This article extends our earlier work From Rotations to Spirals: A Matrix Model of Sentence-Level Semantic Dynamics by introducing the teleological component that had previously been left aside. In the quaternionic extension of the sentence matrix formalism, semantic states are described by a real dimension of actualization and three orthogonal imaginary axes. The axes i and j account for possibilities and goal-orientations, while the real component reflects their stabilization in discourse. Teleological attractors are represented as imaginary targets whose influence is (...) strongest in the distance and vanishes at the point of realization. The resulting dynamics differ fundamentally from gravitational laws: rather than a monotone pull towards what already exists, teleology organizes through the absence of what is not yet realized. Formally, the model is expressed as a drift induced by the gradient of a teleological potential, with feedback on the real component and underdamped oscillations around the attractor. Beyond individual goals, the third imaginary axis k is introduced as the dimension of collective values and norms. These higher-order attractors shape the entire semantic landscape and stabilize discourse over extended timescales. Their detailed mathematical treatment will be developed, however, in a subsequent article. (shrink)

Determining how we use our body to support cognition represents an important part of understanding the embodied and embedded nature of cognition. In the present investigation, we pursue this question in the context of a common perceptual task. Specifically, we report a series of experiments investigating head tilt (i.e., external normalization) as a strategy in letter naming and reading stimuli that are upright or rotated. We demonstrate that the frequency of this natural behavior is modulated by the cost of stimulus (...) rotation on performance. In addition, we demonstrate that external normalization can benefit performance. All of the results are consistent with the notion that external normalization represents a form of cognitive offloading and that effort is an important factor in the decision to adopt an internal or external strategy. (shrink)

In this article, the rotational invariance of entangled quantum states is investigated as a possible cause of the Pauli exclusion principle. First, it is shown that a certain class of rotationally invariant states can only occur in pairs. This is referred to as the coupling principle. This in turn suggests a natural classification of quantum systems into those containing coupled states and those that do not. Surprisingly, it would seem that Fermi–Dirac statistics follows as a consequence of this coupling while (...) the Bose–Einstein follows by breaking it. In Sec. 5, the above approach is related to Pauli's original spin-statistics theorem and finally in the last two sections, a theoretical justification, based on Clebsch–Gordan coefficients and the experimental evidence respectively, is presented. (shrink)

The rotating discs argument against perdurantism has been mostly discussed by metaphysicians, though the argument of course appeals to ideas from classical mechanics, especially about rotation. In contrast, I assess the RDA from the perspective of the philosophy of physics. I argue for three main conclusions. The first conclusion is that the RDA can be formulated more strongly than is usually recognized: it is not necessary to ‘imagine away’ the dynamical effects of rotation. The second is that in (...) general relativity, the RDA fails because of frame-dragging. The third conclusion is that even setting aside general relativity, the strong formulation of the RDA can after all be defeated, namely, by the perdurantist taking objects in classical mechanics to have only temporally extended temporal parts, which immediately blocks the RDA. Admittedly, this version of perdurantism defines persistence in a weaker sense of ‘definition’ than pointilliste versions that aim to define persistence assuming only instantaneous temporal parts. But I argue that temporally extended temporal parts can do the jobs within the endurantism– perdurantism debate that the perdurantist wants temporal parts to do and are supported by both classical and quantum mechanics. Introduction The story so far 2.1 The RDA 2.2 Intrinsic properties and the idea of velocity 2.2.1 The intrinsic–extrinsic distinction 2.2.2 Velocity to the rescue? 2.3 ‘Naturalism’ 2.4 The accompaniments of rotation 2.5 Two kinds of reply: against the consensus Describing rotation 3.1 Rotation is kinematic 3.2 Beware of rigidity 3.3 An improved RDA: allowing the actual accompaniments 3.4 The RDA fails in general relativity Perdurantism without tears: the classical case 4.1 Rejecting instantaneous temporal parts 4.2 Replying to the RDA 4.2.1 ‘Kinematics’ 4.2.2 ‘Dynamics’ 4.2.3 An ‘anti-pointilliste’ objection and reply 4.3 Intrinsic properties of non-instantaneous temporal parts 4.3.1 Can the perdurantist appeal to them? 4.3.2 Temporal intrinsicality at an instant is rare 4.3.3 A better reason for temporal intrinsicality 4.4 Non-instantaneous parts can do the jobs 4.4.1 Humean supervenience revisited 4.4.2 The problem of change 4.4.3 Puzzles of coincidence 4.5 Instantaneous velocity is hardly extrinsic Support from decoherence in quantum theory 5.1 Classical and quantum: relativizing the intrinsic–extrinsic distinction 5.1.1 Unitarity: momentum as temporally intrinsic 5.2 Position and existence as nomically extrinsic. (shrink)

