After briefly discussing the relevance of the notions computation and implementation for cognitive science, I summarize some of the problems that have been found in their most common interpretations. In particular, I argue that standard notions of computation together with a state-to-state correspondence view of implementation cannot overcome difficulties posed by Putnam's Realization Theorem and that, therefore, a different approach to implementation is required. The notion realization of a function, developed out of physical theories, is then introduced as a (...) replacement for the notional pair computation-implementation. After gradual refinement, taking practical constraints into account, this notion gives rise to the notion digital system which singles out physical systems that could be actually used, and possibly even built. (shrink)

The purpose of this paper is to sketch an attack on the general problem of representing a composite physical system in terms of its constituent parts. For quantum-mechanical systems, this is traditionally accomplished by forming either direct sums or tensor products of the Hilbert spaces corresponding to the component systems. Here, a more general mathematical construction is given which includes the standard quantum-mechanical formalism as a special case.

Intentionality is characteristic of many psychological phenomena. It is commonly held by philosophers that intentionality cannot be ascribed to purely physical systems. This view does not merely deny that psychological language can be reduced to physiological language. It also claims that the appropriateness of some psychological explanation excludes the possibility of any underlying physiological or causal account adequate to explain intentional behavior. This is a thesis which I do not accept. I shall argue that physical systems of a (...) specific sort will show the characteristic features of intentionality. Psychological subjects are, under an alternative description, purely physical systems of a certain sort. The intentional description and the physical description are logically distinct, and are not intertranslatable. Nevertheless, the features of intentionality may be explained by a purely causal account, in the sense that they may be shown to be totally dependent upon physical processes. (shrink)

This dissertation elucidates the notion of physical system which opens new conceptual pathways that connect the three realms of physical theory; spacetime, material bodies and their properties, and the laws of nature which govern their evolution. The notion of physical system includes two presuppositions regarding their structure. The first presupposition is a description of isolated systems and their evolution in time, which amounts to a Paradigm of Uniform Motion. The second presupposition describes how parts of (...) a physical system are combined into wholes. This presupposition amounts to a Rule of Composition. Once we make these presuppositions explicit we can derive the spacetime structures and the fundamental equations of motion. "Newtonian" and "relativistic" systems are shown to differ with respect to the paradigm of uniform motion, a difference that leads to the respective structures of Newtonian mechanics and the Special Theory of Relativity. ;The philosophical framework offered in this dissertation provides a new interpretation of the concept of mass, and a new elucidation of the relation between the conservations of mass and momentum. Previous analyses of the concept have claimed that "mass" cannot be defined and broken down to more primitive predicates. The framework offered here, on the other hand, enables the systematic reduction of the concept of mass to motions and the presuppositions we have regarding the nature of physical systems. The new interpretation of mass reveals a surprising connection between mass and inertial reference frames, as they are both shown to be derived, in a similar way, from our definition of physical systems. Mass is by necessity attributed to bodies in virtue of the frame we use to describe their motions. This account also enables us to understand the different conceptual roles of mass and their interconnections. In the context of Newtonian mechanics, the roles of mass as a Quantity of Matter, as the Inertial property of bodies, and as Gravitational mass are shown to be various aspects of a single role the concept has in the new framework offered here. In the context of the Special Theory of Relativity, rest mass and relativistic mass are similarly analyzed as consequences of our presuppositions regarding physical systems. (shrink)

A blockchain can be considered a technological phenomenon that is made up of different interconnected and autonomous systems. Such systems are referred to here as cyber-physical systems: complex interconnections of cyber and physical components. When cyber-physical systems are interconnected, a new whole consisting of a system of systems is created by the autonomous systems and their intercommunication and interaction. In a blockchain, individual systems can independently make decisions on joint information transactions. The decision-making procedures needed for (...) this are executed based on fault-tolerant communication and voting and consensus procedures, while the results of these decision-making procedures are stored in distributed ledgers. Due to the intercommunication, interaction, and independent decision making by autonomous systems, the new whole of a blockchain is a complex entity. Complexity science rather than the usual reductionist scientific approach can help us better understand the behaviour of the new and continuously developing whole of a blockchain as a technological phenomenon. (shrink)

A universal, unified theory of transformations of physical systems based on the propositions of probabilistic physics is developed. This is applied to the treatment of decay processes and intramolecular rearrangements. Some general features of decay processes are elucidated. A critical analysis of the conventional quantum theories of decay and of Slater's quantum theory of intramolecular rearrangements is given. It is explained why, despite the incorrectness of the decay theories in principle, they can give correct estimations of decay rate constants. (...) The reasons for the validity of the Arrhenius formula for the temperature dependence of an intramolecular rearrangement rate constant are discussed. A criterion for the possibility of a proper intramolecular rearrangement is given. The issue of causality in quantum physics is settled. (shrink)

Structural analogies between physical laws have received considerable attention from philosospheres of science. This paper, however, focusses on structural analogies between physical systems; this type of analogy plays an important role in the physical and technological sciences. A formal, set-theoretic description of structural analogies between physical systems is presented, and it is shown that a structural analogy between systems does not require a structural analogy with regard to the laws involved, nor conversely.

