The Emergence of “cyclic” tables in Indian Astronomy in the seventeenth century: Haridatta's Jagadbhusaṇa and its Islamic inspiration

Indian planetary tables can be classified into several distinct types with respect to their underlying mathematicbal structure. One of these, the so-called “cyclic” scheme was inspired by goal-year periods introduced via Islamic channels no later than the early seventeenth century. The first set of such cyclic planetary tables is the Jagadbhusaṇa of Haridatta, composed in Mewar, Rajasthan with an epoch of 31 March 1638. This substantial work, spreading over more than 100 folia in some manuscripts, computes the true longitudes of the planets in a manner similar to those in the Babylonian goal-year texts, Ptolemy, and al- Zarqali. We will consider the inspiration from these earlier sources and how they are incorporated into a distinctly Indian context, with respect to mathematical structure, astronomical foundation, and layout and arrangement of the data in the tabular format

The transmission of Arabic astronomical tables in Sanskrit, Latin, and Chinese. An early step in the internationalization of science?: Introduction

International audienceFrom 2008 to 2013, an international research project entitled History of Numerical Tables supported by the French Agence Nationale de la Recherche under the directorship of Dominique Tournès gathered specialists from a spectrum of scientific traditions. These scholars, ranging from experts in cultures of inquiry at the advent of literacy to the contemporary digital era focused on the study of numerical tables. A key question that arose from the many interactions of this group concerned the transmission and circulation of numerical tables. Preliminary attempts to understand this transmission resulted in the organization of a two-day workshop on the 24th and 25th of October 2012 in Paris, France. The theme was The transmission of Arabic astronomical tables in Sanskrit, Latin, and Chinese: an early step in the internationalization of science?. After highlighted and sharing themes in these areas related to the transmission of numerical tables, the participants wrote up their contributions for this special issue of SUHAYL

On the continuum fallacy: is temperature a continuous function?

It is often argued that the indispensability of continuum models comes from their empirical adequacy despite their decoupling from the microscopic details of the modelled physical system. There is thus a commonly held misconception that temperature varying across a region of space or time can always be accurately represented as a continuous function. We discuss three inter-related cases of temperature modelling — in phase transitions, thermal boundary resistance and slip flows — and show that the continuum view is fallacious on the ground that the microscopic details of a physical system are not necessarily decoupled from continuum models. We show how temperature discontinuities are present in both data (experiments and simulations) and phenomena (theory and models) and how discontinuum models of temperature variation may have greater empirical adequacy and explanatory power. The conclusions of our paper are: a) continuum idealisations are not indispensable to modelling physical phenomena and both continuous and discontinuous representations of phenomena work depending on the context; b) temperature is not necessarily a continuously defined function in our best scientific representations of the world; and c) that its continuity, where applicable, is a contingent matter. We also raise a question as to whether discontinuous representations should be considered truly de-idealised descriptions of physical phenomena

Are mathematical explanations causal explanations in disguise?

There is a major debate as to whether there are non-causal mathematical explanations of physical facts that show how the facts under question arise from a degree of mathematical necessity considered stronger than that of contingent causal laws. We focus on Marc Lange’s account of distinctively mathematical explanations to argue that purported mathematical explanations are essentially causal explanations in disguise and are no different from ordinary applications of mathematics. This is because these explanations work not by appealing to what the world must be like as a matter of mathematical necessity but by appealing to various contingent causal facts

Not so distinctively mathematical explanations: topology and dynamical systems

So-called ‘distinctively mathematical explanations’ (DMEs) are said to explain physical phenomena, not in terms of contingent causal laws, but rather in terms of mathematical necessities that constrain the physical system in question. Lange argues that the existence of four or more equilibrium positions of any double pendulum has a DME. Here we refute both Lange’s claim itself and a strengthened and extended version of the claim that would pertain to any n-tuple pendulum system on the ground that such explanations are actually causal explanations in disguise and their associated modal conditionals are not general enough to explain the said features of such dynamical systems. We argue and show that if circumscribing the antecedent for a necessarily true conditional in such explanations involves making a causal analysis of the problem, then the resulting explanation is not distinctively mathematical or non-causal. Our argument generalises to other dynamical systems that may have purported DMEs analogous to the one proposed by Lange, and even to some other counterfactual accounts of non-causal explanation given by Reutlinger and Rice

Not so distinctively mathematical explanations: topology and dynamical systems

So-called ‘distinctively mathematical explanations’ (DMEs) are said to explain physical phenomena, not in terms of contingent causal laws, but rather in terms of mathematical necessities that constrain the physical system in question. Lange argues that the existence of four or more equilibrium positions of any double pendulum has a DME. Here we refute both Lange’s claim itself and a strengthened and extended version of the claim that would pertain to any n-tuple pendulum system on the ground that such explanations are actually causal explanations in disguise and their associated modal conditionals are not general enough to explain the said features of such dynamical systems. We argue and show that if circumscribing the antecedent for a necessarily true conditional in such explanations involves making a causal analysis of the problem, then the resulting explanation is not distinctively mathematical or non-causal. Our argument generalises to other dynamical systems that may have purported DMEs analogous to the one proposed by Lange, and even to some other counterfactual accounts of non-causal explanation given by Reutlinger and Rice

Review of J. M. Delire (ed.), Astronomy and Mathematics In Ancient India (Leuven, etc.: Peeters, 2012)

Book review

Review of: Dr Sita Sundar Ram, Bījapallava of Kṛṣṇa Daivajña: Algebra in Sixteenth Century India. A Critical Study

Book review