During the 1920s and 1930s geneticist L. C. Dunn of Columbia University cautioned Americans against endorsing eugenic policies and called attention to eugenicists' less than rigorous practices. Then, from the mid-1940s to early 1950s he attacked scientific racism and Nazi Rassenhygiene by co-authoring Heredity, Race and Society with Theodosius Dobzhansky and collaborating with members of UNESCO on their international campaign against racism. Even though shaking the foundations of scientific discrimination was Dunn's primary concern during the interwar and (...) post-World War II years, his campaigns had ancillary consequences for the discipline. He contributed to the professionalization of genetics during the 1920s and 1930s and sought respectability for human genetics in the 1940s and 1950s. My article aims to elucidate the activist scientist's role in undermining scientific discrimination by exploring aspects of Dunn's scientific work and political activism from the 1920s to 1950s. Definitions are provided for scientific discrimination and activist scientist. (shrink)

The English language now dominates scientific communications. Yet, many scientists have English as their second language. Their English proficiency may therefore often be more limited than that of a ‘native speaker’, and their scientific contributions (e.g. manuscripts) in English may frequently contain linguistic features that disrupt the fluency of a reader’s, or listener’s information processing even when the contributions are understandable. Scientific gatekeepers (e.g. journal reviewers) sometimes cite these features to justify negative decisions on manuscripts. Such justifications (...) may rest on the prima facie plausible assumption that linguistic characteristics that hinder fast and easy understandability of scientific contributions are epistemically undesirable in science. I shall raise some doubts about this assumption by drawing on empirical research on processing fluency and its biasing effects. I also argue that directing scientists with English as a foreign language toward approaching ‘native-level’ English can have the negative consequence of reducing their potential to make scientific belief formation more reliable. These points suggest that one seemingly compelling justification for linguistically discriminating against scientific contributions in ‘non-native’ English is questionable and that the common insistence by scientific gatekeepers on ‘native-like’ English may be epistemically harmful to science. (shrink)

Many legal disputes turn on scientific, especially statistical, evidence. Traditionally scientists have accepted only that statistical evidence which satisfies a 95 percent (or 99 percent) rule — that is, only evidence which has less than five percent (or one percent) probability of resulting from chance.The rationale for this rule is the reluctance of scientists to accept anything less than the best-supported new knowledge. The rule reflects the internal needs of scientific practice. However, when uncritically adopted as a rule (...) for admitting legal evidence, the seemingly innocuous 95 percent rule distorts the balance of interests historically protected by the legal system. In particular, plaintiffs in toxic tort and employment discrimination suits are effectively held to a heavier burden of proof in showing that their injuries were more probably than not caused by the defendant's actions. The result is that too many victims of toxic torts or employment discrimination cannot win legal redress for their injuries. (shrink)

We use game theoretic models to take an in-depth look at the dynamics of discrimination and academic collaboration. We find that in collaboration networks, small minority groups may be more likely to end up being discriminated against while collaborating. We also find that discrimination can lead members of different social groups to mostly collaborate with in-group members, decreasing the effective diversity of the social network. Drawing on previous work, we discuss how decreases in the diversity of scientific (...) collaborations might negatively affect the progress of epistemic communities. (shrink)

This essay examines how the American Jewish Congress (AJC) designed a legal attack on discrimination based on social science. This campaign led to the creation in 1945 of two new AJC commissions, t...