Mental rotation of emotional and neutral stimuli The main aim of the study was to create and validate emotional version of mental rotation task (MRT). As all previously conducted experiments utilized neutral material only, such an attempt seemed necessary to confirm the generality of mental rotation effect and its properties. Emotional MRT was constructed using photos of negative facial expressions; a compatible neutral MRT was also created, for detailed comparisons. 2- and 3-dimensional figures (Experiment 1) and hexagrams (...) (Experiment 2 and 3) served as affect-free stimuli. In three experiments, emotional MRT version was proven to be valid, whereas only hexagram-based neutral MRT version yielded the expected results. A number of differences between the two versions emerged, concerning response times, accuracy and difficulty of trials. The neutral/emotional MRT procedure, although needing more research, seems to give stable results, making the study of content-bound imagery possible. (shrink)

The rotating spot method of timing subjective events involves the subject’s watching a rotating spot on a computer and reporting the position of the spot at the instant when the subjective event of interest occurs. We conducted an experiment to investigate factors that may impact on the results produced by this method, using the subject’s perception of when they made a simple finger movement as the subjective event to be timed. Seven aspects of the rotating spot method were investigated, using (...) a factorial experiment. Four of these aspects altered the physical characteristics of the computer generated spot or clock face and the remaining three altered the instructions given to the participant. We found compelling evidence that one factor, whether the subject was instructed to report the instant when the finger movement was initiated or the instant when it was completed, resulted in a systematic shift in the response. Evidence that three other factors affect the observed variability in the response was also found. In addition, we observed that there are substantial systematic differences in the responses made by different subjects. We discuss the implications of our findings and make recommendations about the optimal way of conducting future experiments using the rotating spot method. Our overall conclusion is that our results strongly validate the rotating spot method of timing at least the studied variety of subjective event. (shrink)

Earlier work distinguished between local word-level oscillations and global sentence-level effects, but the latter lacked a rigorous mathematical formulation. In this paper we introduce the sentence matrix St, where each column represents a word vector. Local rotations R(θ) are combined with emergent coupling through the Laplacian. Crucially, the coupling strength η is not imposed externally but derived from the sentence state itself, functioning as a measure of semantic coherence. The resulting update rule combines local word-level rotations with emergent coupling, showing (...) how their interplay transforms neutral cycles into spiral trajectories. Depending on η, three regimes emerge: convergence towards semantic attractors, stagnation, and divergence into incoherence. This framework provides a first precise account of how global sentence-level dynamics arise from local interactions. (shrink)

The proposal to create a chamber selected by sortition would extend this democratic procedure into the legislative branch of government. However, there are good reasons to believe that, as currently conceived by John Gastil and Erik Olin Wright, the proposal will fail to realize sufficiently two fundamental democratic goods, namely, political equality and deliberative reasoning. It is argued through analysis of its historic and contemporary application that sortition must be combined with other institutional devices, in particular, rotation of membership (...) and limited mandate, in order to be democratically effective and to realize political equality and deliberative reasoning. An alternative proposal for a responsive sortition legislature is presented as more realistic and utopian: one that increases substantially the number of members, makes more extensive use of internal sortition and rotation, and recognizes the importance of establishing limited mandates. (shrink)

