The core Oxford Calculators developed a science of kinematics in which the key concept was the "latitude of velocity." Based upon the concept of "latitude," the Calculators developed parts of a mathematical physics in deductive format that could be applied to quite various situations.

In this series of papers, I attempt to provide an answer to the question how the Babylonian scholars arrived at their mathematical theory of planetary motion. Paper I (de Jong in Arch Hist Exact Sci 73:1–37, 2019) was devoted to a study of system A theory of the outer planets. In this second paper, I will study system A theory of the planet Venus. All presently known ephemerides of Venus appear to have been written after 200 BC so that the (...) development of system A theory of Venus may have been a late development. On the other hand, there are several earlier texts in which the motion of Venus, going from one synodic phenomenon to the next one, is parametrized in quite some detail. At least six computational systems of Venus are known of which only two, systems A0 and A3, are genuine type-A systems. Both are based on the hypothesis that in exactly 1151 years Venus experiences 720 synodic phenomena of the same kind and that after this period of 1151 years Venus returns to exactly the same position in the sky. This period relation was probably derived from the observational fact that after 8 years Venus returns to a position in the zodiac that falls on average 2.5° short of its previous position. The study of the Babylonian planetary theory of Venus presented here will be primarily based on the system A3 theory of Venus because it is the most complete of the two systems. The parameters of the four step functions characterizing the system A3 model of the first and last appearances of Venus are known from previous studies of tablet BM 32599 (ACT 1050). Based on a database of synthetic observations of the first and last appearances (morning first, morning last, evening first and evening last) and the two stationary points (morning station and evening station) of Venus between 315 BC and 50 BC, I first discuss the observational material from the point of view of a Babylonian astronomer. This involves deriving synodic time intervals and synodic arcs from the observed dates and longitudes of Venus. Both vary with the position of Venus in the zodiac. This variation shows up most purely in the synodic arcs and synodic time intervals of Venus at its stations. The variation pattern of the synodic arcs and of the synodic time intervals at the first and last appearances of Venus differ considerably because they are strongly affected by atmospheric extinction and by the ecliptic latitude of Venus. A comparison of predictions of the first and last appearances of Venus computed according to system A3 with observations in the synthetic database shows that the models provide fairly accurate fits to the observations of evening last and morning first with typical standard deviations of about 2° but rather poor fits to the observations of morning last and evening first with typical standard deviations of about 7° and 4°. Quite surprisingly, it turns out that the morning first A3 model fits the observed longitudes of Venus at its stations almost perfectly, with standard deviations of about 1°. This suggests that observations of the stations of Venus must have been available to the Babylonian astronomer(s) who constructed the system A3 model of Venus and who computed the longitudes of Venus at its first and last appearances preserved in tablet BM 32599. This is quite puzzling because observations of the stations of Venus were definitely not part of the standard observing program of the Babylonian astronomers as we know it from the Astronomical Diaries. To resolve this problem, I propose that observations could have been made by some individual astronomer for his own use but that these observations never became part of the tradition of what was regularly observed and recorded in the Astronomical Diaries. It turns out that 25 years of observations of Venus (here illustrated for the years 203 BC to 178 BC) is sufficient for the construction of a system A model that perfectly fits the variation of the synodic arcs of Venus at its stations. By combining observed time intervals and known velocities of Venus, observations over this limited timespan can also be used to construct longitudes of Venus at its first and last appearances from previous known positions of Venus based on Normal Stars passages or from known positions at its stations. This is the only way in which positions of Venus at its first and last appearances can be determined because at its first and last appearances the sky is too bright for Normal Stars to be visible. I propose that the Babylonian system A3 models of Venus were based on longitudes constructed in this way. I finally suggest that the tablet, of which BM 32599 is the remainder, was filled line by line starting with a set of initial values in the bottom left-hand corner of the tablet and that the choice of these initial values was based on an observation of Venus at its evening station when it was exceptionally close to the Normal Star η Piscium in February 179 BC. Based on this choice of initial conditions, the tablet covers the years 403 BC to 170 BC and it may have been composed around 170 BC. It was probably computed with the purpose of creating a raster of longitudes with mazes of about 2.5° that could be used to predict future positions of Venus at its first or last appearance once a position at a previous first or last appearance was available. (shrink)

