The size of animal exhibits has important effects on their lives and welfare. However, most references to exhibit size only consider floor space and height dimensions, without considering the space afforded by usable features within the exhibit. In this paper, we develop two possible methods for measuring the usable space of zoo exhibits and apply these to a sample exhibit. Having a metric for usable space in place will provide a better reflection of the quality of different exhibits, and (...) enhance comparisons between exhibits. (shrink)

Space-time intervals are the fundamental components of conscious experience, gravity, and a Theory of Everything. Space-time intervals are relationships that arise naturally between events. They have a general covariance (independence of coordinate systems, scale invariance), a physical constancy, that encompasses all frames of reference. There are three basic types of space-time intervals (light-like, time-like, space-like) which interact to create space-time and its properties. Human conscious experience is a four-dimensional space-time continuum created through the processing of space-time intervals by the brain; (...) space-time intervals are the source of conscious experience (observed physical reality). Human conscious experience is modeled by Einstein’s special theory of relativity, a theory designed specifically from the general covariance of space-time intervals (for inertial frames of reference). General relativity is our most accurate description of gravity. In general relativity, the general covariance of space-time intervals is extended to all frames of reference (inertial and non-inertial), including gravitational reference frames; space-time intervals are the source of gravity in general relativity. The general covariance of space-time intervals is further extended to quantum mechanics; space-time intervals are the source of quantum gravity. The general covariance of space-time intervals seamlessly merges general relativity with quantum field theory (the two grand theories of the universe). Space-time intervals consequently are the basis of a Theory of Everything (a single all-encompassing coherent theoretical framework of physics that fully explains and links together all physical aspects of the universe). This theoretical framework encompasses our observed physical reality (conscious experience) as well; space-time intervals link observed physical reality to actual physical reality. This provides an accurate and reliable match between observed physical reality and the physical universe by which we can carry on our activity. The Minkowski metric, which defines generally covariant space-time intervals, may be considered an axiom (premise, postulate) for the Theory of Everything. (shrink)

This paper aims to show that—and how—Plato’s notion of the receptacle in the Timaeus provides the conditions for developing a mathematical as well as a physical space without itself being space. In response to the debate whether Plato’s receptacle is a conception of space or of matter, I suggest employing criteria from topology and the theory of metric spaces as the most basic ones available. I show that the receptacle fulfils its main task–allowing the elements qua images of (...) the Forms to exist as sensible things by being that in which the elements appear, change and move–in virtue of being pure continuity. All further qualifications required for a full notion of space are derived solely from the content of the receptacle. (shrink)

Geometry was a main source of inspiration for Carnap’s conventionalism. Taking Poincaré as his witness Carnap asserted in his dissertation Der Raum (Carnap 1922) that the metrical structure of space is conventional while the underlying topological structure describes "objective" facts. With only minor modifications he stuck to this account throughout his life. The aim of this paper is to disprove Carnap's contention by invoking some classical theorems of differential topology. By this means his metrical conventionalism turns out to be indefensible (...) for mathematical reasons. This implies that the relation between to-pology and geometry cannot be conceptualized as analogous to the relation between the meaning of a proposition and its expression in some language as logical empiricists used to say. (shrink)

The concept and usage of the word 'metric' within General Relativity is briefly described. The early work of Roy Kerr led to his original 1963 algebraic, rotating metric. This discovery and his subsequent recollection in 2008 are summarised as the motivation for this article. Computer algebra has confirmed that nominal transformations of this early metric can generate further natural algebraic metrics. The algebra is not abstract, nor advanced, and these metrics have been overlooked for many years. The (...) 1916 metric due to Schwarzschild misled Kerr into seeking a similar metric for rotation. The philosophy of astrophysics for Penrose, Hawking and others would have been very different had they used the two lost metrics. (shrink)

Description In this paper, we propose an advanced mathematical framework centered around the Energy Number Field (E), which fundamentally avoids the conventional concept of zero by introducing a neutral ele- ment, νE. Through this approach, we redefine core mathematical constructs, including limits, continuity, differentiation, integration, and series summation, ensuring they operate seamlessly within a zero-less paradigm. We address and redefine matrix operations, topology, metric spaces, and complex analysis, aligning them with the principles of E. Additionally, we explore non-mappable (...) properties of energy numbers in the context of symmetry groups, non-standard fields, fractional calculus, and non-Euclidean geometries. By employing νE as the central element, our framework resolves conventional zero-related sin- gularities and computational anomalies, offering a novel perspective that bridges advanced mathematical theories with practical applications in physics, computational algorithms, and topological transforma- tions. This work paves the way for future research to experimentally validate these formulations and explore potential applications in advanced physics, quantum mechanics, and beyond. (shrink)

Abstract. The aim of this paper is to present a topological method for constructing discretizations (tessellations) of conceptual spaces. The method works for a class of topological spaces that the Russian mathematician Pavel Alexandroff defined more than 80 years ago. Alexandroff spaces, as they are called today, have many interesting properties that distinguish them from other topological spaces. In particular, they exhibit a 1-1 correspondence between their specialization orders and their topological structures. Recently, a special type (...) of Alexandroff spaces was used by Ian Rumfitt to elucidate the logic of vague concepts in a new way. According to his approach, conceptual spaces such as the color spectrum give rise to classical systems of concepts that have the structure of atomic Boolean algebras. More precisely, concepts are represented as regular open regions of an underlying conceptual space endowed with a topological structure. Something is subsumed under a concept iff it is represented by an element of the conceptual space that is maximally close to the prototypical element p that defines that concept. This topological representation of concepts comes along with a representation of the familiar logical connectives of Aristotelian syllogistics in terms of natural settheoretical operations that characterize regular open interpretations of classical Boolean propositional logic. In the last 20 years, conceptual spaces have become a popular tool of dealing with a variety of problems in the fields of cognitive psychology, artificial intelligence, linguistics and philosophy, mainly due to the work of Peter Gärdenfors and his collaborators. By using prototypes and metrics of similarity spaces, one obtains geometrical discretizations of conceptual spaces by so-called Voronoi tessellations. These tessellations are extensionally equivalent to topological tessellations that can be constructed for Alexandroff spaces. Thereby, Rumfitt’s and Gärdenfors’s constructions turn out to be special cases of an approach that works for a more general class of spaces, namely, for weakly scattered Alexandroff spaces. This class of spaces provides a convenient framework for conceptual spaces as used in epistemology and related disciplines in general. Alexandroff spaces are useful for elucidating problems related to the logic of vague concepts, in particular they offer a solution of the Sorites paradox (Rumfitt). Further, they provide a semantics for the logic of clearness (Bobzien) that overcomes certain problems of the concept of higher2 order vagueness. Moreover, these spaces help find a natural place for classical syllogistics in the framework of conceptual spaces. The crucial role of order theory for Alexandroff spaces can be used to refine the all-or-nothing distinction between prototypical and nonprototypical stimuli in favor of a more fine-grained gradual distinction between more-orless prototypical elements of conceptual spaces. The greater conceptual flexibility of the topological approach helps avoid some inherent inadequacies of the geometrical approach, for instance, the so-called “thickness problem” (Douven et al.) and problems of selecting a unique metric for similarity spaces. Finally, it is shown that only the Alexandroff account can deal with an issue that is gaining more and more importance for the theory of conceptual spaces, namely, the role that digital conceptual spaces play in the area of artificial intelligence, computer science and related disciplines. Keywords: Conceptual Spaces, Polar Spaces, Alexandroff Spaces, Prototypes, Topological Tessellations, Voronoi Tessellations, Digital Topology. (shrink)

There are at least two traditional conceptions of numerical degree of similarity. According to the first, the degree of dissimilarity between two particulars is their distance apart in a metric space. According to the second, the degree of similarity between two particulars is a function of the number of (sparse) properties they have in common and not in common. This paper argues that these two conceptions are logically independent, but philosophically inconsonant.