This study examines the spontaneous use of embodied egocentric transformation in understanding false beliefs in the minds of others. EET involves the participants mentally transforming or rotating themselves into the orientation of an agent when trying to adopt his or her visuospatial perspective. We argue that psychological perspective taking such as false belief reasoning may also involve EET because of what has been widely reported in the embodied cognition literature, showing that our processing of abstract, propositional information is often grounded (...) in concrete bodily sensations which are not apparently linked to higher cognition. In Experiment 1, an agent placed a ball into one of two boxes and left. The ball then rolled out and moved either into the other box or back into the original one. The participants were to decide from which box they themselves or the agent would try to recover the ball. Results showed that false belief performance was affected by increased orientation disparity between the participants and the agent, suggesting involvement of embodied transformation. In Experiment 2, false belief was similarly induced and the participants were to decide if the agent would try to recover the ball in one specific box. Orientation disparity was again found to affect false belief performance. The present results extend previous findings on EET in visuospatial perspective taking and suggest that false belief reasoning, which is a kind of psychological perspective taking, can also involve embodied rotation, consistent with the embodied cognition view. (shrink)

This paper concerns the dispute about spaceSpace, timeTime, and motion, about whether space, time, and motion are absolute or relative. This paper focuses on one aspect of the dispute by investigating a kind of motion, the rotationRotation of galaxies with respect to the inertialInertial frame. In rotating universesRotating Universe, distant galaxies rotate with respect to the inertial frameInertial Frame. Our universe does not rotate. Nonetheless, rotating universesRotating Universe throw light on our own, or so this paper argues. First, the paper (...) presents historical evidence of the fundamental theoretical use of the rotating solution in physics. Second, the paper identifies three consequences for time and the causal order. (shrink)

In “Sideways Music”, Ned Markosian uses aesthetic intuitions about temporally-rotated music to argue that the metaphysics of time is different from the metaphysics of space. In response, I use aesthetic intuitions about spatially-rotated paintings to pose a dilemma for Markosian’s argument: either he accepts the intuitions about spatially-rotated paintings, in which case he must give up on some assumptions in his argument, or he rejects intuitions about spatially-rotated paintings, in which case an analogous response can be given regarding intuitions about (...) temporally-rotated music. That is, if Markosian wants to hold on to the assumptions that underwrite his argument, then he thereby offers his opponent the resources with which to resist his conclusion. As such, Markosian’s argument cannot offer a new independent consideration for adjudicating the metaphysical debate between the Dynamic Theorist and the Spacetime Theorist. [Unpublishable 2019]. (shrink)

Two rotational bands have been identified and characterized in the proton-magic N = Z + 1 nucleus Ni-57. These bands complete the systematics of well-and superdeformed rotational bands in the light nickel isotopes starting from doubly magic Ni-56 to Ni-60. High-spin states in Ni-57 have been produced in the fusion-evaporation reaction Si-28(S-32, 2p1n)Ni-57 and studied with the gamma-ray detection array GAMMASPHERE operated in conjunction with detectors for evaporated light charged particles and neutrons. The features of the rotational bands in Ni-57 (...) are compared to those of neighbouring isotopes and interpreted by means of configuration-dependent cranked Nilsson-Strutinsky calculations. The two observed high-spin bands are considered signature partners and assigned to configurations with one 1g(9/2) proton and one 1g(9/2) neutron, resulting in an unambiguous understanding of the energetically favoured signature alpha = -1/2 band but a somewhat less satisfactory description of the signature alpha = +1/2 band. (shrink)

