On the history of the Euclidean Steiner tree problem

The history of the Euclidean Steiner tree problem, which is the problem of constructing a shortest possible network interconnecting a set of given points in the Euclidean plane, goes back to Gergonne in the early nineteenth century. We present a detailed account of the mathematical contributions of some of the earliest papers on the Euclidean Steiner tree problem. Furthermore, we link these initial contributions with results from the recent literature on the problem.     

On Kepler's awareness of the problem of experimental error

This paper is an account of Kepler's explicit awareness of the problem of experimental error. As a study of the Astronomia nova shows, Kepler exploited his awareness of the occurrences of experimental errors to guide him to the right conclusion. Errors were thus employed, so to speak, perhaps for the first time, to bring about a major physical discovery: Kepler's laws of planetary motion. ‘Know then’, to use Kepler's own words, ‘that errors show us the way to truth.’ With a survey of Kepler's revolutionary contribution to optics, the paper demonstrates that Kepler's awareness of the problem of experimental error extended beyond discrepancies between calculations and observations to types of error which pertain to observations and instruments. It emerges that Kepler's belief in the unity of knowledge and physical realism, facilitated—indeed created—the right philosophical posture for comprehending the problem of error in an entirely novel way.     

Ergastoplasmic granules,cytophysiological adaptation of the locusts corpora cardiaca to migratory flights?

Summary A good correlation was shown between the presence of ergastoplasmic granules in the glandular cells of the locusts corpora cardiaca and the flight activity of these insects.Research supported by grants A.T.P. No. 1831 and E.R.A. No. 620 from the Centre National de la Recherche Scientifique, French Ministry.     

On the problem of linear incorporation of amino acids into cell protein

Summary Incorporation of amino acids into mammalian cell protein shows immediate linear kinetics when measured at intervals as small as 5 sec. Free amino acids equilibrate instantaneously across the cell membrane, acting as the precursor supply. Glycine, which does not initially show linear kinetics, may have a significant endogenous precursor supply, but this is not the acid-soluble pool.Acknowledgments. I thank the University of Aberdeen Medical Faculty Endowment Fund for support, and Mrs J. Robertson for technical assistance.     

On de Movire's solutions of the problem of duration of play 1708–1718

Summary I attempt to solve the enigma of how de Moivre derived his recursion formulae and the formulae for the probability of a duration of exactly n games. I believe that he obtained the latter probability by differencing Nicholas Bernoulli's formula for the probability of ruin and that he obtained the recursion formulae by a simple algebraic method and induction.     

Newton's solution of the one-body problem

Communicated by C. A. Wilson     

Galileo and the problem of infinity

During the period before the Greek revolution of 1821, and especially during the years between 1750 and 1821, there were two ways in which European scientific thought was propagated in Greece. The first is traditional. It comes from ancient Greece and, through Byzantium, reaches the period before the Greek revolution. It makes known the thought of Aristotle, Democrititus, and others on ‘natural philosophy’. The second way comes from Europe. The Greek scholars of the period before the Greek revolution, and especially at the end of the eighteenth century, tried to bring to and propagate in Greece the spirit ofthe European Enlightenment, They tried to make known to the Greek people the scientific achievements of Newton, Descartes, Lavoisier, and Laplace. Scientific knowledge is an important weapon against superstition, and Greek students had to learn about science to become free persons in an independent Greek state.     

Behaviour and random mating

Résumé Des expériences portant sur le comportement sexuel chez plusieurs espèces, telles que la drosophile et la souris nous montrent que l'hypothèse qu'elles s'accouplent par hasard, hypothèse dont on fait état assez fréquemment dans la génétique des populations, n'est valable dans cadre des populations naturelles qu'avec de sérieuses restrictions.

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This work was supported by the Australian Research Grants Committee.     