It has been known for long time that the cosmic sound wave was there since the early epoch of the Universe. Signatures of its existence are abound. However, such an acoustic model of cosmology is rarely developed fully into a complete framework from the notion of space, cancer therapy up to the sky. This paper may be the first attempt towards such a complete description of the Universe based on classical wave equation of sound. It is argued that one can (...) arrive at a consistent description of space, elementary particles, Sachs-Wolfe acoustic theorem, up to a novel approach for cancer therapy, starting from this simple classical wave equation of sound. We also discuss a plausible extension of Acoustic Sachs-Wolfe theorem based on its analogue with Klein-Gordon equation to become Acoustic Sachs-Wolfe-Christianto-Smarandache-Umniyati (ASWoCSU) equation. It is our hope that the new proposed equation can be verified with observation data. But we admit that our model is still in its infancy, more researches are needed to fill all the missing details. (shrink)

This paper considers whether an analogy between distance and dissimilarlity supports the thesis that degree of dissimilarity is distance in a metric space. A straightforward way to justify the thesis would be to define degree of dissimilarity as a function of number of properties in common and not in common. But, infamously, this approach has problems with infinity. An alternative approach would be to prove representation and uniqueness theorems, according to which if comparative dissimilarity meets certain qualitative conditions, then (...) it is representable by distance in a metric space. I will argue that this approach faces equally severe problems with infinity. (shrink)

In this paper I argue that the analysis of natural properties as convex subsets of a metric space in which the distances are degrees of dissimilarity is incompatible with both the definition of degree of dissimilarity as number of natural properties not in common and the definition of degree of dissimilarity as proportion of natural properties not in common, since in combination with either of these definitions it entails that every property is a natural property, which is absurd. I (...) suggest it follows that we should think of the convex class analysis of natural properties as a variety of resemblance nominalism. (shrink)

The present paper aims to contribute to the substantivalism versus relationalism debate and to defend general relativity (GR) against pseudoscientific attacks in a novel, especially inclusive way. This work was initially motivated by the desire to establish the incompatibility of any ether theories with accelerated cosmic expansion and inflation (motto: where would a hypothetical medium supposedly come from so fast?). The failure of this program is of interest for emergent GR concepts in high energy particle physics. However, it becomes increasingly (...) important to guard scientific results against their misrepresentation by fundamentally anti-scientific agendas. We therefore argue that although it is not known whether the perceived space-time is fundamental (rather than a condensed state or a particular membrane), in a fundamental theory, space-time must be abstract relational: fundamental space-time is the consistent spatial-temporal arrangement of events. To pursue its own goals, this work should be accessible to a wide audience: physicists, philosophers of science, those being tempted by anti-relativity theories, but also those who vigorously defend some orthodox relativity that is not actually supported by GR. It must thus be extensive in order to satisfy the different parties’ desire to have included and understood their respective positions. (shrink)

There are reports about human experiences of time that are not in line with Einstein’s theory of Special relativity and not in line with the rate of change of the electromagnetic field at the smallest scale size. Some psychological reports describe human experiences about the metric of time that defy physical reality as we know it. These reports question the reliability of our understanding of time.

Special relativity has changed the fundamental view on space and time since Einstein introduced it in 1905. It substitutes four dimensional spacetime for the absolute space and time of Newtonian mechanics. It is believed that the validities of Lorentz invariants are fully confirmed empirically for the last one hundred years and therefore its status are canonical underlying all physical principles. However, spacetime metric is a geometric approach on nature when we interpret the natural phenomenon. A geometric flaw on this (...) will be exhibited and the alternative is suggested. The reasonable geometric model of space and time is a three dimensional space which is translating along the time direction. This model legitimately represents the true characteristic of nature. (shrink)

This paper deals with Gärdenfors’ theory of conceptual spaces. Let \({\mathcal {S}}\) be a conceptual space consisting of 2-type fuzzy sets equipped with several kinds of metrics. Let a finite set of prototypes \(\tilde{P}_1,\ldots,\tilde{P}_n\in \mathcal {S}\) be given. Our main result is the construction of a classification algorithm. That is, given an element \({\tilde{A}}\in \mathcal {S},\) our algorithm classifies it into the conceptual field determined by one of the given prototypes \(\tilde{P}_i.\) The construction of our algorithm uses some physical (...) analogies and the Newton potential plays a significant role here. Importantly, the resulting conceptual fields are not convex in the Euclidean sense, which we believe is a reasonable departure from the assumptions of Gardenfors’ original definition of the conceptual space. A partitioning algorithm of the space \(\mathcal {S}\) is also considered in the paper. In the application section, we test our classification algorithm on real data and obtain very satisfactory results. Moreover, the example we consider is another argument against requiring convexity of conceptual fields. (shrink)

The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence in Stone topology. Presented is a flexible, parametrized family of metrics inducing the latter, used as an analytical aid. We show maps induced by action (...) model transformations continuous with respect to the Stone topology and present results on the recurrent behavior of said maps. (shrink)

The ambition of this paper is extensive: to bring about a new paradigm and firm mathematical foundations to Metaphysics, to aid its progress from the realm of mystical speculation to the realm of scientific scrutiny. -/- More precisely, this paper aims to introduce the field of Metaphysical Cosmology. The Metaphysical Cosmos here refers to the complete structure containing all entities, both existent and non-existent, with the physical universe as a subset. Through this paradigm, future endeavours in Metaphysical Science could thus (...) analyse non-physical parts of the Metaphysical Cosmos. New logical notions are displayed as tools for Metaphysical Cosmology, such as a Metric-Space-based predicate system, as well as a revised version of the Existential Quantifier. -/- A type system is presented to derive a construction of the Metaphysical Cosmos. The system is structured through semantic and syntactic definitions in a coherent way and holds only one proper axiom: the existence of (at least) one entity. This paper itself serves as an empirical proof for this axiom. Formulae and equations that depict a clear logical and mathematical structure of the Metaphysical Cosmos are derived from the definitions of the system and this axiom. -/- This culminates in the "Sixth Theorem", whose proof displays logically that there must be something rather than nothing. A computational simulation of the Sixth Theorem is also provided, alongside with methods for a future Metaphysical Science. Thus, this paper does not aim to provide a traditional philosophical argument but rather a mathematical foundation and new paradigm for the science of Metaphysics. (shrink)

When beliefs are quantified as credences, they are related to each other in terms of closeness and accuracy. The “accuracy first” approach in formal epistemology wants to establish a normative account for credences based entirely on the alethic properties of the credence: how close it is to the truth. To pull off this project, there is a need for a scoring rule. There is widespread agreement about some constraints on this scoring rule, but not whether a unique scoring rule stands (...) above the rest. The Brier score equips credences with a structure similar to metric space and induces a “geometry of reason.” It enjoys great popularity in the current debate. I point out many of its weaknesses in this article. An alternative approach is to reject the geometry of reason and accept information theory in its stead. Information theory comes fully equipped with an axiomatic approach which covers probabilism, standard conditioning, and Jeffrey conditioning. It is not based on an underlying topology of a metric space, but uses a non-commutative divergence instead of a symmetric distance measure. I show that information theory, despite initial promise, also fails to accommodate basic epistemic intuitions; and speculate on its remediation. (shrink)

In this paper I present a problem for the conventionalist regarding temporal metrics, and I defend an objectivist position on the ground of its explanatory force. Roughly, the conventionalist has it that there is no fact of the matter with respect to the truth or falsity of judgments of the kind “event e1 lasted as long as event e2”, while the objectivist thinks that they are grounded in objective features of space-time. I argue that, by positing grounds for judgments of (...) relative temporal length, the objectivist gains an explanatory force that the conventionalist position lacks. (shrink)

