We demonstrate via several examples how the backward error viewpoint can be used in the analysis of solutions obtained by perturbation methods. We show that this viewpoint is quite general and offers several important advantages. Perhaps the most important is that backward error analysis can be used to demonstrate the validity of the solution, however obtained and by whichever method. This includes a nontrivial safeguard against slips, blunders, or bugs in the original computation. We also demonstrate (...) its utility in deciding when to truncate an asymptotic series, improving on the well-known rule of thumb indicating truncation just prior to the smallest term. We also give an example of elimination of spurious secular terms even when genuine secularity is present in the equation. We give short expositions of several well-known perturbation methods together with computer implementations. We also give a generic backward error based method that is equivalent to iteration for regular perturbation. (shrink)

Summary The conical sundial from the museum Thyrrheion is found to be designed with cardinal parametersgeographical latitude ϕ = arc tan(3/5) = 30°57′50″half cone angle α = arc tan(4/9) = 23°57′45″radius at equinox r0 = 4 unciae = 98.7mm (pes monetalis)position of the cone tip h = 18 unciae = 444.3 mmThe half cone angle is equal to the angle of the ecliptic which leads to the special case of a conical sundial with the associated sphere being tangent at the (...) day line of the winter solstice. The ratio of sides in the generating triangle 4:9 may thus be interpreted as an approximation for the angle of ecliptic.The place of finding (operation) is 10° North of the intended latitude (design). The error of the sundial's indications due to the displacement are analyzed. (shrink)

Interest in the computational aspects of modeling has been steadily growing in philosophy of science. This paper aims to advance the discussion by articulating the way in which modeling and computational errors are related and by explaining the significance of error management strategies for the rational reconstruction of scientific practice. To this end, we first characterize the role and nature of modeling error in relation to a recipe for model construction known as Euler’s recipe. We then describe a (...) general model that allows us to assess the quality of numerical solutions in terms of measures of computational errors that are completely interpretable in terms of modeling error. Finally, we emphasize that this type of error analysis involves forms of perturbation analysis that go beyond the basic model-theoretical and statistical/probabilistic tools typically used to characterize the scientific method; this demands that we revise and complement our reconstructive toolbox in a way that can affect our normative image of science. (shrink)

The rapid expansion of computational tools and of data science methods in healthcare has, undoubtedly, raised a whole new set of bioethical challenges. As Laacke and colleagues rightly note,...

Human–robot interactions are often affected by error situations that are caused by either the robot or the human. Therefore, robots would profit from the ability to recognize when error situations occur. We investigated the verbal and non-verbal social signals that humans show when error situations occur in human–robot interaction experiments. For that, we analyzed 201 videos of five human–robot interaction user studies with varying tasks from four independent projects. The analysis shows that there are two types (...) of error situations: social norm violations and technical failures. Social norm violations are situations in which the robot does not adhere to the underlying social script of the interaction. Technical failures are caused by technical shortcomings of the robot. The results of the video analysis show that the study participants use many head movements and very few gestures, but they often smile, when in an error situation with the robot. The results suggest that participants do not see the robot as a social interaction partner with comparable communication skills. Our findings have implications for builders and evaluators of human–robot interaction systems. The builders need to consider including modules for recognition and classification of head movements to the robot input channels. The evaluators need to make sure that the presence of an experimenter does not skew the results of their user studies. (shrink)

The anti-utopian technology critique of Ellul, Postman, and other important social analysts has been the primary mode of critical response to technological developments since the 1950s. However, this mode of technology critique has had a disappointingly small effect on the way we, as a society, receive technology. Rather than attribute this failure to the negativity of the anti-utopian perspective, this article suggests that there are other important and largely overlooked factors at work—in particular, the critics' inability to speak about technology (...) in a way that relates to us as social individuals coping with the contingencies and realities of the day-to-day use of technological devices. The purpose of this analysis is not to suggest that we abandon as irrelevant the work and ideas of technology critics such as Ellul and Postman but, on the contrary, to find a way to reframe their important ideas for wider acceptance. (shrink)

