This article reviews the interactions between Russell and the English mathematician Max Newman. The most substantial one occurred in 1928, when Newman published some penetrating criticisms of Russell’s philosophy of science, and followed up with two long letters to Russell on logical knowledge and on the potential use of topology in physics. The exchange, which opened up some issues in Russell’s philosophy that he did not fully cope with either at the time or later, is transcribed here. Their (...) joint involvements with the Royal Society of London are also recorded. (shrink)

The standard mathematical account of the sub-metrical geometry of a space employs topology, whose foundational concept is the open set. This proves to be an unhappy choice for discrete spaces, and offers no insight into the physical origin of geometrical structure. I outline an alternative, the Theory of Linear Structures, whose foundational concept is the line. Application to Relativistic space-time reveals that the whole geometry of space-time derives from temporal structure. In this sense, instead of spatializing time, Relativity temporalizes (...) space. (shrink)

This commentary starts with a simplified Cartesian vector space of the tristimulus theory of color. This vector space is then further simplified so that bitstrings are used to represent the vector space. The Commission Internationale de l'Eclairage (CIE) diagram is shown to follow directly and simply from this vector space. The Berlin & Kay results are shown to agree quite well with the vector space and the two-dimensional version of it, especially if the dimensions are normalized to take into account (...) the sensitivity of the eye to the different wavelengths comprising color. There is asymmetry with respect to the colors and a similar asymmetry in vocalic phonemes; these effects can be explained in terms of physiology. The (in)famous problem of the color channels is given a unified treatment at various levels. An eight-valued color algebra is created, with addition and multiplication corresponding to additive and subtractive blending of colors. Finally, it is shown that the discrete Hamming metric for colors has a natural toroidal topology. (shrink)

Topology and geometry have played an important role in our theoretical understanding of quantum field theories. One of the most interesting applications of topology has been the quantization of certain coupling constants. In this paper, we present a general framework for understanding the quantization itself in the light of group cohomology. This analysis of the cohomological aspects of physics leads to reconsider the very foundations of mechanics in a new light.

. The deep structural properties of a quantum information theoretic approach to formal languages and universal computation, as well as those of the topology problem of defining the presentation of the Mapping Class Group of a smooth, compact manifold are shown to be grounded in the common categorical features of the two problems.

Hans Reichenbach’s posthumous book The Direction of Time ends somewhere between Socratic aporia and historical irony. Prompted by Feynman’s diagrammatic formulation of quantum electrodynamics, Reichenbach eventually abandoned the delicate balancing between the macroscopic foundation of the direction of time and microscopic descriptions of time order undertaken throughout the previous chapters in favor of an exclusively macroscopic theory that he had vehemently rejected in the 1920s. I analyze Reichenbach’s reasoning against the backdrop of the history of Feynman diagrams and the current (...) practice of particle physics. Building upon the debates about processes and conserved quantities between Wesley Salmon and Phil Dowe in the 1990s, and the exchange between Reichenbach and the gestalt theorist Kurt Lewin during the 1920s about topology and genidentity, I investigate whether the aporia about local time order could be avoided by following a strategy that Reichenbach adopted elsewhere in the book and develop a notion of functional genidentity that captures the practice of present-day elementary particle physics and the fact that Feynman diagrams have to be understood in the context of a complex mathematical description of scattering processes. (shrink)

For the most part, this is a fairly literal translation, but I have opted for a few English idioms for the sake of readability. In that spirit, I have kept the original punctuation, which results in very long sentences, but I have inserted paragraph breaks for readability. I mark these inserted breaks with this sign [¶]; unmarked breaks are in the original. In addition to providing the French for difficult translations, I also interpolate a few English words for readability. Simondon’s (...) notes appear as footnotes; translator’s notes as endnotes. (shrink)

Homologous operational localization processes are effectuated in terms of generalized topological covering systems on structures of physical events. We study localization systems of quantum events' structures by means of Gtothendieck topologies on the base category of Boolean events' algebras. We show that a quantum events algebra is represented by means of a Grothendieck sheaf-theoretic fibred structure, with respect to the global partial order of quantum events' fibres over the base category of local Boolean frames.

This chapter provides a systematic overview of topological explanations in the philosophy of science literature. It does so by presenting an account of topological explanation that I (Kostić and Khalifa 2021; Kostić 2020a; 2020b; 2018) have developed in other publications and then comparing this account to other accounts of topological explanation. Finally, this appraisal is opinionated because it highlights some problems in alternative accounts of topological explanations, and also it outlines responses to some of the main criticisms raised by the (...) so-called new mechanists. (shrink)

In this paper, I present a general theory of topological explanations, and illustrate its fruitfulness by showing how it accounts for explanatory asymmetry. My argument is developed in three steps. In the first step, I show what it is for some topological property A to explain some physical or dynamical property B. Based on that, I derive three key criteria of successful topological explanations: a criterion concerning the facticity of topological explanations, i.e. what makes it true of a particular system; (...) a criterion for describing counterfactual dependencies in two explanatory modes, i.e. the vertical and the horizontal; and, finally, a third perspectival one that tells us when to use the vertical and when to use the horizontal mode. In the second step, I show how this general theory of topological explanations accounts for explanatory asymmetry in both the vertical and horizontal explanatory modes. Finally, in the third step, I argue that this theory is universally applicable across biological sciences, which helps to unify essential concepts of biological networks. (shrink)

