Physical Facts Research Articles

Indexing and Mathematical Explanation

We discuss a recent attempt by Chris Daly and Simon Langford to do away with mathematical explanations of physical phenomena. Daly and Langford suggest that mathematics merely indexes parts of the physical world, and on this understanding of the role of mathematics in science, there is no need to countenance mathematical explanation of physical facts. We argue that their strategy is at best a sketch and only looks plausible in simple cases. We also draw attention to how frequently Daly and Langford find themselves in conflict with mathematical and scientific practice.

The physical, gain–loss model for the stochasticity of the phase velocity of a wind-driven water wave

Mathematical-model study of the behavior of a ship in an irregular sea (e.g., the roll motion) includes an analysis of the particular case where the stochastic wind-driven wave is a plane wave, i.e. the wave traveling in one spatial direction. The stochasticity of a wind-driven wave is solely due to the stochasticity of wind. By using the basic physical facts on the water-surface/wind interaction, more specifically, the rates of the gain and loss of the wave energy, the present work derives a dynamical model for the phase velocity of a water wave. The model is a linear ordinary differential equation for the cubed phase velocity. This equation which includes the velocity of wind becomes stochastic when the wind is a stochastic process, for example, is described by the first-order Itô’s stochastic differential equation (ISDE). In this case, the water-wave phase velocity appears to be a solution of the second-order ISDE. The derivation of the model implies an analytical relation which explicitly couples the parameters “alpha” and “beta” of the well-known Pierson–Moskowitz spectral function. It is shown that the derived relation agrees well with the experimentally obtained values of the parameters. The derived model can be used not only in models for the ship dynamics in a stochastic sea but also in a number of other ocean problems where the prediction of water waves by mere measurement of the wind is an advantage. These problems in particular include the real-time control of the stochastic water load on the ocean structures by sensing the stochastic wind rather than sensing stochastic waves thereby creating an alternative to more complex and expensive methods.

INTEGRATING MECHANICAL CONTROL THEORY INTO MODELS OF BIOLOGICAL DEVELOPMENT — ANALYTICAL REVIEW

This paper presents both a general review on developmental biomechanics and a concrete proposition for the computation of a symmetry breaking instability of a model of biological development in terms of self-organization theory. The necessary biological and physical facts taken from the literature are described and discussed in the context of a unified statement of the problems for mathematical modeling of pattern formation. This is then applied to planar cell polarization (PCP) of the Drosophila wing. In this way, the process is modeled by an elastopolarization equation. In terms of this statement, the mechanical specificity (interaction with basal plate) of wing PCP is characterized. Some aspects of modeling somite formation as well as other developmental processes are also concerned.

Kathleen P. Whitley. The Gilded Page: The History and Technique of Manuscript Gilding. New Castle, Del.: Oak Knoll Press; London: The British Library, 2010. xv, 233p. ISBN (USA; hardcover) 978-1-58456-239-9; (USA; paperback) 978-1-58456-241-2; (UK; paperback) 978-0-7123-5066-2. $49.95; $34.95

Kathleen Whitley’s The Gilded Page is a mixture of excellent and wretched, satisfying and frustrating.Let’s look at the excellent first. The content is amazing, filled with an abundance of information on the history and technique of gilding, coming from an experienced gilder. In 1969, D.F. McKenzie wrote his landmark essay “Printers of the Mind: Some Notes on Bibliographical Theories and Printing-House Practices”1 in which he talks about “the need for what might be called ‘scientific’ investigation in bibliography” which comes from “a strict regard for certain fixed bounds of physical fact” (p. 1). Among many other things this article . . .

