An isomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That isomorphism can be interpreted physically as the invariance between a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting another way for proving it, more concise and meaningful physically. Mathematically, the isomorphism means (...) the invariance to choice, the axiom of choice, well-ordering, and well-ordering “theorem” (or “principle”) and can be defined generally as “information invariance”. (shrink)

A homeomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That homeomorphism can be interpreted physically as the invariance to a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting at another way for proving it, more concise and meaningful physically. Furthermore, the conjecture (...) can be generalized and interpreted in relation to the pseudo-Riemannian space of general relativity therefore allowing for both mathematical and philosophical interpretations of the force of gravitation due to the mismatch of choice and ordering and resulting into the “curving of information” (e.g. entanglement). Mathematically, that homeomorphism means the invariance to choice, the axiom of choice, well-ordering, and well-ordering “theorem” (or “principle”) and can be defined generally as “information invariance”. Philosophically, the same homeomorphism implies transcendentalism once the philosophical category of the totality is defined formally. The fundamental concepts of “choice”, “ordering” and “information” unify physics, mathematics, and philosophy and should be related to their shared foundations. (shrink)

1. Schrodinger Equation, fragmentalism, total time T, Euclidean space 2. Does the A-series have the properties of qualia?

Relativistic quantum theories are equipped with a background Minkowski spacetime and non-relativistic quantum theories with a Galilean space-time. Traditional investigations have distinguished their distinct space-time structures and have examined ways in which relativistic theories become sufficiently like Galilean theories in a low velocity approximation or limit. A different way to look at their relationship is to see that both kinds of theories are special cases of a certain five-dimensional generalization involving no limiting procedures or approximations. When one (...) compares them, striking features emerge that bear on philosophical questions, including the ontological status of the wave function and time reversal invariance. (shrink)

We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in Maudlin and Malament. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of Tarski : a predicate of betwenness and (...) a four place predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional ‘vector space’ that can be decomposed everywhere into a spacelike hyperplane—which obeys the Euclidean axioms in Tarski and Givant, 175–214 1999)—and an orthogonal timelike line. The length of other ‘vectors’ are calculated according to Pythagoras’ theorem. We conclude with a Representation Theorem relating models \ of our system \ that satisfy second order continuity to the mathematical structure \, called ‘Minkowski spacetime’ in physics textbooks. (shrink)

Here we discuss and hope to solve a problem rooted in the necessity of the study of historical science, the slow deviation of physics education over the past century, and how the loss of crucial contextual tool has debilitated discussion of a very important yet specialized physics sub-topic: the isotropy of the one-way speed of light. Most notably, the information that appears to be most commonly missing is not simply the knowledge of the historical fact that Poincare and Lorentz presented (...) a mathematically equivalent representation of relativity theory contemporary with Einstein’s publication, but the most deleterious outcome is a lack of understanding of how that theory worked within a mechanical wave system to give the same results in all known experiments via an instrumentation-based illusion. Unfortunately those well educated in relativity theory, often haven’t been granted the advantage of contrast this history of development of the theory gives and thus some of the most direct and critical implications of modern theory are often lost on even graduate students. Chief among the implications that should be trivial to a student of relativity is the incompatibility of a mechanical wave concept of light with the modern assumptions of relativity. However, one should also be able to expect a graduate student to also easily comprehend the mathematical necessity of conjoining space with time is only descended from the presumption of isotropic constancy specifically, and further that the mechanics are one and the same as the relativity of simultaneity. However, many published papers appear to lack this understanding. The result is that the modern consensus appears to have arrived at the conclusion that the one-way speed of light is intrinsically untestable and therefore the physics community has accidentally pushed Minkowski spacetime, and most directly, the relativity of simultaneity, into the domain of pseudoscience, leaving only the historical relativistic “ether” described by Mansouri-Sexl test theory (AKA Lorentz Ether Theory) as the only workable alternative. This situation must be re-examined at the lowest possible level to arrive at an appropriate experimental regime. (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 essay explores Kaila's interpretation of the special theory of relativity. Although the relevance of his work to logical empiricism is well-known, not much has been written on what Kaila calls the ‘Einstein-Minkowski invariance theory’. Kaila's interpretation focuses on two salient features. First, he emphasizes the importance of the invariance of the spacetime interval. The general point about spacetime invariance has been known at least since Minkowski, yet Kaila applies his overall tripartite theory of invariances to space, (...) time and spacetime in an original way. Second, Kaila provides a non-conventionalist argument for the isotropic speed of electromagnetic signals. The standard Einstein synchrony is not a mere convention but a part of a larger empirical theory. According to Kaila's holistic principle of testability, which stands in contrast to the theses of translatability and verification, different items in the theory cannot be sharply divided into conventional and empirical. Kaila's invariantism/non-conventionalism about relativity reflects an interesting case in the gradual transition from positivism to realism within the philosophy of science. (shrink)

A-theoretic presentness is commonly regarded as non-solipsist and non-relative. The non-solipsism of a non-relative, A-theoretic presentness requires at least two space-like separated things to be present simpliciter together – this co-presentness further implies the global, non-relative, non-conventional simultaneity of them. Yet, this implication clashes with the general view that there is no global, non-relative, non-conventional simultaneity in Minkowski space-time. In order to resolve this conflict, this paper explores the possibility that the non-solipsism of a non-relative, A-theoretic presentness (...) does not require at least two space-like separated things to be present simpliciter together. This can be done by holding exclusive disjunctivism –that mutually space-like separated things are present simpliciter exclusively disjunctively, and each one of them gets to be present simpliciter in a non-successive way (just like mutually time-like related things are present simpliciter exclusively disjunctively, and each one of them gets to be present simpliciter, but in a successive way). (shrink)

Temporality and Spatiality have been extensively addressed in philosophy, and their disturbances have been extensively studied in psychopathology (e.g. Wyllie 2005). Mental health patients: (1) describe pathological experiences of Time and Space (Gallagher and Varela 2003); (2) show disturbed timing (Tysk 1984); (3) experience psychopathological phenomena that could be the cause of changes in temporality and spatiality. These topics will be discussed in the case of mood disorders, in particular euphoric and dysphoric mania episodes. Any phenomenological study in mood (...) disorders is delicate as affective disorders are in themselves phenomenologically diverse, because they have obscure meaning, multitude of criteria and inconsistent reference norms. Also, psychoanalytical, colloquial and cognitive psychologies keep instilling comprehensive and epistemological structures onto both mood and time/space notions. Nevertheless, bridging philosophical phenomenology and epistemology on time and temporality with mood psychopathology and taxonomy constitutes an on-going project. Theories by Heidegger, Husserl and Merleau-Ponty as well as by Minkowsky, Binswanger, Fuchs, Parnas, and Sass could help to describe this relation deepened into many other Twentieth-Century philosophical papers. A similar account of space and spatiality will be brought about. We will reason about the concept that they provide evidence to address current conceptualization of “bipolar” disorder and the hierarchical grouping of dysphoric and euphoria mania. (shrink)

This essay explores theories of place, or lived-space, as regards the role of objectivity and the problem of relativism. As will be argued, the neglect of mathematics and geometry by the lived-space theorists, which can be traced to the influence of the early phenomenologists, principally the later Husserl and Heidegger, has been a major contributing factor in the relativist dilemma that afflicts the lived-space movement. By incorporating various geometrical concepts within the analysis of place, it is demonstrated (...) that the lived-space theorists can gain a better insight into the objective spatial relationships among individuals and within groups—and, more importantly, this appeal to mathematical content need not be construed as undermining the basic tenants of the lived-space approach. (shrink)