Pure science and the problem of progress

How should we understand scientific progress? Kuhn famously discussed science as its own internally driven venture, structured by paradigms. He also famously had a problem describing progress in science, as problem-solving ability failed to provide a clear rubric across paradigm change—paradigm changes tossed out problems as well as solving them. I argue here that much of Kuhn’s inability to articulate a clear view of scientific progress stems from his focus on pure science and a neglect of applied science. I trace the history of the distinction between pure and applied science, showing how the distinction came about, the rhetorical uses to which the distinction has been put, and how pure science came to be both more valued by scientists and philosophers. I argue that the distinction between pure and applied science does not stand up to philosophical scrutiny, and that once we relinquish it, we can provide Kuhn with a clear sense of scientific progress. It is not one, though, that will ultimately prove acceptable. For that, societal evaluations of scientific work are needed.     

Beating the random walk in Central and Eastern Europe

We compare the accuracy of vector autoregressive (VAR), restricted vector autoregressive (RVAR), Bayesian vector autoregressive (BVAR), vector error correction (VEC) and Bayesian error correction (BVEC) models in forecasting the exchange rates of five Central and Eastern European currencies (Czech Koruna, Hungarian Forint, Slovak Koruna, Slovenian Tolar and Polish Zloty) against the US Dollar and the Euro. Although these models tend to outperform the random walk model for long‐term predictions (6 months ahead and beyond), even the best models in terms of average prediction error fail to reject the test of equality of forecasting accuracy against the random walk model in short‐term predictions. Copyright © 2005 John Wiley & Sons, Ltd.     

Galileo and the problem of concentric circles

In 1892, Eliakim Hastings Moore accepted the task of building a mathematics department at the University of Chicago. Working in close conjuction with the other original department members, Oskar Bolza and Heinrich Maschke, Moore established a stimulating mathematical environment not only at the University of Chicago, but also in the Midwest region and in the United States in general. In 1893, he helped organize an international congress of mathematicians. He followed this in 1896 with the organization of the Midwest Section of the New York City-based American Mathematical Society. He became the first editor-in-chief of the Society's Transactions in 1899, and rose to the presidency of the Society in 1901.     

Chemotactic and random movement of cord-blood granulocytes

Summary Chemotactic responsiveness and random movement of cord-blood granulocytes were studied with a modified Boyden's method. Cord-blood granulocytes were less active chemotactically than granulocytes from healthy children and adults, whereas the random filter movement of the cells from all three sources was about the same. In cord sera, concentrations of cell directed chemotaxis inhibitors were equal to those in sera from other age groups. Compared with the situation in healthy children and adults, the generation of chemotactic factors in cord-blood sera was impaired. This impairment was not related to an increased activity of chemotactic factor inactivators. Measurement of the cyclic nucleotide levels in granulocytes from cord-blood and from children belonging to various age groups revealed that the cord granulocytes have significantly lower concentrations of cAMP and cGMP, which could have been responsible for the decreased chemotactic responsiveness.     

Isaac Newton and the problem of the earth's shape

In this article I discuss the theory of the earth's shape presented by Isaac Newton in Book III of his Principia. I show that the theory struck even the most reputable continental mathematicians of the day as incomprehensible. I examine the many obstacles to understanding the theory which the reader faced — the gaps, the underived equations, the unproven assertions, the dependence upon corollaries to practically incomprehensible theorems in Book I of the Principia and the ambiguities of these corollaries, the conjectures without explanations of their bases, the inconsistencies, and so forth. I explain why these apparent drawbacks are, historically considered, strengths of Newton's theory of the earth's shape, not weaknesses.     

Chemotactic and random movement of cord-blood granulocytes

Chemotactic responsiveness and random movement of cord-blood granulocytes were studied with a modified Boyden's method. Cord-blood granulocytes were less active chemotactically than granulocytes from healthy children and adults, whereas the random filter movement of the cells from all three sources was about the same. In cord sera, concentrations of cell directed chemotaxis inhibitors were equal to those in sera from other age groups. Compared with the situation in healthy children and adults, the generation of chemotactic factors in cord-blood sera was impaired. This impairment was not related to an increased activity of chemotactic factor inactivators. Measurement of the cyclic nucleotide levels in granulocytes from cord-blood and from children belonging to various age groups revealed that the cord granulocytes have significantly lower concentrations of cAMP and cGMP, which could have been responsible for the decreased chemotactic responsiveness.