'Natural Supernaturalism?' The Tagore-Gandhi Debate on the Bihar Earthquake

This article is a study of the confrontation between Rabindranath Tagore (1861–1941) and Mohandas Karamchand Gandhi (1869–1948) on the Bihar earthquake of January 1934. Gandhi who was then campaigning against untouchability in South India called the earthquake ‘a divine chastisement for the great sin we have committed and are still committing against those whom we describe as untouchables … ’. Reading this statement in the press, Tagore wrote to Gandhi pointedly disagreeing with him: ‘I am compelled to utter a truism in asserting that physical catastrophes have their inevitable and exclusive origin in certain combinations of physical facts’. This article examines the differences in their position over this topic and discusses the implications of their contrasting stands on it. In addition, I also look at Gandhi’s other statements on the earthquake as I do at Tagore’s exchanges with Einstein on the relationship between the observer and the phenomenal world. Perhaps no other disagreement between Gandhi and Tagore better illustrates the differences in their attitudes to life, their notions of what constitutes the relationship between physical phenomena and the realm of human morals, or between nature and God, within a broadly Hindu framework of understanding. But departing from the conventional view that Tagore’s position is rational–scientific–modern, while Gandhi’s is religious–superstitious–traditional, I argue that the contestations are not as much between rationality and faith, science and superstition, or modernity and tradition as between two kinds of rationality, two ideas of science, and two approaches to modernity. I try to show how both Tagore’s and Gandhi’s positions are intellectually more complex, nuanced, and compelling than might appear at first. Ultimately, both Gandhi and Tagore contributed, even with their contrasting perspectives, to the richness that made up Indian modernity, with its unique attempts to integrate rationality with a spiritual view of the world.

O faktach instytucjonalnych

The principal aim of this article is to analyze the structure of institutional facts. These are facts whose essential part is a particular social context. The physical facts that present the background of institutional facts are called “brute facts”. In the article I define the link between them and institutional facts. I first analyze the concept of the brute fact using Elizabeth Anscombe’s article On brute facts (1958). I discuss in detail the structure of institutional facts and define their relation to brute facts. Then I take up the analysis of the contemporary theory of institutional facts presented by John Searle in his book The Construction of Social Reality (1995). I first distinguish between regulative and constitutive rules and analyze more closely the structure of such constitution. Next, I introduce the concept of institution which according to Searle means a particular pattern of behavior that is defined by a set of constitutive rules. In the end I take up the issue of the ontological foundation of the institution, i.e. of collective consciousness.

Optimus prime: paraphrasing prime number talk

Baker (Mind 114:223–238, 2005; Brit J Philos Sci 60:611–633, 2009) has recently defended what he calls the “enhanced” version of the indispensability argument for mathematical Platonism. In this paper I demonstrate that the nominalist can respond to Baker’s argument. First, I outline Baker’s argument in more detail before providing a nominalistically acceptable paraphrase of prime-number talk. Second, I argue that, for the nominalist, mathematical language is used to express physical facts about the world. In endorsing this line I follow moves made by Saatsi (Brit J Philos Sci 62(1):143–154, 2011). But, unlike Saatsi, I go on to argue that the nominalist requires a paraphrase of prime-number talk, for otherwise we lack an account of what that ‘physical fact’ is in the case of mathematics that seemingly makes reference to prime numbers.

Björn Olof Roos (1937–2010)

Björn Roos was one of the most prominent theoretical chemists of the 20th and early 21st century. His membership in the International Academy of Quantum Molecular Sciences (IAQMS) honored perhaps more the IAQMS than it honored Björn Roos himself. Also, he was an active member of the Bureau of that Academy, in addition to important positions of trust in Sweden. Björn was a Ph.D. student of Inga Fischer-Hjalmars, who in turn had studied with Charles Coulson. It is interesting to ask whether his combination of intellectual rigor and sense for the physical and chemical facts can be partially derived from his academic ancestry. He started with semiempirical methods but switched to ab initio method development in 1968. After only a few years, in 1972, he had his first permanent achievement, the direct Configuration Interaction (CI) method. The Complete Active Space method followed in 1980 and CASPT2 in 1990. His scientific oeuvre is discussed by others in this volume. As a scientist, he only improved with age. One must record here his last “heat” with heavy-element chemistry, when he introduced relativistic terms in the MOLCAS package, single-handedly developed basis sets, and ran a number of classical applications. Perhaps, the crowning achievement was the understanding of the chemical bond in U2, published in Nature in 2005. His last papers are still appearing posthumously. Björn's scientific competence and intellectual discipline had as their vehicle an outspoken personality. This made his surrounding a magic circle that was free of any pretensions or ambiguities. We miss his sardonic laughter. Björn's last decade was shadowed by cancer. He is missed by his wife Ingela, and by five children from two marriages.