It is no surprise that empirical psychology refutes, again and again, assumptions of uneducated common sense. But some puzzlement tends to arise when scientific results appear to call into question the very conceptual framework of the mental to which we have become accustomed. This paper shall examine a case in point: Experiments on colour-discrimination have recently been taken to refute an assumption of first-person authority that appears to be constitutive of our ordinary notion of perceptual experience. The paper (...) is to show that those experiments do not refute this assumption, and will suggest that the impression to the contrary is, ultimately, due to two factors: to misleading imagery and, above all, to mistaken translation from the technical idiom of empirical psychology into the plain English we use every day. This is to take the mystery out of what we shall see to constitute a pretty puzzle; it is to remind us just how careful we need to be when drawing conclusions from results of scientific psychology; and it is to bring out the virtues of methods commonly lumped together under the entirely misleading label of 'ordinary language philosophy', of methods far more useful than their common caricature would make one think. (shrink)

The vegan ideal is entailed by arguments for ethical veganism based on traditional moral theory (rights and/or utilitarianism) extended to animals. The most ideal lifestyle would abjure the use of animals or their products for food since animals suffer and have rights not to be killed. The ideal is discriminatory because the arguments presuppose a male physiological norm that gives a privileged position to adult, middle-class males living in industrialized countries. Women, children, the aged, and others have substantially different nutritional (...) requirements and would bear a greater burden on vegetarian and vegan diets with respect to health and economic risks, than do these males. The poor and many persons in Third World nations live in circumstances that make the obligatory adoption of such diets, where they are not already a matter of sheer necessity, even more risky.Traditional moral theorists (such as Evelyn Pluhar and Gary Varner whose essays appear in this issue) argue that those who are at risk would beexcused from a duty to attain the virtue associated with ethical vegan lifestyles. The routine excuse of nearly everyone in the world besides adult, middle-class males in industrialized countries suggests bias in the perspective from which traditional arguments for animal rights and (utilitarian) animal welfare are formulated. (shrink)

The true story of Dr. Caroline Crocker's experience as an adjunct science professor at George Mason University. Addresses her teaching techniques, methodology, and perceived discrimination. Also provides a semi-biographical account of her experience with students.

Experiences of discrimination such as everyday racism can negatively affect the mental and physical health of children and adolescents with an immigrant background and impair their integration process in the host societies. Although experiences of racism are part of the everyday life of many minors affected by the process of “Othering”, an overview of empirical findings is missing for this age group worldwide. A systematic review was conducted to identify and analyze international research on the impact of discrimination (...) on the developmental outcomes and integration of immigrant children and adolescents. Three scientific databases were systematically searched up to June 11, 2021. A total of k = 4,769 identified publications were reviewed based on inclusion and exclusion criteria in terms of the PICOS format by independent reviewers. Thirty-four primary studies published between 1998 and 2021 met all inclusion criteria. The samples examined were mainly migrant youth, with only k = 2 studies assessing refugee youth and k = 1 study assessing both migrant and refugee youth. The majority of included studies assessed perceived discrimination, with only k = 1 study directly assessing experiences of racism. The association between discrimination or racism and developmental outcomes was assessed by the included studies within the three main topics of mental and physical health-related outcomes, school-related outcomes, and other developmental outcomes. Data collection procedures were implemented, and findings on minors’ developmental outcomes and integration process who experience discrimination and racism were summarized and discussed. The current review suggests experienced discrimination as a negative predictor of children and adolescents’ health-related outcomes, while no clear results could be found for the association between discrimination and school-related outcomes. A need for more empirical research focusing on the path and indirect link between discrimination and children and adolescents’ school-related outcomes as well as resulting school recommendations and the chosen career path was derived.Systematic Review Registration[https://www.crd.york.ac.uk/prospero/display_record.php?RecordID=260291], identifier [CRD42021260291]. (shrink)

In the recent past a number of empirical studies provided evidence that increasing genetic knowledge leads to new forms of exclusion, disadvantage and stigmatisation. As a consequence, many states have inaugurated special legislation to fight "genetic discrimination".This article focuses on some theoretical, normative and practical problems in the scientific and political debate on genetic discrimination. It puts forward the thesis that the existing antidiscrimination approach is based on the implicit idea that genes are the essence of (human) (...) life. Since genes are held responsible for individual development and personal identity, genetic discrimination is granted a privileged legal status in comparison to other forms of discrimination. As a result the analytical and political concentration on processes of genetic discrimination may reinforce the "geneticization" of body, illness and deviance. (shrink)

