paths. This permits the introduction of a new parametric representation of the Schrödinger equation, denoted as GLP-parametrization, (...) and of the associated quantum hydrodynamic equations. The remarkable aspect of the GLP approach presented here is that it realizes at the same time also a new solution method for the N-body Schrödinger equation. As an application, Gaussian-like particular solutions for the quantum probability density function are considered, which are proved to be dynamically consistent. For them, the Schrödinger equation is reduced to a single Hamilton–Jacobi evolution equation. Particular solutions of this type are explicitly constructed, which include the case of free particles occurring in 1- or N-body quantum systems as well as the dynamics in the presence of suitable potential forces. In all these cases the initial Gaussian PDFs are shown to be free of the spreading behavior usually ascribed to quantum wave-packets, in that they exhibit the characteristic feature of remaining at all times spatially-localized. (shrink)

Because of the gradual aging of the population, hospital facilities for socio-sanitary care of the elderly are quite scarce relative to the very high number of elderly people present in the country. This has pushed a high number of families to privately hire home-care workers. The scientific literature gives a picture of the psycho-physical risks that this type of profession is exposed to; however, there is still a need for a more systemic reflection with regard to representations about their (...) role and competences. The aim of the present study is to outline the representations of the role and the skills it requires from home-care workers’ point of view. We reconstructed how home-care workers perceive and define the profession, and understand the necessary skills required from their point of view. Our results show that the professional profile of home-care workers still remains poorly defined and that professionals themselves struggle to find value and recognition, and to articulate what the skill set they develop is formed of. (shrink)

We generalize the results of Ref. 7 for the coherent states of a spin-1 entity to spin-S entities with S > 1 and to noncoherent spin states: through the introduction of “hidden correlations” (see Ref. 8) we introduce a representation for a spin-S entity as a compound system consisting of 2S “individual” spin-1/2 entities, each of them represented by a “proper state,” and such that we are able to consider a measurement on the spin-S entity as a measurement on (...) each of the individual spin1/2 entities. If the spin-S entity is in a maximal spin state, the 2S individual spin1/2 entities behave as a collection of indistinguishable but separated entities. If not so, we have to introduce the same kind of hidden correlations as required for a hidden correlation representation of a compound quantum system described by a symmetrical superposition. Moreover, by applying the Majorana representation of Ref. 11 and Aerts' representation for a spin-1/2 entity of Ref. 3, this hidden correlation representation yields a classical mechanistic representation of a spin-S entity in $ \mathbb{R}^{\text{3}} $. (shrink)

The representation of physics problems in relation to the organization of physics knowledge is investigated in experts and novices. Four experiments examine the existence of problem categories as a basis for representation; differences in the categories used by experts and novices; differences in the knowledge associated with the categories; and features in the problems that contribute to problem categorization and representation. Results from sorting tasks and protocols reveal that experts and novices begin their problem representations with specifiably (...) different problem categories, and completion of the representations depends on the knowledge associated with the categories. For, the experts initially abstract physics principles to approach and solve a problem representation, whereas novices base their representation and approaches on the problem's literal features. (shrink)

BACON.3 is a production system that discovers empirical laws. Although it does not attempt to model the human discovery process in detail, it incorporates some general heuristics that can lead to discovery in a number of domains. The main heuristics detect constancies and trends in data, and lead to the formulation of hypotheses and the definition of theoretical terms. Rather than making a hard distinction between data and hypotheses, the program represents information at varying levels of description. The lowest levels (...) correspond to direct observations, while the highest correspond to hypotheses that explain everything so for observed. To take advantage of this representation, BACON.3 has the ability to carry out and relate multiple experiments, collapse hypotheses with identical conditions, ignore differences to let similar concepts be treated as equal, and to discover and ignore irrelevant variables. BACON.3 has shown its generality by rediscovering versions of the ideal gas law, Kepler's third law of planetary motion, Coulomb's law, Ohm's law, and Galileo's laws for the pendulum and constant acceleration. (shrink)