Does Mary know I experience plus rather than quus? A new hard problem

Realism about cognitive or semantic phenomenology, the view that certain conscious states are intrinsically such as to ground thought or understanding, is increasingly being taken seriously in analytic philosophy. The principle aim of this paper is to argue that it is extremely difficult to be a physicalist about cognitive phenomenology. The general trend in later 20th century/early 21st century philosophy of mind has been to account for the content of thought in terms of facts outside the head of the thinker at the time of thought, e.g. in terms of causal relations between thinker and world, or in terms of the natural purposes for which mental representations have developed. However, on the assumption that consciousness is constitutively realised by what is going on inside the head of a thinker at the time of experience, the content of cognitive phenomenology cannot be accounted for in this way. Furthermore, any internalist account of content is particularly susceptible to Kripkensteinian rule following worries. It seems that if someone knew all the physical facts about what is going on in my head at the time I was having a given experience with cognitive phenomenology, they would not thereby know whether that state had ‘straight’ rather than ‘quus-like’ content, e.g. whether the experience was intrinsically such as the ground the thought that two plus two equals four or intrinsically such as to ground the thought that two quus two equals four. The project of naturalising consciousness is much harder for realists about cognitive phenomenology.

Compressible turbulence: Multi-fractal scaling in the transition to the dissipative regime

Multi-fractal scaling in the transition to the dissipative regime for fully-developed compressible turbulence is considered. The multi-fractal power law scaling behavior breaks down for very small length scales thanks to viscous effects. However, the effect of compressibility is found to extend the single-scaling multi-fractal regime further into the dissipative range. In the ultimate compressibility limit, thanks to the shock waves which are the appropriate dissipative structures, the single-scaling regime is found to extend indeed all the way into the full viscous regime. This result appears to be consistent with the physical fact that vortices become more resilient and stretch stronger in a compressible fluid hence postponing viscous intervention. The consequent generation of enhanced velocity gradients in a compressible fluid appears to provide an underlying physical basis for the previous results indicating that fully-developed compressible turbulence is effectively more dissipative than its incompressible counterpart.

Stringency in Qumran?

AbstractSome scholars allege a stringent ideology behind the severe Qumranic halakhot in contrast to putative leniencies in parallel rabbinic rulings. Vered Noam contends that the rabbinic propensity for leniency and innovativeness, versus the opposite Qumranic approach are the source of their disputes. Thus, Qumranic strictness is not “objective” but relative to the lenient rabbinic law. This paper critically scrutinizes Noam’s thesis, and will posit that the halakhot of Qumran are founded on a literal adherence to Scripture versus rabbinic pragmatism. The study discusses Noam’s cited examples, offering contrasting explanations. It deliberates about the difference between disputes concerning interpretations and physical facts, the rationales behind the various classifications, and the relationship between the degrees of holiness and the degrees of impurity.

The fallacy of Oppenheimer Snyder collapse: no general relativistic collapse at all, no black hole, no physical singularity

By applying Birkhoff’s theorem to the problem of the general relativistic collapse of a uniform density dust, we directly show that the density of the dust ρ=0 even when its proper number density n would be assumed to be finite! The physical reason behind this exact result can be traced back to the observation of Arnowitt et al. (Phys. Rev. Lett. 4: 375, 1960) that the gravitational mass of a neutral point particle is zero: m=0. And since, a dust is a mere collection of neutral point particles, unlike a continuous hydrodynamic fluid, its density ρ=mn=0. It is nonetheless found that for k=−1, a homogeneous dust can collapse and expand special relativistically in the fashion of a Milne universe. Thus, in reality, general relativistic homogeneous dust collapse does not lead to the formation of any black hole in conformity of many previous studies (Logunov et al., Phys. Part. Nucl. 37: 317, 2006; Kiselev et al., Theor. Math. Phys. 164: 972, 2010; Mitra, J. Math. Phys. 50: 042502, 2009a; Suggett, J. Phys. A 12: 375 1979b). Interestingly, this result is in agreement with the intuition of Oppenheimer and Snyder (Phys. Rev. 56: 456, 1939) too:“Physically such a singularity would mean that the expressions used for the energy-momentum tensor does not take into account some essential physical fact which would really smooth the singularity out. Further, a star in its early stages of development would not possess a singular density or pressure, it is impossible for a singularity to develop in a finite time.”