Biological modalities, i.e., biologically possible, impossible, or necessary states of affairs have not received much attention from philosophers. Yet, it is widely agreed that there are biological constraints on physically possible states of affairs, such that not everything that is physically possible is also biologically possible, even if everything that is biologically possible is also physically possible. Furthermore, biologists use concepts that appear to be modal in nature, such as the concept of evolvability in evolutionary developmental biology, or “evo-devo.” The (...) present chapter investigates what kind of modality underlies the concept of evolvability. This concept tries to capture the capacity of an organism or a lineage to sustain genetic changes that enable it to evolve or to evolve adaptively. The basic idea of the proposed approach is to construe evolvability as a kind of accessibility in a modal space. The difficult part is to specify this modal space and the relevant accessibility relation. While there may not be a general way of defining such a relation, there exist model systems for which it is possible, e.g., evolving small RNAs. The modal space in such cases turns out to be quite distinct from those constructed by philosophers, e.g., David Lewis’s similarity metric for possible worlds. Even though the biological case examined here is quite special, attending to the way in which biological possibilities are modeled in this case harbors some general lessons about biological modalities, in particular their dependence on the explanatory goals of the models modeling modality. (shrink)

An operational approach to quantum mechanics has been developed in the past decades in our group in Brussels. A similar approach is taken in this work, making use of the extra operational depth offered by this approach, to show that the construction of spacetime is specific to each observer. What is usually referred to as the block universe then emerges by noting that parts of the past and future are also contained in the present, but without the limitations that a (...) four-dimensional block universe usually implies, of a reality in which change would be impossible. In our operational approach, reality remains dynamic, with free choice playing a central role in its conceptualization. We also show that, when operationally analyzed, the theory implies that objects move not only in space, but also and especially in time, and more generally in spacetime, with their rest mass being a measure of their kinetic time energy. We therefore claim that Einstein’s relativity revolution has not been fully realized, since most physicists are not ready to accept these consequences of the theory although the formula’s showing them, when operationally analyzed, are in every relativity textbook. In particular, when relativistic motion is revisited as a genuine four-dimensional motion, it becomes possible to reinterpret the parameter c associated with the coordinate speed of light, which becomes the magnitude of the four-velocity of all material entities. We observe that this four-dimensional motion in Minkowski space can also be better understood if placed in the broader perspective of quantum mechanics, provided that non-locality is interpreted as non-spatiality, thus indicating the existence of an underlying non-spatial reality, the nature of which could be conceptual, consistent with the conceptuality interpretation of quantum mechanics. This hypothesis is reinforced by noting that when observers, or experiencers, as they will be referred to in this article, are described by acknowledging their cognitive nature of entities moving in a semantic space, Minkowski metric emerges in a natural way. (shrink)

Numerous high-profile ethics scandals, rising inequality, and the detrimental effects of climate change dramatically underscore the need for business schools to instill a commitment to social purpose in their students. At the same time, the rising financial burden of education, increasing competition in the education space, and overreliance on graduates’ financial success as the accepted metric of quality have reinforced an instrumentalist climate. These conflicting aims between social and financial purpose have created an existential crisis for business education. To (...) resolve this impasse, we draw on the concept of moral self-awareness to offer a system-theoretical strategy for crowding-in a culture of ethics within business schools. We argue that to do so, business schools will need to (1) reframe the purpose of business, (2) reframe the meaning of professional success, and (3) reframe the ethos of business education itself. (shrink)

Most current techniques to deal with invasive species are ineffective or have highly damaging side effects. To this end suppression-drives based on clustered regularly inter-spaced short palindromic repeats (CRISPR/Cas9) have been touted as a potential silver bullet for the problem, allowing for a highly focused, humane and cost-effective means of removing a target species from an environment. Suppression-drives come with serious risks, however, such that the precautionary principle seems to warrant us not deploying this technology. The focus of this paper (...) is on one such risk – the danger of a suppression-drive escaping containment and wiping out the target species globally. Here, I argue that in most cases this risk is significant enough to warrant not using a gene-drive. In some cases, however, we can bypass the precautionary principle by using an approach that hinges on what I term the ‘Worst-Case Clause’. This clause, in turn, provides us with a litmus test that can be fruitfully used to determine what species are viable targets for suppression-drives in the wild. Using this metric in concert with other considerations, I suggest that only three species are currently possible viable targets – the European rabbit, ship rat and Caribbean Tree Frog. (shrink)

Climate change and decarbonization raise complex justice questions that researchers and policymakers must address. The distributions of greenhouse gas emissions rights and mitigation efforts have dominated justice discourses within scenario research, an integrative element of the IPCC. However, the space of justice considerations is much larger. At present, there is no consistent approach to comprehensively incorporate and examine justice considerations. Here we propose a conceptual framework grounded in philosophical theory for this purpose. We apply this framework to climate mitigation scenarios (...) literature as proof of concept, enabling a more holistic and multidimensional investigation of justice. We identify areas of future research, including new metrics of service provisioning essential for human well-being. [Can be freely read by clicking the ReadCube link below.]. (shrink)

This short article pairs the realms of “Mathematics”, “Philosophy”, and “Poetry”, presenting some corners of intersection of this type of scientocreativity. Poetry have long been following mathematical patterns expressed by stern formal restrictions, as the strong metrical structure of ancient Greek heroic epic, or the consistent meter with standardized rhyme scheme and a “volta” of Italian sonnets. Poetry was always connected to Philosophy, and further on, notable mathematicians, like the inventor of quaternions, William Rowan Hamilton, or Ion Barbu, the creator (...) of the Barbilian spaces, have written appreciated poems. We will focus here on an avant-garde movement in literature, art, philosophy, and science, called Paradoxism, founded in Romania in 1980 by a mathematician, philosopher and poet, and on the laboured writing exercises of the Oulipo group, founded in Paris in 1960 by mathematicians and poets, both of them still in act. (shrink)

Open theists argue that God's relationship to time, as conceived in classical theism, is erroneous. They explain that it is contradictory for an atemporal being to act in a temporal universe, including experiencing its temporal successions. Contrary to the atemporalists, redemptive history has shown that God interacts with humans in time. This relational nature of God nullifies the classical notion of God as timelessly eternal. Therefore, it lacks a philosophical and theological basis. Because God is in time, He does not (...) know all future contingencies and, therefore, changes. This study examines open theism's appropriation of the A and B theories of time to the divine-human relationship. The study argues that divine temporality does not solve the tension of divine-human relationships, especially in relation to the future. Further, historical divine temporality does not negate the fact of divine atemporality. It mainly stems from God's choice to create temporal creatures and His relationship with them. Furthermore, if it is not logically and metaphysically contradictory for an omnipresent being to act in space, then it follows that an atemporal being can act in time. Whether time is understood from the metric or psychological point of view, it does not transcend God, and therefore, the limitation it places on human creatures with respect to the future does not apply to God. Lastly, although a few philosophers reject the notion of eternity as timelessly eternal, the doctrine has a philosophical and theological basis in the Scripture. (shrink)