We analyse a finite spinning cosmic string in the jump-rope (troposkein) configuration as a source of closed timelike curves (CTCs) in General Relativity and Einstein–Cartan (EC) theory. The troposkein is the equilibrium surface of revolution swept by a flexible string spinning at constant angular velocity Ωrot between two fixed endpoints (“handles”); it is neither straight nor cylindrical, but bows outward from the rotation axis, reaching maximum radius Rtrop at the midplane z = 0 and returning to r = 0 (...) at the endpoints z = ±L/2. In the weak-field, fast-rotation limit the linearized metric admits the form ds2 = −dt2 − 2ω(r, z) dt dϕ + (r2 − ω2) dϕ2 + dr2 + dz2, where ω(r, z) ∼ ω0 Ψ(z) (r/Rtrop)2 near the axis, Ψ(z) encodes the troposkein profile with Ψ(0) = 1 and Ψ(±L/2) = 0. The r2 scaling follows from the dipole character of the gravitomagnetic field of a finite loop source. We prove: (i) CTCs exist in an annular region r− c (z) < r < r+ c (z) bounded in both r and z, existing only where the local frame-dragging is sufficient; (ii) the chronology horizon H is a closed compact surface of revolution by the geometry of the troposkein — no endcap matching argument is required, and no approximation is invoked; (iii) the exterior is exactly Minkowski because the string terminates at the endpoints and ω → 0 there; (iv) the NEC is violated in the CTC annulus and satisfied everywhere outside it; (v) EC torsion enhances the effective frame-dragging; (vi) the KRW theorem applies in full, and the back-reaction timescale τBR ∼ r4 c/(Gℏ) is cosmologically large for macroscopic rc. The linearized regime requires relativistic tip speeds to achieve ω0 > Rtrop; this is resolved by a three-layer exact construction (Section III): (L1) the truncated Lanczos–Van Stockum rotating dust interior is an exact nonlinear solution — no approximation used — with r2 frame-dragging, CTCs sourced by positive-density ordinary matter, and a compact cylindrical chronology horizon; (L2) the troposkein z-profile continuously deforms this exact solution, preserving CTCs and closing the horizon into a compact surface of revolution; (L3) the linearized metric is the weak-field limit of (L1), analytically tractable for computing CJR. The jump-rope troposkein provides a finite, single-source CTC construction with a naturally compact horizon and an exact nonlinear existence proof from ordinary matter (via the truncated Lanczos–Van Stockum construction, Layer L1). Whether it survives quantum back-reaction depends on CJR (Claim 1), which has not been computed. (shrink)

Galaxy dynamics present a cascade of puzzles: flat rotation curves requiring invisible mass; the extraordinarily tight Baryonic Tully-Fisher Relation (V⁴ ∝ M_baryon) with minimal scatter; the Radial Acceleration Relation showing universal correlation between observed and baryonic gravitational acceleration; thousands of predicted dark matter subhalos that don't exist (missing satellites); and wild diversity in dwarf galaxy dark matter content despite similar visible mass. ΛCDM explains each poorly or requires fine-tuning, while MOND fits the relations beautifully but fails for clusters and (...) lacks theoretical grounding. This work resolves all puzzles through one principle: "dark matter" is not particulate but the gravitational shadow of coherence—the Mθ attractor structure generated by baryonic organization itself. A galaxy's Mθ contribution is not independent of its baryonic content but caused by it; the depth and shape of the Mθ well depend on the system's integrated history, stability, and recursive self-reference (spectral concentration κ). This immediately explains the tight BTFR (baryonic mass and "dark matter" correlate perfectly because one generates the other, with no scatter from independent halo variation), the RAR universality (the same κ-generating baryonic physics operates everywhere), missing satellites (empty halos don't exist because halos require baryonic structure to generate them), and dwarf diversity (different formation histories produce different κ). The framework derives the MOND acceleration scale a₀ ≈ 1.2 × 10⁻¹⁰ m/s² from first principles as the holographic horizon limit: a₀ = cH₀/2π, where the Unruh thermal wavelength equals the cosmic horizon—not a fitted parameter but an emergent property of the universe's causal structure. Critically, the framework explains why high-redshift galaxies appear baryon-dominated: young, turbulent, merger-active systems haven't accumulated sufficient κ; they're "naked baryons" that haven't built their shadow yet. Dark matter content is a function of dynamical age (quiescence), not just mass—distinguishing this framework from both ΛCDM and standard MOND. Predictions include dark matter profiles tracking coherence metrics (age, stability) not just mass; tidal dwarf galaxies following BTFR despite lacking primordial halos; continued non-detection of dark matter particles; and systematic differences between settled disks and merger remnants at equal mass and redshift. (shrink)