Non-commuting quantities and hidden parameters – Wave-corpuscular dualism and hidden parameters – Local or nonlocal hidden parameters – Phase space in quantum mechanics – Weyl, Wigner, and Moyal – Von Neumann’s theorem about the absence of hidden parameters in quantum mechanics and Hermann – Bell’s objection – Quantum-mechanical and mathematical incommeasurability – Kochen – Specker’s idea about their equivalence – The notion of partial algebra – Embeddability of a qubit into a bit – Quantum computer is not Turing machine (...) – Is continuality universal? – Diffeomorphism and velocity – Einstein’s general principle of relativity – „Mach’s principle“ – The Skolemian relativity of the discrete and the continuous – The counterexample in § 6 of their paper – About the classical tautology which is untrue being replaced by the statements about commeasurable quantum-mechanical quantities – Logical hidden parameters – The undecidability of the hypothesis about hidden parameters – Wigner’s work and и Weyl’s previous one – Lie groups, representations, and psi-function – From a qualitative to a quantitative expression of relativity − psi-function, or the discrete by the random – Bartlett’s approach − psi-function as the characteristic function of random quantity – Discrete and/ or continual description – Quantity and its “digitalized projection“ – The idea of „velocity−probability“ – The notion of probability and the light speed postulate – Generalized probability and its physical interpretation – A quantum description of macro-world – The period of the as-sociated de Broglie wave and the length of now – Causality equivalently replaced by chance – The philosophy of quantum information and religion – Einstein’s thesis about “the consubstantiality of inertia ant weight“ – Again about the interpretation of complex velocity – The speed of time – Newton’s law of inertia and Lagrange’s formulation of mechanics – Force and effect – The theory of tachyons and general relativity – Riesz’s representation theorem – The notion of covariant world line – Encoding a world line by psi-function – Spacetime and qubit − psi-function by qubits – About the physical interpretation of both the complex axes of a qubit – The interpretation of the self-adjoint operators components – The world line of an arbitrary quantity – The invariance of the physical laws towards quantum object and apparatus – Hilbert space and that of Minkowski – The relationship between the coefficients of -function and the qubits – World line = psi-function + self-adjoint operator – Reality and description – Does a „curved“ Hilbert space exist? – The axiom of choice, or when is possible a flattening of Hilbert space? – But why not to flatten also pseudo-Riemannian space? – The commutator of conjugate quantities – Relative mass – The strokes of self-movement and its philosophical interpretation – The self-perfection of the universe – The generalization of quantity in quantum physics – An analogy of the Feynman formalism – Feynman and many-world interpretation – The psi-function of various objects – Countable and uncountable basis – Generalized continuum and arithmetization – Field and entanglement – Function as coding – The idea of „curved“ Descartes product – The environment of a function – Another view to the notion of velocity-probability – Reality and description – Hilbert space as a model both of object and description – The notion of holistic logic – Physical quantity as the information about it – Cross-temporal correlations – The forecasting of future – Description in separable and inseparable Hilbert space – „Forces“ or „miracles“ – Velocity or time – The notion of non-finite set – Dasein or Dazeit – The trajectory of the whole – Ontological and onto-theological difference – An analogy of the Feynman and many-world interpretation − psi-function as physical quantity – Things in the world and instances in time – The generation of the physi-cal by mathematical – The generalized notion of observer – Subjective or objective probability – Energy as the change of probability per the unite of time – The generalized principle of least action from a new view-point – The exception of two dimensions and Fermat’s last theorem. (shrink)

The paper continues the consideration of Hilbert mathematics to mathematics itself as an additional “dimension” allowing for the most difficult and fundamental problems to be attacked in a new general and universal way shareable between all of them. That dimension consists in the parameter of the “distance between finiteness and infinity”, particularly able to interpret standard mathematics as a particular case, the basis of which are arithmetic, set theory and propositional logic: that is as a special “flat” case of Hilbert (...) mathematics. The following four essential problems are considered for the idea to be elucidated: Fermat’s last theorem proved by Andrew Wiles; Poincaré’s conjecture proved by Grigori Perelman and the only resolved from the seven Millennium problems offered by the Clay Mathematics Institute (CMI); the four-color theorem proved “machine-likely” by enumerating all cases and the crucial software assistance; the Yang-Mills existence and mass gap problem also suggested by CMI and yet unresolved. They are intentionally chosen to belong to quite different mathematical areas (number theory, topology, mathematical physics) just to demonstrate the power of the approach able to unite and even unify them from the viewpoint of Hilbert mathematics. Also, specific ideas relevant to each of them are considered. Fermat’s last theorem is shown as a Gödel insoluble statement by means of Yablo’s paradox. Thus, Wiles’s proof as a corollary from the modularity theorem and thus needing both arithmetic and set theory involves necessarily an inverse Grothendieck universe. On the contrary, its proof in “Fermat arithmetic” introduced by “epoché to infinity” (following the pattern of Husserl’s original “epoché to reality”) can be suggested by Hilbert arithmetic relevant to Hilbert mathematics, the mediation of which can be removed in the final analysis as a “Wittgenstein ladder”. Poincaré’s conjecture can be reinterpreted physically by Minkowski space and thus reduced to the “nonstandard homeomorphism” of a bit of information mathematically. Perelman’s proof can be accordingly reinterpreted. However, it is valid in Gödel (or Gödelian) mathematics, but not in Hilbert mathematics in general, where the question of whether it holds remains open. The four-color theorem can be also deduced from the nonstandard homeomorphism at issue, but the available proof by enumerating a finite set of all possible cases is more general and relevant to Hilbert mathematics as well, therefore being an indirect argument in favor of the validity of Poincaré’s conjecture in Hilbert mathematics. The Yang-Mills existence and mass gap problem furthermore suggests the most general viewpoint to the relation of Hilbert and Gödel mathematics justifying the qubit Hilbert space as the dual counterpart of Hilbert arithmetic in a narrow sense, in turn being inferable from Hilbert arithmetic in a wide sense. The conjecture that many if not almost all great problems in contemporary mathematics rely on (or at least relate to) the Gödel incompleteness is suggested. It implies that Hilbert mathematics is the natural medium for their discussion or eventual solutions. (shrink)

The purpose of this paper is to show that the Elementary Process Theory (EPT) agrees with the knowledge of the physical world obtained from the successful predictions of Special Relativity (SR). For that matter, a recently developed method is applied: a categorical model of the EPT that incorporates SR is fully specified. Ultimate constituents of the universe of the EPT are modeled as point-particles, gamma-rays, or time-like strings, all represented by integrable hyperreal functions on Minkowski space. This proves (...) that the EPT agrees with SR. -/- Edit: this preprint differs significantly from the published chapter. (shrink)

The way, in which quantum information can unify quantum mechanics (and therefore the standard model) and general relativity, is investigated. Quantum information is defined as the generalization of the concept of information as to the choice among infinite sets of alternatives. Relevantly, the axiom of choice is necessary in general. The unit of quantum information, a qubit is interpreted as a relevant elementary choice among an infinite set of alternatives generalizing that of a bit. The invariance to the axiom of (...) choice shared by quantum mechanics is introduced: It constitutes quantum information as the relation of any state unorderable in principle (e.g. any coherent quantum state before measurement) and the same state already well-ordered (e.g. the well-ordered statistical ensemble of the measurement of the quantum system at issue). This allows of equating the classical and quantum time correspondingly as the well-ordering of any physical quantity or quantities and their coherent superposition. That equating is interpretable as the isomorphism of Minkowski space and Hilbert space. Quantum information is the structure interpretable in both ways and thus underlying their unification. Its deformation is representable correspondingly as gravitation in the deformed pseudo-Riemannian space of general relativity and the entanglement of two or more quantum systems. The standard model studies a single quantum system and thus privileges a single reference frame turning out to be inertial for the generalized symmetry [U(1)]X[SU(2)]X[SU(3)] “gauging” the standard model. As the standard model refers to a single quantum system, it is necessarily linear and thus the corresponding privileged reference frame is necessary inertial. The Higgs mechanism U(1) → [U(1)]X[SU(2)] confirmed enough already experimentally describes exactly the choice of the initial position of a privileged reference frame as the corresponding breaking of the symmetry. The standard model defines ‘mass at rest’ linearly and absolutely, but general relativity non-linearly and relatively. The “Big Bang” hypothesis is additional interpreting that position as that of the “Big Bang”. It serves also in order to reconcile the linear standard model in the singularity of the “Big Bang” with the observed nonlinearity of the further expansion of the universe described very well by general relativity. Quantum information links the standard model and general relativity in another way by mediation of entanglement. The linearity and absoluteness of the former and the nonlinearity and relativeness of the latter can be considered as the relation of a whole and the same whole divided into parts entangled in general. (shrink)