In this paper we intend to discuss the importance of providing a physical representation of quantum superpositions which goes beyond the mere reference to mathematical structures and measurement outcomes. This proposal goes in the opposite direction to the project present in orthodox contemporary philosophy of physics which attempts to “bridge the gap” between the quantum formalism and common sense “classical reality”—precluding, right from the start, the possibility of interpreting quantum superpositions through non-classical notions. We will argue that in (...) order to restate the problem of interpretation of quantum mechanics in truly ontological terms we require a radical revision of the problems and definitions addressed within the orthodox literature. On the one hand, we will discuss the need of providing a formal redefinition of superpositions which captures explicitly their contextual character. On the other hand, we will attempt to replace the focus on the measurement problem, which concentrates on the justification of measurement outcomes from “weird” superposed states, and introduce the superposition problem which focuses instead on the conceptual representation of superpositions themselves. In this respect, after presenting three necessary conditions for objective physical representation, we will provide arguments which show why the classical representation of physics faces severe difficulties to solve the superposition problem. Finally, we will also argue that, if we are willing to abandon the presupposition according to which ‘Actuality = Reality’, then there is plenty of room to construct a conceptual representation for quantum superpositions. (shrink)

The concept of representation has been a key element in the scientific study of mental processes, ever since such studies commenced. However, usage of the term has been all but too liberal—if one were to adhere to common use it remains unclear if there are examples of physical systems which cannot be construed in terms of representation. The problem is considered afresh, taking as the starting point the notion of activity spaces—spaces of spatiotemporal events produced by (...) dynamical systems. It is argued that representation can be analyzed in terms of the geometrical and topological properties of such spaces. Several attributes and processes associated with conceptual domains, such as logical structure, generalization and learning are considered, and given analogues in structural facets of activity spaces, as are misrepresentation and states of arousal. Based on this analysis, representational systems are defined, as is a key concept associated with such systems, the notion of representational capacity. According to the proposed theory, rather than being an all or none phenomenon, representation is in fact a matter of degree—that is can be associated with measurable quantities, as is behooving of a putative naturalistic construct. (shrink)

1. Throughout the paper, and especially in the section called "LISP vs. DST", I worried that there was not enough focus on EXPLANATION. For the real question, it seems to me, is not whether some dynamical system can implement human cognition, but whether the dynamical description of the system is more explanatorily potent than a computational/representational one. Thus we know, for example, that a purely physical specification can fix a system capable of computing any LISP function. But from this (...) it doesn't follow that the physical description is the one we need to understand the power of the system considered as an information processing device. In the same way, I don't think your demonstration that bifurcating attractor sets can yield the same behavior as a LISP program goes any way towards showing that we should not PREFER the LISP description. To reduce symbolic stories to a subset of DST (as hinted in that section) requires MORE than showing this kind of equivalence: it requires showing that there is explanatory gain, or at the very least, no explanatory loss, at that level. I append an extract from a recent paper of mine that touches on these issues, in case it helps clarify what I am after here. (shrink)

The representation of a rose varies considerably across philosophical, religious, and scientific schools of thought. While many would suggest that a rose exists objectively, as a physical object in geometric space reducible to fundamental particles such as atoms or quarks, others propose that a rose is an emergent whole that exists meaningfully when experienced subjectively for its sweet fragrance and red hue, its soft petals and thorny stem. Some might even maintain that a rose is “consciousness-only,” having no (...) existence apart from conscious perception. Thus, we find a spectrum of realist to idealist perspectives. Even in Dharma studies, with a common basis in Indian thought, the Vaiśeṣikas, Vaibhāṣikas, and the vijñaptimātra doctrine of the Yogācārin-Vijñānavādins entertain diverging perspectives. On one hand, the Vaiśeṣikas, a school of Vedic philosophy, propounded a theory of reality in the form of indivisible, eternal atoms, a metaphysical approach counter to the doctrine of not-self (anātman) in Buddhism. The Vaibhāṣikas, a school of early Buddhist atomism, on the other hand, denied the existence of a true self or eternal soul (ātman) as substratum for reality but maintained their own theory of atomism. For the Vaibhāṣikas, the flow of consciousness may be segmented into discrete moments, yet unlike many of their Buddhist contemporaries from other schools, they asserted that all cognizable phenomena are truly existent insofar as they consist of physically irreducible atoms. Among their objectors were the Yogācārin-Vijñānavādins who proposed the theory of consciousness-only (vijñaptimātra), rejecting the independent existence of indivisible atoms and discrete moments of time. This paper introduces the dialectic that formed between these schools through Vasubandhu’s fourth century C.E. text Twenty Verses on Consciousness-Only (Viṃśikāvijñaptimātratāsiddhi). While the gulf between the realist and idealist positions may seem, at times, irreconcilable, we integrate findings from the field of physics, particularly quantum mechanics (and several philosophical interpretations thereof) within the realm of modern science as a possible bridge between these otherwise seemingly disparate systems of Dharma. (shrink)

A purely probabilistic-informational model of evolutions is sketched, basically free of any assumption concerning the nature and structure of the evolving system but apt to incorporatea posteriori any such assumptions needed for application to a specified evolution. The model produces an abstract extension of the second principle of thermodynamics. It also leads to an outline of a typology of irreversible evolutions.