In this series of papers, I attempt to provide an answer to the question how the Babylonian scholars arrived at their mathematical theory of planetary motion. Paper I (de Jong in Arch Hist Exact Sci 73:1–37, 2019) was devoted to a study of system A theory of the outer planets. In this second paper, I will study system A theory of the planet Venus. All presently known ephemerides of Venus appear to have been written after 200 BC so that the (...) development of system A theory of Venus may have been a late development. On the other hand, there are several earlier texts in which the motion of Venus, going from one synodic phenomenon to the next one, is parametrized in quite some detail. At least six computational systems of Venus are known of which only two, systems A0 and A3, are genuine type-A systems. Both are based on the hypothesis that in exactly 1151 years Venus experiences 720 synodic phenomena of the same kind and that after this period of 1151 years Venus returns to exactly the same position in the sky. This period relation was probably derived from the observational fact that after 8 years Venus returns to a position in the zodiac that falls on average 2.5° short of its previous position. The study of the Babylonian planetary theory of Venus presented here will be primarily based on the system A3 theory of Venus because it is the most complete of the two systems. The parameters of the four step functions characterizing the system A3 model of the first and last appearances of Venus are known from previous studies of tablet BM 32599 (ACT 1050). Based on a database of synthetic observations of the first and last appearances (morning first, morning last, evening first and evening last) and the two stationary points (morning station and evening station) of Venus between 315 BC and 50 BC, I first discuss the observational material from the point of view of a Babylonian astronomer. This involves deriving synodic time intervals and synodic arcs from the observed dates and longitudes of Venus. Both vary with the position of Venus in the zodiac. This variation shows up most purely in the synodic arcs and synodic time intervals of Venus at its stations. The variation pattern of the synodic arcs and of the synodic time intervals at the first and last appearances of Venus differ considerably because they are strongly affected by atmospheric extinction and by the ecliptic latitude of Venus. A comparison of predictions of the first and last appearances of Venus computed according to system A3 with observations in the synthetic database shows that the models provide fairly accurate fits to the observations of evening last and morning first with typical standard deviations of about 2° but rather poor fits to the observations of morning last and evening first with typical standard deviations of about 7° and 4°. Quite surprisingly, it turns out that the morning first A3 model fits the observed longitudes of Venus at its stations almost perfectly, with standard deviations of about 1°. This suggests that observations of the stations of Venus must have been available to the Babylonian astronomer(s) who constructed the system A3 model of Venus and who computed the longitudes of Venus at its first and last appearances preserved in tablet BM 32599. This is quite puzzling because observations of the stations of Venus were definitely not part of the standard observing program of the Babylonian astronomers as we know it from the Astronomical Diaries. To resolve this problem, I propose that observations could have been made by some individual astronomer for his own use but that these observations never became part of the tradition of what was regularly observed and recorded in the Astronomical Diaries. It turns out that 25 years of observations of Venus (here illustrated for the years 203 BC to 178 BC) is sufficient for the construction of a system A model that perfectly fits the variation of the synodic arcs of Venus at its stations. By combining observed time intervals and known velocities of Venus, observations over this limited timespan can also be used to construct longitudes of Venus at its first and last appearances from previous known positions of Venus based on Normal Stars passages or from known positions at its stations. This is the only way in which positions of Venus at its first and last appearances can be determined because at its first and last appearances the sky is too bright for Normal Stars to be visible. I propose that the Babylonian system A3 models of Venus were based on longitudes constructed in this way. I finally suggest that the tablet, of which BM 32599 is the remainder, was filled line by line starting with a set of initial values in the bottom left-hand corner of the tablet and that the choice of these initial values was based on an observation of Venus at its evening station when it was exceptionally close to the Normal Star η Piscium in February 179 BC. Based on this choice of initial conditions, the tablet covers the years 403 BC to 170 BC and it may have been composed around 170 BC. It was probably computed with the purpose of creating a raster of longitudes with mazes of about 2.5° that could be used to predict future positions of Venus at its first or last appearance once a position at a previous first or last appearance was available. (shrink)

A theoretical and experimental search for the so-called Weyssenhof behavior of a spinning particle, due to the noncollinearity of its velocity and momentum, has been undertaken. Z-independent solutions of Maxwell's equations had previously been produced with a nonzeros z component of the Poynting vector; indeed, Imbert emphasized that the spatial exponential damping of Fresnel's evanescent wave would entail a nonzero value for the integral ε εs z dx dy. Excellent experimental verifications of this point have been obtained by Imbert. (...) Besides having noz component of their momentum, the energy-momentum quanta inside Fresnel's evanescent wave have typical tachyon properties, the imaginary character of theiry component (normal to the reflecting surface) entailing that (in units such thatc=1) theirx component islarger than the energy quanta. Imbert is now planning experiments to test these interesting properties. Thus, the two main aspects of noncollinearity of velocity and momentum of spinning particles would be displayed. (shrink)