In an earlier article on this journal I argued that the problem of empirical underdetermination can for the largest part be solved by theoretical virtues, and for the remaining part it can be tolerated. Here I confront two further challenges to scientific realism based on underdetermination. First, there are four classes of theories which may seem to be underdetermined even by theoretical virtues. Concerning them I argue that (i) theories produced by trivial permutations and (ii) “equivalent descriptions” are compatible (...) with the truth of standard theories; instead (iii) “as if” versions of standard theories are much worse from the point of view of theoretical virtues; finally (iv) mathematically intertranslatable theories either may become empirically decidable in the future, or can be discriminated by theoretical virtues, or realists may simply plead ignorance about their claims. Secondly, I consider Stanford’s underdetermination with respect unconceived alternatives, arguing that it essentially relies on the pessimistic meta-induction from the falsity of all past theories. Therefore, it can be resisted by (a) considering the radical advancement of present with respect to past science, and (b) arguing with selective realism that past successful theories, even if false, always included some true components. (shrink)

Cultural accounts of scientific ideas and practices have increasingly come to be welcomed as a corrective to previous—and still widely held—theories of scientific knowledge and practices as universal. The editors caution, however, against the temptation to overgeneralize the work of culture, and to lapse into a kind of essentialism that flattens the range and variety of scientific work. The book refers to this tendency as culturalism. The contributors to the volume model a new path where historicized and (...) cultural accounts of scientific practice retain their specificity and complexity without falling into the traps of culturalism. They examine, among other issues, the potential of using notions of culture to study behavior in financial markets; the ideology, organization, and practice of earthquake monitoring and prediction during China's Cultural Revolution; the history of quadratic equations in China; and how studying the "glass ceiling" and employment discrimination became accepted in the social sciences. Demonstrating the need to understand the work of culture as a fluid and dynamic process that directly both shapes and is shaped by scientific practice, Cultures without Culturalism makes an important intervention in science studies. Contributors. Bruno Belhoste, Karine Chemla, Caroline Ehrhardt, Fa-ti Fan,Kenji Ito, Evelyn Fox Keller, Guillaume Lachenal, Donald MacKenzie, Mary S. Morgan, Nancy J. Nersessian, David Rabouin, Hans-Jörg Rheinberger, Claude Rosental, Koen Vermeir. (shrink)

In the last few years, we have witnessed a surge in scholarly interest and scientific evidence of how algorithms can produce discriminatory outcomes, especially with regard to gender and race. However, the analysis of fairness and bias in AI, important for the debate of AI for social good, has paid insufficient attention to the category of age and older people. Ageing populations have been largely neglected during the turn to digitality and AI. In this article, the concept of AI (...) ageism is presented to make a theoretical contribution to how the understanding of inclusion and exclusion within the field of AI can be expanded to include the category of age. AI ageism can be defined as practices and ideologies operating within the field of AI, which exclude, discriminate, or neglect the interests, experiences, and needs of older population and can be manifested in five interconnected forms: (1) age biases in algorithms and datasets (technical level), (2) age stereotypes, prejudices and ideologies of actors in AI (individual level), (3) invisibility of old age in discourses on AI (discourse level), (4) discriminatory effects of use of AI technology on different age groups (group level), (5) exclusion as users of AI technology, services and products (user level). Additionally, the paper provides empirical illustrations of the way ageism operates in these five forms. (shrink)