This paper argues that ordinary object languages for fundamental physics are incomplete, essentially because they are extensional, and consequently lack any adequate formal representation of contingency. It is shown that it is impossible to formulate adequate deduction systems for general transformations in such languages. This is argued in detail for the time reversal transformation. Two important controversies about the application of time reversal in quantum mechanics are summarized at the start, to provide the context of this problem, and (...) show its serious implications, but the aim here is not to solve these problems. The flaw is not special to quantum mechanics: it is a general feature traced to extensionality, and demonstrated through a simple example in classical physics. It is proposed that this defect can be overcome by extending to an intensional semantics, but this involves extending the usual formalism of physics. A detailed proposal for such an extension is given in Part 2. (shrink)

The Vitruvian Man of Leonardo da Vinci is one of the most famous and most studied drawings over the world as well as one of the most reproduced ones, e.g. in coins, space suit patches, books and movies. The aim of the present work is to discuss the Vitruvian Man as a figurative representation of the Leonardo’s scientific method. Our analysis is based on scientific elements both present in the drawing and provided by Leonardo in his approach to this (...) drawing. Our thesis is that the square symbolizes the measurable physical world and that the man inscribed within the square refers to the physics measurement process based on the operational definition of quantities, including the measurement unit system and the quantities conversion factors. Therefore, the measurement process is fundamental for the Leonardo’s approach to the scientific knowledge, albeit, the drawing also suggests that this latter does not correspond with the true knowledge. The circle, which has a different center with respect to the square, symbolizes the truth, to which the man inscribed in the square yearns, without ever achieving it, the truth being reachable only by the man inscribed within the circle. (shrink)

We introduce an explicit definition for “hidden correlations” on individual entities in a compound system: when one individual entity is measured, this induces a well-defined transition of the “proper state” of the other individual entities. We prove that every compound quantum system described in the tensor product of a finite number of Hilbert spaces can be uniquely represented as a collection of individual entities between which there exist such hidden correlations. We investigate the significance of these hidden correlation representations within (...) Aerts' creation-discovery approach and in particular their compatibility with the hidden measurement formalism. This leads us to the introduction of the notions of “soft” and “hard” “acts of creation” and to the observation that our approach can be seen as a theory of individuals when it is compared to the standard quantum theory. (shrink)

This paper deals with the question: what are the key requirements for a physical system to perform digital computation? Time and again cognitive scientists are quick to employ the notion of computation simpliciter when asserting basically that cognitive activities are computational. They employ this notion as if there was or is a consensus on just what it takes for a physical system to perform computation, and in particular digital computation. Some cognitive scientists in referring to digital computation simply (...) adhere to Turing’s notion of computability . Classical computability theory studies what functions on the natural numbers are computable and what mathematical problems are undecidable. Whilst a mathematical formalism of computability may perform a methodological function of evaluating computational theories of certain cognitive capacities, concrete computation in physical systems seems to be required for explaining cognition as an embodied phenomenon . There are many non-equivalent accounts of digital computation in physical systems. I examine only a handful of those in this paper: (1) Turing’s account ; (2) The triviality “account”; (3) Reconstructing Smith’s account of participatory computation ; (4) The Algorithm Execution account . My goal in this paper is twofold. First, it is to identify and clarify some of the underlying key requirements mandated by these accounts. I argue that these differing requirements justify a demand that one commits to a particular account when employing the notion of computation in regard to physical systems. Second, it is to argue that despite the informative role that mathematical formalisms of computability may play in cognitive science, they do not specify the relationship between abstract and concrete computation. (shrink)

Incorporating a discussion of physical and emotional trauma in medical education can help prepare students for their encounters with trauma survivors in clinical practice. A pedagogical approach begins with an inquiry into the purpose of historical or current representations of torture. Justifications include rationalizing state-sponsored torture, providing an outlet for critique and protest, and organizing representations of the enemy. Discussions of torture must further address the emotional and symbolic effects of clinical work with torture survivors on the caregiver. Introductory (...) workshops using visual representations can trigger pain, fear and anger in the viewer. Images of torture, war, and genocide may also invoke ethical concerns relating to the impact of visual images, where viewing can elicit an ambiguous response, casting the viewer into the role of voyeur. At the same time, learners should recognize that indifference or inattention to the provocations mediated through images has its own liabilities, signaling defensiveness. Discussions about the respective roles of perpetrators, victims and observers offer opportunities for the viewer to engage in self-reflection. Artistic representations also offer opportunities for advocacy on the survivor’s behalf, sometimes facilitated by dissemination of visual representations, but also by involving the survivors themselves in activities that exploit the healing power of art. (shrink)