Indeterminism, understood as a notion that an event may be continued in a few alternative ways, invokes the question what a region of chanciness looks like. We concern ourselves with its topological and spatiotemporal aspects, abstracting from the nature or mechanism of chancy processes. We first argue that the question arises in Montague-Lewis-Earman conceptualization of indeterminism as well as in the branching tradition of Prior, Thomason and Belnap. As the resources of the former school are not rich enough to study (...) topological issues, we investigate the question in the framework of branching space-times of Belnap (Synthese 92:385–434, 1992). We introduce a topology on a branching model as well as a topology on a history in a branching model. We define light-cones and assume four conditions that guarantee the light-cones so defined behave like light-cones of physical space-times. From among various topological separation properties that are relevant to our question, we investigate the Hausdorff property. We prove that each history in a branching model satisfies the Hausdorff property. As for the satisfaction of the Hausdorff property in the entire branching model, we prove that it is related to the phenomenon of passive indeterminism, which we describe in detail. (shrink)

Must space be a unity? This question, which exercised Aristotle, Descartes and Kant, is a specific instance of a more general one; namely, can the topology of physical space change with time? In this paper we show how the discussion of the unity of space has been altered but survives in contemporary research in theoretical physics. With a pedagogical review of the role played by the Euler characteristic in the mathematics of relativistic spacetimes, we explain how classical general (...) relativity (modulo considerations about energy conditions) allows virtually unrestrained spatial topology change in four dimensions. We also survey the situation in many other dimensions of interest. However, topology change comes with a cost: a famous theorem by Robert Geroch shows that, for many interesting types of such change, transitions of spatial topology imply the existence of closed timelike curves or temporal non-orientability. Ways of living with this theorem and of evading it are discussed. (shrink)

It is universally accepted that genetic control over basic aspects of cell and molecular biology is the primary organizing principle in development and homeostasis of living systems. However, instances do exist where important aspects of biological order arise without explicit genetic instruction, emerging instead from simple physical principles, stochastic processes, or the complex self‐organizing interaction between random and seemingly unrelated parts. Being mostly resistant to direct genetic dissection, the analysis of such emergent processes falls into a grey area between mathematics, (...) physics and molecular cell biology and therefore remains very poorly understood. We recently proposed a mathematical model predicting the emergence of a specific non‐Gaussian distribution of polygonal cell shapes from the stochastic cell division process in epithelial cell sheets; this cell shape distribution appears to be conserved across a diverse set of animals and plants.1 The use of such topological models to study the process of cellular morphogenesis has a long history, starting almost a century ago, and many insights from those original works influence current experimental studies. Here we review current and past literature on this topic while exploring some new ideas on the origins and implications of topological order in proliferating epithelia. BioEssays 30:260–266, 2008. © 2008 Wiley Periodicals, Inc. (shrink)

The quantization of the magnetic flux in superconducting rings is studied in the frame of a topological model of electromagnetism that gives a topological formulation of electric charge quantization. It turns out that the model also embodies a topological mechanism for the quantization of the magnetic flux with the same relation between the fundamental units of magnetic charge and flux as there is between the Dirac monopole and the fluxoid.

This article draws upon recent theorising of the ‘becoming topological’ of space– specifically, how new social spaces are constituted through relations rather than physical locations – to explore how standardised data, and specifically test data, have influenced teachers’ work and learning. We outline the varied ways in which teacher practices at a primary school in Queensland, Australia, were actively constituted through processes of ‘tracking data’ and ‘keeping data on-track’, and how teachers were simultaneously being disciplined, or ‘tracked’, by these very (...) same data. Our analyses suggest that what appear to be more ‘technical’ activities and tasks of ‘using’ data are, in fact, actively constituted modes of governance, enabled through and deployed by ongoing practices of comparison and topological respatialisation. (shrink)

The general aim of this paper is to introduce some ideas of the theory of infinite topological games into the philosophical debate on supertasks. First, we discuss the elementary aspects of some infinite topological games, among them the Banach-Mazur game.Then it is shown that the Banach-Mazur game may be conceived as a Newtonian supertask.In section 4 we propose to conceive physical experiments as infinite games. This leads to the distinction between determined and undetermined experiments and the problem of how it (...) is related to that between determinism and indeter-minism. Finally the role of the Axiom of Choice as a source of indetermi-nacy of supertasks is discussed. (shrink)

Violence, as a concept, has shaped most of human history and discourse. Over the centuries, the concept has gone through dynamic evolutions and should be understood in relation to diverse agents such as nation, nostalgia, and culture. Modern society’s tendency to impede and constrain overt forms of violence has paved the way for covert forms to exist in socio-cultural spheres. Cultural violence is one such realization where aggression gets exercised covertly through heterogenous mediums such as language, regulations, mass media, and (...) most importantly cultural practices. Its topological structures can be traced in national imagination and a sense of cultural nostalgia originating out of it, that ultimately formulates cultural “otherness.” In Gandhian philosophy, the absence of physical aggression is insignificant, if not complemented with the eradication of violence from the cultural and intellectual strata. Gandhi’s critique of exclusive nationalism and narrowness is reflective of a distinct kind of cultural topology that generates structural violence and with the due course of history it gets legitimacy to exert power over the cultural binary it constructed. The fundamental questions of the paper are associated with assessing the role of national imagination and cultural imperatives in germinating the structures of violence in culture, exclusive nationalism, and Gandhian reconsideration of peace in the context of covert violence in the material and intellectual realms. (shrink)