This article conducts a literature review of current and future challenges in the use of artificial intelligence in cyber physical systems. The literature review is focused on identifying a conceptual framework for increasing resilience with AI through automation supporting both, a technical and human level. The methodology applied resembled a literature review and taxonomic analysis of complex internet of things interconnected and coupled cyber physical systems. There is an increased attention on propositions on models, infrastructures and frameworks of (...) IoT in both academic and technical papers. These reports and publications frequently represent a juxtaposition of other related systems and technologies. We review academic and industry papers published between 2010 and 2020. The results determine a new hierarchical cascading conceptual framework for analysing the evolution of AI decision-making in cyber physical systems. We argue that such evolution is inevitable and autonomous because of the increased integration of connected devices in cyber physical systems. To support this argument, taxonomic methodology is adapted and applied for transparency and justifications of concepts selection decisions through building summary maps that are applied for designing the hierarchical cascading conceptual framework. (shrink)

This book provides an introduction to applied statistical mechanics by considering physically realistic models. It provides a simple and accessible introduction to theories of thermal fluctuations and diffusion, and goes on to apply them in a variety of physical contexts. The first part of the book is devoted to processes in thermal equilibrium, and considers linear systems. Ideas central to the subject, such as the fluctuation dissipation theorem, Fokker-Planck equations and the Kramers-Kroenig relations are introduced during the course of (...) the exposition. The scope is then expanded to include non-equilibrium systems and also illustrates simple nonlinear systems. This book will be of interest to final year undergraduate and graduate students studying statistical mechanics, plasma physics, basic electronics, solid state physics and anyone who wants an accessible introduction to the subject. (shrink)

We present a content markup language for physics realized by extending the OMDoc format by an infrastructure for the principal concepts of physics: observables, physical systems, and experiments.

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)

The relationship between abstract formal procedures and the activities of actual physical systems has proved to be surprisingly subtle and controversial, and there are a number of competing accounts of when a physical system can be properly said to implement a mathematical formalism and hence perform a computation. I defend an account wherein computational descriptions of physical systems are high-level normative interpretations motivated by our pragmatic concerns. Furthermore, the criteria of utility and success vary according to (...) our diverse purposes and pragmatic goals. Hence there is no independent or uniform fact to the matter, and I advance the ‘anti-realist’ conclusion that computational descriptions of physical systems are not founded upon deep ontological distinctions, but rather upon interest-relative human conventions. Hence physical computation is a ‘conventional’ rather than a ‘natural’ kind. (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)

The determination of the past and the future of a physical system are complementary aims of measurements. An optimal determination of the past of a system can be achieved by an informationally complete set of physical quantities. Such a set is always strongly noncommutative. An optimal determination of the future of a physical system can be obtained by a Boolean complete set of quantities. The two aims can be reconciled to a reasonable degree with (...) using unsharp measurements. (shrink)

Physical systems without time and dynamics have been considered. The principle of how to construct spacetime in a physical system without time and dynamics has been proposed. It has been found what can be objects in such a spacetime, and what can be an interaction between such objects. Within the framework of the considered class of systems, answers to the following problems of philosophy and physics have been found: the nature of consciousness and the connection of body (...) and consciousness (mind-body problem), the nature of time, the anthropic principle and the problem of fine-tuning the universe, the effectiveness of mathematics in describing physical phenomena, the limits of knowledge. There are a number of indications that our Universe is not based on one of the systems of the class considered. The considered class of systems makes it possible to find answers to questions that cannot be answered for our Universe. This shows that it is fundamentally possible to find answers to these questions for our Universe as well. (shrink)