This communication is part I of a series of papers which explore the theoretical possibility of generalizing quantum dynamics in such a way that the predicted motions of an isolated system would include the irreversible (entropy-increasing) state evolutions that seem essential if the second law of thermodynamics is ever to become a theorem of mechanics. In this first paper, the general mathematical framework for describing linear but not necessarily Hamiltonian mappings of the statistical operator is reviewed, with particular attention to (...) detailed representations of the Kossakowski conditions for the case of a two-level system. (shrink)

It is often supposed that we can use mathematics to capture the time evolution of any physical system. By this, I mean that we can capture the basic truths about the time evolution of a physical system with a set of mathematical assertions, which can then be used as premises in arbitrary mathematical arguments to deduce more complex properties of the system. ;I would like to argue that this picture of the role of mathematics in physics is incorrect. (...) Specifically, I shall assert: ;The Deduction Failure Thesis: Bodies of knowledge in physics are generally not closed under otherwise valid mathematical argument forms. ;The Representation Failure Thesis: We cannot assume that the state of any system, together with its fundamental laws, can be captured by some set of mathematical assertions or equations. In fact, it is more likely that the world is not representable by a set of mathematical assertions or equations than that it is. ;The dissertation largely consists of arguments for these two theses. (shrink)

In this paper, we argue for the centrality of prediction in the use of computational models in science. We focus on the consequences of the irreversibility of computational models and on the conditional or ceteris paribus, nature of the kinds of their predictions. By irreversibility, we mean the fact that computational models can generally arrive at the same state via many possible sequences of previous states. Thus, while in the natural world, it is generally assumed that physical states have (...) a unique history, representations of those states in a computational model will usually be compatible with more than one possible history in the model. We describe some of the challenges involved in prediction and retrodiction in computational models while arguing that prediction is an essential feature of non-arbitrary decision making. Furthermore, we contend that the non-predictive virtues of computational models are dependent to a significant degree on the predictive success of the models in question. (shrink)

1. Throughout the paper, and especially in the section called "LISP vs. DST", I worried that there was not enough focus on EXPLANATION. For the real question, it seems to me, is not whether some dynamical system can implement human cognition, but whether the dynamical description of the system is more explanatorily potent than a computational/representational one. Thus we know, for example, that a purely physical specification can fix a system capable of computing any LISP function. But from this (...) it doesn't follow that the physical description is the one we need to understand the power of the system considered as an information processing device. In the same way, I don't think your demonstration that bifurcating attractor sets can yield the same behavior as a LISP program goes any way towards showing that we should not PREFER the LISP description. To reduce symbolic stories to a subset of DST (as hinted in that section) requires MORE than showing this kind of equivalence: it requires showing that there is explanatory gain, or at the very least, no explanatory loss, at that level. I append an extract from a recent paper of mine that touches on these issues, in case it helps clarify what I am after here. (shrink)

We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in [Maudlin 2012] and [Malament, unpublished]. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of [Tarski 1959]: a predicate of betwenness and (...) a four place predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional ‘vector space’ that can be decomposed everywhere into a spacelike hyperplane - which obeys the Euclidean axioms in [Tarski and Givant, 1999] - and an orthogonal timelike line. The length of other ‘vectors’ are calculated according to Pythagora’s theorem. We conclude with a Representation Theorem relating models of our system that satisfy second order continuity to the mathematical structure called ‘Minkowski spacetime’ in physics textbooks. (shrink)

Given that theoretical analysis and empirical validation is fundamental to any model, whether conceptual or formal, it is surprising that these two tools of scientific discovery are so often ignored in contemporary studies of communication. In this paper, we pursued the ideas of a) correcting and expanding the modeling approaches of linguistics, which are otherwise inapplicable, to the general case of hypermedia-based communication, and b) developing techniques for empirical validation of semiotic models, which are nowadays routinely used to explore internal (...) mechanisms of complex systems, yet on a purely speculative basis. This study thus offers two experimentally tested substantive contributions: the formal representation of communication as the mutually-orienting behavior of coupled autonomous systems, and the mathematical interpretation of the semiosis of communication, which together offer a concrete and parsimonious understanding of diverse communication phenomena. (shrink)