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation (...) can be also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators on it. One can interpret special Minkowski space involved by special relativity and the qubit Hilbert space of quantum information as Fourier counterparts immediately noticing that general relativity means gravitation as the Fourier counterpart of non-Hermitian operators implying non-unitarity and the violation of energy conservation and thus destroying Pauli’s particle paradigm. Since the Standard model obeys it, this explains the impossibility of “quantum gravitation” in any framework conservatively generalizing the Standard model so that it would include gravitation along with electromagnetic, weak, and strong interactions. Einstein’s geometrization of gravitation can be continued into a purely mathematical theory of it following Euclid’s realization for geometry to be exhaustively built in a deductive and axiomatic way as well as Riemann’s parametrization of all the class of Euclidean and non-Euclidean geometries by “space curvature”, then being generalized to Minkowski space as the operators on pseudo-Riemannian space as the Einstein field equation means gravitation. The transition from mathematical gravitation to logical one can rely on the historical lesson of the pair of Lobachevski’s and Riemann’s approaches now “reversely”, i.e., from the latter to the former. Logical gravitation is linkable to Hegel’s dialectical logic and ontological dialectics abandoning their interpretations as a new zero logic substituting classical propionyl logic. The approach of ontomathematics generalizing that of ontology, traceable even to Aristotle’s reformation of Plato’s doctrine, needs Hegel’s doctrine to be formalized as a first-order logic naturally containing Boolean algebra, isomorphic to both classical propositional logic and set theory being the class of all first-order logics, as a sub-logic along with Peano arithmetic as another sub-logic. The first-order logic at issue is called Hilbert arithmetic and elaborated in detail in other papers. It allows for both self-foundation of mathematics to be internally proved as complete and furthermore, quantum mechanics reinterpreted as quantum information to be included by the qubit Hilbert space interpretable in turn as a dual and physical counterpart of Hilbert arithmetic in a narrow sense, that is, both counterparts constitute Hilbert arithmetic in a wide sense, being mathematical and physical simultaneously and thus overcoming the Cartesian dualism of “body” gapped from “mind” by an abyss. Then, the proper philosophical interpretation of gravitation to be the fundamental ontomathematical force or interaction overcomes the ridiculous belief of the Big Bang wrongly alleged to be a scientific theory. Ontomathematical gravitation suggests an omnipresent and omnitemporal medium of “God’s” creation “ex nihilo” following only the natural necessity of quantum-information conservation particularly and locally manifested as energy conservation. (shrink)

This paper develops a Fragmentalist theory of Presentism and shows how it can help to develop a interpretation of quantum mechanics. There are several fragmental interpretations of physics. In the interpretation of this paper, each quantum system forms a fragment, and fragment f1 makes a measurement on fragment f2 if and only if f2 makes a corresponding measurement on f1. The main idea is then that each fragment has its own present (or ‘now’) until a mutual quantum measurement—at which time (...) they come (‘become’) to share the same ‘now’. The theory of time developed here will make use of both McTaggart’s A-series (in the form of future-present-past) and B-series (earlier-times to later-times). An example of an application is that a Bell pair of electrons does not take on definite spin values until measurement because the measuring system and the Bell pair do not share the same present (‘now’) until mutual quantum measurement, i.e. until they ‘become’ to share the same A-series. Before that point the ‘now’ of the opposing system is not in the reference system’s fragment. Relativistic no-signaling is preserved within each fragment, which will turn out to be sufficient for the general case. Several issues in the foundations of quantum mechanics are canvassed, including Schrodinger’s cat, the Born rule, modifications to Minkowski space that accommodate both the A-series and the B-series, and entropy. (shrink)

This book is devoted to the presentation of the new quantum mechanical formalism based on the probability representation of quantum states. In the 20s and 30s it became evident that some properties in quantum mechanics can be assigned only to the quantum mechanical system, but not necessarily to its constituents. This led Einstein, Podolsky and Rosen (EPR) to their remarkable 1935 paper where they concluded that quantum mechanics is not a complete theory of nature (EPR paradox). In order to avoid (...) the contradiction which arises from instantaneous action at a distance mentioned above we introduce an extension of the canonical relativity by using measure algebra of physical events in Minkowski space-time. The canonical QM formalism is extended by additional new postulate of EPRB nonlocality for continuous and discrete observables, chapter I. The postulate of EPRB nonlocality is supported by new quantum mechanical formalism based on the probability representation of quantum states. Chapter II is devoted to the new quantum mechanical formalism based on the probability representation of quantum states. Chapter III is devoted to the Einstein's 1927 gedanken experiment resolution. Chapter IV is devoted to the EPR paradox resolution. Chapter V is devoted to the EPR-B paradox resolution. Chapter VI is devoted to the Schrödinger's cat (measured spin) paradox resolution. Chapter VII is devoted to the Bell inequalities revisited. Remind that the canonical arguments which were presented by many authors, namely, that violations of Bell type inequalities signal us that the classical Kolmogorovian model of probability is inapplicable to quantum phenomena. We claimed that the canonical assumption, under which Bell type inequalities were derived, is not supported by real physical nature of the EPRB experiments. The fundamental physical nature violations of the canonical Bell type inequalities explained by Postulate of EPR-Nonlocality and Heisenberg noise-disturbance uncertainty relations. (shrink)

The concept of quantum information is introduced as both normed superposition of two orthogonal sub-spaces of the separable complex Hilbert space and in-variance of Hamilton and Lagrange representation of any mechanical system. The base is the isomorphism of the standard introduction and the representation of a qubit to a 3D unit ball, in which two points are chosen. The separable complex Hilbert space is considered as the free variable of quantum information and any point in it (a wave (...) function describing a state of a quantum system) as its value as the bound variable. A qubit is equivalent to the generalization of ‘bit’ from the set of two equally probable alternatives to an infinite set of alternatives. Then, that Hilbert space is considered as a generalization of Peano arithmetic where any unit is substituted by a qubit and thus the set of natural number is mappable within any qubit as the complex internal structure of the unit or a different state of it. Thus, any mathematical structure being reducible to set theory is re-presentable as a set of wave functions and a subspace of the separable complex Hilbert space, and it can be identified as the category of all categories for any functor represents an operator transforming a set (or subspace) of the separable complex Hilbert space into another. Thus, category theory is isomorphic to the Hilbert-space representation of set theory & Peano arithmetic as above. Given any value of quantum information, i.e. a point in the separable complex Hilbert space, it always admits two equally acceptable interpretations: the one is physical, the other is mathematical. The former is a wave function as the exhausted description of a certain state of a certain quantum system. The latter chooses a certain mathematical structure among a certain category. Thus there is no way to be distinguished a mathematical structure from a physical state for both are described exhaustedly as a value of quantum information. This statement in turn can be utilized to be defined quantum information by the identity of any mathematical structure to a physical state, and also vice versa. Further, that definition is equivalent to both standard definition as the normed superposition and in-variance of Hamilton and Lagrange interpretation of mechanical motion introduced in the beginning of the paper. Then, the concept of information symmetry can be involved as the symmetry between three elements or two pairs of elements: Lagrange representation and each counterpart of the pair of Hamilton representation. The sense and meaning of information symmetry may be visualized by a single (quantum) bit and its interpretation as both (privileged) reference frame and the symmetries of the Standard model. (shrink)

Sir Roger Penrose and prof. Stuart Hameroff had substantiated a theory that a human brain performs quantum computations. Logically, a question comes what information does then the brain compute and what is the result of such a quantum computing? To answer this, it is tempting to exploit isomorphism between complex hermitian 2 × 2 matrices and R4, more specifically a real vector representation of qubit states. P Arrighi proposed that "qubit states may be viewed as spatio-temporal objects, or indeed as (...) four-vectors of a Minkowski space-time." Under Orch OR theory assumptions, a very large number of entangled qubits is involved in a massive and highly complex computing task. What does this gigantic quantum computing machinery produce as the final outcome of its coordinated computations? The answer is obvious - it is the physical world as we see it, or the so called an external, to the human brain, reality (Minkowski space). Accordingly, underlying Orch OR brain computing concept is a mathematical connection between a qubit (qm) and relativity (Minkowski space). It is a connection between our mind, or the consciousness, and a physical reality the way we see it as the result of quantum computations of our brain. Does this mean that a physical reality as we see it, is being internally quantum computed and represented to us as a Minkowski space? That is, can a physical classical world be viewed as the result of our internal measurement leading to collapse of the quantum computed wave function? This abstract omits this question as irrelevant to the subject matter of a paper. The most important question is the aforementioned mathematical connection between quantum mechanics and relativity, it is a foundation which proves that Orch OR theory is correct. I propose that enormous quantum computing power in human brain does produce the Minkowski space, a representation of the physical reality. Mathematically, it is done by integrating, or encoding, the information about external physical world, into a qubit wave function vectors. I believe that probability distribution functions of pairs of fermions and bosons serve as the hidden variables encoding information about external world, into a qubit wave function vectors. They are hidden for two reasons. First is that these variables are not obvious as an intrinsic part of a qubit equation defining human brain quantum computing. Traditional way of thinking does not easily accommodate these variables into a qubit equation. The second reason they are hidden is because Einstein was desperately looking for them to make quantum mechanics complete. Simply, Sir Roger Penrose and prof. Stuart Hameroff had made a breakthrough that will have a very far reaching implications, including but not limited to Einstein hidden variables discovery. Quantum mechanics and relativity can be easily unified should indeed these variables be encoded into qubit as the carriers of information of the classical physical world. (shrink)