According to the standard interpretation of Einstein’s field equations, gravity consists of mass-energy curving spacetime, and an additional physical force or entity—denoted by Λ (the ‘cosmological constant’)—is responsible for the Universe’s metric-expansion. Although General Relativity’s direct predictions have been systematically confirmed, the dominant cosmological model thought to follow from it—the ΛCDM (Lambda cold dark matter) model of the Universe’s history and composition—faces considerable challenges, including various observational anomalies and experimental failures to detect dark matter, dark energy, or inflation-field candidates. (...) This paper shows that Einstein’s Equivalence Principle entails two possible physical interpretations of General Relativity’s field equations. Although the field equations facially appear to support the standard interpretation—that gravity consists of mass-energy curving spacetime—the field equations can be equivalently understood as holding that gravitational effects instead result from mass-energy accelerating the metric-expansion of a second-order spacetime fabric superimposed upon an absolute, first-order Euclidean space, resulting in the observational appearance of spacetime curvature. This alternative interpretation of relativity is shown to be empirically equivalent to the standard interpretation of relativity, albeit with a changing value for Λ (which is similar to how Λ is understood in the conception of Λ as ‘quintessence’, but in this case takes Λ to be gravity). The reconceptualization is then shown to potentially resolve major observational anomalies for the ΛCDM model, including recent observations conflicting with ΛCDM predictions, as well as failures to directly detect dark matter, dark energy, and inflation field/particle candidates. (shrink)

Gödel's Philosophical Legacy Kurt Gödel's contributions to philosophy extend beyond his incompleteness theorems. He engaged deeply with the work of other philosophers, including Immanuel Kant and Edmund Husserl, and explored topics such as the nature of time, the structure of the universe, and the relationship between mathematics and reality. Gödel's philosophical writings, though less well-known than his mathematical work, offer rich insights into his views on the nature of existence, the limits of human knowledge, and the interplay between the finite (...) and the infinite. His work continues to inspire and challenge philosophers, mathematicians, and scientists, inviting them to explore the profound and often enigmatic questions at the heart of human understanding. -/- Kurt Gödel's Broader Contributions to Philosophy Kurt Gödel, while primarily known for his monumental incompleteness theorems, made significant contributions that extended beyond the realm of mathematical logic. His philosophical pursuits deeply engaged with the works of eminent philosophers like Immanuel Kant and Edmund Husserl. Gödel's explorations into the nature of time, the structure of the universe, and the relationship between mathematics and reality reveal a profound and multifaceted intellectual legacy. -/- Engagement with Immanuel Kant Gödel held a deep interest in the philosophy of Immanuel Kant. He admired Kant's critical philosophy, particularly the distinction between the noumenal and phenomenal worlds. Kant posited that human experience is shaped by the mind’s inherent structures, leading to the conclusion that certain aspects of reality (the noumenal world) are fundamentally unknowable. Gödel’s incompleteness theorems echoed this Kantian theme, illustrating the limits of formal systems in capturing the totality of mathematical truth. Gödel believed that mathematical truths exis t independently of human thought, akin to Kant's noumenal realm. This philosophical alignment provided a robust foundation for Gödel's Platonism, which asserted the existence of mathematical objects as real, albeit abstract, entities. -/- Influence of Edmund Husserl Gödel was also profoundly influenced by Edmund Husserl, the founder of phenomenology. Husserl's phenomenology emphasizes the direct investigation and description of phenomena as consciously experienced, without preconceived theories about their causal explanation. Gödel saw Husserl's work as a pathway to bridge the gap between the abstract world of mathematics and concrete human experience. Husserl's ideas about the structures of consciousness and the intentionality of thought resonated with Gödel's views on mathematical intuition. Gödel believed that human minds could access mathematical truths through intuition, a concept that draws on Husserlian phenomenological methods. -/- The Nature of Time and the Universe Gödel's philosophical inquiries extended to the nature of time and the structure of the universe. His collaboration with Albert Einstein at the Institute for Advanced Study led to the development of the "Gödel metric" in 1949. This solution to Einstein's field equations of general relativity described a rotating universe where time travel to the past was theoretically possible. Gödel's model challenged conventional notions of time and causality, suggesting that the universe might have a more intricate structure than previously thought. Gödel's exploration of time was not just a mathematical curiosity but a profound philosophical statement about the nature of reality. He questioned whether time was an objective feature of the universe or a construct of human consciousness. His work hinted at a timeless realm of mathematical truths, aligning with his Platonist view. -/- Mathematics and Reality Gödel's philosophical outlook extended to the broader relationship between mathematics and reality. He believed that mathematics provided a more profound insight into the nature of reality than empirical science. For Gödel, mathematical truths were timeless and unchangeable, existing independently of human cognition. This perspective led Gödel to critique the materialist and mechanistic views that dominated 20th-century science and philosophy. He argued that a purely physicalist interpretation of the universe failed to account for the existence of abstract mathematical objects and the human capacity to understand them. Gödel's philosophy suggested a more integrated view of reality, where both physical and abstract realms coexist and inform each other. -/- Gödel's Exploration of Time Kurt Gödel, one of the most profound logicians of the 20th century, ventured beyond the confines of mathematical logic to explore the nature of time. His inquiries into the concept of time were not merely theoretical musings but were grounded in rigorous mathematical formulations. Gödel's exploration of time challenged conventional views and opened new avenues of thought in both physics and philosophy. -/- Gödel and Einstein Gödel’s interest in the nature of time was significantly influenced by his friendship with Albert Einstein. Both were faculty members at the Institute for Advanced Study in Princeton, where they engaged in deep discussions about the nature of reality, time, and space. Gödel's exploration of time culminated in his solution to Einstein's field equations of general relativity, known as the Gödel metric. -/- The Gödel Metric In 1949, Gödel presented a model of a rotating universe, which became known as the Gödel metric. This solution to the equations of general relativity depicted a universe where time travel to the past was theoretically possible. Gödel’s rotating universe contained closed timelike curves (CTCs), paths in spacetime that loop back on themselves, allowing for the possibility of traveling back in time. The Gödel metric posed a significant philosophical challenge to the conventional understanding of time. If time travel were possible, it would imply that time is not linear and absolute, as commonly perceived, but rather malleable and subject to the geometry of spacetime. This raised profound questions about causality, the nature of temporal succession, and the very structure of reality. -/- Philosophical Implications Gödel’s exploration of time extended beyond the mathematical implications to broader philosophical inquiries: Nature of Time: Gödel questioned whether time was an objective feature of the universe or a construct of human consciousness. His work suggested that our understanding of time as a linear progression from past to present to future might be an illusion, shaped by the limitations of human perception. -/- Causality and Free Will: The existence of closed timelike curves in Gödel’s model raised questions about causality and free will. If one could travel back in time, it would imply that future events could influence the past, potentially leading to paradoxes and challenging the notion of a deterministic universe. -/- Temporal Ontology: Gödel's work contributed to debates in temporal ontology, particularly the debate between presentism (the view that only the present exists) and eternalism (the view that past, present, and future all equally exist). Gödel’s rotating universe model seemed to support eternalism, suggesting a block universe where all points in time are equally real. Philosophy of Science: Gödel’s exploration of time had implications for the philosophy of science, particularly in the context of understanding the limits of scientific theories. His work underscored the importance of considering philosophical questions when developing scientific theories, as they shape our fundamental understanding of concepts like time and space. -/- Legacy Gödel’s exploration of time remains a significant and controversial contribution to both physics and philosophy. His work challenged established notions and encouraged deeper inquiries into the nature of reality. Gödel’s rotating universe model continues to be a topic of interest in theoretical physics and cosmology, inspiring new research into the nature of time and the possibility of time travel. In philosophy, Gödel’s inquiries into time have prompted ongoing debates about the nature of temporal reality, the relationship between mathematics and physical phenomena, and the limits of human understanding. His work exemplifies the intersection of mathematical rigor and philosophical inquiry, demonstrating the profound insights that can emerge from such an interdisciplinary approach. The Temporal Ontology of Kurt Gödel Kurt Gödel's profound contributions to mathematics and logic extend into the realm of temporal ontology—the philosophical study of the nature of time and its properties. Gödel's insights challenge conventional perceptions of time and suggest a more intricate, layered understanding of temporal reality. This essay explores Gödel's contributions to temporal ontology, particularly through his engagement with relativity and his philosophical reflections. -/- Gödel's Rotating Universe One of Gödel’s most notable contributions to temporal ontology comes from his work in cosmology, specifically his solution to Einstein’s field equations of general relativity, known as the Gödel metric. Introduced in 1949, the Gödel metric describes a rotating universe with closed timelike curves (CTCs). These curves imply that, in such a universe, time travel to the past is theoretically possible, presenting a significant challenge to conventional views of linear, unidirectional time. -/- Implica tions for Temporal Ontology Gödel's rotating universe model has profound implications for our understanding of time: Eternalism vs. Presentism: Gödel’s model supports the philosophical stance known as eternalism, which posits that past, present, and future events are equally real. In contrast to presentism, which holds that only the present moment exists, eternalism suggests a "block universe" where time is another dimension like space. Gödel’s rotating universe, with its CTCs, reinforces this view by demonstrating that all points in time could, in principle, be interconnected in a consistent manner. Non-linearity of Time: The possibility of closed timelike curves challenges the idea of time as a linear sequence of events. In Gödel’s universe, time is not merely a straight path from past to future but can loop back on itself, allowing for complex interactions between different temporal moments. This non-linearity has implications for our understanding of causality and the nature of temporal succession. Objective vs. Subjective Time: Gödel’s work invites reflection on the distinction between objective time (the time that exists independently of human perception) and subjective time (the time as experienced by individuals). His model suggests that our subjective experience of a linear flow of time may not correspond to the objective structure of the universe. This raises questions about the relationship between human consciousness and the underlying temporal reality. -/- Gödel and Philosophical Reflections on Time Gödel’s engagement with temporal ontology was not limited to his cosmological work. He also reflected deeply on philosophical questions about the nature of time and reality, drawing on the ideas of other philosophers and integrating them into his own thinking. Kantian Influences: Gödel was influenced by Immanuel Kant’s distinction between the noumenal world (things as they are in themselves) and the phenomenal world (things as they appear to human observers). Gödel’s views on time echoed this distinction, suggesting that our perception of time might be a phenomenon shaped by the limitations of human cognition, while the true nature of time (the noumenal aspect) might be far more complex and non-linear. Husserlian Phenomenology: Gödel’s interest in Edmund Husserl’s phenomenology also informed his views on time. Husserl’s emphasis on the structures of consciousness and the intentionality of thought resonated with Gödel’s belief in the importance of intuition in accessing mathematical truths. Gödel’s reflections on time incorporated a phenomenological perspective, considering how temporal experience is structured by human consciousness. Mathematical Platonism: Gödel’s Platonist views extended to his understanding of time. Just as he believed in the independent existence of mathematical objects, Gödel saw time as an objective entity with a structure that transcends human perception. His work on the Gödel metric can be seen as an attempt to uncover this objective structure, revealing the deeper realities that underlie our experience of time. (shrink)

