1. Time until Newton

‘Time until Newton’ begins by describing the historical origin of calendars and mathematical ways of representing time. It discusses the Aristotelian worldview, which formed the dominant understanding of the Universe in the West from the time of Aristotle until the 17th century when Newton proposed his theory of motion. This was the first physical theory in the mathematical form that we expect nowadays and by making space and time subjects of scientific investigation Newton forever changed the way that people studied space and time. After the publication of his theory, a debate about whether space and time were entities or systems of relations broke out between Newton and the philosopher Gottfried Wilhelm Leibniz. A series of letters between Leibniz and the philosopher Samuel Clarke focusing on this question introduced the mathematical tools of symmetry and invariance that would become important in subsequent study of the structure of space and time.

2. From space and time to spacetime: the era of Einstein

Isaac Newton’s theory of motion was superseded by Albert Einstein’s theories of relativity. By the early 20th century, it was clear that there was something wrong with Newton’s theory. Newton’s theory together with Maxwell’s newly proposed equations of electromagnetism predicted that the speed of light should depend on the motion of the observer, but experiments found that the velocity of light is independent of the motion of the observer. Einstein proposed the special theory of relativity in 1905 which merged space and time into a four-dimensional structure known as spacetime. Ten years later he proposed the general theory which extended the special theory to include gravity. With Einstein’s theories, an ancient philosophical debate between Heraclitus and Parmenides on change as the fundamental character of time was revived.

Proofs Of Incorporeality of God In Islam And Judaism: Analysis On The Discourse Of Al-Ghazālī And Maimonides

This study aims to examine the concept of incorporeality of God according to al-Ghazālī and Maimonides. Due to the existence of ‘human-like’ attributes and actions in the Hebrew Bible, it entails to various interpretations towards anthropomorphic verses within Muslim and Jewish society. During the golden age of Islamic civilization, fellow Jews and Christian were seen to be engaged in theological discourse with Muslim scholars. The emerging trend during that time in inculcating rational interpretations into religion has triggered scholars to be engaged in the inter-theological dialogue. Prior to this critical situation, al-Ghazālī and Maimonides were seen playing vital roles in affirming the incorporeality of God and refuting anthropomorphism in their respective religions. Therefore, this study will highlight their methods in affirming the incorporeality of God. In sum, it can be observed that al-Ghazālī employed kalām’s method of arguments on jawhar fard while Maimonides’ methods reciprocate Aristotle’s argument on the theory of motion. Through their propositions, both scholars denounced God to be associated to any form of substance, accident and body. Both argued that God is an incorporeal being that does not possess any forms or figures. However, Maimonides arguing through the theory of motion led to the concept of God as the First Mover. Meanwhile al-Ghazālī opposed against the former concept and argued that God particularized (mukhaşşiş) of every creations. In sum, it is apparent that the argument of incorporeality that serves as the fundamental proposition is essential in having the right understanding on the concept of God. Despite having the similarities in arguing on the incorporeality of God, both al- Ghazālī and Maimonides differ in comprehending the concept of God.

Multifractality through Non-Markovian Stochastic Processes in the Scale Relativity Theory. Acute Arterial Occlusions as Scale Transitions

By assimilating biological systems, both structural and functional, into multifractal objects, their behavior can be described in the framework of the scale relativity theory, in any of its forms (standard form in Nottale’s sense and/or the form of the multifractal theory of motion). By operating in the context of the multifractal theory of motion, based on multifractalization through non-Markovian stochastic processes, the main results of Nottale’s theory can be generalized (specific momentum conservation laws, both at differentiable and non-differentiable resolution scales, specific momentum conservation law associated with the differentiable–non-differentiable scale transition, etc.). In such a context, all results are explicated through analyzing biological processes, such as acute arterial occlusions as scale transitions. Thus, we show through a biophysical multifractal model that the blocking of the lumen of a healthy artery can happen as a result of the “stopping effect” associated with the differentiable-non-differentiable scale transition. We consider that blood entities move on continuous but non-differentiable (multifractal) curves. We determine the biophysical parameters that characterize the blood flow as a Bingham-type rheological fluid through a normal arterial structure assimilated with a horizontal “pipe” with circular symmetry. Our model has been validated based on experimental clinical data.