According to pancomputationalism, all physical systems – atoms, rocks, hurricanes, and toasters – perform computations. Pancomputationalism seems to be increasingly popular among some philosophers and physicists. In this paper, we interpret pancomputationalism in terms of computational descriptions of varying strength—computational interpretations of physical microstates and dynamics that vary in their restrictiveness. We distinguish several types of pancomputationalism and identify essential features of the computational descriptions required to support them. By tying various pancomputationalist theses directly to notions of what (...) counts as computation in a physical system, we clarify the meaning, strength, and plausibility of pancomputationalist claims. We show that the force of these claims is diminished when weaknesses in their supporting computational descriptions are laid bare. Specifically, once computation is meaningfully distinguished from ordinary dynamics, the most sensational pancomputationalist claims are unwarranted, whereas the more modest claims offer little more than recognition of causal similarities between physical processes and the most primitive computing processes. (shrink)

One of the main driving forces in the era of cyber-physical systems is the introduction of massive sensor networks into manufacturing processes, connected cars, precision agriculture, and so on. Therefore, large amounts of sensor data have to be ingested at the server side in order to generate and make the “twin digital model” or virtual factory of the existing physical processes for predictive simulation and scheduling purposes usable. In this paper, we focus on our ultimate goal, a novel (...) software container-based approach with cloud agnostic orchestration facilities that enable the system operators in the industry to create and manage scalable, virtual IT platforms on-demand for these two typical major pillars of CPS: server-side framework for sensor networks and configurable simulation tool for predicting the behavior of manufacturing systems. The paper discusses the scalability of the applied discrete-event simulation tool and the layered back-end framework starting from simple virtual machine-level to sophisticated multilevel autoscaling use case scenario. The presented achievements and evaluations leverage on the synergy of the existing EasySim simulator, our new CQueue software container manager, the continuously developed Occopus cloud orchestrator tool, and the latest version of the evolving MiCADO framework for integrating such tools into a unified platform. (shrink)

Nunez's description of the brain as a medium capable of wave propagation has provided some fundamental insights into its dynamics. This approach soon reaches the descriptive limits of the brain as a physical system, however. We point out some biological constraints which differentiate the brain from physical systems and we elaborate on its consequences for future research.

When people make judgments about the effects of a perturbation on populations of species in a food web, their judgments exhibit the dissipation effect: a tendency to judge that effects of the perturbation weaken or dissipate as they spread out through the food web from the locus of the perturbation. In the present research evidence for two more phenomena is reported. Terminal locations are points in the food web with just a single connection to the rest of the web. Judged (...) changes tended to be higher for species at terminal locations than for species the same distance from the perturbation but at nonterminal locations. Branches are points in the web where a route splits into two or more routes. Judged changes tended to be lower for species following branching points than for species the same distance from the perturbation but not following branching points. It is proposed that the findings can be explained as effects of a mental model employing concepts of influence and resistance. Under this model a perturbation is a change in energy level at a point in the system that acts as an influence affecting the rest of the system. The basic concepts in this model are domain‐general and on that basis it is predicted that the dissipation effect should be found in judgments of any physical system to which notions of influence and resistance can be applied. (shrink)

The Gibbs' Paradox is commonly explained by invoking some type of "principle of indistinguishability," which asserts that the interchange of identical particles is not a real physical event, i.e., is operationally meaningless. However, if this principle is to provide a satisfactory resolution of the Paradox, it must be operationally possible to determine whether, in fact, two given systems are identical or not. That is, the assertion that the Gibbs' Paradox is resolvable by an indistinguishability principle actually is an assertion (...) that we can in principle possess a complete set of effective procedures for determining the identity or non-identity of arbitrary physical systems. We show that, in rather general situations, an assertion of this type is not well founded. It is further pointed out that a failure to recognize an incomplete set of "sameness criteria" can lead to serious blunders in physics and in biology. (shrink)

From the perspective of the system of systems development, system-level functional testing is required for designing subsystems. This study utilizes modeling and simulation techniques to analyze the operational behaviors of the subsystems and confirm data communication between them. The targeted system in the study is a naval combat system, which is a typical type of defense cyber-physical system. Three types of models were designed for the simulation testing of the NCS: a combat-management model for (...) simulating the overall computational activities, physical models to confirm the intrasubsystem behaviors, and data integration models to test the intersubsystem communications. These models are realized with the Model-View-ViewModel design pattern, which strongly facilitates graphical user interfaces being decoupled from model logic and data. We consider underwater combat scenarios as an application. Six significant physical subsystems within the NCS are simulated and tested: a ship-steering system, an inertial navigation system, a global navigation satellite system, a periscope, sonar systems, and a plotting board. We expect that the proposed work will play a principal role when analyzing the behaviors and communications of defense CPSs and providing an environment for functional testing as a digital twin. (shrink)

The connection of the structure of statistical selection procedures with measure theory is investigated. The methods of measure theory are applied in order to analyze a mathematical description of preparation and registration of physical systems that is used by G. Ludwig for a foundation of quantum mechanics.