We present a deductive theory of space-time which is realistic, objective, and relational. It is realistic because it assumes the existence of physical things endowed with concrete properties. It is objective because it can be formulated without any reference to cognoscent subjects or sensorial fields. Finally, it is relational because it assumes that space-time is not a thing but a complex of relations among things. In this way, the original program of Leibniz is consummated, in the sense that space is (...) ultimately an order of coexistents, and time is an order of succesives. In this context, we show that the metric and topological properties of Minkowskian space-time are reduced to relational properties of concrete things. We also sketch how our theory can be extended to encompass a Riemannian space-time. (shrink)

Understanding of time, construed as movement, change and becoming, is explained taking examples from natural sciences. Durational and metrical aspects of time are elaborated. General assumptions about passage of time are listed. Indian, Chinese and later insights of path of passage of time are figured. Physical and psychological times are differentiated and explained using Energy-Presence (Being) and Energy-Transformation (Becoming) concepts. Concepts of Time at rest and Time in motion are proposed. -/- . The meanings of time-space, time-flow, different phases of (...) time-conscious and time-transcendent mind and thought processes are interpreted from basic physics principles and Upanishadic awareness -/- An attempt is made to present a comprehensive insight of nature of time, thought process and conscious states (phases) of mind. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Newton's Metaphysics: Essays by Eric SchliesserMarius StanEric Schliesser. Newton's Metaphysics: Essays. Oxford: Oxford University Press, 2021. Pp. 328. Hardback, $99.90.Newton owes his high regard to the quantitative science he left us, but his overall picture of the world had some robustly metaphysical threads woven in as well. Posthumous judgment about the value of these threads has varied wildly. Christian Wolff thought him a metaphysical rustic, as did Hans (...) Reichenbach some two centuries later ("Die Bewegungslehre bei Newton, Leibniz und Huygens," Kant-Studien 29 [1924]: 416–38). In the 1960s, the tide would turn, as Howard Stein and James Edward McGuire separately began to show that Newton's metaphysics was not just sophisticated, but often more compelling than its early modern alternatives (see respectively "Newtonian Spacetime," Texas Quarterly 10 [1967]: 174–200; and Tradition and Innovation: Newton's Metaphysics of Nature [Dordrecht: Kluwer Academic Publishers, 1995]). Eric Schliesser's book unfolds in that same register of appreciative, high scholarship, and it attests to the enduring attraction of its subject.The book grew out of previous discrete papers, to which he added a few more for this occasion. Accordingly, it does not come with a master argument. Rather, it is an in-depth exploration of some key metaphysical themes in Newton. As such, it befits its subject figure, who reflected on themes and concepts while stopping short of working out systems.The first major theme is Newton and Spinozism. The latter does not denote Spinoza's metaphysics. In fact, Schliesser explains, Newton shared with Spinoza some weighty commitments, for example, to space being actually infinite, and to substance monism: "for Newton, there is strictly speaking only one genuine substance," namely, God (33). Rather, "Spinozism" is an interpreter's category for a bundle of three theses: identifying God and nature; denying final causation in the physical world; and the assumption of "blind" metaphysical necessity. Some counted Hobbes and John Toland as Spinozist in this sense, and even Epicurus, avant la lettre. Newton and his followers argued vehemently against this package, as Schliesser shows in chapters 4, 5, and 8. Their chief complaint was that Spinozism is unable to account for the "origin of motion," for a certain type of order, and for the stability of cosmological structure—and to do so in a way that "meets the standards of Newtonian mechanics" (122). This interpretive lens allows Schliesser to draw Kant in, by reading his youthful Theory of Heaven as a possible Spinozist reply to their objections (chapter 3). [End Page 157]A second theme is the metaphysics of mechanics, where Schliesser weaves together several strands. One is the ontology of gravity, for which he offers a novel construal: for Newton, gravity counts as real, but in a qualified sense. Namely, it is not essential and not intrinsic: "even after creation, a lonely partless particle of matter in the universe would not be said to gravitate." And gravity is relational: a "shared quality" of two or more bits of matter, which obtains in virtue of their sharing a nature (19). Another strand is Newton's ontology of time—really, a subtle, difficult topic long neglected. Famously, Newton in Principia defends absolute, true, and mathematical time. The question is what these three qualifiers denote, and whether Newton thought they were synonymous. Schliesser in chapter 7 argues for the provocative view that "absolute" and "true" time are not identical concepts; rather, they pick out different entities. These entities share a common structure, namely, metric and topological. That makes them species of "mathematical" time (179). But, Schliesser contends, Newton has unequal warrant for his two concepts of time.Yet another theme is formal causation. It comes to the fore in chapter 5, which grapples with Newton's opaque idea that space is an "emanative effect." Schliesser explains that here, "emanation picks out a species of formal causation" (147), but in a novel, early modern sense that comes from Bacon, not Aristotle. If space has a formal cause, then so has its twin brother, time, the topic of chapter 7. God is their common formal cause. Then in chapter 6 (coauthored with Zvi Biener) Schliesser adds that, for Newton, laws... (shrink)