In a recent article [1], Wiseman has proposed the use of so-called weak measurements for the determination of the velocity of a quantum particle at a given position, and has shown that according to quantum mechanics the result of such a procedure is the Bohmian velocity of the particle. Although Bohmian mechanics is empirically equivalent to variants based on velocity formulas different from the Bohmian one, and although it has been proven that the velocity in Bohmian (...) mechanics is not measurable, we argue here for the somewhat paradoxical conclusion that Wiseman’s weak measurement procedure indeed constitutes a genuine measurement of velocity in Bohmian mechanics. We reconcile the apparent contradictions and elaborate on some of the different senses of measurement at play here. (shrink)

The Einstein law of velocity addition is well-known. Consider three inertial reference frames S, K, and M, with X axes parallel in the same sense. Let K have velocity v1 along the X axis of S, and M have velocity v2 along the X axis of K. Then, according to the Einstein formula, the velocity v3 of M along the X axis of S is If v2 is the velocity of an object at rest in (...) M as measured by an observer in K, then v3 is the velocity of the same object as measured by an observer in S. The formula is valid for a change in reference frame of the observer. (shrink)

Some authors have recently arguedthat an objects velocity is logicallyindependent of its locations throughout time.Their aim is to deny the Russellianview that motion is merely a change oflocation, and to promote a rival account onwhich the connection between velocities andtrajectories is provided by the laws ofnature. I defend the Russellian view of motionagainst these attacks.

This paper is concerned with the interpretation of velocity eigenstates for unstable quantons, their relationship to space-like momentum eigenstates for such quantons and the explanation of Shirokov’s contracting lifetimes for such velocity eigenstates. It is an elaboration of a portion of the authors earlier study.

Bošković’s distinction between two kinds of velocities – velocity in the first act, or potential velocity, and velocity in the second act, or actual velocity – is considered in respect to the concept of instantaneous velocity as defined by calculus differentialis. Contrary to the seeming inconsistency of Bošković’s duality of velocities and the concept of instantaneous velocity, due to a critical examination of logical and methodological foundations of the calculus, the article shows that the (...) duality of velocities is consistent with the interpretations of instantaneous velocity given by Oresme, Euler and Maclaurin, as with the definition of instantaneous velocity according to the rigorous Cauchyan founding of the calculus. Bošković’s duality of velocities is also shown to be consistent with Aristotelian-scholastic doctrine of potentiality and actuality, especially in its domain related to the nature of continuous motion. (shrink)

In recent years, the debate on emotions has been influenced by postconstructionist research, particularly the use of performativity as a key concept. According to Judith Butler (1993, 1997) the construction of emotions is a process open to constant change and redefinition. The final result of emotionlanguage “natural” development is what is known as technoscience. New ways of naming emotions have emerged within technoscience. In our research on the use of information and communication technologies (ICT) by cyber-café and call shop users, (...) we came to understand how these technologies are significant in those users’ daily life. The emphasis will be on analyzing emotions related to the use of ICT in the aforementioned settings. Using the concept of performance (Butler, 1990), we will explore how narratives create a need for particular emotions, which did not exist before they were performed. To understand this performance, we use an ad hoc tool called Membership Categorization Analysis (MCA) as it is used by the Manchester School. Analysis has revealed the existence of a membership category in which velocity is salient as performance. This ‘velocity’ seems to follow the evolution of technoscience in the social sciences. We will observe velocity in the context created by two concepts, Donna Haraway’s (1990) cyborg and Alessandro Baricco’s (2007) mutant. (shrink)

Some variants in the materials related to the planetary latitudes, including computational procedures, underlying parameters, numerical tables, and so on, may be addressed in the corpus of the astronomical tables preserved from the medieval Islamic period, which have already been classified comprehensively by Van Dalen. Of these, the new values obtained for the planetary inclinations and the longitude of their ascending nodes might have something to do with actual observations in the period in question, which are the main concern of (...) this paper. The paper is in the following sections. In the first section, Ptolemy’s latitude models and their reception in Islamic astronomy are briefly reviewed. In the next section, the medieval non-Ptolemaic values for the inclinations and the longitudes of the nodal lines are introduced. The paper ends with the discussion and some concluding remarks. The derivation of the underlying inclination values from the medieval planetary latitude tables and determining the accuracy of the tables are postponed to “Appendix” in the end of the paper. (shrink)