WHOLE ANALYSIS APPROACH FOR RESIDUE TIME DISTRIBUTION CURVE IN MULTI--STRAND CONTINUOUS CASTING TUNDISH

The study of residue time distribution(RTD) curve is usually one of the effective methods to estimate the flow characteristics in the continuous casting tundish.In the past,the analysis model for RTD curve of one-strand is usually applied to estimate the individual strand data in multi-strand tundish,but the result obtained by such a model can not agree with the physical fact sometimes. In this paper,an analysis model is proposed to analyze flow characteristics in multi-strand tundish. First,the whole RTD curve of multi-strand tundish is obtained by the individual strand data.Second, classic analysis model is applied to analyze the whole RTD curve of multi-strand tundish.Third, average residence time is chosen as a key parameter to estimate the similarity of flow characteristics of each strand in the multi-strand tundish.Such an analysis approach can avoid the occurrence of the negative dead zone.And the volume ratio of dead zone satisfies the physical facts.

Disability Studies in India: The Kerala Experience

The study of disability as difference is not new. Disability theory is currently divided between those who insist it reflects a physical fact affecting life quality, and those who believe disability is defined by social prejudice. Notwithstanding a dialogue spanning bioethical, medical and social scientific literatures, the differences between opposing views remains persistent. Moreover, the issue of disability is dogged by the controversy of ‘normality’ and ‘abnormality’. Disability as ‘difference’, is often used in this context.

Potential of very high resolution SAR for persistent scatterer interferometry in urban areas

Persistent scatterer interferometry (PSI) has matured to an established method for detection of large-scale and small-scale deformation phenomena in urban areas and of man-made infrastructure. Deformation regimes originating from oil, gas, or water extraction, storage of gas underground, CO2 sequestration, loading of dams and dykes, and mining activities are prominent examples for investigations that have been carried out successfully applying the PSI technique to ERS or ENVISAT data stacks. Due to the sparse spatial distribution of persistent scatterers (PSs) and the moderate resolution of the mentioned satellites it has usually not been possible to track down the source of scattering in detail. The use of PSs was also opportunistic, that is, the PSI monitoring of individual buildings or specific parts of infrastructure was not always been guaranteed. This situation changes dramatically if PSI is applied to very high resolution data obtained from modern radar satellites like TerraSAR-X or COSMO-Skymed. For example, TerraSAR-X is able to deliver images with a resolution of up to 1 m in azimuth and 0.6 m in slant range when operated in the so-called high-resolution spotlight mode with 300 MHz bandwidth. This kind of data provide much more details of single objects and at the same time much higher PS densities. Compared to ERS or ENVISAT type data, the PS density can increase by factors of 100–200 on the same area. This is caused by the physical fact that at higher resolution and shorter wavelength, small scatterers (e.g., trihedrals) show higher signal-to-clutter ratio. Often, several tens to more than a hundred PSs can be found on a single large building facade or roof. Thus, individual buildings and infrastructure can be monitored in terms of structural stress and seasonal deformation, which is also supported by the short revisiting time of only 11 days of TerraSAR-X. Besides on resolution, the density of these points also depends on additional acquisition parameters like incidence angle or polarization and also on the three-dimensional (3D) structure of the given scene, as regions of layover areas and shadow are closely related to the geometrical configuration. The dependence of PS density on these parameters is discussed in this article utilizing results of PSI analysis of different high-resolution TerraSAR-X spotlight data stacks. In addition to this increase of resolution, TerraSAR-X products benefit from a high absolute slant range georeferencing accuracy of 0.5–1 m, which supports a very precise absolute 3D localization of the PSs on the same order. Hence, the physical nature of a PS can be investigated in more detail helping the understanding of the scattering source of the man-made infrastructure. Results of 3D localization and deformation assessment on several test sites are presented in this article.

Geometrical simplification of the dipole–dipole interaction formula

Many students meet dipole–dipole potential energy quite early on when they are taughtelectrostatics or magnetostatics and it is also a very popular formula, featured inencyclopedias. We show that by a simple rewriting of the formula it becomes apparentthat, for example, by reorienting the two dipoles, their attraction can become exactly twiceas large. The physical facts are naturally known, but the transformation presented seems tounderline the geometrical features in a rather unexpected way. The consequence of thefeatures discussed is the so-called magic angle which appears in many applications. Thepresent discussion contributes to an easier introduction of this feature. We also discuss thepossibility of designing educational toys and try to suggest why this formula has notbeen written down frequently before this work. A similar transformation is alsopossible for the field of a single dipole. In this case we found one such formula onthe Web, but we could not find any published detailed discussion for this caseeither.