It is commonly the case that a problem concerning a mathematical or physical system can be solved in two quite different ways--by an internal or an external approach. For example, the area of a triangle can be found by integration or by showing it to be half that of a certain rectangle. In general, the first approach is, to analyse the given system into component parts, and the second approach is to deal with the system as (...) a whole. It seems that even in cases where solutions to physical problems obtained according to these two approaches are equally valid, and are equally good as explanations, scientists prefer the solution obtained by the internal approach. The reasons for this preference are examined. And it is suggested that whatever the reasons, this preference may have been partly responsible for the 19th century preference for the Kinetic Theory rather than Thermodynamics. (shrink)

When we are concerned with the logical form of a computation and its formal properties, then it can be theoretically described in terms of mathematical and logical functions and relations between abstract entities. However, actual computation is realised by some physical process, and the latter is of course subject to physical laws and the laws of thermodynamics in particular. An issue that has been the subject of much controversy is that of whether or not there are any systematic (...) connections between the logical properties of computations considered abstractly and the thermodynamical properties of their concrete physical realizations. Landauer [R. Landauer, Irreversibility and heat generation in the computing process, IBM Journal of Research and Development 5 183–191. Reprinted in Leff and Rex ] proposed such a general connection, known as Landauer’s Principle. To resolve this matter an analysis of the notion of the implementation of a computation by a physical system is clearly required. Another issue that calls for an analysis of implementation is that of realism about computation. The account of implementation presented here is based on the notion of an L-machine. This is a hybrid physical-logical entity that combines a physical device, a specification of which physical states of that device correspond to various logical states, and an evolution of that device which corresponds to the logical transformation L. The most general form of Landauer’s Principle can be precisely stated in terms of L-machines, namely that the logical irreversibility of L implies the thermodynamic irreversibility of every corresponding L-machine. (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)

Speculations about the role of consciousness in physical systems are frequently observed in the literature concerned with the interpretation of quantum mechanics. While only three experimental investigations can be found on this topic in physics journals, more than 800 relevant experiments have been reported in the literature of parapsychology. A well-defined body of empirical evidence from this domain was reviewed using meta-analytic techniques to assess methodological quality and overall effect size. Results showed effects conforming to chance expectation in control (...) conditions and unequivocal non-chance effects in experimental conditions. This quantitative literature review agrees with the findings of two earlier reviews, suggesting the existence of some form of consciousness-related anomaly in random physical systems. (shrink)

The implementation of cyber-physical and similar systems depends on prevailing social and economic conditions. It is here argued that, if the effect of these technologies is to be benign, the current neo-liberal economy must change to a radically more cooperative model. In this paper, economy change means a thorough change to a qualitatively different kind of economy. It is contrasted with economic change, which is the kind of minor change usually considered in mainstream discourse. The importance of language is (...) emphasised, including that of techno-optimism and that of economic conservatism. Problems of injustice, strife, and ecological overload cannot be solved by conventional growth together with technical efficiency gains. Rather, a change is advocated from economics-as-usual to a broader concept, oikonomia, which takes into account all that contributes to a good life, including what cannot be represented quantitatively. Some elements of such a broader economy are discussed. It is argued that the benefits of technology can be enhanced and the ills reduced in such an economy. This is discussed in the case of cyber-physical systems under the headings employment, security, standards and oligopoly, and energy efficiency. The paper concludes that such systems, and similar technological developments, cannot resolve the problems of sustainability within an economy-as-usual model. If, however, there is the will to create a cooperative and sustainable economy, technology can contribute significantly to the resolution of present problems. (shrink)

When dealing with a certain class of physical systems, the mathematical characterization of a generic system aims to describe the phase portrait of all its possible states. Because they are defined only up to isomorphism, the mathematical objects involved are “schematic structures”. If one imposes the condition that these mathematical definitions completely capture the physical information of a given system, one is led to a strong requirement of individuation for physical states. However, we show there (...) are not enough qualitatively distinct properties in an abstract Hilbert space to fulfill such a requirement. It thus appears there is a fundamental tension between the physicist’s purpose in providing a mathematical definition of a mechanical system and a feature of the basic formalism used in the theory. We will show how group theory provides tools to overcome this tension and to define physical properties. (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)

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)