We consider the historic Harress-Sagnac experiment in the light of our absolute space-time theory, proposing two modifications, and we give an account of its recent practical performance. We show that the effect of the rotating disk experiment is a direct result of the light velocity's direction dependence and we point out that our recently performed coupled-mirrors experiment, with whose help for the first time we have measured the Earth's absolute velocity, can be considered as a logical result of the rotating (...) disk experiment. (shrink)

Motor imagery provides a direct insight into action representations. The aim of the present study was to investigate the level of impairment of action monitoring in schizophrenia by evaluating the performance of schizophrenic patients on mental rotation tasks. We raised the following questions: Are schizophrenic patients impaired in motor imagery both at the explicit and at the implicit level? Are body parts more difficult for them to mentally rotate than objects? Is there any link between the performance and the (...) hallucinating symptom profile? The schizophrenic patients displayed the same pattern of performance as the control subjects . More particularly, schizophrenic patients’ reaction time varied as a function of the angular disparity of the stimuli. On the other hand, they were significantly slower and less accurate. Interestingly, patients suffering from hallucinations made significantly more errors than non-hallucinatory patients. We discussed these latter results in terms of deficit of the forward model. We emphasized the necessity to distinguish different levels of action, more or less impaired in schizophrenia. (shrink)

The disk that rotates in an inertial frame in special relativity has long been analysed by assuming a Lorentz contraction of its peripheral elements in that frame, which has produced widely varying views in the literature. We show that this assumption is unnecessary for a disk that corresponds to the simplest form of rotation in special relativity. After constructing such a disk and showing that observers at rest on it do not constitute a true rotating frame, we choose a (...) “master” observer and calculate a set of disk coordinates and spacetime metric pertinent to that observer. We use this formalism to resolve the “circular twin paradox”, then calculate the speed of light sent around the periphery as measured by the master observer, to show that this speed is a function of sent-direction and disk angle traversed. This result is consistent with the Sagnac Effect, but constitutes a finer analysis of that effect, which is normally expressed using an average speed for a full trip of the periphery. We also use the formalism to give a resolution of “Selleri’s paradox”. (shrink)

Etch pits with edges parallel to directions on (001) surface of sodium chloride have been observed by using ethyl alcohol as an etchant. It has been found that ethyl alcohol can distinguish between annealed and fresh dislocations. It is shown that by varying the concentration of mercuric chloride in ethyl alcohol, etch pits with edges parallel to and directions can be obtained. The reason for the rotation of etch pits is explained on the basis of the change in the (...) lateral displacement velocity of surface steps along different directions. (shrink)

We investigate how a uniformly rotating frame is defined as the rest frame of an observer rotating with constant angular velocity Ω around the z axis of an inertial frame. Assuming this frame to be a Lorentz one, we second quantize a free massless scalar field in the rotating frame and obtain that creation-annihilation operators of the field are not the same as those of an inertial frame. This leads to a new vacuum state—a rotating vacuum. After this, introducing an (...) apparatus device coupled linearly with the field, we obtain that there is a strong correlation between the number of Trocheries-Takeno particles (in a given state) obtained via canonical quantization and the response function of the rotating detector. Finally, we analyze polarization effects in circular accelerators in the proper frame of the electron, making a connection with the inertial frame point of view. (shrink)

The title of our volume on interdisciplinary semiotics is situated in a geographical metaphor and points to the possibility of uncovering meanings through shifting perspectives as well as to the possibility of understanding how these various modes of meaning are articulated and framed in particular cultural instances. Regardless of medium, semiotic rotations permit play between the surface and underlying levels of a communication, reveal the relationship between open and closed systems of signification, and modulate shades of meaning caught between the (...) visible and invisible. Readerly play in these sets of apparent oppositions reveals that the less each pairing is held to be a coupling of oppositions and the more they are observed through perspectives gained by semiotic rotations, then the more complex and rich the modes of meaning may become. (shrink)