The issue of death due to medical errors is not new. We have all heard horror stories about patients dying in the hospital because of a drug mix-up or a surgery patient having the wrong limb amputated. Most people believed these stories were the exception to the rule until November 1999, when the Institute of Medicine issued a report entitled To Err Is Human: Building A Safer Health System. This report focused on medical errors and patient safety in U.S. hospitals. (...) The report indicated that as many as 44,000 to 98,000 people die each year in hospitals as a result of medical errors. These numbers suggest that more Americans are killed in U.S.hospitals every 6 months than died in the entire Vietnam War, and some have compared the alleged rate to fully loaded jumbo jets crashing every other day. This report was not without its critics. (shrink)

The issue of death due to medical errors is not new. We have all heard horror stories about patients dying in the hospital because of a drug mix-up or a surgery patient having the wrong limb amputated. Most people believed these stories were the exception to the rule until November 1999, when the Institute of Medicine issued a report entitled To Err Is Human: Building A Safer Health System. This report focused on medical errors and patient safety in U.S. hospitals. (...) The report indicated that as many as 44,000 to 98,000 people die each year in hospitals as a result of medical errors. These numbers suggest that more Americans are killed in U.S.hospitals every 6 months than died in the entire Vietnam War, and some have compared the alleged rate to fully loaded jumbo jets crashing every other day. This report was not without its critics. (shrink)

Probabilistic reasoning is heavily investigated in decision research. Violations of probability theory have been demonstrated numerously, for instance, the tendency to overestimate the joint probab...

Compared to other health care professions such as medicine, nursing and pharmacy, few studies have been conducted to examine the nature of practice errors in occupational and physical therapy. In an ongoing study to determine root causes, typographies and impact of occupational and physical therapy error on patients, focus group interviews have been conducted across the United States. A substantial number of harmful practice errors and/or other patient safety events (deviations or accidents) have been identified. Often these events have (...) had moral dimensions that troubled the therapist involved. In this article, six of these transcribed cases are analyzed, using predominant bioethical theories, ethical principles and professional codes of ethics. The cases and their analyses are intended to be exemplary, improving the readers’ ability to discern and critically address similar such events. Several patient safety strategies are suggested that might have prevented the events described in these cases. (shrink)

Dealing with errors in psychotherapy is challenging, both ethically and practically. There is almost no empirical research on this topic. We aimed (1) to explore psychotherapists’ self-reported ways of dealing with an error made by themselves or by colleagues, and (2) to reconstruct their reasoning according to the two principle-based ethical approaches that are dominant in the ethics discourse of psychotherapy, Beauchamp & Childress (B&C) and Lindsay et al. (L).

Generalized structured component analysis (GSCA) is a component-based approach to structural equation modeling (SEM), where latent variables are approximated by weighted composites of indicators. It has no formal mechanism to incorporate errors in indicators, which in turn renders components prone to the errors as well. We propose to extend GSCA to account for errors in indicators explicitly. This extension, called GSCA_M, considers both common and unique parts of indicators, as postulated in common factor analysis, and estimates a weighted (...) composite of indicators with their unique parts removed. Adding such unique parts or uniqueness terms serves to account for measurement errors in indicators in a manner similar to common factor analysis. Simulation studies are conducted to compare parameter recovery of GSCA_M and existing methods. These methods are also applied to fit a substantively well-established model to real data. (shrink)

Libertarians are mistaken to seek foundations, to take sides over moral approaches, and to have no proper theory of liberty.

Thelen et al. criticize “spatial coding” approaches to the A-not-B error. However, newer thinking about spatial coding provides more precise analytic categories and recognizes that different spatial coding systems normally coexist. Theorizing about spatial coding is largely compatible with dynamic-systems theory, augmenting it with an analysis of what one means when discussing “location at A” (or B).