The question whether Kuhn's theory of scientific revolutions could be applied to mathematics caused many interesting problems to arise. The aim of this paper is to discuss whether there are different kinds of scientific revolution, and if so, how many. The basic idea of the paper is to discriminate between the formal and the social aspects of the development of science and to compare them. The paper has four parts. In the first introductory part we discuss some of (...) the questions which arose during the debate of the historians of mathematics. In the second part, we introduce the concept of the epistemic framework of a theory. We propose to discriminate three parts of this framework, from which the one called formal frame will be of considerable importance for our approach, as its development is conservative and gradual. In the third part of the paper we define the concept of epistemic rupture as a discontinuity in the formal frame. The conservative and gradual nature of the changes of the formal frame open the possibility to compare different epistemic ruptures. We try to show that there are four different kinds of epistemic rupture, which we call idealisation, re-presentation, objectivisation and re-formulation. In the last part of the paper we derive from the classification of the epistemic ruptures a classification of scientific revolutions. As only the first three kinds of rupture are revolutionary (the re-formulations are rather cumulative), we obtain three kinds of scientific revolution: idealisation, re-presentation, and objectivisation. We discuss the relation of our classification of scientific revolutions to the views of Kuhn, Lakatos, Crowe, and Dauben. (shrink)

COVID-19 vaccine requirements have generated significant debate. Here, we argue that, on the evidence available, such policies should have recognised proof of natural immunity as a sufficient basis for exemption to vaccination requirements. We begin by distinguishing our argument from two implausible claims about natural immunity: natural immunity is superior to ‘artificial’ vaccine-induced immunity simply because it is ‘natural’ and it is better to acquire immunity through natural infection than via vaccination. We then briefly survey the evidence base for the (...) comparison between naturally acquired immunity and vaccine-induced immunity. While we clearly cannot settle the scientific debates on this point, we suggest that we lack clear and convincing scientific evidence that vaccine-induced immunity has a significantly higher protective effect than natural immunity. Since vaccine requirements represent a substantial infringement of individual liberty, as well as imposing other significant costs, they can only be justified if they are necessary for achieving a proportionate public health benefit. Without compelling evidence for the superiority of vaccine-induced immunity, it cannot be deemed necessary to require vaccination for those with natural immunity. Subjecting them to vaccine mandates is therefore not justified. We conclude by defending the standard of proof that this argument from necessity invokes, and address other pragmatic and practical considerations that may speak against natural immunity exemptions. There are no data in this work. (shrink)

Theories of partial reference have been developed in order to retrospectively interpret rather stubborn past scientific theories like Newtonian dynamics and the phlogiston theory in a realist way, i.e., as approximately true. This is done by allowing for a term to refer to more than one entity at the same time and by providing semantic structures that determine the truth values of sentences containing partially referring terms. Two versions of theories of partial reference will be presented, a conjunctive (by (...) Hartry Field, 1973) and a disjunctive one (by Christina McLeish, 2006). In this paper, I will analyze them with regard to modal and epistemic aspects of those theories. It will be argued that a) theories of partial reference are (surprisingly) compatible with the rigidity of natural kind terms but face a weaker form of the so called “no-failures-of-reference-problem” and b) that the disjunctive account of partial reference suffers from a serious weakness: the impossibility of discriminating between descriptions that fix the reference of a term and those merely associated with it leads to the unacceptable result that past scientific theories containing such partially referring terms will come out as epistemically necessary, i.e., as a priori true. (shrink)

This paper discusses the relationship between internationalisation, mobility, quality and equality in the context of recent developments in research policy in the European Research Area (ERA). Although these developments are specifically concerned with the growth of research capacity at European level, the issues raised have much broader relevance to those concerned with research policy and highly skilled mobility. The paper draws on a wealth of recent research examining the relationship between mobility and career progression with particular reference to a recently (...) completed empirical study of doctoral mobility in the social sciences (Ackers et al. Doctoral Mobility in the Social Sciences. Report to the NORFACE ERA-Network, 2007). The paper is structured as follows. The first section introduces recent policy developments including the European Charter for Researchers and Code of Conduct for the Recruitment of Researchers and the European Commission’s Green Paper on the ERA. The discussion focuses on concerns around the definition of ‘mobility’ and the tendency (in both policy circles and academic research) to conflate different forms of mobility and to equate these with notions of excellence or quality. Scientific mobility is shaped as much by ‘push’ factors (limited opportunity) as it is by the ‘draw’ of excellence. Scientists are exercising a degree of ‘choice’ within a specific and individualised framework of constraints. The following sections consider some of the ‘professional’ and ‘personal’ factors shaping scientific mobility and the influence that these have on the relationship between mobility, internationalisation and excellence. The paper concludes that mobility is not an outcome in its own right and must not be treated as such (as an implicit indicator of internationalisation). To do so contributes to differential opportunity in scientific labour markets reducing both efficiency and equality. (shrink)