Theory of networks serves as a mathematical foundation for the construction and modeling of chemical structures and complicated networks. In particular, chemical networking theory has a wide range of utilizations in the study of chemical structures, where examination and manipulation of chemical structural information are made feasible by utilizing the numerical graph invariants. A network invariant or a topological index is a numerical measure of a chemical compound which is capable to describe the chemical structural properties such as melting point, (...) freezing point, density, pressure, tension, and temperature of chemical compounds. Wiener initiated the first distance-based TI which is considered to be the most important TI to preserve the chemical and physical properties of chemical structures. Later on, degree-based TI was introduced to find the π -electron energy of molecules. Recently, connection number-based TIs are studied which are more efficient than degree and distance-based TIs. In this paper, we compute the connection number-based TIs of the structure of crystal cubic carbons which are one of the most significant and interesting composites in modern resources of science due to the involvement of carbon atoms. (shrink)

The unified treatment of the Dirac monopole, the Schwinger monopole, and the Aharonov-Bohm problem by Barut and Wilson is revisited via a path integral approach. The Kustaanheimo-Stiefel transformation of space and time is utilized to calculate the path integral for a charged particle in the singular vector potential. In the process of dimensional reduction, a topological charge quantization rule is derived, which contains Dirac's quantization condition as a special case. “Everything that is made beautiful and fair and lovely is made (...) for the eye of one who sees.” Jelaluddin Rumi,Mathnawi [I, 2383]. (shrink)

Our greatest certainty and greatest mystery is our mortality. In this book, Steven M. Rosen explores the profound mystery of death and rebirth from psychological, philosophical, and alchemical perspectives. To model, embody, and contain the paradoxical transformations involved in the death-rebirth enigma, Rosen employs a paradoxical form of mathematics: the topology of the Moebius strip and Klein bottle. As we follow this alchemical odyssey, the author makes himself transparent through his dreams and brings himself tangibly into his text so (...) as to enact a dialectic of ego and Self. "In tackling the subject of death and rebirth Steven Rosen writes about our modern state of mind, how we got like this and where we need to go from here. He does all this with a psychotherapeutic insight that begins with his own subjectivity--and his own dreams--and ends with the subjectivity of the modern world. Using myths, dreams, and alchemical symbolism as well as psychological research and Jungian insights, Rosen speaks to us all from the self and the Self. A book to be read immediately, and then read again." --Christopher Hauke, Jungian analyst and author of Jung and the Postmodern: The Interpretation of Realities "How does a mental-spiritual ego, the creation of our post-Renaissance world, embrace the body as a living partner? In Dreams, Death, Rebirth, Steven M. Rosen offers a topological analysis that meets the challenge of this daunting endeavor. It is a remarkable accomplishment, and vital for the advancement of psychotherapy." --Nathan Schwartz-Salant, Jungian analyst and author of The Black Nightgown: The Fusional Complex and the Unlived Life Steven M. Rosen is professor emeritus of psychology at the College of Staten Island of the City University of New York. After receiving his PhD in psychology in 1971, he began exploring the foundations, frontiers, and poetics of science, and his work became transdisciplinary and philosophical in nature. His essays have appeared in journals and collections spanning the fields of psychology, philosophy, theoretical physics, education, semiotics, and ecology. He is the author of Science, Paradox, and the Moebius Principle (1994), Dimensions of Apeiron (2004), Topologies of the Flesh (2006), and The Self-Evolving Cosmos (2008). (shrink)

We are used to regarding actions and other events, such as Brutus’ stabbing of Caesar or the sinking of the Titanic, as occupying intervals of some underlying linearly ordered temporal dimension. This attitude is so natural and compelling that one is tempted to disregard the obvious difference between time periods and actual happenings in favor of the former: events become mere “intervals cum description”.1 On the other hand, in ordinary circumstances the point of talking about time is to talk about (...) what actually happens or might happen at some time or another. We talk about ‘now’ and ‘then’ in an effort to put some order in our description of what goes on. And since different events seem to overlap in so many different ways, a full account of their temporal relations seems to run afoul of a reductionist strategy. This raises two philosophical questions. The first is whether we can actually go beyond time, as it were, i.e., whether we can take events as bona fide entities and deal with them directly, just as we can deal with spatial entities such as physical bodies or masses without confining ourselves to their spatial representations. This is a controversial issue (though probably not as controversial as it used to be), and ties in with a number of unsettled problems concerning, e.g., the structure of causality or the definition of adequate identity and individuation criteria for events. 2 The second question is whether we can perhaps do without time, i.e., whether we can dispense with time points or intervals as an independent ontological category and focus only on actual or potential happenings, in opposition to the form of reductionism mentioned above—in short, whether we can account for the temporal dimension in terms of suitable relations among events. This is also a highly controversial issue, and relates to the classical dispute concerning relational vs. absolutist conceptions of (space and) time.3 It is this second question that we intend to focus on here.. (shrink)

