Giora Hon

Towards a typology of experimental errors: An epistemological view

Abstract This paper is concerned with the problem of experimental error. The prevalent view that experimental errors can be dismissed as a tiresome but trivial blemish on the method of experimentation is criticized. It is stressed that the occurrence of errors in experiments constitutes a permanent feature of the attempt to test theories in the physical world, and this feature deserves proper attention. It is suggested that a classification of types of experimental error may be useful as a heuristic device in studying the nature of these errors. However, the standard classification of systematic and random errors is mathematically based does not focus on the causes of the errors, their origins, or the contexts in which they arise. A new typology of experimental errors is therefore proposed whose criterion is epistemological. This typology reflects the various stages that can be discerned in the execution of an experiment, each stage constituting a category of a certain type of experimental error. The proposed classification consists of four categories which are illustrated by historical cases.

On Kepler's awareness of the problem of experimental error

Summary This paper is an account of Keplers 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: Keplers laws of planetary motion. ‘Know then’, to use Keplers own words, ‘that errors show us the way to truth.’ With a survey of Keplers revolutionary contribution to optics, the paper demonstrates that Keplers 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 Keplers 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.

Geometry of Light and Shadow: Francesco Maurolyco (1494–1575) and the Pinhole Camera

Summary In his Theoremata de lumine, et umbre (1521), Francesco Maurolyco (1494–1575) discussed, inter alia, the problem of the pinhole camera. Maurolyco outlined a framework based on Euclidean geometry in which he applied the rectilinear propagation of light to the casting of shadow on a screen behind a pinhole. We limit our discussion to the problem of how the image behind an aperture is formed, and follow the way Maurolyco combined theory with instrument to solve the problem of the projection of light through small apertures. We show that Maurolyco not only reformed the classical sources which, he thought, were no longer the authoritative code of textual knowledge, but also established with the dioptra a novel linkage of method, theory, and instrument. He thereby demonstrated the importance of optics to the science of astronomy.

Kepler's Move from Orbs to Orbits: Documenting a Revolutionary Scientific Concept

This study of the concept of orbit is intended to throw light on the nature of revolutionary concepts in science. We observe that Kepler transformed theoretical astronomy that was understood in terms of orbs [Latin:orbes](spherical shells to which the planets were attached) and models (called hypotheses at the time), by introducing a single term, orbit [Latin:orbita], that is, the path of a planet in space resulting from the action of physical causes expressed in laws of nature. To demonstrate the claim that orbit is a revolutionary concept we pursue three lines of argument. First we trace the origin of the term;second, we document its development and specify the meaning of the novel term as it was introduced into astronomy by Kepler in his Astronomia nova (1609). Finally, in order to establish in what sense the concept is revolutionary, we pay attention to the enduring impact that the concept has had on the relevant sciences, in this case astronomy and indeed physics. We claim that orbit is an instance of a revolutionary concept whose provenance and use can provide the insights we are seeking.

Going amiss in experimental research

Introduction Giora Hon, Jutta Schickore, and Friedrich Steinle Error as an object of study Giora Hon Error: The long neglect, the one-sided view, and a typology Jutta Schickore Error as historiographical challenge: The infamous globule hypothesis Learning from error Erez Braun and Shimon Marom Learning without error Giora Hon Living extremely flat: the life of automaton John von Neumanns conception of error of (in)animate systems Concepts and dead ends Hans-Jorg Rheinberger Experimental reorientations Karin Nickelsen and Gerd Grasshoff Concepts from the bench: Krebs and the Urea cycle Friedrich Steinle How experiments make concepts fail: Faraday and magnetic curves Kostas Gavroglu A pioneer who never got it right: James Dewar and the elusive phenomena of cold Instrumental artifacts Wendy Parker Distinguishing real results from instrumental artifacts: The case of the missing rain Jan Frercks Going right and making it wrong: The reception of Fizeaus ether-drift experiment of 1859 Allan Franklin The spectrum of ss decay: continuous or discrete? A variety of errors in experimental investigation Surprise and puzzlement Christoph Hoffmann The scent of filth: Experiments, waste, and the set-up Ursula Klein In the thick of organic matter Epilogue Giora Hon, Jutta Schickore, and Friedrich Steinle