Scientific realists argue that present theories are more successful than past theories, so present theories will not be superseded by alternatives, even though past theories were superseded by alternatives. Alai (2016) objects that although present theories are more successful than past theories, they will be replaced by future theories, just as past theories were replaced by present theories. He contends, however, that past theories were partly true, and that present theories are largely true. I argue that Alai’s discrimination (...) between past and present theories is subject to his own criticism against realists’ discriminations between past and present theories, and also subject to other criticisms that philosophers have raised against scientific realism and pessimism. (shrink)

The aim of the paper is to clarify Kuhn’s theory of scientific revolutions. We propose to discriminate between a scientific revolution, which is a sociological event of a change of attitude of the scientific community with respect to a particular theory, and an epistemic rupture, which is a linguistic fact consisting of a discontinuity in the linguistic framework in which this theory is formulated. We propose a classification of epistemic ruptures into four types. In the paper, each (...) of these types of epistemic ruptures is illustrated by examples from physics. The classification of epistemic ruptures can be used as a basis for a classification of scientific revolutions and thus for a refinement of our view of the progress of science. (shrink)

The consideration of racial differences in the biology of disease and treatment options is a hallmark of modern medicine. However, this time-honored medical tradition has no scientific basis, and the premise itself, that is, the existence of biological differences between the commonly known races, is false inasmuch as races are only sociocultural constructions. It is time to rid medical research of the highly damaging exercise of searching for supposed racial differences in the biological manifestations of disease. The practice not (...) only condoned but required by the National Institutes of Health of utilizing racial identification as a demographic characteristic with assumed biological implications is at best badly flawed, and at worst unintentionally contributes to perpetuating the fallacy of natural differences between persons of different skin color, which has been used in the past to advance the cause of racial discrimination. (shrink)

Existential phenomenologists hold that the two most basic forms of intelligent behavior, learning, and skillful action, can be described and explained without recourse to mind or brain representations. This claim is expressed in two central notions in Merleau-Ponty's Phenomenology of Perception: the intentional arc and the tendency to achieve a maximal grip. The intentional arc names the tight connection between body and world, such that, as the active body acquires skills, those skills are stored, not as representations in the mind, (...) but as dispositions to respond to the solicitations of situations in the world. A phenomenology of skill acquisition confirms that, as one acquires expertise, the acquired know-how is experienced as finer and finer discriminations of situations paired with the appropriate response to each. Maximal grip names the body's tendency to refine its responses so as to bring the current situation closer to an optimal gestalt. Thus, successful learning and action do not require propositional mental representations. They do not require semantically interpretable brain representations either.Simulated neural networks exhibit crucial structural features of the intentional arc, and Walter Freeman's account of the brain dynamics underlying perception and action is structurally isomorphic with Merleau-Ponty's account of the way a skilled agent is led by the situation to move towards obtaining a maximal grip. (shrink)

Commentary on four articles in a special issue on “theories of emotion,” comparing the theories with respect to five conceptual contrasts. The first four contrasts are essentialism versus nonessentialism, discriminative versus integrative theories, individual versus social focus, and instrumentalism versus scientific realism. Although scientific psychologists appear to have reached consensus in favor of nonessentialism and they freely use both realist and instrumentalist interpretations, there is no consensus on the other two contrasts. The final contrast explored addresses attitudes toward (...) the use of philosophy in scientific theorizing, and whether philosophy is best kept in the background or brought into the foreground. (shrink)