The logical theory of branching space-times, which provides a relativistic framework for studying objective indeterminism, remains mostly disconnected from discussions of space-time theories in philosophy of physics. Earman has criticized the branching approach and suggested “pruning some branches from branching space-time.” This article identifies the different—order-theoretic versus topological—perspective of both discussions as a reason for certain misunderstandings and tries to remove them. Most important, we give a novel, topological criterion of modal consistency that usefully generalizes an earlier criterion, and (...) we introduce a differential-geometrical version of branching space-times as a non-Hausdorff (generalized) manifold. (shrink)

In this research work, we have explored the physical and topological properties of the crystal structure of metal-insulator transition superlattice. In recent times, two-dimensional substantial have enamored comprehensive considerations owing to their novel ophthalmic and mechanical properties for anticipated employment. Recently, some researchers put their interest in modifying this material into useful forms in human life. Also, Metal-Insulator Transition Superlattice is useful in form of a thin film to utilize as two-dimensional transition metal dichalcogenides. Moreover, we have defined the computed-based (...) bond properties such as the degree constructed topological indices and their heat of formation for single crystal and monolayered structure of Ge-Sb-Te. Also, this structure is one of the most interesting composites in modern resources of science. (shrink)

Quantum contextuality and its ontological meaning are very controversial issues, and they relate to other problems concerning the foundations of quantum theory. I address this controversy and stress the fact that contextuality is a universal topological property of quantum processes, which conflicts with the basic metaphysical assumption of the definiteness of being. I discuss the consequences of this fact and argue that generic quantum potentiality as a real physical indefiniteness has nothing in common with the classical notions of possibility and (...) counterfactuality, and that also it reverses, in a way, the classical mirror-like relation between actuality and definite possibility. (shrink)

This review investigates the potential of non-orientable topology as a fundamental framework for understanding the Poincaré conjecture and its implications across various scientific disciplines. Integrating insights from Dokuchaev (2020), Rapoport, Christianto, Chandra, Smarandache (under review), and other pioneering works, this article explores the theoretical foundations linking non-orientable spaces to resolving the Poincaré conjecture and its broader implications in theoretical physics, geology, cosmology, and biology.

A topological index can be focused on uprising of a chemical structure into a real number. The degree-based topological indices have an active place among all topological indices. These topological descriptors intentionally associate certain physicochemical assets of the corresponding chemical compounds. Graph theory plays a very useful role in such type of research directions. The hex-derived networks have vast applications in computer science, physical sciences, and medical science, and these networks are constructed by hexagonal mesh networks. In this paper, we (...) determined the exact values of vertex-edge-degree-based topological descriptors for hex-derived networks HDN 1 p and HDN 2 p, which are generated by the hexagonal network of dimension p. (shrink)

This article, written in honor of Fritz Rohrlich, briefly surveys the role of topology in physics.

Topological indices are numeric parameters which portray the topology of a subatomic structure. In QSAR/QSPR analysis, topological descriptors play a vital role to examine the topology of a network. An interconnection network is a structure whose components are connected physically according to some pattern. In this paper, an interconnection network, ternary hypertree, which is a structural combination of complete ternary tree and hypertree, is introduced. We have evaluated the topological descriptors grounded on the distances for the ternary hypertree. (...) The analytical expressions for Wiener, different types of Szeged, and Mostar indices are determined. (shrink)

Our reality constitutes itself as being one of pictures. Landscape is a product of aesthetic reflection as well as the perception of reality and virtual reality of the first order (VR 1). Pictorial representation of a landscape is virtual reality of the second order (VR 2). A picture is a structure of relations with a specific topology or an interrelationship. A picture is set in relation. Topology relates to relational similarities and differences as well as their transfer into (...) other interrelationships, other topologies. The differences between nature, landscape (VR 1), metaphor of landscape and pictorial representation of landscape, etc. (VR 2) describe a change of the interrelationship. These changes happen in a physical-psychic-mental production of reality. We are involved in the events of particular relationships of the picture. The Topology of Being and Appearance reflects the inconspicuous similarities of relations and proportions in the relationship of the world in association with our physical-psychic-mental existential orientation in the world. (shrink)

Foundations of Relational Realism presents an intuitive interpretation of quantum mechanics, based on a revised decoherent histories interpretation, structured within a category theoretic topological formalism. -/- If there is a central conceptual framework that has reliably borne the weight of modern physics as it ascends into the twenty-first century, it is the framework of quantum mechanics. Because of its enduring stability in experimental application, physics has today reached heights that not only inspire wonder, but arguably exceed the limits (...) of intuitive vision, if not intuitive comprehension. For many physicists and philosophers, however, the currently fashionable tendency toward exotic interpretation of the theoretical formalism is recognized not as a mark of ascent for the tower of physics, but rather an indicator of sway—one that must be dampened rather than encouraged if practical progress is to continue. -/- In this unique two-part volume, designed to be comprehensible to both specialists and non-specialists, the authors chart out a pathway forward by identifying the central deficiency in most interpretations of quantum mechanics: That in its conventional, metrical depiction of extension, inherited from the Enlightenment, objects are characterized as fundamental to relations—i.e., such that relations presuppose objects but objects do not presuppose relations. The authors, by contrast, argue that quantum mechanics exemplifies the fact that physical extensiveness is fundamentally topological rather than metrical, with its proper logico-mathematical framework being category theoretic rather than set theoretic. -/- By this thesis, extensiveness fundamentally entails not only relations of objects, but also relations of relations. Thus, the fundamental quanta of quantum physics are properly defined as units of logico-physical relation rather than merely units of physical relata as is the current convention. Objects are always understood as relata, and likewise relations are always understood objectively. In this way, objects and relations are coherently defined as mutually implicative. The conventional notion of a history as “a story about fundamental objects” is thereby reversed, such that the classical “objects” become the story by which we understand physical systems that are fundamentally histories of quantum events. -/- These are just a few of the novel critical claims explored in this volume—claims whose exemplification in quantum mechanics will, the authors argue, serve more broadly as foundational principles for the philosophy of nature as it evolves through the twenty-first century and beyond. (shrink)