The central nervous system uses feedback processes that occur at multiple time scales to control interactions with the environment. The long-latency response is the fastest process that directly involves cortical areas, with a motoneuron response measurable 50 ms following an imposed limb displacement. Several behavioral factors concerning perturbation mechanics and the active role of muscles prior or during the perturbation can modulate the long-latency response amplitude in the upper limbs, but the interactions among many of these factors had not been (...) systematically studied before. We conducted a behavioral study on thirteen healthy individuals to determine the effect and interaction of four behavioral factors – background muscle torque, perturbation direction, perturbation velocity, and task instruction – on the LLRa evoked from the flexor carpi radialis and extensor carpi ulnaris muscles after velocity-controlled wrist displacements. The effects of the four factors were quantified using both a 0D statistical analysis on the average perturbation-evoked EMG signal in the period corresponding to an LLR, and using a timeseries analysis of EMG signals. All factors significantly modulated LLRa, and their combination nonlinearly contributed to modulating the LLRa. Specifically, all the three-way interaction terms that could be computed without including the interaction between instruction and velocity significantly modulated the LLR. Analysis of the three-way interaction terms of the 0D model indicated that for the ECU muscle, the LLRa evoked when subjects are asked to maintain their muscle activation in response to the perturbations was greater than the one observed when subjects yielded to the perturbations, but this effect was not measured for muscles undergoing shortening or in absence of background muscle activation. Moreover, higher perturbation velocity increased the LLRa evoked from the stretched muscle in presence of a background torque, but no effects of velocity were measured in absence of background torque. Also, our analysis identified significant modulations of LLRa in muscles shortened by the perturbation, including an interaction between torque and velocity, and an effect of both torque and velocity. The time-series analysis indicated the significance of additional transient effects in the LLR region for muscles undergoing shortening. (shrink)

This article surveys measurements of celestial (chiefly solar) altitudes documented from twelfth- and thirteenth-century Latin Europe. It consists of four main parts providing (i) an overview of the instruments available for altitude measurements and described in contemporary sources, viz. astrolabes, quadrants, shadow sticks, and the torquetum; (ii) a survey of the role played by altitude measurements in the determination of geographic latitude, which takes into account more than 70 preserved estimates; (iii) case studies of four sets of measured solar (...) altitudes in twelfth-century Latin sources; (iv) an in-depth discussion of the evidence relating to altitude measurements performed in Paris in the period 1281–1290. The findings from the last part indicate that by the end of the thirteenth century Parisian astronomer had developed rigorous standards of observational practice in which altitudes were typically measured to a precision of minutes of arc and with a level of accuracy higher than ± 0;5°, and sometimes exceeding ± 0;1°. (shrink)

Using a model quantum clock, I show how the velocity of a relativistic particle can be measured. The results are used to analyse the long-standing problem of the velocity..

The connection between the Minkowskian geometry of the plane and its projective geometry is exemplified by the Einstein velocity addition theorem.

There are indications that simple reaction time might have slowed in Western countries, based on both cohort- and multi-study comparisons. A possible limitation of the latter method in particular is measurement error stemming from methods variance, which results from the fact that instruments and experimental conditions change over time and between studies. We therefore set out to measure the simple auditory reaction time (SRT) of 7,081 individuals (2,997 males and 4,084 females) born in Sweden 1959-1985 (subjects were aged between 27 (...) and 54 years at time of measurement). Depending on cut-offs and adjustment for ageing related slowing on SRT, the data suggest that SRT has increased between 3 and 16 ms in the 27 birth years covered in the present sample. The slowing is unlikely to be explained by attrition, as evaluated by comparing the general intelligence × birth-year interactions and standard deviations for both male participants and dropouts, utilizing military conscript cognitive ability data. The present result is consistent with previous studies employing alternative methods, and may result from several synergistic factors, such as possible recent micro-evolutionary trends favouring lower g in Sweden and the effects of industrially produced neurotoxic substances on peripheral nerve conduction velocity. (shrink)

Irregularity may occur on the earth’s surface in the form of mountains due to the imperfection of the earth’s crust. To explore the influence of horizontally polarized shear waves on mountains, we considered the fluid-saturated porous medium over an orthotropic semi-infinite medium with rigid and soft mountain surfaces for wave propagation. The mountain surface is defined mathematically as a periodic function of the time domain. The physical interpretation of materials’ structure has been explained in rectangular Cartesian coordinate system originated at (...) the contact interface of layer and half-space. The displacement of the mountains has been derived by solving energy equations analytically. The influence of rigid and soft mountain surfaces on the phase velocity of shear waves has been demonstrated graphically. (shrink)