An Algorithm for the Factorization of Split Quaternion Polynomials

We present an algorithm to compute all factorizations into linear factors of univariate polynomials over the split quaternions, provided such a factorization exists. Failure of the algorithm is equivalent to non-factorizability for which we present also geometric interpretations in terms of rulings on the quadric of non-invertible split quaternions. However, suitable real polynomial multiples of split quaternion polynomials can still be factorized and we describe how to find these real polynomials. Split quaternion polynomials describe rational motions in the hyperbolic plane. Factorization with linear factors corresponds to the decomposition of the rational motion into hyperbolic rotations. Since multiplication with a real polynomial does not change the motion, this decomposition is always possible. Some of our ideas can be transferred to the factorization theory of motion polynomials. These are polynomials over the dual quaternions with real norm polynomial and they describe rational motions in Euclidean kinematics. We transfer techniques developed for split quaternions to compute new factorizations of certain dual quaternion polynomials.

Some Consequences of Physics for the Comparative Metaphysics of Quantity

According to comparativist theories of quantities, their intrinsic values are not fundamental. Instead, all the quantity facts are grounded in scale-independent relations like “twice as massive as” or “more massive than.” I show that this sort of scale independence is best understood as a sort of metaphysical symmetry—a principle about which transformations of the non-fundamental ontology leave the fundamental ontology unchanged. Determinism—a core scientific concept easily formulated in absolutist terms—is more difficult for the comparativist to define. After settling on the most plausible comparativist understanding of determinism, I offer some examples of physical systems that the comparativist must count as indeterministic, although the relevant physical theory gives deterministic predictions. Several morals are drawn. In particular: comparativism is metaphysically contingent if true, and it is most natural for a comparativist to accept an at-at theory of motion.

Investigation of solutions of weakly perturbed boundary value problems for systems with impulse action

The paper is devoted to the investigation of the existence and construction of solutions of weakly perturbed linear boundary value problems for systems with impulse action in the case when the generating boundary value problem with impulse action has no solutions for arbitrary right-hand sides. The relevance of this topic is due primarily to the importance of practical application of the theory of boundary value problems in various fields of science and technology - the theory of nonlinear oscillations, the theory of motion stability, control theory, a variety of geophysical problems. On the other hand, the question of the existence and construction of solutions of boundary value problems occupies one of the central and fundamentally important places in the qualitative theory of ordinary differential equations.

Marx and Motion

This chapter explains Marx’s theory of motion first as it is developed in his dissertation on Epicurus, Democritus, and Lucretius and then as it is developed in his books leading up to the Capital volumes. The argument is that Marx developed an original dialectics of motion that stayed with him throughout his life and work. In short, his materialist naturalism was the foundation for his critique of capitalism and economics. Marx’s interest in motion preceded his analysis and critique of capitalism and is the larger framework within which his economic and social critique should be understood.

Alexander Crum Brown: A Forgotten Pioneer in Vestibular Sciences

Although vestibular anatomy was described in the Renaissance period, research in vestibular physiology began in the 1820s and was spearheaded by Purkinje and Flourens. This was subsequently expanded by Ménière, Helmholtz, Goltz, Mach, Breuer, Ewald, and Hogyes, who are regarded as the early pioneers in research on vestibular physiology in the 19th century. The relationship of endolymphatic flow and semicircular canal function is termed the Mach-Breuer hypothesis. What is less well known is that a Scottish chemist, Alexander Crum Brown, arrived at similar conclusions as Mach and Breuer at the same time quite independently. In fact, he pioneered several concepts in vestibular physiology that included pairing of semicircular canals for function, the vestibular pathway, optic fixation elimination in vestibular experimentation, the theory of motion intolerance, and study in deaf mutes for insights into vestibular pathology and vestibular compensation. This article is a tribute to this forgotten pioneer in vestibular research.