Since its discovery in 1959 the Aharonov-Bohm effect has continuously been the cause for controversial discussions of various topics in modern physics, e.g. the reality of gauge potentials, topological effects and nonlocalities. In the present paper we juxtapose the two rival interpretations of the Aharonov-Bohm effect. We show that the conception of nonlocality encountered in the Aharonov-Bohm effect is closely related to the nonseparability which is common in quantum mechanics albeit distinct from it due to its topological nature. We (...) propose a third alternative interpretation based on the loop space of holonomies which serves to solve some of the problems and we trace back the topological nonlocality and thereby the Aharonov-Bohm effect to their quantum mechanical origin. All three discussed interpretations are, of course, empirically equivalent. In fact, they present us with an instructive case study for the thesis of theory underdetermination by empirical data. (shrink)

A chemical compound in the form of graph terminology is known as a chemical graph. Molecules are usually represented as vertices, while their bonding or interaction is shown by edges in a molecular graph. In this paper, we computed various connectivity indices based on degrees of vertices of a chemical graph of indium phosphide. Afterward, we found the physical measures like entropy and heat of formation of InP. Then, we fitted curves between different indices and the thermodynamical properties, namely, heat (...) of formation and entropy. Curve fitting was done in MATLAB through different methods based on linearity and nonlinearity. Furthermore, we depicted our results numerically and graphically. These numerical systems may give an approach to concentrate on the thermodynamical properties of the compound design of InP at an exceptional level that will help understand the connection between framework measurement and these actions. (shrink)

Whereas decades of research have cataloged striking errors in physical reasoning, a resurgence of interest in intuitive physics has revealed humans’ remarkable ability to successfully predict the unfolding of physical scenes. A leading interpretation intended to resolve these opposing results is that physical reasoning recruits a general-purpose mechanism that reliably models physical scenarios (explaining recent successes), but overly contrived tasks or impoverished and ecologically invalid stimuli can produce poor performance (accounting for earlier failures). But might there be tasks that (...) persistently strain physical understanding, even in naturalistic contexts? Here, we explore this question by introducing a new intuitive physics task: evaluating the strength of knots and tangles. Knots are ubiquitous across cultures and time-periods, and evaluating them correctly often spells the difference between safety and peril. Despite this, 5 experiments show that observers fail to discern even very large differences in strength between knots. In a series of two-alternative forced-choice tasks, observers viewed a variety of simple “bends” (knots joining two pieces of thread) and decided which would require more force to undo. Though the strength of these knots is well-documented, observers’ judgments completely failed to reflect these distinctions, across naturalistic photographs (E1), idealized renderings (E2), dynamic videos (E3), and even when accompanied by schematic diagrams of the knots’ structures (E4). Moreover, these failures persisted despite accurate identification of the topological differences between the knots (E5); in other words, even when observers correctly perceived the underlying structure of the knot, they failed to correctly judge its strength. These results expose a blindspot in physical reasoning, placing new constraints on general-purpose theories of scene understanding. (shrink)

The boundary problem is related to the binding problem, part of a family of puzzles and phenomenal experiences that theories of consciousness (ToC) must either explain or eliminate. By comparison with the phenomenal binding problem, the boundary problem has received very little scholarly attention since first framed in detail by Rosengard in 1998, despite discussion by Chalmers in his widely cited 2016 work on the combination problem. However, any ToC that addresses the binding problem must also address the boundary problem. (...) The binding problem asks how a unified first person perspective (1PP) can bind experiences across multiple physically distinct activities, whether billions of individual neurons firing or some other underlying phenomenon. To a first approximation, the boundary problem asks why we experience hard boundaries around those unified 1PPs and why the boundaries operate at their apparent spatiotemporal scale. We review recent discussion of the boundary problem, identifying several promising avenues but none that yet address all aspects of the problem. We set out five specific boundary problems to aid precision in future efforts. We also examine electromagnetic (EM) field theories in detail, given their previous success with the binding problem, and introduce a feature with the necessary characteristics to address the boundary problem at a conceptual level. Topological segmentation can, in principle, create exactly the hard boundaries desired, enclosing holistic, frame-invariant units capable of effecting downward causality. The conclusion outlines a programme for testing this concept, describing how it might also differentiate between competing EM ToCs. (shrink)