Lewisian reference magnetism about linguistic content determination [Lewis 1983 has been defended in recent work by Weatherson [2003] and Sider [2009], among others. Two advantages claimed for the view are its capacity to make sense of systematic error in speakers' use of their words, and its capacity to distinguish between verbal and substantive disagreements. Our understanding of both error and disagreement is linked to the role of usage and first order intuitions in semantics and in linguistic theory more (...) generally. I argue, partially on the basis of these more general considerations, that reference magnetism delivers implausible results. Specifically, I argue that the proponent of reference magnetism maintains her analysis of genuinely systematic error at the cost of an empirically unjustifiable error theory regarding ordinary usage. In response, I describe an alternative view of content determination—MUMPS, or Meaning is Use Minus Pragmatics—which is not committed to such error theories. Despite this advantage, MUMPS has high prima facie costs. On such a view, there is a great deal of variation in linguistic meaning across speakers and times. As a result, a large number of seemingly mistaken claims are analysed as expressing true propositions. Correspondingly, a large number of seemingly substantive disagreements are analysed as terminological. However, I argue that these consequences are not as costly as they seem. Despite appearances, MUMPS is consistent with objective, metaphysically realist adjudication of disagreements, even in cases where meanings are not shared and where both parties to a dispute speak truly. MUMPS thus allows for a more nuanced understanding of linguistic usage, change, and variation, without imposing a commitment to any form of metaphysical anti-realism. (shrink)

This text provides a critique of the subjective Bayesian view of statistical inference, and proposes the author's own error-statistical approach as an alternative framework for the epistemology of experiment. It seeks to address the needs of researchers who work with statistical analysis.

This article scrutinizes in detail much of the extant historiography on the controversy between biometricians and Mendelians, considering in particular how this controversy is related to the evolutionary synthesis. While the historiographic critique concentrates on William Provine’s standard account, it also extends to the proposal by Donald MacKenzie and Barry Barnes. What Provine and these sociologists of scientific knowledge have in common is a set of unquestioned assumptions about the nature of Darwinism, about William Bateson’s anti-Darwinism, and about the very (...) idea of an evolutionary “synthesis.” While these assumptions make for a compelling history of the synthesis, they engender an endemically asymmetrical perspective and bias historiography toward the mere confirmation of antecedent expectations, which renders the years from 1859 to 1929 an age of ignorance and misunderstanding. In contrast, a return to what was probably the original meaning of evolutionary “synthesis” allows for a symmetrical account. It yields an appreciation of the positive contributions made both by Mendelians and biometricians to the gradual development of Darwinism. The article concludes with a synopsis of this alternative account. (shrink)

Error is protean, ubiquitous and crucial in scientific process. In this paper it is argued that understanding scientific process requires what is currently absent: an adaptable, context-sensitive functional role for error in science that naturally harnesses error identification and avoidance to positive, success-driven, science. This paper develops a new account of scientific process of this sort, error and success driving Self-Directed Anticipative Learning (SDAL) cycling, using a recent re-analysis of ape-language research as test example. The (...) example shows the limitations of other accounts of error, in particular Mayo’s (Error and the growth of experimental knowledge, 1996) error-statistical approach, and SDAL cycling shows how they can be fruitfully contextualised. (shrink)

What is the correct concept behind measures of inflation? Does money cause business activity or is it the other way around? Shall we stimulate growth by raising aggregate demand or rather by lowering taxes and thereby providing incentives to produce? Policy-relevant questions such as these are of immediate and obvious importance to the welfare of societies. The standard approach in dealing with them is to build a model, based on economic theory, answer the question for the model world and then (...) apply the results to economic phenomena outside. Data come in, if at all, only in testing a limited number of the model's consequences. Despite some critical voices, economic methodology too has by and large subscribed to a "theory first" approach to applied economics. Error in Economics systematically develops an alternative to the theory-based orthodoxy. It places the methodical study of evidence at the centre of the scientific enterprise and thus provides a foundation for a methodology of evidence-based economics. But the book does not stop at the truism that claims should be based on the best available evidence. Rather, detailed studies in the areas of measurement, causal inference and policy analysis show what it means for a claim to be evidence-based in the context of a concrete case. The examples discussed concern topics as diverse as consumer price indices, radio spectrum auctions, the transmission mechanism, natural experiments on minimum wages and the evaluation of counterfactuals for policy. Error in Economics is essential reading for economic methodologists, philosophers of science and anyone interested in how claims about socio-economic matters are validated. (shrink)

I consider the error-statistical account as both a theory of evidence and as a theory of inference. I seek to show how inferences regarding the truth of hypotheses can be upheld by avoiding a certain kind of alternative hypothesis problem. In addition to the testing of assumptions behind the experimental model, I discuss the role of judgments of implausibility. A benefit of my analysis is that it reveals a continuity in the application of error-statistical assessment to low-level (...) empirical hypotheses and highly general theoretical principles. This last point is illustrated with a brief sketch of the issues involved in the parametric framework analysis of tests of physical theories such as General Relativity and of fundamental physical principles such as the Einstein Equivalence Principle. (shrink)