This article puts forward a novel smooth rotated hyperbola model for support vector machine (RHSSVM) for classification. As is well known, the Support vector machine (SVM) is based on Statistical Learning Theory and performs its high precision on data classification. However, the objective function is non-differentiable at the zero point. Therefore the fast algorithms cannot be used to train and test the SVM. To deal with it, the proposed method is based on the approximation property of the hyperbola to its (...) asymptotic lines. Firstly, we describe the development of RHSSVM from the basic linear SVM optimization programming. Then we extend the linear model to non-linear model. We prove the solution of RHSSVM is convergent, unique, and global optimal. We show how RHSSVM can be practically implemented. At last, the theoretical analysis illustrates that compared with other three typical models, the rotated hyperbola model has the least error on approximating the plus function. Meanwhile, computer simulations show that the RHSSVM can reduce the consuming time at most 54.6% and can efficiently handle large scale and high dimensional programming. -/- . (shrink)

ε-support vector regression (ε-SVR) as a constrained minimization problem can be converted into an unconstrained convex quadratic programming. Smooth function is the essence of the ε-smooth support vector regression (ε-SSVR). In this paper, a new rotated hyperbola function is proposed to replace the ε-insensitive loss function. The ε-rotated hyperbola smooth support vector regression (ε-RHSSVR) model is presented. Theoretical analyses show that the derived smooth function has improved approximation precision compared with other smooth approximate functions. The Newton-Armijo algorithm is applied to (...) train the new model. Numerical results and comparisons are given to demonstrate the effectiveness and speed of the method. -/- . (shrink)

Alternative theories of relativistic rotation considered viable as of 2004 are compared in the light of experiments reported in 2005. En route, the contentious issue of simultaneity choice in rotation is resolved by showing that only one simultaneity choice, the one possessing continuous time, gives rise, via the general relativistic equation of motion, to the correct Newtonian limit Coriolis acceleration. In addition, the widely dispersed argument purporting Lorentz contraction in rotation and the concomitant curved surface of a (...) rotating disk is analyzed and argued to be lacking for more than one reason. It is posited that not by theoretical arguments, but only via experiment can we know whether such effect exists in rotation or not. The Coriolis/simultaneity correlation, and the results of the 2005 experiments, support the Selleri theory as being closest to the truth, though it is incomplete in a more general applicability sense, because it does not provide a global metric. Two alternatives, a modified Klauber approach and a Selleri–Klauber hybrid, are presented which are consistent with recent experiment and have a global metric, thereby making them applicable to rotation problems of all types. (shrink)

The dynamics of rapidly rotating bodies is formulated in a rotationally invariant form in all frames rotating with constant angular velocities relative to each other. This includes the energy, angular momentum, rotational frequency, and moment of inertia. The transformation between these quantities, when expressed in different frames, is then given explicitly and expressed in terms of both the angular momentum and the rotational frequency variables. Comparison with the approximate formula for the Routhian is made, and some consequences of physical interest (...) are drawn. (shrink)

The effect of the rotating-wave approximation (RWA) on the coupling between an atom and the electromagnetic field is studied in the dipole approximation. It is demonstrated that use of the RWA results in an explicitly nonlocal interaction.