The nonadditive properties of mass make it desirable to abandon mass as a basis unit in physics and to replace it by a unit of the dimension of the quantum of action [h]. The ensuing four-unit system of action, charge, length, and time [h, q, l, t] interacts in a much more elucidating fashion with experiment and with the fundamental structure of physics. All space-time differential forms expressing fundamental laws of physics are forms of physical dimensions, h, (...) h/q, or q. Their occurrence as periods (residues) of period integrals of forms makes h and q topological invariants in space-time and stresses in general the global nature of quantization. The coordinate dimensions [l] and [t] only come into play for the form-coefficients, the metric tensor, and their tensorial relatives. One thus obtains a very natural guidance for implementing the principle of general covariance, when coordinate-based descriptions are necessary. The consequences for the general theory of relativity are discussed. (shrink)

Evidence is presented that the singularities induced in causal Lorentzian spacetimes by changes in 3-space topology give rise to infinite particle and energy production under reasonable laws of quantum field propagation. In the case of the gravitational field, if 3-space is compact the total energy must vanish. A topological transition therefore induces a violent collapse that effectively aborts the transition, since the collapse mode is the only mode carrying the negative energy needed to compensate the associated infinite energy production. (...) The existence of the Hamiltonian constraint of general relativity suggests that topological stability is a local property of the quantum theory that is maintained even when 3-space is noncompact. (shrink)

In 1974 perfect crystal interferometry has been developed and immediately afterwards the 4π-symmetry of spinor wave-functions has been verified. The new method opened a new access to the observation of intrinsic quantum phenomena. Spin-superposition, quantum state reconstruction and quantum beat effects are examples of such investigations. In this connection efforts have been made to separate and measure various dynamical and geometrical phases. Non-cyclic and non-adiabatic topological phases have been identified and their stability against various fluctuations and dissipative forces has been (...) investigated by means of ultra-cold neutrons. An entanglement between different degrees of freedom of a single neutron system demonstrated the contextuality feature of quantum mechanics. In its continuation this yields to Kochen-Specker theorem like investigations providing a new basis for information processing and for the understanding of quantum physics in general. All investigations show the equivalence of various phase spaces and show how physical phenomena are correlated by quantum laws. Some curiosa occurred during the experiments and some epistemological aspects will be discussed as well. (shrink)

The mathematical structure of realist quantum theories has given rise to a debate about how our ordinary 3-dimensional space is related to the 3N-dimensional configuration space on which the wave function is defined. Which of the two spaces is our (more) fundamental physical space? I review the debate between 3N-Fundamentalists and 3D-Fundamentalists and evaluate it based on three criteria. I argue that when we consider which view leads to a deeper understanding of the physical world, especially given the deeper topological (...) explanation from the unordered configurations to the Symmetrization Postulate, we have strong reasons in favor of 3D-Fundamentalism. I conclude that our evidence favors the view that our fundamental physical space in a quantum world is 3-dimensional rather than 3N-dimensional. I outline lines of future research where the evidential balance can be restored or reversed. Finally, I draw lessons from this case study to the debate about theoretical equivalence. (shrink)

A generic non-conservative force, applied to an interferometer particle for a period in the past and then turned off, leaves stationary phase and fringe shifts in the now force-free interferometer. Both Aharonov-Bohm and Aharonov-Casher topological phase and fringe shifts can be created in this way. The specific sources of the non-conservative forces behind Aharonov-Bohm and Aharonov-Casher stationary fringe shifts are, respectively, Faraday induction fields and Maxwell displacement currents, now off.

Stuart Hameroff opens with an extended and updated exposition of the Penrose/Hameroff Orch-OR model, and subsequently addresses recent criticisms of quantum approaches to the brain. Evan Walker presents his view on consciousness from the perspective of a new approach to the integration of quantum theory and relativity. Friedrich Beck elaborates on the Beck/Eccles quantum approach to consciousness. Karl Pribram puts the holographic view on consciousness in perspective of his life long work. Peter Marcer and Edgar Mitchell explain the relevance of (...) quantum holography for consciousness. Gordon Globus discusses the relation between postmodern philosophical theories and quantum consciousness. Chris Clarke develops a theory in terms of a specific type of formal logic to reconcile the phenomenology of consciousness with the physical world. Ilya Prigogine summarizes his view on complexity, and on the future of quantum theory, which goes beyond the present formalism, and goes on to comment on the problem of consciousness. Matti Pitkanen identifies the place for consciousness in a unifying topological geometro-dynamics theory. Colin McGinn argues against classical materialism. Dick Bierman gives an overview of anomalous phenomena. He identifies a decline effect, and discusses different possible interpretations. Philip Van Loocke closes the volume with a discussion on how deep teleology in cellular systems may relate to consciousness. (shrink)

Causal set theory and the theory of linear structures (which has recently been developed by Tim Maudlin as an alternative to standard topology) share some of their main motivations. In view of that, I raise and answer the question how these two theories are related to each other and to standard topology. I show that causal set theory can be embedded into Maudlin’s more general framework and I characterise what Maudlin’s topological concepts boil down to when applied to (...) discrete linear structures that correspond to causal sets. Moreover, I show that all topological aspects of causal sets that can be described in Maudlin’s theory can also be described in the framework of standard topology. Finally, I discuss why these results are relevant for evaluating Maudlin’s theory. The value of this theory depends crucially on whether it is true that (a) its conceptual framework is as expressive as that of standard topology when it comes to describing well-known continuous as well as discrete models of spacetime and (b) it is even more expressive or fruitful when it comes to analysing topological aspects of discrete structures that are intended as models of spacetime. On the one hand, my theorems support (a): the theory is rich enough to incorporate causal set theory and its definitions of topological notions yield a plausible outcome in the case of causal sets. On the other hand, the results undermine (b): standard topology, too, has the conceptual resources to capture those topological aspects of causal sets that are analysable within Maudlin’s framework. This fact poses a challenge for the proponents of Maudlin’s theory to prove it fruitful. (shrink)