Albert Einstein's bold assertion of the form-invariance of the equation of a spherical light wave with respect to inertial frames of reference became, in the space of six years, the preferred foundation of his theory of relativity. Early on, however, Einstein's universal light-sphere invariance was challenged on epistemological grounds by Henri Poincaré, who promoted an alternative demonstration of the foundations of relativity theory based on the notion of a light-ellipsoid. Drawing in part on archival sources, this paper shows how (...) an informal, international group of physicists, mathematicians, and engineers, including Einstein, Paul Langevin, Poincaré, Hermann Minkowski, Ebenezer Cunningham, Harry Bateman, Otto Berg, Max Planck, Max Laue, A. A. Robb, and Ludwig Silberstein, employed figures of light during the formative years of relativity theory in their discovery of the salient features of the relativistic worldview. (shrink)

From the geometric formulation of gravity, according to the Einstein-Grosmann-Hilbert equations, of November 1915, as the geodesic movement in the semirimennian manifold of positive curvature, spacetime, where due to absence of symmetries, the conservation of energy-impulse is not possible taking together the material processes and that of the gravitational geometric field, however, given those symmetries in the flat Minkowski spacetime, using the De Sitter model, Einstein linearizing gravitation, of course, really in the absence of gravity, in 1916, purged of (...) some mathematical errors in 1918, he introduced "gravitational waves" as disturbances in the curvature of space, and in the absence of knowing physically what spacetime is and philosophically in dispute, that previously in 1936 and definitively in 1937, Einstein showed they did not exist. It was through the works arising from the dynamics of academic discourse, from the perspective not of Einstein but of Weyl, that Bondi, Pirani, Robinson and Trautman, in the 1950s, after Einstein's death, "gravitational waves" were reintroduced and led to experimental search. In 2002, from Sergei Kopeikin's VLBI experiment, its supposed speed was established, without obtaining unanimous recognition from the community of scientists but rather dividing them. And it was in February 2016 that the aLIGO-aVirgo collaboration announced that they had detected them for the first time. In this work, the history that led to this supposed discovery is presented and it is stated that the waves detected are really from the quantum vacuum in which everything that exists is immersed, the author's thesis exposed immediately in response to that 2016 announcement. (shrink)

The purpose of this note is to show how an 'AB-series' interpretation of time, given in a companion paper, leads, surprisingly, directly to the physicists' important AdS5 geometry. This is not a theory of 2 time dimensions. Rather, it is a theory of 1 time dimension that has both B-series and A-series characteristics. -/- To summarize the result, a spacetime in terms of 1. the earlier-to-later aspect of time, and 2. the related future-present-past aspect of time, and 3. 3-d (...) class='Hi'>space, automatically gives us AdS_5. (shrink)

According to the conventionalist doctrine of space elaborated by the French philosopher-scientist Henri Poincaré in the 1890s, the geometry of physical space is a matter of definition, not of fact. Poincaré's Hertz-inspired view of the role of hypothesis in science guided his interpretation of the theory of relativity (1905), which he found to be in violation of the axiom of free mobility of invariable solids. In a quixotic effort to save the Euclidean geometry that relied on this axiom, (...) Poincaré extended the purview of his doctrine of space to cover both space and time. The centerpiece of this new doctrine is what he called the "principle of physical relativity," which holds the laws of mechanics to be covariant with respect to a certain group of transformations. For Poincaré, the invariance group of classical mechanics defined physical space and time (Galilei spacetime), but he admitted that one could also define physical space and time in virtue of the invariance group of relativistic mechanics (Minkowski spacetime). Either way, physical space and time are the result of a convention. (shrink)

Tschumi believes that the quality of architecture depends on the theoretical factor it contains. Such a view led to the creation of architecture that would achieve visibility and comprehensibility only after its interpretation. On his way to creating such an architecture he took on a purely philosophical reflection on the basic building block of architecture, which is space. In 1975, he wrote an essay entitled Questions of Space, in which he included several dozen questions about the nature of (...) space. The questions he formulated could be regarded as analogous to the situation in the philosophy of the time, in which the interest in questioning the most obvious forms of understanding the world and intellectual categories increased. The research on space is an area common to many fields of natural sciences, humanities and artistic creation, but it also deals with other problems, such as issues of experience. The concept of space-time continuum proposed by Hermann Minkowski drew attention to the identity of time and space with the events taking place. Probably regardless of the postulates of physicists commenting on Einstein’s discoveries, also in philosophy it increased the importance of the concept of the event which became dominant in Heidegger’s latest work Contributions of Philosophy. Of the event. Furthermore, Tschumi’s reflections on space entered into relation with the problem of experience, which aroused the interest of a group of French philosophers trying to assimilate Georges Bataille’s concept of “inner experience”. Both Tschumi and Derrida referred to Bataille because his views could be used not only to modify the concept of the subject, but also to change the understanding of what constitutes the area of architecture. The discussion on experience has led to the recognition that the subject is not sovereign, but actually a form of what is on their outside. Such insights make it possible to treat the area of the Parc de La Villette as existing mainly when it is organised by its users. The decisive features of the Park are its assumptions, according to which it is a variety of active void that leads to agreeing new social relations with it. The park does not force to participate in already existing moral or political communities, but tries to move into an unknown future in which the scope of free functioning of individuals will be increased. Doubts about the principles of functioning of the individual self and its discovery as a whole composed of non-coherent parts, as well as its dependence on its own depth full of disordered forces, influenced the understanding of architecture as a set of contradictions whose source is a fundamental void anticipating the empty phenomenal space. The use of this phenomenal void in architecture, as well as the rejection of the whole and unity, had a specific political purpose and drew its inspiration from political analyses. In the Parc de La Villette, metaphysics and politics were brought closer together because the philosophy of void was used to create new conditions for community action. It can be argued that the source of this philosophy was the perception of errors in existing societies dependent on the shortcomings of traditional metaphysics. Spacing (espacement) was one of the key terms in Derrida’s philosophy, which was also combined with the concepts of différance and chôra. The study of the nature of space, especially its transition from the level of pure possibility to the level of sensual phenomenon, also contributes to understanding how well designed space can have an impact on its audience. This explanation is based on Tschumi’s assumption that the space of the Parc de La Villette contradicts the integrating approaches and instead exposes contradictions, but it does so in a way that combines incompatible properties into a single piece of architecture. The specificity of such integration is similar to the invention of a musical phrase, which is an ideological message: moral and political. Such a thesis may raise doubts, however, if both the clearly adopted assumptions and those deduced from the work allow for their ↪Quart Nr 2(52)/2019 logically ordered presentation then to a limited extent it may be assumed that the work has achieved a connection between a specific philosophy of space and its practical application. Derrida combined the problem of spatiality with the problem of transcendental imagination in Kant’s philosophy, who in the first version of Critique of Pure Reason assumed that pure imagination precedes the appearance of time and space, even in their transcendental forms. The imagination in such a situation can be described as a factor activating time and space, which indicates what function is played by movement in this activity. This leads us to recognize that the ultra originary source of pure forms of sensual intuition is movement, which in early Greek philosophy was identified with void and its lack of resistance to phenomena occurring in it. Derrida’s philosophy in search of a certain super-transcendental source of time and space pointed to différance which, like void or the chôra, does not have material features or even any other form of being. Différance is the primary cause of the disruption of motionlessness and the introduction of activity into motionless time and space, thus its activity can be described as spacing (espacement). Derrida’s discoveries in this respect are not entirely original, because Hegel already pointed out when examining the present that it is primarily a differential relation (differente Beziehung), which, being seemingly neutral, influences the present with supernatural force and makes it unidentifiable with itself. Differente Beziehung must similarly influence the originary space, negating its initial character by multiplying its divisions and expanding its boundaries. Différance acts by revealing contradictions wherever there is apparent undifferentiation. Tschumi, composing the Parc de La Villette as a variety of void and a set of incompatible layers, followed the rules of différance or the chôra: he made void visible together with its saturation with contradictions. If space can be considered to be the result of the activity of difference, such activity has a certain regularity, which influences the behaviour of its observers. Differences or contradictions fall into a certain rhythm, which can be considered a manifestation of transcendent order. The problem is that what can be considered the source of such order, namely the logos or God, is partly disorder and error. According to descriptions contained in Timaeus, the world is a combination of forces that drive to order with forces of erroneous necessity that resounds in every order and forces it to return to disorder. Derrida denied the possibility of understanding différance as a theological value, even if it were a negative or apophatic theology, but no categorical denial could be perfect. The assumption that différance or the chôra are not endowed with any substance properties cannot deny their activity, and thus a certain force. Already since Democritus, philosophy has multiplied the names of such a force and the contradictory variety of its manifestations, never forgetting also the necessity for reason to withdraw from the possibility of giving its correct characteristics. Such a withdrawal may be interpreted as an expression of respect and, in certain situations, as a cult of the force that precedes reasonableness. The Parc de La Villette, which is an artistic divagation about the contradictions and forces behind them, can be considered as a place of their sublimation, and therefore as a variation of the temple of what differs from order and disorder. (shrink)