A methodological model of origin and settlement of theory-choice situations (previously tried on the theories of Einstein and Lorentz in electrodynamics) is applied to modern Theory of Gravity. The process of origin and growth of empirically-equivalent relativistic theories of gravitation is theoretically reproduced. It is argued that all of them are proposed within the two rival research programmes – (1) metric (A. Einstein et al.) and (2) nonmetric (H. Poincare et al.). Each programme aims at elimination of the cross-contradiction (...) between the special theory of relativity and Newton’s theory of gravitation. New arguments in favor of Einstein’s programme are given. Nevertheless, this does not imply the necessity to rule out all the nonmetric theories, since Einstein’s and Poincare’s programmes are alternative only as different tools of the cross-contradiction elimination. In the other respects these programmes are complementary: description, explanation and prediction of gravitational experimental data entails the usage of the languages of nonmetric theories as well as of metric ones. The part of the present investigation elucidating the necessity of nonmetric theories is an implementation of the ideas of A.Z. Petrov, the founder of Kazan University Relativity Department. Late Alexei Zinovievich had frequently punctuated that the notion of Riemann space-time continuum common for all metric theories obfuscates all the gravitational notions considerably and hampers the analogies with other physical theories at hand. Since the ambiguity is a hallmark of all the general relativism notions, approach to their definitions “should be determined not by analogies and contingent facts, but by general considerations linked the physical measurements theory… No matter how far the events lie out of the frames of classical physical explanations, all the experimental data should be described by classical notions” (Petrov, 1965,pp. 59,66). Key words: Kip S. Thorne, A.P. Lightman, Stepin, theory of gravity . (shrink)

In this work we study dimensional theoretical properties of some a±ne dynamical systems. By dimensional theoretical properties we mean Hausdor® dimension and box- counting dimension of invariant sets and ergodic measures on theses sets. Especially we are interested in two problems. First we ask whether the Hausdor® and box- counting dimension of invariant sets coincide. Second we ask whether there exists an ergodic measure of full Hausdor® dimension on these invariant sets. If this is not the case we ask the (...) question, whether at least the variational principle for Haus- dor® dimension holds, which means that there is a sequence of ergodic measures such that their Hausdor® dimension approximates the Hausdor® dimension of the invariant set. It seems to be well accepted by experts that these questions are of great importance in developing a dimension theory of dynamical systems (see the book of Pesin about dimension theory of dynamical systems [PE2]). Dimensional theoretical properties of conformal dynamical systems are fairly well understood today. For example there are general theorems about conformal repellers and hyperbolic sets for conformal di®eomorphisms (see chapter 7 of [PE2]). On the other hand the existence of two di®erent rates of expansion or contraction forces problems that are not captured by a general theory this days. At this stage of de- velopment of the dimension theory of dynamical systems it seems natural to study non conformal examples. This is the ¯rst step to understand the mechanisms that determine dimensional theoretical properties of non conformal dynamical systems. A±ne dynamical systems represent simple examples of non conformal systems. They are easy to de¯ne, but studying their dimensional theoretical properties does never- theless provide challenging mathematical problems and exemplify interesting phe- nomena. We consider here a special class of self-a±ne repellers in dimension two, depending on four parameters (see 2.1.). Furthermore we study a class of attractors of piecewise a±ne maps in dimension three depending on four parameters as well. The last object of our work are projections of these maps that are known as gener- alized Baker's transformations (see 2.2.). The contents of our work is the following: In chapter two we give an overview about some main results in the area of di- mension theory of a±ne dynamical systems and de¯ne the systems we study in this work. We will explain, what is known about the dimensional theoretical properties of these systems and describe what our new results are. In chapter three we then apply symbolic dynamics to our systems. We will introduce explicit shift codings 4 and ¯nd representations of all ergodic measures for our systems using these codings. From chapter four to chapter eight we study dimensional theoretical properties, which our systems generally or generically have. In chapter four we will prove a formula for the box-counting dimension of the repellers and the attractors (see the- orem 4.1.). Then in chapter ¯ve we apply general dimensional theoretical results for ergodic measures found by Ledrappier and Young [LY] and Barreira, Schmeling and Pesin [BPS] to our systems. These results relate the dimension of ergodic measures to metric entropy and Lyapunov exponents. Using this approach we will be able to reduce questions about the dimension of ergodic measures in our context to ques- tions about certain overlapping and especially overlapping self-similar measures on the line. These overlapping self-similar measures are studied in chapter six. Our main theorem extends a result of Peres and Solomyak [PS2] concerning the absolute continuity resp. singularity of symmetric self-similar measures to asymmetric ones (see theorem 6.1.3.). In chapter seven we bring our results together. We prove that we generically (in the sense of Lebesgue measure on a part of the parameter space) have the iden- tity of box-counting and Hausdor® dimension for the repellers and the attractors. (see theorem 7.1.1. and corollary 7.1.2.). This result suggest that one can expect that the identity of box-counting dimension and Hausdor® dimension holds at least generically in some natural classes of non conformal dynamical systems. Furthermore we will see in chapter seven that there generically exists an ergodic measure of full Hausdor® dimension for the repellers. On the other hand the vari- ational principle for Hausdor® dimension is not generic for the attractors. It holds only if we assume a certain symmetry (see theorem 7.1.1.). For generalized Baker's transformations we will ¯nd a part of the parameter space where there generically is an ergodic measure of full dimension and a part where the variational principle for Hausdor® dimension does not hold (see theorem 7.1.3.). Roughly speaking the reason why the variational principle does not hold here is, that if there exists both a stable and an unstable direction one can not generically maximize the dimension in the stable and in the unstable direction at the same time. In an other setting this phenomenon was observed before by Manning and McCluskey [MM]. In chapter eight we extend some results of the last section to invariant sets that correspond to special Markov chains instead of full shifts (see theorem 8.1.1.). In the last two chapters of our work we are interested in number theoretical excep- tions to our generic results. The starting point of our considerations in section nine are results of ErdÄos [ER1] and Alexander and Yorke [AY] that establish singularity and a decrease of dimension for in¯nite convolved Bernoulli measures under special conditions. Using a generalized notion of the Garsia entropy ([GA1/2]) we are able 5 to understand the consequences of number theoretical peculiarities in broader class of overlapping measures (see theorem 9.1.1.). In chapter ten we then analyze number theoretical peculiarities in the context of our dynamical systems. We restrict our attention to a symmetric situation where we generically have the existence of a Bernoulli measure of full dimension and the identity of Hausdor® and box-counting dimension for all of our systems. In the ¯rst section of chapter ten we ¯nd parameter values such that the variational principle for Hausdor® dimension does not hold for the attractors and for the Fat Baker's transformations (see theorem 10.1.1.). These are the ¯rst known examples of dynamical systems for which the variational principle for Hausdor® dimension does not hold because of number theoretical peculiarities of parameter values. For the repellers we have been able to show that under certain number theoretical conditions there is at least no Bernoulli measure of full Hausdor® dimension; the question if the variational principle for Hausdor® dimension holds remains open in this situation. In the second section of chapter ten we will show that the identity for Hausdor® and box-counting dimension can drops because there are number theoretical pecu- liarities. In the context of Weierstrass-like functions this phenomenon was observed by Przytycki and Urbanski [PU]. Our theorem extends this result to a larger class of sets, invariant under dynamical systems (see theorem 10.2.1). At the end of this work the reader will ¯nd two appendices, a list of notations and the list of references. In appendix A we introduce the notions of dimension we use in this work and collect some general facts in dimension theory. In appendix B we state the facts about Pisot-Vijayarghavan number, we need in our analysis of number theoretical peculiarities. The list of notations contains general notations and a table with a summary of notations we use to describe the dynamical systems that we study. Acknowledgments I wish to thank my supervisor JÄorg Schmeling for a lot of valuable discussion and all his help. Also thanks to Luis Barreira for his great hospitality in Lisboa and many interesting comments. This work was done while I was supported by "Promotionstipendium gem. NaFÄoG der Freien UniversitÄat Berlin". (shrink)