Existential phenomenologists hold that the two most basic forms of intelligent behavior, learning, and skillful action, can be described and explained without recourse to mind or brain representations. This claim is expressed in two central notions in Merleau-Ponty's Phenomenology of Perception: the intentional arc and the tendency to achieve a maximal grip. The intentional arc names the tight connection between body and world, such that, as the active body acquires skills, those skills are “stored”, not as representations in the mind, (...) but as dispositions to respond to the solicitations of situations in the world. A phenomenology of skill acquisition confirms that, as one acquires expertise, the acquired know-how is experienced as finer and finer discriminations of situations paired with the appropriate response to each. Maximal grip names the body's tendency to refine its responses so as to bring the current situation closer to an optimal gestalt. Thus, successful learning and action do not require propositional mental representations. They do not require semantically interpretable brain representations either.Simulated neural networks exhibit crucial structural features of the intentional arc, and Walter Freeman's account of the brain dynamics underlying perception and action is structurally isomorphic with Merleau-Ponty's account of the way a skilled agent is led by the situation to move towards obtaining a maximal grip. (shrink)

By a close examination of changes in analytical chemistry between the years 1920 and 1950, I document the case that natural science has undergone and continues to undergo a major revolution. The central feature of this transformation is the rise in importance of scientific instrumentation. Prior to 1920, analytical chemists determined the chemical constitution of some unknown by treating it with a series of known compounds and observing the kind of reactions it underwent. After 1950, analytical chemists determined the (...) chemical constitution of an unknown by using a variety of instruments which allow one to discriminate chemicals in terms of their physical properties. This transformation involved changes in the practice of analytical chemistry. It involved the development of a new family of scientific instrument-making companies, and a new level of capital expenditure necessary to do analytical chemistry. It involved the development of new means to disseminate information about scientific instruments. While I do not document the broader case, these changes have been widespread throughout the natural sciences. It is the rise in the importance of instrumentation which is the key conceptual change in what has been identified as the fourth big scientific revolution. (shrink)

The article combines a criticism of public understanding of science with the sociology of expectations to examine how particular expectations toward scientific progress have performative effects for the construction of publics as citizens of science. By analyzing a particular controversy about gene therapy in Denmark, the article demonstrates how different sets of expectations can be used to discriminate among three different assemblages: the assemblage of consumption, the assemblage of comportment, and the assemblage of heroic action. Each of these assemblages (...) makes medical science, scientific citizenship, politics, patients, doctors, and expectations toward the future emerge in particular ways. By their radically different expectations toward science and their different constructions of what it means to be a scientific citizen, the assemblages construct the objectives of the governance of science in three very different ways. (shrink)

In the 1920s, scientists at the University of Cambridge’s Sir William Dunn Institute of Biochemistry made major contributions to the emerging discipline of biochemistry while also devoting considerable time and energy to the production of a humor journal entitled Brighter Biochemistry. Although humor is frequently regarded as peripheral to the work of science, the journal provides an opportunity to understand how it contributes to the social infrastructure of scientific communities as modern workplaces. Taking methodological cues from cultural history, ethnography, (...) and humor studies, this essay conducts a close and contextual reading of Brighter Biochemistry. This reading demonstrates how humor served as a central means through which members of the Dunn confronted workplace issues, including creating cooperative work teams, responding to gender discrimination, addressing funding anxiety, and defining professional identity. These conclusions provide a new perspective on the well-documented history of the Dunn and also offer a model for how historians of science can approach humor when its traces are encountered in other settings. (shrink)