This chapter discusses the roles of ether and electrons in relativity theory. One of the most radical moves made by Albert Einstein was to dismiss the ether from electrodynamics. His fellow physicists felt challenged by Einstein’s view, and they came up with a variety of responses, ranging from enthusiastic approval, to dismissive rejection. Among the naysayers were the electron theorists, who were unanimous in their affirmation of the ether, even if they agreed with other aspects of Einstein’s theory of relativity. (...) The eventual success of the latter theory (circa 1911) owed much to Hermann Minkowski’s idea of four-dimensional spacetime, which was portrayed as a conceptual substitute of sorts for the ether. (shrink)

The Shadow of God in the Philosopher’s Garden. The Parc de La Villette in Paris in the context of the philosophy of chôra I Bernard Tschumi’s project of the Parc de La Villette could have won the competition and was implemented thanks to the political atmosphere that accompanied the victory of the left-wing candidate in the French presidential elections in 1981. François Mitterand’s revision of the political programme and the replacement of radical reforms with the construction of prestigious architectural objects (...) and urban assumptions in the French capital gave Tschumi a unique opportunity to realise ideas that polemicised with traditional forms of social life, questioned the basic principles of architecture and included architectural work in the philosophical disputes over the issues of metaphysics. Tschumi’s theoretical assumptions put forward during the design of the Parc de La Villette highlighted the questions of conflict between the main components of the project and suggested that the intensification of differences was analogous to Jacques Derrida’s creation of the concept of différance. It was this philosopher who in a special commentary to Derrida’s project also introduced the concept of maintenant, which aimed at demonstrating that the architect’s polemical inclinations remain in a hidden balance with his inclinations to affirmation of architectural principles. During the discussion between Derrida and Peter Eisenman, who was to take part in the design of the Parisian park, the concept of the chôra was also put forward, which in the course of the debate led to an additional confusion of architectural and philosophical problems. II In the period from the Antiquity to the Renaissance, the dialogue Timaeus was the most frequently commented work of Plato. At present, the most frequently discussed is the issue of the chôra included in it, which aroused fascination among philosophers, researchers of rhetoric, religion, feminism, but also architecture. The work on the chôra also influenced the development of the interpretation of the Parc de La Villette, among which the topics related to the beginning and the change were highlighted. In early uses of the word chôra in Greek, as in Homer’s 18th Book of Iliad, it meant both dancing and a place to dance. On this occasion, it can be seen that it is not possible to determine which phenomenon took precedence in the creation of the name. It cannot be denied, however, that the word concerned a specific movement, as if circular and returning to an indefinable beginning. Despite gaining more and more general meanings, the word chôra has retained its connection with the dance of people on the threshing floor, the dance of bees (choros meliton) or the dance of stars (choros astron). In Timaeus, the chôra is a space filled with movement with an effect similar to shaking the sieve to husk the grain: it separates similar elements from the dissimilar ones. The juxtaposition of the Parc de La Villette and the chôra already at this stage leads to the suggestion that the park was treated by the architect as a place of dynamic changes leading to the establishment of new social solutions. In his statements, the architect confirmed that the park was to be a space of new politics and ethics. The book by Julia Kristeva La Révolution du langage poétique contributed to the spread of the belief that works of art can play a role as factors of political revolution. In this work, the author put forward the thesis that the chôra is a kind of space, the character of which has a destructive influence on attempts to conclude language games. The chôra gives beginning to words, but at the same time, by leaving a trace of this beginning it forces us to renew their meanings. The chôra understood in this way, turns out to be an irremovable beginning, to which one has to return all the time. Kristeva found manifestations of the chôra’s activity in avant-garde French poetry, to which she attributed the role of a mediator between criticism of metaphysics and aspirations for social change. The chôra, violating the language, introduces some voids into it, as if traces of the abyss, which direct the consciousness towards understanding the necessity of political changes. The Parc de La Villette was to pursue similar objectives in the city space. In his essays, Tschumi considered the problems of creating spaces that would give rise to a radical democracy. The proposed rebellious spaces should have the characteristics of a void, in which contradictory forces would occur as forms of pure activity. The means of achieving this goal was to concentrate contradictions and make them visible. The Parc de La Villette was supposed to collect differences as indelible and at the same time by showing them it was supposed to raise awareness of the social world as a conglomerate of differences. Saturation of the space of the park with subversive values results from the character of this space suppressed in the consciousness, as well as from the social diversity which has not been taken into account so far. The main contradictions contained in space relate to the division that exists between its presentation as a mental problem and a sensual one. The park was the deliberate creation of a place that transcends such a division and creates a separate space for negotiation between architectural theories and its practical applications. The purpose of the park was to become a place of future events, which would not hide their conflicting character coming from diversity of both space and society. The method of composition usually aimed at achieving a harmonious whole has been replaced by Tschumi with a system of juxtaposition of non-coherent elements or those resulting from variations and transformations. Tschumi did not seek direct influence on politics in the Parc de La Villette, but made room for thinking about the possibilities of the future. He introduced problems rather than showed solutions to them. The task of the park was to put the principles of architecture into a kind of vibration that would inspire users to participate in the new community. III Tschumi believes that the quality of architecture depends on the theoretical factor it contains. Such a view led to the creation of architecture that would achieve visibility and comprehensibility only after its interpretation. On his way to creating such an architecture he took on a purely philosophical reflection on the basic building block of architecture, which is space. In 1975, he wrote an essay entitled Questions of Space, in which he included several dozen questions about the nature of space. The questions he formulated could be regarded as analogous to the situation in the philosophy of the time, in which the interest in questioning the most obvious forms of understanding the world and intellectual categories increased. The research on space is an area common to many fields of natural sciences, humanities and artistic creation, but it also deals with other problems, such as issues of experience. The concept of space-time continuum proposed by Hermann Minkowski drew attention to the identity of time and space with the events taking place. Probably regardless of the postulates of physicists commenting on Albert Einstein’s discoveries, also in philosophy it increased the importance of the concept of the event which became dominant in Martin Heidegger’s latest work Contributions of Philosophy: Of the event. Furthermore, Tschumi’s reflections on space entered into relation with the problem of experience, which aroused the interest of a group of French philosophers trying to assimilate Georges Bataille’s concept of “inner experience”. Both Tschumi and Derrida referred to Bataille because his views could be used not only to modify the concept of the subject, but also to change the understanding of what constitutes the area of architecture. The discussion on experience has led to the recognition that the subject is not sovereign, but actually a form of what is on their outside. Such insights make it possible to treat the area of the Parc de La Villette as existing mainly when it is organised by its users. The decisive features of the park are its assumptions, according to which it is a variety of active void that leads to agreeing new social relations with it. The park does not force to participate in already existing moral or political communities, but tries to move into an unknown future in which the scope of free functioning of individuals will be increased. Doubts about the principles of functioning of the individual self and its discovery as a whole composed of non-coherent parts, as well as its dependence on its own depth full of disordered forces, influenced the understanding of architecture as a set of contradictions whose source is a fundamental void anticipating the empty phenomenal space. The use of this phenomenal void in architecture, as well as the rejection of the whole and unity, had a specific political purpose and drew its inspiration from political analyses. In the Parc de La Villette, metaphysics and politics were brought closer together because the philosophy of void was used to create new conditions for community action. It can be argued that the source of this philosophy was the perception of errors in existing societies dependent on the shortcomings of traditional metaphysics. Spacing (espacement) was one of the key terms in Derrida’s philosophy, which was also combined with the concepts of différance and chôra. The study of the nature of space, especially its transition from the level of pure possibility to the level of sensual phenomenon, also contributes to understanding how well designed space can have an impact on its audience. This explanation is based on Tschumi’s assumption that the space of the Parc de La Villette contradicts the integrating approaches and instead exposes contradictions, but it does so in a way that combines incompatible properties into a single piece of architecture. The specificity of such integration is similar to the invention of a musical phrase, which is an ideological message: moral and political. Such a thesis may raise doubts, however, if both the clearly adopted assumptions and those deduced from the work allow for their logically ordered presentation then to a limited extent it may be assumed that the work has achieved a connection between a specific philosophy of space and its practical application. Derrida combined the problem of spatiality with the problem of transcendental imagination in the philosophy of Immanuel Kant, who in the first version of Critique of Pure Reason assumed that pure imagination precedes the appearance of time and space, even in their transcendental forms. The imagination in such a situation can be described as a factor activating time and space, which indicates what function is played by movement in this activity. This leads us to recognize that the ultra originary source of pure forms of sensual intuition is movement, which in early Greek philosophy was identified with void and its lack of resistance to phenomena occurring in it. Derrida’s philosophy in search of a certain super-transcendental source of time and space pointed to différance which, like void or the chôra, does not have material features or even any other form of being. Différance is the primary cause of the disruption of motionlessness and the introduction of activity into motionless time and space, thus its activity can be described as spacing (espacement). Derrida’s discoveries in this respect are not entirely original, because Georg Wilhelm Friedrich Hegel already pointed out when examining the present that it is primarily a differential relation (differente Beziehung), which, being seemingly neutral, influences the present with supernatural force and makes it unidentifiable with itself. Differente Beziehung must similarly influence the originary space, negating its initial character by multiplying its divisions and expanding its boundaries. Différance acts by revealing contradictions wherever there is apparent undifferentiation. Tschumi, composing the Parc de La Villette as a variety of void and a set of incompatible layers, followed the rules of différance or the chôra: he made void visible together with its saturation with contradictions. If space can be considered to be the result of the activity of difference, such activity has a certain regularity, which influences the behaviour of its observers. Differences or contradictions fall into a certain