This volume develops a fundamentally different categorical framework for conceptualizing time and reality. The actual taking place of reality is conceived as a “constellatory self-unfolding” characterized by strong self-referentiality and occurring in the primordial form of time, the not yet sequentially structured “time-space of the present.” Concomitantly, both the sequentially ordered aspect of time and the factual aspect of reality appear as emergent phenomena that come into being only after reality has actually taken place. In this new framework, time functions (...) as an ontophainetic [H1] platform, i.e., as the stage on which reality can first occur. Events are merely the “tracks” that the actual taking place of reality leaves behind on the co-emergent “canvas’’ of local spacetime. -/- The view of time proposed here is particularly relevant to the recent debate over the “ER=EPR” conjecture targeting the relation between quantum physics and general relativity theory. The novelty of this radically different framework is that it allows quantum reduction and singularities to be addressed as inverse transitions into and out of the factual layer of reality: In quantum physical state reduction, reality “gains” the chrono-ontological format of facticity, and the sequential aspect of time becomes applicable. In singularities, by contrast, the opposite happens: Reality loses its local spacetime formation and reverts back to its primordial, pre-local shape – making the use of causality relations, Boolean logic and the dichotomization of subject and object obsolete in the process. -/- For our understanding of the relation between quantum and relativistic physics, this new view opens up fundamentally new perspectives: Both are legitimate views of time and reality; they simply address very different chrono-ontological portraits, and thus should not lead us to erroneously prefer one view over the other. -/- The task of the book is to provide a formal framework in which this radically different view of time and reality can be suitably addressed. The mathematical approach is based on the logical and topological features of the Borromean Rings, and draws upon concepts and methods from algebraic and geometric topology – especially the theory of sheaves and links, group theory, logic and information theory in relation to the standard constructions employed in quantum mechanics and general relativity, shedding new light on the problems of their compatibility. The intended audience includes physicists, mathematicians and philosophers with an interest in the conceptual and mathematical foundations of modern physics. (shrink)

The unified theory of dose and effect, as indicated by the median-effect equation for single and multiple entities and for the first and higher order kinetic/dynamic, has been established by T.C. Chou and it is based on the physical/chemical principle of the massaction law (J. Theor. Biol. 59: 253-276, 1976 (質量作用中效定理) and Pharmacological Rev. 58: 621-681, 2006) (普世中效指數定理). The theory was developed by the principle of mathematical induction and deduction (數學演繹歸納法). Rearrangements of the median-effect equation lead to Michaelis-Menten, Hill, Scatchard, (...) and Henderson-Hasselbalch equations. The “median” serves as the universal reference point and the “common link” for the relationship of all entities and is also the “harmonic mean” of kinetic dissociation constants. Over 300 mechanism-specific equations have been derived and published using the mathematical induction-deduction process. These equations can be deduced into several general equations, including the median-mediated whole/part equation, combination index theorem, isobologram equation, and polygonogram. It is proven that “dose” and “effect” are interchangeable, thus, “substance” and “function” are interchangeable, which leads to “the unity theory” (劑效、心物、知行一元論) in quantitative mathematical philosophy (數學的定量哲學) in functional context. Therefore, a general theory centered on the “median” and based on equilibrium dynamics has evolved. In other words: [「中」的宇宙觀： 以「中」爲基凖的動力學生態平衡]. Based on the median-effect equation of the mass-action law, the fundamental claim is that we can draw “a specific cure” for only two data points, if they are determined accurately. This claim has far reaching consequences since it defies the general held belief that two points can dray only a straight line. Remarkably, the unity theory (一元論) providesscientific/mathematical interpretation in equations and in graphics of Chinese ancient philosophy, including Fu-Si Ba Gua (伏羲八卦), Dao’s Harmony (和諧), the Confucian doctrine of the mean (儒家中庸之道), Chou Dun-Yi’s (周敦頤, 1017-1073) From Wu-ji to Tai-ji and Taiji Tu Sho (無極而太極及太極圖說). The moderntopological analysis for trinity yields an exact correspondence to the Ba-Gua, which was introduced over 4,000 years ago. Furthermore, the median-centered algorithm, promotes modern ecological content (生態學) in the equilibral dynamic state of harmony. It is concluded that Western science and Eastern philosophy are directly linked and complementary to each other. Since the truth in mathematical quantitative philosophy (數學的定量哲學) has no boundaries, East and West philosophies can flourish together for the common goal and ideal in science and in humanity (世界大同). (shrink)