Much indirect evidence supports the hypothesis that transformations of mental images are at least in part guided by motor processes, even in the case of images of abstract objects rather than of body parts. For example, rotation may be guided by processes that also prime one to see results of a specific motor action. We directly test the hypothesis by means of a dual-task paradigm in which subjects perform the Cooper-Shepard mental rotation task while executing an unseen motor (...) rotation in a given direction and at a previously learned speed. Four results support the inference that mental rotation relies on motor processes. First, motor rotation that is compatible with mental rotation results in faster times and fewer errors in the imagery task than when the two rotations are incompatible. Second, the angle through which subjects rotate their mental images, and the angle through which they rotate a joystick handle are correlated, but only if the directions of the two rotations are compatible. Third, motor rotation modifies the classical inverted V-shaped mental rotation response time function, favoring the direction of the motor rotation; indeed, in some cases motor rotation even shifts the location of the minimum of this curve in the direction of the motor rotation. Fourth, the preceding effect is sensitive not only to the direction of the motor rotation, but also to the motor speed. A change in the speed of motor rotation can correspondingly slow down or speed up the mental rotation. (shrink)

Several arguments suggest that motor planning may share embodied neural mechanisms with mental rotation (MR). However, it is not well established whether this overlap occurs regardless of the type of stimulus that is manipulated, in particular manipulable or non-manipulable objects and body parts. We here used high-density electroencephalography (EEG) to examine the cognitive similarity between MR of objects that do not afford specific hand actions (chairs) and bodily stimuli (hands). Participants had identical response options for both types of stimuli, (...) and they gave responses orally in order to prevent possible interference with motor imagery. MR of hands and chairs generated very similar behavioral responses, time-courses and neural sources of evoked-response potentials (ERPs). ERP segmentation analysis revealed distinct time windows during which differential effects of stimulus type and angular disparity were observed. An early period (90–160 ms) differentiated only between stimulus types, and was associated with occipito-temporal activity. A later period (290–330 ms) revealed strong effects of angular disparity, associated with electrical sources in the right angular gyrus and primary motor/somatosensory cortex. These data suggest that spatial transformation processes and motor planning are recruited simultaneously, supporting the involvement of motor emulation processes in MR. (shrink)

A gedanken experiment that distinguishes locally between acceleration of rotation and linear acceleration is described and discussed.

New arguments against Bayesian regularity and an otherwise plausible domination principle are offered on the basis of rotational symmetry. The arguments against Bayesian regularity work in very general settings.

We generalize the notions of Girard algebras and MV-algebras by introducing rotation-invariant semigroups. Based on a geometrical characterization, we present five construction methods which result in rotation-invariant semigroups and in particular, Girard algebras and MV-algebras. We characterize divisibility of MV-algebras, and point out that integrality of Girard algebras follows from their other axioms.

Recent work in the physics literature demonstrates that, in particular classes of rotating spacetimes, physical light rays in general do not traverse null geodesics. Having presented this result, we discuss its philosophical significance, both for the clock hypothesis (and, in particular, a recent purported proof thereof for light clocks), and for the operational meaning of the metric field. 1Introduction 2Fletcher's Theorem 2.1Maudlin on the clock hypothesis in special relativity 2.2Fletcher’s result in special relativity 2.3Fletcher’s theorem in general relativity 3Electromagnetism and (...) the Geometrical-Optical Limit 3.1Maxwell’s equations in curved spacetime 3.2The geometrical-optical limit 3.3Rotating spacetimes 3.4Aren’t Gödel spacetimes unphysical? 4The Clock Hypothesis and Chronogeometry 4.1Natural and mathematical observations 4.2Clock registry discord 4.3Chronogeometry 5Conclusion. (shrink)

Regenerative agriculture is an approach that places soil conservation at the center of its practices. As part of this approach, regenerative agriculture seeks to address concerns related to environmental and socio-economic dimensions of food production through the promotion of a range of best management practices. While regenerative agriculture has received support at various levels in many countries, including Canada, adoption remains low. Systems thinking strength has been recognized as facilitating farmer adoption of several regenerative agricultural practices including rotational grazing (RG). (...) However, few approaches have examined multiple types of systems thinking nor the breadth of a system which may underlay the diverse ways that systems thinking influences agricultural practice adoption and persistence. Furthermore, few studies have taken a quantitative approach into understanding how different systems are emphasized by adopters of RG within the context of systems thinking. Using survey data from program participants in a national producer training program, we explored the use of two measures of systems thinking, systems thinking strength and diversity of a system in RG adopters. Our research highlights how the inclusion of the breadth of systems farmers consider can help us better understand RG adopters and support efforts to recruit new adopters. Furthermore, our results suggest that adopters are not homogenous in the types of systems they emphasize in their farming nor in the strength of their systems thinking. Future training programs can utilize these insights to leverage existing system emphases of RG producers and integrate them in the development of training programs to attract potential adopters. (shrink)