rhythm, which can be considered a manifestation of transcendent order. The problem is that what can be considered the source of such order, namely the logos or God, is partly disorder and error. According to descriptions contained in Timaeus, the world is a combination of forces that drive to order with forces of erroneous necessity that resounds in every order and forces it to return to disorder. Derrida denied the possibility of understanding différance as a theological value, even if it were a negative or apophatic theology, but no categorical denial could be perfect. The assumption that différance or the chôra are not endowed with any substance properties cannot deny their activity, and thus a certain force. Already since Democritus, philosophy has multiplied the names of such a force and the contradictory variety of its manifestations, never forgetting also the necessity for reason to withdraw from the possibility of giving its correct characteristics. Such a withdrawal may be interpreted as an expression of respect and, in certain situations, as a cult of the force that precedes reasonableness. The Parc de La Villette, which is an artistic divagation about the contradictions and forces behind them, can be considered as a place of their sublimation, and therefore as a variation of the temple of what differs from order and disorder. IV In the texts that presented the theoretical assumptions of the Parc de La Villette, Tschumi used a large number of terms that contradicted not only the traditional principles of composing architecture, but also negated the rules of social order and the foundations of Western metaphysics. Tschumi’s statements, which are a continuation of his leftist political fascinations from the May 1968 revolution, as well as his interest in the philosophy of French poststructuralism and his collaboration with Derrida, prove that terms such as “disruption”, “dissociation”, “disfunction”, “disjunction” and “dispersion” not only referred to architectural problems but also applied to political criticism and the deepest foundations of thinking itself. His collaboration with Derrida manifested itself primarily in the publication La Case Vide: La Villette 1985, in which the architect’s design drawings and texts explaining his concepts related to the Parc de La Villette were accompanied by an extensive essay by Derrida, which included theoretical problems taken up by Tschumi in a philosophical context. Architectural and philosophical issues were also combined during seven discussion meetings organised by Eisenman, invited by Tschumi to collaborate on the design of the Parc de La Villette. Eisenman, who, like Tschumi, invited Derrida to participate in the design of the park and also led to the publication of Chora L Works: Jacques Derrida and Peter Eisenman, in which his ideas were confronted with Derrida’s philosophical text. In this case, Derrida’s essay was not a direct commentary on the architect’s concepts, but rather a reflection on the question of the chôra presented by Plato in Timaeus. During the discussion and in his essay, Derrida pointed out that the chôra is a component of the created world, yet it does not belong to it, but precedes it. The originality of the chôra is so radical that she also precedes all the factors of creating the world, including ideas and the Demiurge. Thus athesis appeared in the metaphysics of the West that the chôra is a form of active abyss, in relation to which all beings are secondary, both those perfect (as ideas or God) and those created, such as the world, things, people or language. This leads to the conclusion that the chôra does not exist, because all existence is a derivative of the chôra. Nor could the chôra be described, since it is a form of developing a space that is preceded by a lack of space characteristic of the chôra. Derrida intended the chôra to be an instance with an exceptional degree of transcendentalism, an anti-metaphysical instance, but also an a-theological one. However, this attempt failed, both in the field of secular philosophy and in the field of theology. Derrida’s characteristics of the chôra to strengthen its transcendentalism and negation of metaphysics had to be expressed in a language that immediately produces new concepts and a new metaphysics that reproduces the categories of the beginning, the origin or the foundation known from earlier philosophical traditions. All forms of criticism of metaphysics are also inspired by negative, apophatic and mystical theology. The undermining of many concepts of permanent meaning and the introduction of new concepts of unstable meaning, characteristic of the philosophy of deconstruction, had many features of originality, but it was directed towards problems whose solutions repeat, with the use of new vocabulary, the findings known in culture since Democritus. Thus, if apophatic philosophy can be regarded as deconstruction avant la lettre, then deconstruction itself in its late versions began to take on the features of a new religion. The exchange of inspiration between theology and deconstruction was manifested in a series of scientific conferences and publications in which Derrida’s philosophical concepts were interpreted within the scope of religious thought. Theological threads began to be found in such concepts of deconstruction as différance or the chôra, while at the same time Derrida himself undertook in his philosophy to study problems such as the Other (L’Autre) or the Impossible (Impossible), which belonged to newer theological traditions. As a consequence of the new problems, the deconstruction became closer to the features of a new religion. Philosophy, at least from Kant’s time, has tried to create a system that would take over from religion the tasks of setting moral and political goals. Similarly, Derrida has directed his interest towards the problems of democracy and ethics, which would enable their renewal. Attempts to create a new religion (cleared of old metaphors), a new community or a new democracy bring problems and threats which may be no less troublesome than the previous systems. All promises of freedom carry with them threats, the greater the more they strive for perfection. The renewal of existential orders, sometimes carried out by means of violent changes, is a certain repetitive feature of human cultures. Deep changes, however, do not protect against the return of both old gods and old demons. Tschumi and Derrida were shaped in their youth by the atmosphere of leftist rebellion against the moral and political limitations of ossified communities and the imperfections of democracy. The ethical theme distinguishes many of their works, including the Parc de La Villette. The opposition to the metaphysical traditions of philosophy and architecture contained in this park was prompted by specific political situations and resulted from bringing political issues to the level of philosophical considerations. Achievements made at the level of pure concepts were then subject to elevation, to a kind of sacralization, which made them religious concepts. The deconstruction reached for the status of the new religion especially when it found its followers and began to generate moral obligations. In the new situation, terms such as the chôra, l’Autre or the Impossible were absolutized and in relation to them a cult and attitude of adoration emerged. The Parc de La Villtette then gained new post-secular meanings, which allow it to be assigned the function of a Temple of Otherness (L’Autre) and Impossible. V In the traditional sense, a work of art creates an illustration of the outside world, or of a certain text or doctrine. Sometimes it is considered that such an illustration is not literal, but is an interpretation of what is visible, or an interpretation of a certain literary or ideological message. It can also be assumed that a work of art creates its own visual world, a separate story or a separate philosophical statement. Parc de La Villette represents the last of these possibilities: it is a philosophical statement that develops the premises derived from poststructuralist philosophies and the philosophy of deconstruction. The uniqueness of its being status, however, is that it does so not only at the level of the theoretical assumptions, but also through its functioning as an active philosophical work. This means that a park is a happening philosophy. Its activity, however, does not refer only to the present tense, but is also an attempt to penetrate the future, all otherness and impossibility. This kind of activity assumes that the work, in a sense, does not yet fully exist, but is also still produced in the processes of its interpretation. The theoretical foundations of the park included texts by Tschumi, in which he questioned traditional ways of creating a work of architecture, postulating in return the use of a long series of negations, which were comparable to the crisis of metaphysics characteristic of contemporary philosophy. It is therefore no coincidence that the publication containing Tschumi’s theoretical text on Parc de La Villette was accompanied by an essay by Derrida developing some of the architect’s concepts. The next step in integrating philosophy into the process of park design was a series of discussions between Eisenman and Derrida, who completely moved the creation of the park into the world of thoughts, without accentuating the need for their realization in the material reality. The main topic of these discussions was the problem of the chôra, which was taken up by later commentators and used to interpret the park as a work in which the philosophy of the beginning is manifested relating to issues of politics, morality and religion. The park was therefore interpreted as a space of invention within the scope of creating new rules of functioning of the community and democracy. Thinking about the political future may, however, exceed the horizon of ordinary expectations. Although philosophical thought is always connected with contemporary problems and metaphysics sometimes intertwines with current politics, yet at the same time the customs of philosophy also include crossing horizons and thinking about absolute otherness and impossibility. Initially, the chôra, différance, absolute otherness (tout autre) and the Impossible were concepts of pure philosophy of atheistic character, but with the further development of the discussion, more and more theological motifs began to emerge. One of the reasons for this phenomenon was the fact that radical negations of all being, which were contemplated in contemporary philosophy (by Heidegger and Derrida, among others), had previously been manifested in negative and apophatic theologies (by Master Eckhart, among others).Also the category of the “Other”, taken from Emmanuel Levinas, was clearly connected with the thought about God. A further reason for connecting the chôra with the theological thought was the interest in the philosophy of deconstruction expressed by some theologians. John Caputo in particular managed to persuade Derrida to participate in discussions on the current status of religion. In the late period of Derrida’s writing, further statements on religious topics appeared. All these reasons led to posing a question about the identity of the chôra and God. Although there were no satisfactory conclusions on this issue, the discussion was also important to create an interpretation of the park as a place of worship. The chôra, representing, according to Plato, the preoriginal emptiness is the place of every beginning, but it turns out that it is not neutral to the being created in it. The chôra deposits itself in every being as an irremovable beginning that interferes with its stability. The chôra, therefore, forces us into a palintropical movement, but it also turns out to be a pure compulsion, an erring necessity and a fundamental force from which, in the human perception, motifs useful to the individual and to the community are extracted. All definitions of this force, including its anthropomorphisation, are formulated in such a way that they allow for building private and collective morality upon them. Such definitions are changed depending on variable political situations. It is difficult to determine whether in the processes of changes in the formulation of “God’s names” any essential value is retained, which is not subject to change. The current definitions of the chôra (God?), which can be found, for example, in the philosophy of Caputo, stress that she is a combination of various and contradictory forces. This characteristic inherits much of Plato’s concept, reminds us of Master Eckhart’s views on Gottheit and, at the same time, is not unfamiliar to Tschumi, whose essays were an apologia of contradictions. The current concept of chôra, transferred into the sphere of politics, is the praise of social diversity and the protection of the difference from the forces of order. In the Parc de La Villette, the future community and democracy were elevated as a system of safe existence of individuals in all their singularity. The park is a temple of a future community in which individual beings have nothing in common. (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)

