Giora Hon

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.

The attempt to narrow the general discourse of the problem of error and to focus it on the specific problem of experimental error may be approached from different directions. One possibility is to establish a focusing process from the standpoint of history; such an approach requires a careful scrutiny of the history of science with a view to identifying the juncture when the problem of experimental error was properly understood and accounted for. In a study of this kind one would have to examine the evolution of the method of experimentation and related topics so that clear criteria would underlie the analysis.

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.

The claim that Galileo Galilei transformed the spyglass into an astronomical instrument has never been disputed and is considered a historical fact. However, the question what was the procedure which Galileo followed is moot, for he did not disclose his research method. On the traditional view, Galileo was guided by experience, more precisely, systematized experience, which was current among northern Italian artisans and men of science. In other words, it was a trial-and-error procedure—no theory was involved. A scientific analysis of the optical properties of Galileo’s first improved spyglass shows that his procedure could not have been an informed extension of the traditional optics of spectacles. We argue that most likely Galileo realized that the objective and the eyepiece form a system and proceeded accordingly.

In 1646, Francesco Fontana (1580–1656) published his Novae Coelestium Terresriumque Rerum Observationes which includes discussions of optical properties of systems of lenses, e.g., telescope and microscope. Our study of the Novae Coelestium shows that the advance Fontana made in optics could not have been accomplished on the basis of the traditional spectacle optics which was the dominant practice at his time. Though spectacle and telescope making share the same optical elements, improving eyesight and constructing telescope are different practices based on different principles. The production of powerful astronomical telescopes demanded objective lenses with much longer focal length and eyepiece lenses with much shorter focal length than the range of focal length of lenses used for spectacles, respectively. Moreover, higher standard of precision and purity of the glass was required. The transition from the practice by which optical components were chosen from ready-made spectacle lenses to lenses which were produced according to predetermined specifications (e.g., calculation of focal length) was anything but straight forward. We argue that Fontana developed the optical knowledge necessary for improving the performance of optical systems. Essentially, he formulated—based on rich practical experience—a set of rules of calculation by which optical properties of a lens system could be determined and adjusted as required.

Descartes’s Cogito, “I am thinking, therefore I exist,” is perhaps the most famous assertion in the history of philosophy. Thirteen hundred years earlier, St. Augustine formulated a similar claim, arguing “if I am mistaken, I am.” Did St. Augustine anticipate Descartes? We show that Descartes’s dictum is a novel insight and less vulnerable to criticism than the claim of St. Augustine. Whereas Descartes searched for one true proposition on which he could base scientificknowledge, St. Augustine sought to refute the skeptics who had denied the possibility of knowledge. By a twist of irony, the skeptics and St. Augustine reached contradictory (ethical) conclusions based, however, on similar reasoning.

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 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, 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 Kepler's scheme: they impose constraints on theory, but at the same time render astronomical knowledge secure. To get a comprehensive grasp of Kepler's 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.

The term “analogy” stands for a variety of methodological practices all related in one way or another to the idea of proportionality. We claim that in his first substantial contribution to electromagnetism James Clerk Maxwell developed a methodology of analogy which was completely new at the time or, to borrow John North’s expression, Maxwell’s methodology was a “newly contrived analogue”. In his initial response to Michael Faraday’s experimental researches in electromagnetism, Maxwell did not seek an analogy with some physical system in a domain different from electromagnetism as advocated by William Thomson; rather, he constructed an entirely artificial one to suit his needs. Following North, we claim that the modification which Maxwell introduced to the methodology of analogy has not been properly appreciated. In view of our examination of the evidence, we argue that Maxwell gave a new meaning to analogy; in fact, it comes close to modeling in current usage.

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] and models , 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 . 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

: 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

We call attention to the historical fact that the meaning of symmetry in antiquity—as it appears in Vitruvius’s De architectura—is entirely different from the modern concept. This leads us to the question, what is the evidence for the changes in the meaning of the term symmetry, and what were the different meanings attached to it? We show that the meaning of the term in an aesthetic sense gradually shifted in the context of architecture before the image of the balance was attached to the term in the middle of the 18th century and well before the first modern scientific usage by Legendre in 1794.Keywords: Symmetry; Vitruvius; Claude Perrault; Charles-Louis de Secondat Baron de Montesquieu; Balance in architecture.

Can a theory turn back, as it were, upon itselfand vouch for its own features? That is, canthe derived elements of a theory be the veryprimitive terms that provide thepresuppositions of the theory? This form of anall-embracing feature assumes a totality inwhich there occurs quantification over thattotality, quantification that is defined bythis very totality. I argue that the Machprinciple exhibits such a feature ofall-embracing nature. To clarify the argument,I distinguish between on the one handcompleteness and on the other wholeness andtotality, as different all-embracing features:the former being epistemic while the latter –ontological.I propose an analogy between the Mach principleas a possible selection principle in generalrelativity, and the vicious-circle principle infoundations of mathematics. I finally concludewith a consequence of this analogyvis-à-vis completeness and totality,viz., both should be constrained if they wereto be valid concepts for a physical theory.

Hermann Weyl succeeded in presenting a consistent overarching analysis that accounts for symmetry in material artifacts, natural phenomena, and 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”. 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.