Absolute velocities in Newtonian mechanics are commonly regarded as unmeasurable. Roberts (Br J Philos Sci 59(2):143–168, 2008) provides a justification for this thesis which appeals to the observational indistinguishability of boost-related models of Newtonian mechanics. Middleton and Murgueitio Ramírez (Australas J Philos, 2020) criticise his argumentation by pointing out that his analysis of the notion of measurement is too restrictive, and that, under a weaker analysis (based on counterfactuals), absolute velocities are measurable. Jacobs (Australas J Philos, 2020) opposes their view, (...) arguing that, on a properly formulated counterfactual-based account of measurement, absolute velocities are unmeasurable. However, in his argument, observational indistinguishability plays no role, even though, intuitively, it is very relevant for the issue of (un)measurability. This paper’s aim is to bring observational indistinguishability back to this discussion. I build upon the observation that there is an analogy between possible views on knowledge and justification on the one hand, and on measurement on the other. In particular, I explore the distinction between externalist and internalist approaches. Counterfactual-based accounts are all externalist, whereas the observational indistinguishability of boost-related models becomes relevant if we are interested in an internalist concept of measurement. (shrink)

The experimental situation proposed by Fisk consists of a light source in a system S which sends a signal to two observers, one located at a distance x1 from the source and at rest in S, and the other moving away from the source at a speed v, in such a manner that its position coincides with the point x1 when the light signal reaches x1. The moving observer's coordinate system may be designated as S'. Further, it is assumed that (...) there is a half-silvered mirror associated with the moving observer, and that the light signal reaches the mirror so that part of the signal is received by the S' observer and part is received by the stationary S observer; each observer considers the light to reach him when he is at point x1. (shrink)

In connection with another article by the author, we show how it might be possible to travel faster than the speed of light. We show that for clocks and rods moving faster than the speed of light, we get instead of “time dilation” and “Lorentz contraction,” respectively, “time contraction” and “Lorentz expansion,” respectively. It is shown that this paper is in confirmation with earlier articles dealing with this subject.

이 논문은 俛宇(郭鍾錫, 1846-1919)의 사단칠정설을 ‘氣의 經緯說’에서 주목하여 조명하고 있다. 논문에 따르면, 면우의 경위설은 ‘理自發’과 ‘性發爲情’을 사단과 칠정에 고루 적용하면서도 四七양자를 구별하는 논리적 장치였다. 그는 이 이론에 입각하여 사단과 칠정의 의미에 대해 새로운 이해를 제시하였고 나아가 도덕감정 이론에서 의미 있는 진전을 보여주었다고 이 논문은 주장한다. 이 논문은 먼저 農巖의 경위설에 대한 면우의 비판과 계승을 살펴보고 그 의의를 분석한다. 면우에 따르면, 농암의 이론은 성발위정에 위배될 뿐 아니라 칠정의 도덕적 가능성을 간과하는 것이었다. 그래서 그는 새로운 경위설을 제시하여 그 오류들을 수정하고 사단칠정의 구조를 (...) 재정립하였다. 이어서 이 논문은 면우가 四端不中節의 문제를 해결해가는 과정과 그 의의를 살펴보고 있다. 면우는 사단의 무오류성을 적극 천명하고 측은지심의 무한 확장을 주장하였다. 마지막으로 이 논문은 그가 사단의 완전성에 대한 믿음에 기초하여 達道의 七情을 강조하고 칠정의 도덕적 가능성을 천명한 것을 고찰한다. 그리고 면우의 사단칠정론이 공공의 감정론으로 귀결된다는 점에 주목한다. (shrink)

We investigate the novel problem of what happens in special relativity and in relativistic field theories whenthree-dimensional space is quantized. First we examine the equation for elastic waves on a linear chain, the simplest example of a quantized medium, and propose, on its analogy, a nonlinearp-k relationp=ħk(sinhkl)/kl for light and material waves. Here,kl is a new variable which represents the space-quantization effect on the plane wave of wave numberk=|k|. (Note thatkl=0 givesp=ħk.) This relation makes the light velocity in vacuum (...) dependent onkl. We postulate, however, that the phase and group velocities of each individual light wave are still invariant, and try to generalize special relativity to the case ofkl ≠ 0. This can be simply done if the invariance ofkl is assumed. Our results suggest that “localization” might be a relative concept. One interesting consequence of our proposal is that relativistic field theories become automatically finite. This comes out without violating unitarity or causality. A precise measurement of velocities of high-energy photons or massive particles is desirable for checking our proposal. (shrink)

Agendanken experiment is proposed for distinguishing between two models accounting for the macroscopic arrow of time. The experiment involves the veloeity revesal of components of an isolated system, and the two models give contrasting predictions as to its behavior.