Searching for Asses, Finding a Kingdom: The Story of the Invention of the Scanning Tunnelling Microscope (STM)

Summary We offer a novel historical-philosophical framework for discussing experimental practice which we call ‘Generating Experimental Knowledge’. It combines three different perspectives: experimental systems, concept formation, and the pivotal role of error. We then present an historical account of the invention of the Scanning Tunnelling Microscope (STM), or Raster-Tunnelmikroskop, and interpret it within the proposed framework. We show that at the outset of the STM project, Binnig and Rohrer—the inventors of the machine—filed two patent disclosures; the first is dated 22 December 1978 (Switzerland), and the second, two years later, 12 September 1980 (US). By studying closely these patent disclosures, the attempts to realize them, and the subsequent development of the machine, we present, within the framework of generating experimental knowledge, a new account of the invention of the STM. While the realization of the STM was still a long way off, the patent disclosures served as blueprints, marking the changes that had to be introduced on the way from the initial idea to its realization.

Kepler's Optical Part of Astronomy (1604): Introducing the Ecliptic Instrument

The year 2009 marks the 400th anniversary of the publication of one of the most revolutionary scientific texts ever written. In this book, appropriately entitled, Astronomia nova, Johannes Kepler (15711630) developed an astronomical theory which departs fundamentally from the systems of Ptolemy and Copernicus. One of the great innovations of this theory is its dependence on the science of optics. The declared goal of Kepler in his earlier publication, Paralipomena to Witelo whereby The Optical Part of Astronomy is Treated (Ad Vitellionem Paralipomena, quibus astronomiae pars optica traditvr, 1604), was to solve difficulties and expose illusions astronomers face when conducting astronomical observations with optical instruments. To avoid observational errors that had plagued the antiquated measuring techniques for calculating the apparent diameter and angular position of the luminaries, Kepler designed a novel device: the ecliptic instrument. In this paper we seek to shed light on the role optical instruments play in Keplers scheme: they impose constraints on theory, but at the same time render astronomical knowledge secure. To get a comprehensive grasp of Keplers astonishing achievements it is required to widen the approach to his writings and study Kepler not only as a mathematico-physical astronomer, but also as a designer of instruments and a practicing observer.

Celestial charts and spherical triangles : The unifying power of Symmetry

It comes as a surprise to many scholars that before 1794 the term symmetry (or symmetric) was not used in its modern sense; rather, beginning in Antiquity, it meant either commensurate (as in Euclid’s Elements) or well proportioned (as in Vitruvius’s De architectura). In astronomy the term symmetry is rarely encountered before the end of the eighteenth century with the notable exceptions of Copernicus and Galileo but, as we have shown, they do not invoke the modern sense of this term. In 1794 Adrien-Marie Legendre (1752–1833) introduced a modern definition of symmetry in his Éléments de géométrie that applied to geometric solids: “Two equal solid angles which are formed (by the same plane angles) but in the inverse order will be called angles equal by symmetry, or simply symmetric angles”, and then:

Unpacking "For Reasons of Symmetry": Two Categories of Symmetry Arguments

Hermann Weyl succeeded in presenting a consistent overarching analysis that accounts for symmetry in (1) material artifacts, (2) natural phenomena, and (3) physical theories. Weyl showed that group theory is the underlying mathematical structure for symmetry in all three domains. But in this study Weyl did not include appeals to symmetry arguments which, for example, Einstein expressed as “for reasons of symmetry” (wegen der Symmetrie; aus Symmetriegründen). An argument typically takes the form of a set of premises and rules of inference that lead to a conclusion. Symmetry may enter an argument both in the premises and the rules of inference, and the resulting conclusion may also exhibit symmetrical properties. Taking our cue from Pierre Curie, we distinguish two categories of symmetry arguments, axiomatic and heuristic; they will be defined and then illustrated by historical cases.

Hertz's study of propagation vs. Rutherford's study of structure : Two modes of experimentation and their theoretical underpinnings

Hertz’s experimental studies are essentially studies of propagation. They were carried out in a rich theoretical context with a view to judging which of the competing theories was the correct one. The principal theoretical difficulty was to formulate the most appropriate problem amenable to experimental testing, given the sensitivity of the available instruments. I argue that Hertz abstracted from this experience the philosophical principles which he presented in the Introduction to his Principles of Mechanics.