Fatigue growth prediction of elliptical cracks in welded joint structure: Hybrid and energy density approach

A hybrid weight function approach (HWFM) is presented for the fatigue life prediction of infinite body and welded joint structure containing elliptical cracks. A self-containing computer code has been developed for this purpose. Numerical computations were first conducted on cracked infinite body showing a physical fact, that the elliptical shape of the crack becomes circular during its evolution. The prediction of the fatigue crack growth shows that the present results are in perfect concordance with those reported in the literature. Then, numerical tests were carried out on two types of specimens of welded joint structure. The present results were compared to the experimental and predicted ones of other authors, demonstrating that the hybridization method is a powerful numerical technique, and that the SEDF approach (using the Sih’s law) is more valid for the critical cases of welded joints than the SIF approach (using the Paris law). A parametric study has been conducted on the stress ratio “ R” showing that the fatigue life to failure decreases with the increase of “ R”.

Analysis of Phase Distribution of Focused Light in High Numerical Aperture Systems

High numerical aperture focusing is becoming increasingly important for nanotechnology related applications. Rigorous, vector evaluation of the focused field, in such cases, is usually performed using the Richards-Wolf method which is based on the Debye approach. The resulting field is known to have a piecewise quasi planar phase. A corresponding result, produced by a Fresnel-Kirchhoff integral for aplanatic optical systems of medium and low numerical apertures, leads to the well known physical fact that a quadratic phase exists when the entrance pupil is not located at the front focal plane. Yet, the amplitudes produced in both ways are in a good agreement. In this work we investigated the difference, presented above, in a 2D system with the help of the Stratton-Chu diffraction integral. The amplitude obtained by the Stratton-Chu integral was quite similar to the classic results while the phase exhibited a quadratic behavior, with the quadratic coefficient depending on the numerical aperture of the optical system. For lower numerical apertures it approached the result obtained by the Fresnel-Kirchhoff integral while for higher numerical apertures it was approaching the Richards-Wolf result. A mathematical expression for the quadratic coefficient was derived and verified for various values of numerical aperture.

Spectral Automorphisms in Quantum Logics

In quantum mechanics, the Hilbert space formalism might be physically justified in terms of some axioms based on the orthomodular lattice (OML) mathematical structure (Piron in Foundations of Quantum Physics, Benjamin, Reading, 1976). We intend to investigate the extent to which some fundamental physical facts can be described in the more general framework of OMLs, without the support of Hilbert space-specific tools. We consider the study of lattice automorphisms properties as a “substitute” for Hilbert space techniques in investigating the spectral properties of observables. This is why we introduce the notion of spectral automorphism of an OML. Properties of spectral automorphisms and of their spectra are studied. We prove that the presence of nontrivial spectral automorphisms allow us to distinguish between classical and nonclassical theories. We also prove, for finite dimensional OMLs, that for every spectral automorphism there is a basis of invariant atoms. This is an analogue of the spectral theorem for unitary operators having purely point spectrum.

How Could There Be True Causal Claims Without There Being Special Causal Facts in the World?

Some philosophers of physics recently expressed their skepticism about causation (Norton 2003b, 2007). However, this is not new. The view that causation does not refer to any ontological category perhaps can be attributed to Hume, Kant and Russell. On the other hand, some philosophers (Wesley Salmon and Phil Dowe) view causation as a physical process and some others (Cartwright) view causation as making claims about capacities possessed by objects. The issue about the ontological status of causal claims involves issues concerning the ontological status of capacity, modality and dispositional claims. In this paper, my goal is to show that without engaging metaphysical debates about the ontological status of causal claims, it can be shown that we can objectively assign truth values to these statements. I argue that for causal claims to be objective we don't need to postulate the existence of special facts (specific to causal claims) in addition to ordinary physical facts described by physical theories. This, I think, is enough to justify the usefulness of this concept in certain branches (may be all) of science. Once this is achieved, there is no need to engage in unnecessary metaphysical debates. So, even if advanced physical theories don't mention this notion, causal reasoning can still be important in understanding the world not in the sense that science discovers special ontological category called causation but in the sense that we come to know certain facts about the world.