In the following we will apply the manipulability theory of causation of Woodward (2004) to physical systems, and show that, in the context of physical systems, the theory can be simplified. Elaborating on an argument by Cartwright, we will argue that the notions of ‘modularity’ and ‘intervention’ of the cited work should be adapted for typical physical systems, in order to take into account the coupling of system equations. We will show that this allows the reduction (...) of all cause types discussed in Woodward (2004) to only one, namely that of ‘total cause’. We therefore claim that the manipulability account can be drastically simplified when applied to coupled physical systems. (shrink)

The system reachability set is calculated by covering all possible behaviours of the system through a finite number of simulation steps to ensure that the system trajectory stays within a set safety region. In this paper, the theory of the game method is applied to the design of the controller, a very small controller is designed, and good control results are obtained by simulation. The system gradually shows a divergent trend and cannot achieve stable control. A (...) multihop channel reservation Medium Access Control protocol based on a parallel mechanism is proposed. The multihop channel reservation mechanism is proposed based on periodic node sleep, and the node uses the reservation frame to make the reservation of the channel and transmits the data according to the reservation information; the parallel mechanism is used to make the reservation information and data transmission simultaneously. (shrink)

Human contact is a key issue in social interactions for autonomous systems since robots are increasingly appearing everywhere, which has led to a higher risk of conflict. Particularly in the real world, collisions between humans and machines may result in catastrophic accidents or damaged goods. In this paper, a novel stop strategy related to autonomous systems is proposed. This control method can eliminate the vibrations produced by a system’s movement by analysing the poles and zeros in the model of (...) autonomous vehicles and goods. Using the pole placement technique, the motion of a system is guaranteed to be more stable, more flexible and smoother. Moreover, several control profiles are employed in the switching mechanism to choose the proper vibration-free effect. The main contributions of this paper are the recommendation of an active stopping planner using different smooth generators from a modelling study, the validation of their physical characteristics and the launching of a switching algorithm based on the socially aware navigation framework of a robot. This theoretical work is based on the virtual environment of MATLAB, and the experiment is implemented in the practical platform of an automated guided vehicle. From these results, it can be seen that the proposed approach is robust, effective and feasible for applications in storehouse management, public transportation or factory manufacturing. (shrink)

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)

The canonical proper time formulation of relativistic dynamics provides a framework from which one can describe the dynamics of classical and quantum systems using the clock of those very systems. The framework utilizes a canonical transformation on the time variable that is used to describe the dynamics, and does not transform other dynamical variables such as momenta or positions. This means that the time scales of the dynamics are described in terms of the natural local time coordinates, which is the (...) most meaningful parameterization of phenomena such as the approach to equilibrium, or the back reaction of interacting systems. We summarize the formalism of the canonical proper time framework, and provide example calculations of the eigenvalues of the hydrogen atom and near horizon description of a scalar field near a Schwarzschild black hole. (shrink)

We consider consciousness attributed to systems in space-time which can be purely physical without biological background and focus on the mathematical understanding of the phenomenon. It is shown that the set theory based on sets in the foundations of mathematics, when switched to set theory based on ZFC models, is a very promising mathematical tool in explaining the brain/mind complex and the emergence of consciousness in natural and artificial systems. We formalise consciousness-supporting systems in physical space-time, but this (...) is localised in open domains of spatial regions and the result of this process is a family of different ZFC models. Random forcing, as in set theory, corresponds precisely to the random influence on the system of external stimuli, and the principles of reflection of set theory explain the conscious internal reaction of the system. We also develop the conscious Turing machines which have their external ZFC environment and the dynamics is encoded in the random forcing changing models of ZFC in which Turing machines with oracles are formulated. The construction is applied to cooperating families of conscious agents which, due to the reflection principle, can be reduced to the implementation of certain concurrent games with different levels of self-reflection. (shrink)

Despite an increasing role of machine learning in science, there is a lack of results on limits of empirical exploration aided by machine learning. In this paper, we construct one such limit by proving undecidability of learnability of state spaces of physical systems. We characterize state spaces as binary hypothesis classes of the computable Probably Approximately Correct learning framework. This leads to identifying the first limit for learnability of state spaces in the agnostic setting. Further, using the fact that (...) finiteness of the combinatorial dimension of hypothesis classes is undecidable, we derive undecidability for learnability of state spaces as well. Throughout the paper, we try to connect our formal results with modern neural networks. This allows us to bring the limits close to the current practice and make a first step in connecting scientific exploration aided by machine learning with results from learning theory. (shrink)

There are two kinds of such limiting results that must be carefully distinguished. Results of the first kind state the nonexistence of any algorithm for determining whether any statement among a given set of statements is true or false.