"There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact" Mark Twain-Life on the Mississippi -/- This is a lovely book full of fascinating info on the evolution of physics and cosmology. Its main theme is how the idea of higher dimensional geometry created by Riemann, recently extended to 24 dimensions by string theory, has revolutionized our understanding of the universe. Everyone knows that Riemann created multidimensional geometry in 1854 (...) but it is amazing to learn that he also was a physicist who believed that it held the key to explaining the fundamental laws of physics. Maxwell´s equations did not exist then and Riemann´s untimely death at age 39 prevented his pursuit of these ideas. Both he and his British translator Clifford believed that magnetic and electric fields resulted from the bending of space in the 4th dimension-more than 50 years before Einstein! The fourth dimension became a standard subject in the popular media for the next 50 years with several stories by HG Wells using it and even Lenin wrote about it. The American mathematician Hinton had widely publicized his idea that light is a vibration in the 4th spatial dimension. Amazingly, physicists and most mathematicians forgot about it and when Einstein was looking for the math needed to encompass general relativity 60 years later, he had never heard of Riemannian geometry. He spent 3 years trying to find the equations for general relativity and only after a math friend told him about Riemann was he able to complete his work. Riemann´s equations with four dimensional metric tensors describing every point in space were incorporated almost unchanged into relativity. And on and on it goes. Since this review I have written a great deal on the language games of math and science, uncertainty, incompleteness, the limits of computation etc., so those interested should find them useful since this volume like most science frequently wanders across the line into philosophy (scientism). -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

We indicate a new way in the solution of the problem of the quantum measurement . In past papers we used the well-known formalism of the density matrix using an algebraic approach in a two states quantum spin system S, considering the particular case of three anticommuting elements. We demonstrated that, during the wave collapse, we have a transition from the standard Clifford algebra, structured in its space and metrics, to the new spatial structure of the Clifford dihedral algebra. This (...) structured geometric transition, which occurs during the interaction of the S system with the macroscopic measurement system M, causes the destruction of the interferential factors. In the present paper we construct a detailed model of the (S+M) interaction evidencing the particular role of the Time Ordering in the (S+M) coupling since we have a time asymmetric interaction . We demonstrate that , during the measurement , the physical circumstance that the fermion creation and annihilation operators of the S system must be destroyed during such interaction has a fundamental role . (shrink)

General Relativity defines gravity like the metric of a Lorentzian manifold. Einstein formulated spacetime as quality structural of gravity, i.e, circular definition between gravity and spacetime, also Einstein denoted "Space and time are modes by which we think, not conditions under which we live" and “We denote everything but the gravitational field as matter”, therefore, spacetime is nothing and gravity in first approximation an effect of coordinates, and definitely a geometric effect. The mathematical model generates quantitative predictions coincident in (...) high grade with observations without physical meaning. Philosophy intervened: in Substantivalism, spacetime exists in itself while in Relationalism as metrical relations. But, it does not know what spacetime. The outcomes of model have supported during a century, validity of the General Relativity, interpreted arbitrarily. Einstein formulated, from quadrupoles of energy, the formation of ripples in spacetime propagating as gravitational waves abandoned, in 1938, when he said that they do not exist. LIGO announced the first detection of gravitational waves from a pair of merging black holes. They truly are waves of quantum vacuum. (shrink)

The question of time travel stimulates the imagination and provides material for whimsical stories. A work on the topic of "time travel" forces us to deal with the concept of "time". The complexity and the antinomic character of this concept make it difficult to grasp "time" more precisely. We encounter time as a form of perception in its deeply subjective aspect, as a biological rhythm, as a social phenomenon in the sense of a collective determination of time, but also as (...) a physical quantity. Einstein's theory of relativity revolutionized our ideas of space and time. His Special Theory of Relativity (1905) allows "travel into the future" through the effect of time dilation he predicted, and Einstein's theory of gravity allows for closed time lines as solutions to its equations (e.g., Gödel cosmos, anti-de Sitter cosmos). However, traveling in a time loop would immediately lead to a number of paradoxes (e.g., grandfather paradox, information paradox). Although, surprisingly, the basic laws of physics (apart from extremely rare and macroscopically non-appearing quantum mechanical effects) would not be violated in a time reversal, there seems to be a fundamental prohibition of traveling into the past in nature. (shrink)

Dwork, Hardt, Pitassi, Reingold, & Zemel [6] introduced two notions of fairness, each of which is meant to formalize the notion of similar treatment for similarly qualified individuals. The first of these notions, which we call additive metric fairness, has received much attention in subsequent work studying the fairness of a system composed of classifiers which are fair when considered in isolation [3, 4, 7, 8, 12] and in work studying the relationship between fair treatment of individuals and fair (...) treatment of groups [6, 7, 13]. Here, we extend these lines of research to the second, less-studied notion, which we call multiplicative metric fairness. In particular, we exactly characterize the fairness of conjunctions and disjunctions of multiplicative metric fair classifiers, and the extent to which a classifier which satisfies multiplicative metric fairness also treats groups fairly. This characterization reveals that whereas additive metric fairness becomes easier to satisfy when probabilities of acceptance are small, leading to unfairness under functional and group compositions, multiplicative metric fairness is better-behaved, due to its scale-invariance. (shrink)

‘Space does not exist fundamentally: it emerges from a more fundamental non-spatial structure.’ This intriguing claim appears in various research programs in contemporary physics. Philosophers of physics tend to believe that this claim entails either that spacetime does not exist, or that it is derivatively real. In this article, I introduce and defend a third metaphysical interpretation of the claim: reductionism about space. I argue that, as a result, there is no need to subscribe to fundamentality, layers of reality and (...) emergence in order to analyse the constitution of space by non-spatial entities. It follows that space constitution, if borne out, does not provide empirical evidence in favour of a stratified, Aristotelian in spirit, metaphysics. The view will be described in relation to two particular research programs in contemporary physics: wave function realism and loop quantum gravity. (shrink)

Research assessment and grant funding are vital to higher education. However, the reliance on quantitative metrics in these processes has raised concerns about their validity and potential negative consequences. This study aims to investigate the game of numbers in research assessment and grant funding, focusing on the perspectives of experienced researchers from around the globe. Accidental sampling elicited responses from more than 15 experienced researchers across different academic disciplines, institutions, and countries. The data were collected from the popular “Reviewer 2 (...) Must be Stopped!” Facebook platform, which includes more than 135,000 members across the globe. Two posts were made, allowing participants to share their experiences, perspectives, and concerns related to metrics and numbers in research assessment and grant funding. The results from the thematic analysis revealed diverse perspectives among experienced researchers. Some participants expressed concerns about the dominance of quantitative metrics, highlighting the limitations and potential biases associated with their use. Others acknowledged the value of certain indicators in showcasing research impact. Moreover, the impact of metrics on grant funding awards was also documented. The study highlights the necessity for a more balanced and context-aware approach to research assessment and grant funding, incorporating qualitative measures and acknowledging the diverse nature of research impact. (shrink)