Accelerating Expansion explores some of the philosophical implications of modern cosmology, focused on the significance that the discovery of the accelerating expansion of the Universe has for our understanding of time, geometry, and physics. The appearance of the cosmological constant in the equations of general relativity allows one to model universes in which space has an inherent tendency towards expansion. This constant, introduced by Einstein but subsequently abandoned by him, returned to centre stage with the discovery of the accelerating (...) expansion. This pedagogically-oriented essay begins with a study of the most basic and elegant relativistic world that involves a positive cosmological constant, de Sitter spacetime. It then turns to the relatives of de Sitter spacetime that dominate modern relativistic cosmology. Some of the topics considered include: the nature of time and simultaneity in de Sitter worlds; the sense in which de Sitter spacetime is a powerful dynamical attractor; the limited extent to which observation can give us information about the topology of space in a world undergoing accelerated expansion; and cosmologists' favourite sceptical worry about the reliability of evidence and the possibility of knowledge, the problem of Boltzmann brains. (shrink)

We think of the world around us as divided into physical objects like toasters and daisies, rather than solely as a smear of properties like yellow and smooth. How do we single out these objects? One theory of object concepts uses part‐of relations and relations of connectedness. According to this proposal, an object is a connected spatial item of maximal extent: Any other connected item that overlaps (i.e., shares a part with) the object must be a part of that object. (...) This article reports four experiments that test this proposal. Participants see descriptions or diagrams of spatial items that vary across trials in their relative positions. In separate experiments, participants decide whether the items are physical objects, whether they are wholes, or how many objects are present. All experiments find support for connectedness as a contributor to object status, but they find little support for maximality. The results suggest that maximality is not a necessary feature of wholes or of objects. (shrink)

Stephen Hawking, among others, has proposed that the topological stability of a property of space-time is a necessary condition for it to be physically significant. What counts as stable, however, depends crucially on the choice of topology. Some physicists have thus suggested that one should find a canonical topology, a single ‘right’ topology for every inquiry. While certain such choices might be initially motivated, some little-discussed examples of Robert Geroch and some propositions of my own show that (...) the main candidates—and each possible choice, to some extent—faces the horns of a no-go result. I suggest that instead of trying to decide what the ‘right’ topology is for all problems, one should let the details of particular types of problems guide the choice of an appropriate topology. (shrink)

So-called ‘distinctively mathematical explanations’ (DMEs) are said to explain physical phenomena, not in terms of contingent causal laws, but rather in terms of mathematical necessities that constrain the physical system in question. Lange argues that the existence of four or more equilibrium positions of any double pendulum has a DME. Here we refute both Lange’s claim itself and a strengthened and extended version of the claim that would pertain to any n-tuple pendulum system on the ground that such explanations are (...) actually causal explanations in disguise and their associated modal conditionals are not general enough to explain the said features of such dynamical systems. We argue and show that if circumscribing the antecedent for a necessarily true conditional in such explanations involves making a causal analysis of the problem, then the resulting explanation is not distinctively mathematical or non-causal. Our argument generalises to other dynamical systems that may have purported DMEs analogous to the one proposed by Lange, and even to some other counterfactual accounts of non-causal explanation given by Reutlinger and Rice. (shrink)

In this paper we study the emergence of Minkowski space–time from a discrete causal network representing a classical information flow. Differently from previous approaches, we require the network to be topologically homogeneous, so that the metric is derived from pure event-counting. Emergence from events has an operational motivation in requiring that every physical quantity—including space–time—be defined through precise measurement procedures. Topological homogeneity is a requirement for having space–time metric emergent from the pure topology of causal connections, whereas physically homogeneity (...) corresponds to the universality of the physical law. We analyze in detail the case of 1+1 dimensions. If we consider the causal connections as an exchange of classical information, we can establish coordinate systems via an Einsteinian protocol, and this leads to a digital version of the Lorentz transformations. In a computational analogy, the foliation construction can be regarded as the synchronization with a global clock of the calls to independent subroutines in a parallel distributed computation. Thus the Lorentz time-dilation emerges as an increased density of leaves within a single tic-tac of a clock, whereas space-contraction results from the corresponding decrease of density of events per leaf. The operational procedure of building up the coordinate system introduces an in-principle indistinguishability between neighboring events, resulting in a network that is coarse-grained, the thickness of the event being a function of the observer's clock. The illustrated simple classical construction can be extended to space dimension greater than one, with the price of anisotropy of the maximal speed, due to the Weyl-tiling problem. This issue is cured if the causal network is quantum, as e.g. in a quantum cellular automaton, and isotropy is recovered by quantum coherence via superposition of causal paths. We thus argue that in a causal network description of space–time, the quantum nature of the network is crucial. (shrink)

Classical cognitive science assumes that intelligently behaving systems must be symbol processors that are implemented in physical systems such as brains or digital computers. By contrast, connectionists suppose that symbol manipulating systems could be approximations of neural networks dynamics. Both classicists and connectionists argue that symbolic computation and subsymbolic dynamics are incompatible, though on different grounds. While classicists say that connectionist architectures and symbol processors are either incompatible or the former are mere implementations of the latter, connectionists reply that neural (...) networks might be incompatible with symbol processors because the latter cannot be implementations of the former. In this contribution, the notions of 'incompatibility' and 'implementation' will be criticized to show that they must be revised in the context of the dynamical system approach to cognitive science. Examples for implementations of symbol processors that are incompatible with respect to contextual topologies will be discussed. (shrink)