A rotating disk with angular acceleration is given a relativistic description as observed from the rotating rest frameR of the disk. It is shown how a non-Euclidean intrinsic spatial geometry develops inR, as the disk gets an angular velocity. The explanation of this as given by anR-observer is discussed. A recent description of the geometry inR presented by Grünbaum and Janis is criticized. The motion of light as described by use of coordinate clocks inR is discussed in connection with some (...) recent work by R. C. Jennison and coworkers. The significance of the difference between directed signals and circular waves when clocks inR are to be synchronized by means of light emitted from the axis inR is made clear. (shrink)

Rotation in a general relativistic framework is examined. This concept, combined with the appropriate mechanical work concept, is used to show how the Euclidean group of transformations, serving as an invariance requirement associated with the principle of objectivity, can lead to erroneous conclusions.

A 14th-century Persian medical manual known as the _Tānksūqnāmah_ and commissioned by the vizier and physician Rashīd al-Dīn Hamadānī (1247–1318) explicitly states that blood “makes rounds” within the body, flowing from the liver to the heart, then to the lungs, and returning again to the liver. This account, grounded in a cosmological model that links bodily processes to celestial movements, does not correspond to Ibn al-Nafīs’s philosophical description of pulmonary transit, nor does it anticipate William Harvey’s (1578–1657) quantitative theory of (...) systemic circulation, for it is rooted in an astrological understanding of motion and causality. Even though it draws on Chinese cosmology and medicine and the Graeco-Arabic medical heritage, the _Tānksūqnāmah_ ultimately advances its own conception of blood movement—one that diverges from both—indicating a deliberate reinterpretation rather than simple continuity. The _Tānksūqnāmah_ is therefore best understood as a product of Mongol-era Iran’s unique cross-cultural milieu, where heterogeneous concepts were consciously recombined within a shared intellectual setting. Seen in this light, the text exemplifies how scientific ideas could emerge through reinterpretation in cultural and scientific contact zones rather than through the transmission and adaptation of knowledge within a single lineage. (shrink)

is the thesis that everything supervenes upon the spatiotemporal distribution of local intrinsic qualities. A recent threat to HS, originating in thought experiments by Armstrong and Kripke, claims that the mere possibility of rotating homogeneous discs proves HS false. I argue that the rotating disc argument (RDA) fails. If I am right, Humeans needn't abandon or alter HS to make sense of rotating homogeneous discs. Homogeneous discs, as necessarily understood by RDA, are not the sorts of things in which we (...) should believe. These discs do not belong in our ontology - not because there is a problem with their homogeneity, but (surprisingly) because there is a problem with their rotation. RDA is shown to be a kind of parody of classic arguments for spatial substantivalism. (shrink)

The mental rotation ability is an essential spatial reasoning skill in human cognition and has proven to be an essential predictor of mathematical and STEM skills, critical and computational thinking. Despite its importance, little is known about when and how mental rotation processes are activated in games explicitly targeting spatial reasoning tasks. In particular, the relationship between spatial abilities and TetrisTM has been analysed several times in the literature. However, these analyses have shown contrasting results between the effectiveness (...) of Tetris-based training activities to improve mental rotation skills. In this work, we studied whether, and under what conditions, such ability is used in the TetrisTM game by explicitly modelling mental rotation via an ACT-R based cognitive model controlling a virtual agent. The obtained results show meaningful insights into the activation of mental rotation during game dynamics. The study suggests the necessity to adapt game dynamics in order to force the activation of this process and, therefore, can be of inspiration to design learning activities based on TetrisTM or re-design the game itself to improve its educational effectiveness. (shrink)