According to representionalists, qualia-the introspectible properties of sensory experience-are exhausted by the representational contents of experience. Representationalists typically advocate an informational psychosemantics whereby a brain state represents one of its causal antecedents in evolutionarily determined optimal circumstances. I argue that such a psychosemantics may not apply to certain aspects of our experience, namely, our experience of space in vision, hearing, and touch. I offer that these cases can be handled by supplementing informational psychosemantics with a procedural psychosemantics whereby a representation (...) is about its effects instead of its causes. I discuss conceptual and empirical points that favor a procedural representationalism for our experience of space. (shrink)

Security and privacy are the major concerns in the internet of things (IoT) which are uncertain and unpredictable. Trust aware routing is one of the recent and effective strategies which ensure better resilience for IoT nodes from different security threats. Towards such concern, this paper proposes a new strategy called independent onlooker withstanding trust aware routing (IOWTAR) for IoT. IOWTAR introduced a new compound trust metric by combining three individual metrics namely independent trust, onlooker trust, and withstanding trust (a (...) combination of resilient trust and immovability trust). Independent trust and onlooker trust are assessed based on direct and indirect experiences of nodes about their neighbor nodes. Withstanding trust is assessed based on the stability and resilience of nodes towards dynamic topological changes and network failures respectively. Further, this work adapted the Firefly algorithm (FFA) to optimize the weights of individual trusts and establishes a secure path. Simulation experiments carried out over the proposed method had shown its superiority in terms of packet delivery ratio, delay, and throughput. The proposed method has gained an average improvement in the throughput is of 23.71%, 20.18%, 17.27%, and 2.88% from PSO, GSA, WOA, and CBBMOR-TSM-IOT methods respectively. (shrink)

There are few notions in philosophy seen more clearly, and in parallel so laden with confusion, than that of space and time. The subjective nature of analyses is most likely to blame. As it stands, a universal agreement has not yet been reached. My position is simply that the mind, when passive, has no qualms with space and time itself, nor is it concerned with its principles. It is only when our passions are ignited, and our judgment is utilized, i.e. (...) when we begin to actively think about space and time, that the notion becomes confounded. Any further digression into semantics of the issue by trying to give a ‘say all end all’ explanation will always lead to a dead end. Both space and time are ideas of an infinite nature and can never be visited manifestly since the mind itself is undeniably finite. (shrink)

There is a growing body of scholarship that is addressing the ethics, in particular, the bioethics of space travel and colonisation. Naturally, a variety of perspectives concerning the ethical issues and moral permissibility of different technological strategies for confronting the rigours of space travel and colonisation have emerged in the debate. Approaches ranging from genetically enhancing human astronauts to modifying the environments of planets to make them hospitable have been proposed as methods. This paper takes a look at a critique (...) of human bioenhancement proposed by Mirko Garasic who argues that the bioenhancement of human astronauts is not only functional but necessary and thus morally permissible. However, he further claims that the bioethical arguments proposed for the context of space do not apply to the context of Earth. This paper forwards three arguments for how Garasic’s views are philosophically dubious: (1) when he examines our responsibility towards future generations he refers to a moral principle (which we will call the principle of mere survival) which, besides being vague, is not morally acceptable; (2) the idea that human bioenhancement is not natural is not only debatable but morally irrelevant; and (3) it is not true that the situations that may arise in space travel cannot occur on Earth. We conclude that not only is the (bio)enhancement of humans on Earth permissible but perhaps even necessary in certain circumstances. (shrink)

Distributive justice deals with allocations of goods and bads within a group. Different principles and results of distributions are seen as possible ideals. Often those normative approaches are solely framed verbally, which complicates the application to different concrete distribution situations that are supposed to be evaluated in regard to justice. One possibility in order to frame this precisely and to allow for a fine-grained evaluation of justice lies in formal modelling of these ideals by metrics. Choosing a metric that (...) is supposed to map a certain ideal has to be justified. Such justification might be given by demanding specific substantiated axioms, which have to be met by a metric. This paper introduces such axioms for metrics of distributive justice shown by the example of needs-based justice. Furthermore, some exemplary metrics of needs-based justice and a three dimensional method for visualisation of non-comparative justice axioms or evaluations are presented. Therewith, a base worth discussing for the evaluation and modelling of metrics of distributive justice is given. (shrink)

I motivate and defend a previously underdeveloped functionalist account of the metaphysics of color, a view that I call ‘quality-space functionalism’ about color. Although other theorists have proposed varieties of color functionalism, this view differs from such accounts insofar as it identifies and individuates colors by their relative locations within a particular kind of so-called ‘quality space’ that reflects creatures’ capacities to discriminate visually among stimuli. My arguments for this view of color are abductive: I propose that quality-space functionalism best (...) captures our commonsense conception of color, fits with many experimental findings, coheres with the phenomenology of color experience, and avoids many issues for standard theories of color such as color physicalism and color relationalism. (shrink)

This paper provides a method for characterizing space events using the framework of conceptual spaces. We focus specifically on estimating and ranking the likelihood of collisions between space objects. The objective is to design an approach for anticipatory decision support for space operators who can take preventive actions on the basis of assessments of relative risk. To make this possible our approach draws on the fusion of both hard and soft data within a single decision support framework. Contextual data (...) is also taken into account, for example data about space weather effects, by drawing on the Space Domain Ontologies, a large system of ontologies designed to support all aspects of space situational awareness. The framework is coupled with a mathematical programming scheme that frames a mathematically optimal approach for decision support, providing a quantitative basis for ranking potential for collision across multiple satellite pairs. The goal is to provide the broadest possible information foundation for critical assessments of collision likelihood. (shrink)

A distorted representation of one's own body is a diagnostic criterion and core psychopathology of both anorexia nervosa (AN) and bulimia nervosa (BN). Despite recent technical advances in research, it is still unknown whether this body image disturbance is characterized by body dissatisfaction and a low ideal weight and/or includes a distorted perception or processing of body size. In this article, we provide an update and meta-analysis of 42 articles summarizing measures and results for body size estimation (BSE) from 926 (...) individuals with AN, 536 individuals with BN and 1920 controls. We replicate findings that individuals with AN and BN overestimate their body size as compared to controls (ES= 0.63). Our meta-regression shows that metric methods (BSE by direct or indirect spatial measures) yield larger effect sizes than depictive methods (BSE by evaluating distorted pictures), and that effect sizes are larger for patients with BN than for patients with AN. To interpret these results, we suggest a revised theoretical framework for BSE that accounts for differences between depictive and metric BSE methods regarding the underlying body representations (conceptual vs. perceptual, implicit vs. explicit). We also discuss clinical implications and argue for the importance of multimethod approaches to investigate body image disturbance. (shrink)

This paper argues that all of the standard theories about the divisions of space and time can benefit from, and may need to rely on, parsimony considerations. More specifically, whether spacetime is discrete, gunky or pointy, there are wildly unparsimonious rivals to standard accounts that need to be resisted by proponents of those accounts, and only parsimony considerations offer a natural way of doing that resisting. Furthermore, quantitative parsimony considerations appear to be needed in many of these cases.

Ian Stoner has recently argued that we ought not to colonize Mars because doing so would flout our pro tanto obligation not to violate the principle of scientific conservation, and there is no countervailing considerations that render our violation of the principle permissible. While I remain agnostic on, my primary goal in this article is to challenge : there are countervailing considerations that render our violation of the principle permissible. As such, Stoner has failed to establish that we ought not (...) to colonize Mars. I close with some thoughts on what it would take to show that we do have an obligation to colonize Mars and related issues concerning the relationship between the way we discount our preferences over time and projects with long time horizons, like space colonization. (shrink)