Beginning with the premise that the principal function of a criminal trial is to find out the truth about a crime, Larry Laudan examines the rules of evidence and procedure that would be appropriate if the discovery of the truth were, as higher courts routinely claim, the overriding aim of the criminal justice system. Laudan mounts a systematic critique of existing rules and procedures that are obstacles to that quest. He also examines issues of error distribution by offering the (...) first integrated analysis of the various mechanisms - the standard of proof, the benefit of the doubt, the presumption of innocence and the burden of proof - for implementing society's view about the relative importance of the errors that can occur in a trial. (shrink)

In _Error,_ Nicholas Rescher presents a fresh analysis of the occurrence, causality, and consequences of error in human thought, action, and evaluation. Rescher maintains that error-avoidance and truth-achievement are distinct but equally important factors for rational inquiry, and that error is inherent in the human cognitive process. He defines three main categories of error: cognitive ; practical ; and axiological, and articulates the factors that contribute to each. His discussion also provides a historical perspective on (...) the treatment of error in Greek philosophy, and by later thinkers such as Aquinas, Descartes, Spinoza, Leibniz, James, Royce, Moore, and Russell. _Error _is an important reexamination of the significance of error to the fields of philosophical anthropology, epistemology, ontology, and theology. As Rescher’s study argues, truth and error are inexorably intertwined—one cannot exist without the other. Error is an unavoidable occurrence in the cognitive process—without missteps on the path to truth, truth itself cannot be attained. The risk of error is inherent in the quest for truth. (shrink)

Many of the errors that occur in children' subtraction are due to the use of incorrect strategies rather than to the incorrect recall of number facts. A production system is presented for performing written subtraction which is consistent with an earlier analysis of the nature of such a cognitive skill. Most of the incorrect strategies used by schoolchildren can be accounted for in a principled way by simple changes in the production system, such as the omission of individual rules (...) or the inclusion of rules appropriate to other arithmetical tasks. The production system model is evaluated against a corpus of over 1500 subtraction problems done by 10‐year olds and is shown to account for about two‐thirds of the (nonnumber fact) errors. It also provides an alternative, simpler interpretation of the subtraction errors analysed by Brown and Burton (1978). Some implications for teaching are discussed. (shrink)

ABSTRACTIn this essay, I review Suits’ classic description of games and cite three kinds of problems—mischaracterizations, omissions, and ambiguities. I build on previous criticisms by myself and others leveled at his definition. However, in contrast to much of this previous work, I will present what I hope is an improved description. The latter part of the essay is devoted to defending this alternate characterization. I conclude by arguing that my revisionist work paradoxically both supports and undermines the merits of Suits’ (...) anti-Wittgensteinian efforts to identify the necessary and sufficient conditions for games. (shrink)

This paper argues, first, that recent studies of experimentation, most notably by Deborah Mayo, provide the conceptual resources to describe scientific discovery's early stages as error-probing processes. Second, it shows that this description yields greater understanding of those early stages, including the challenges that they pose, the research strategies associated with them, and their influence on the rest of the discovery process. Throughout, the paper examines the phenomenon of "chemical hormesis" (i.e., anomalous low-dose effects from toxic chemicals) as a (...) case study that is important not only for the biological sciences but also for contemporary public policy. The resulting analysis is significant for at least two reasons. First, by elucidating the importance of discovery's earliest stages, it expands previous accounts by philosophers such as William Wimsatt and Lindley Darden. Second, it identifies the discovery process as yet another philosophical topic on which the detailed studies of the "new experimentalists" can shed new light. (shrink)

The view is advocated that to preserve a deductivist account of science against recent criticism, it is necessary to incorporate experimental error, or imprecision, in the deductive structure. The sources of imprecision in empirical variables are analyzed, and the notion of conceptual imprecision introduced and illustrated. This is then used to clarify the notion of the acceptable range of a functional law. It is further shown that imprecision may be ascribed to parameters in laws and theories without rendering the (...) deductive structure untestable. It is claimed that this analysis explicates the relation between laws and theories in a way that invalidates certain arguments against its deductive nature. (shrink)