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)

During the last decades, many cognitive architectures (CAs) have been realized adopting different assumptions about the organization and the representation of their knowledge level. Some of them (e.g. SOAR [35]) adopt a classical symbolic approach, some (e.g. LEABRA[ 48]) are based on a purely connectionist model, while others (e.g. CLARION [59]) adopt a hybrid approach combining connectionist and symbolic representational levels. Additionally, some attempts (e.g. biSOAR) trying to extend the representational capacities of CAs by integrating diagrammatical representations and reasoning are (...) also available [34]. In this paper we propose a reflection on the role that Conceptual Spaces, a framework developed by Peter G¨ardenfors [24] more than fifteen years ago, can play in the current development of the Knowledge Level in Cognitive Systems and Architectures. In particular, we claim that Conceptual Spaces offer a lingua franca that allows to unify and generalize many aspects of the symbolic, sub-symbolic and diagrammatic approaches (by overcoming some of their typical problems) and to integrate them on a common ground. In doing so we extend and detail some of the arguments explored by G¨ardenfors [23] for defending the need of a conceptual, intermediate, representation level between the symbolic and the sub-symbolic one. In particular we focus on the advantages offered by Conceptual Spaces (w.r.t. symbolic and sub-symbolic approaches) in dealing with the problem of compositionality of representations based on typicality traits. Additionally, we argue that Conceptual Spaces could offer a unifying framework for interpreting many kinds of diagrammatic and analogical representations. As a consequence, their adoption could also favor the integration of diagrammatical representation and reasoning in CAs. (shrink)

Achieving space domain awareness requires the identification, characterization, and tracking of space objects. Storing and leveraging associated space object data for purposes such as hostile threat assessment, object identification, and collision prediction and avoidance present further challenges. Space objects are characterized according to a variety of parameters including their identifiers, design specifications, components, subsystems, capabilities, vulnerabilities, origins, missions, orbital elements, patterns of life, processes, operational statuses, and associated persons, organizations, or nations. The Space Object Ontology (...) provides a consensus-based realist framework for formulating such characterizations in a computable fashion. Space object data are aligned with classes and relations in the Space Object Ontology and stored in a dynamically updated Resource Description Framework triple store, which can be queried to support space domain awareness and the needs of spacecraft operators. This paper presents the core of the Space Object Ontology, discusses its advantages over other approaches to space object classification, and demonstrates its ability to combine diverse sets of data from multiple sources within an expandable framework. Finally, we show how the ontology provides benefits for enhancing and maintaining longterm space domain awareness. (shrink)

This paper is a brief (and hopelessly incomplete) non-standard introduction to the philosophy of space and time. It is an introduction because I plan to give an overview of what I consider some of the main questions about space and time: Is space a substance over and above matter? How many dimensions does it have? Is space-time fundamental or emergent? Does time have a direction? Does time even exist? Nonetheless, this introduction is not standard because I (...) conclude the discussion by presenting the material with an original spin, guided by a particular understanding of fundamental physical theories, the so-called primitive ontology approach. (shrink)

One of the greatest achievements of modern physics is the discovery of spacetime by Hermann Minkowski. Still, talking about the ”discovery” of spacetime cannot be done without further questioning its ontological status. Did Minkowski discover a real physical substrate? What is the creative role of his scientific imagination in the process of discovery? To what extent the explanatory power of spacetime supports the conclusion that it is a true description of the physical world? I consider those questions in (...) that paper, and I claim that for Minkowski’s discovery of spacetime, imagination and explanation work together in a fictionalist strategy. I explain why there is no reason to doubt the veracity of the discovery of spacetime and its physical reality. (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)

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)

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- (...) class='Hi'>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)

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)

Henri Lefebvre has considerable claims to be the greatest living philosopher. His work spans some sixty years and includes original work on a diverse range of subjects, from dialectical materialism to architecture, urbanism and the experience of everyday life. The Production of Space is his major philosophical work and its translation has been long awaited by scholars in many different fields. The book is a search for a reconciliation between mental space and real space. In the course (...) of his exploration, Henri Lefebvre moves from metaphysical and ideological considerations of the meaning of space to its experience in the everyday life of home and city. He seeks, in other words, to bridge the gap between the realms of theory and practice, between the mental and the social, and between philosophy and reality. In doing so, he ranges through art, literature, architecture and economics, and further provides a powerful antidote to the sterile and obfuscatory methods and theories characteristic of much recent continental philosophy. This is a work of great vision and incisiveness. It is also characterized by its author's wit and by anecdote, as well as by a deftness of style which Donald Nicholson-Smith's sensitive translation precisely captures. (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.

The article fits into the debate regarding space, time and nature in dialogue with the world lived by subjects that build up themselves or are built as mythological heroes, source of speech and spacial concrete practices. It's a poorly explored field in Geography that recently approaches to the cultural dynamic debate, to the symbolic field and also to their spacialization processes. The aim is to discuss the possibility of understanding in the present time about the space organization processes (...) related to the society's previous moments, in a space/time dialectics which articulate the present and past times in a complex and non linear way. Methodologically, starting from a literature review about the theme, the present study was linked to the field and documental research about migration to the vicinal ways of Transamazônica Highway (BR-230 Highway), the creation of the "Centro Espírita União do Vegetal", a religion that arises in the Amazon and set up its headquarters in Brasília and the construction of Brasilia as a modern metropolis without a past. The conclusion points at the possibility of space/time nexuses linking the Myth of Nature to the Creation of Heroes, constantly appropriated and with new meanings, in order to support speeches and new actions dialectically throughout the Brazilian contemporaneous space. (shrink)

We provide a new perspective on the relation between the space of description of an object and the appearance of novelties. One of the aims of this perspective is to facilitate the interaction between mathematics and historical sciences. The definition of novelties is paradoxical: if one can define in advance the possibles, then they are not genuinely new. By analyzing the situation in set theory, we show that defining generic (i.e., shared) and specific (i.e., individual) properties of elements of (...) a set are radically different notions. As a result, generic and specific definitions of possibilities cannot be conflated. We argue that genuinely stating possibilities requires that their meaning has to be made explicit. For example, in physics, properties playing theoretical roles are generic; then, generic reasoning is sufficient to define possibilities. By contrast, in music, we argue that specific properties matter, and generic definitions become insufficient. Then, the notion of new possibilities becomes relevant and irreducible. In biology, among other examples, the generic definition of the space of DNA sequences is insufficient to state phenotypic possibilities even if we assume complete genetic determinism. The generic properties of this space are relevant for sequencing or DNA duplication, but they are inadequate to understand phenotypes. We develop a strong concept of biological novelties which justifies the notion of new possibilities and is more robust than the notion of changing description spaces. These biological novelties are not generic outcomes from an initial situation. They are specific and this specificity is associated with biological functions, that is to say, with a specific causal structure. Thus, we think that in contrast with physics, the concept of new possibilities is necessary for biology. (shrink)

Choreographing Space is a reflection on the collaborative work of e+i studio, a New York City based architecture practice. Founders Eva Perez de Vega and Ian Gordon guide the reader through a dynamic selection of projects, each one opening us up to their relationship with the choreography of human and nonhuman forces at play. -/- Born as a retrospective and future-oriented book, it engages philosophical thought with architectural projects located in Europe, Asia, and the US, as well as speculative (...) scenarios that offer an alternative, less human-centric way of practicing architecture. -/- Organised into four parts, each part opens with a philosophical text that acts as an insightful prelude to the topics, questions and reflections posed by each project. Each part concludes with a speculative scenario, where one of the projects is imagined thriving in a future where life is now almost extinct. These are not intended as apocalyptic or even nostalgic scenarios, but rather as affirmative alternatives to the bleak imaginary arising from the world’s current climate crisis. (shrink)

This paper develops the ontology of space objects for theoretical and computational ontology applied to the space (astronautical/astronomical) domain. It follows “An ontological architecture for Orbital Debris Data” (Rovetto, 2015) and “Preliminaries of a Space Situational Awareness Ontology” (Rovetto, Kelso, 2016). Important considerations for developing a space object ontology, or more broadly, a space domain ontology are presented. The main category term ‘Space Object’ is analyzed from a philosophical perspective. The ontological commitments of legal (...) definitions for artificial space objects are also discussed. Space object taxonomies are offered and space object terms are defined. (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)

Modern cosmology treats space and time, or rather space-time, as concrete particulars. The General Theory of Relativity combines the distribution of matter and energy with the curvature of space-time. Here space-time appears as a concrete entity which affects matter and energy and is affected by the things in it. I question the idea that space-time is a concrete existing entity which both substantivalism and reductive relationism maintain. Instead I propose an alternative view, which may be (...) called non-reductive relationism, by arguing that space and time are abstract entities based on extension and changes. (shrink)

Newton had a fivefold argument that true motion must be motion in absolute space, not relative to matter. Like Newton, Kant holds that bodies have true motions. Unlike him, though, Kant takes all motion to be relative to matter, not to space itself. Thus, he must respond to Newton’s argument above. I reconstruct here Kant’s answer in detail. I prove that Kant addresses just one part of Newton’s case, namely, his “argument from the effects” of rotation. And, to (...) show that rotation is relative to matter, Kant changes the meaning of ‘relative motion.’ However, that change puts Kant’s doctrine in deep tension with Newton’s science. Based on my construal, I correct earlier readings of Kant by John Earman and Martin Carrier. And, I argue that we need to revise Michael Friedman’s influential view of Kant. Kant’s struggle, I conclude, illustrate the difficulties that early modern relationists faced as they turned down Newtonian absolute space ; and it typifies their selective engagement with Newton’s case for it. (shrink)

Shepard’s (1987) universal law of generalisation (ULG) illustrates that an invariant gradient of generalisation across species and across stimuli conditions can be obtained by mapping the probability of a generalisation response onto the representations of similarity between individual stimuli. Tenenbaum and Griffiths (2001) Bayesian account of generalisation expands ULG towards generalisation from multiple examples. Though the Bayesian model starts from Shepard’s account it refrains from any commitment to the notion of psychological similarity to explain categorisation. This chapter presents the conceptual (...) spaces theory (Gärdenfors 2000, 2014) as a mediator between Shepard’s and Tenenbaum & Griffiths’ conflicting views on the role of psychological similarity for a successful model of categorisation. It suggests that the conceptual spaces theory can help to improve the Bayesian model while finding an explanatory role for psychological similarity. (shrink)

We live in an age in which outer space has changed from a theme for flights of science fiction to the actual locus of exploration and travel.1 Space no longer has merely speculative significance for thinking about possible worlds; it has become a real factor in understanding the nature and conditions of the human world that we are constantly refashioning. Our entry into outer space brings with it changes in conditions and experience that require us to rethink (...) the concepts through which we comprehend environment and act environmentally. (shrink)

This paper examines connections between concepts of space and extension on the one hand and immaterial spirits on the other, specifically the immanentist concept of spirits as present in rerum natura. Those holding an immanentist concept, such as Thomas Aquinas, typically understood spirits non-dimensionally as present by essence and power; and that concept was historically linked to holenmerism, the doctrine that the spirit is whole in every part. Yet as Aristotelian ideas about extension were challenged and an actual, infinite, (...) dimensional space readmitted, a dimensionalist concept of spirit became possible—that asserted by the mature Henry More, as he repudiated holenmerism. Despite More’s intentions, his dimensionalist concept opens the door to materialism, for supposing that spirits have parts outside parts implies that those parts could in principle be mapped onto the parts of divisible bodies. The specter of materialism broadens our interest in More’s unconventional ideas, for the question of whether other early modern thinkers, including Isaac Newton, followed More becomes a question of whether they too unwittingly helped usher in materialism. This paper shows that More’s attack upon holenmerism fails. He illegitimately injects his dimensionalist concept of spirit into the doctrine, failing to recognize it as a consequence of the non-dimensionalist concept of spirit, which in itself secures indivisibility. The interpretive consequence for Newton is that there is no prima facie reason to suppose that the charitable interpretation takes him to deny holenmerism. (shrink)