I analyse Kripke’s modal argument against the mind-brain identity theories. Specifically, he argues against the identity between pain and C-fibres simulation by pointing out the difference between this identity claim and the theoretical identifications, such as ‘Water is H2O’ and ‘Lightning is a motion of electric charges’. Kripke’s argument relies on the assumption that the experience of pains is a simple and homogenous phenomenon, but scientific research shows that it is in fact a quite complex one. We can distinguish (...) at least three components: sensory-discriminative, motivational-affective and cognitive. This discovery makes it possible to reject Kripke’s argument, but it also uncovers a major flaw that is common to all modal arguments against physicalism. They proclaim to answer the fundamental question about the nature of our world by relying on our powers of imagination and without having the relevant factual knowledge. (shrink)

In recent years, the study of women entrepreneurship has experienced great growth, gaining a broad consensus among academics and contributing above all to understanding all those factors that explain the difficulty of women in undertaking an entrepreneurial career. This document tries to contribute to the field of study, thanks to a systematic analysis through the publications present in the topic. For this purpose, 2,848 peer-reviewed articles were analyzed, published between 1950 and 2019, using the Scopus database (SCImago Research Group). Through (...) the use of a series of bibliometric indicators it was possible to define the current state of research on the international scene. The analysis revealed that it is a multidisciplinary field of study and that has started to expand further since 2006, culminating in 2019, which makes it become a current and valid object of study. The analysis of the clusters allowed to isolate 6 different lines of research in which emerged, on the one hand, the importance of entrepreneurial education, social entrepreneurship and the socio-cultural context of reference (e.g. culture, family and institutional support) as tools to overcome the gender gap, on the other, the importance that women entrepreneurship assumes in the economic growth of the country (especially in developing economies), promoting social inclusion and combating poverty and discrimination. The study presents an important contribution to reflect on current policies and to outline future lines of investigation. (shrink)

This essay examines the symbolic significance of blood in the twentieth century and its role in determining the composition of a national community along racial lines. By drawing parallels between Nazi notions of blood and racial purity and historically contemporaneous U.S. policies regarding blood and blood products, Polsky reveals a disturbing proximity in discourse and policy. While the Nazis attempted to locate Jewish racial essence and inferiority in blood and instituted eugenic measures and laws forbidding racial admixture, similar policies existed (...) in the U.S. based on the so-called one drop rule that systematically discriminated against African Americans. (shrink)

Almost everyone has an intuitive notion of what a random number is. For example, consider these two series of binary digits: 01010101010101010101 01101100110111100010 The first is obviously constructed according to a simple rule; it consists of the number 01 repeated ten times. If one were asked to speculate on how the series might continue, one could predict with considerable confidence that the next two digits would be 0 and 1. Inspection of the second series of digits yields no such comprehensive (...) pattern. There is no obvious rule governing the formation of the number, and there is no rational way to guess the succeeding digits. The arrangement seems haphazard; in other words, the sequence appears to be a random assortment of 0's and 1's. (shrink)

What could be more certain than the fact that 2 plus 2 equals 4? Since the time of the ancient Greeks mathematicians have believed there is little---if anything---as unequivocal as a proved theorem. In fact, mathematical statements that can be proved true have often been regarded as a more solid foundation for a system of thought than any maxim about morals or even physical objects. The 17th-century German mathematician and philosopher Gottfried Wilhelm Leibniz even envisioned a ``calculus'' of reasoning such (...) that all disputes could one day be settled with the words ``Gentlemen, let us compute!'' By the beginning of this century symbolic logic had progressed to such an extent that the German mathematician David Hilbert declared that all mathematical questions are in principle decidable, and he confidently set out to codify once and for all the methods of mathematical reasoning. (shrink)

Human beings are strange animals. Although evolutionary theory has brilliantly accounted for the features we share with other creatures—from the genetic code that directs the construction of our bodies to the details of how our muscles and neurons work—we still stand out in countless ways. Our brains are exceptionally large, we alone have truly grammatical language, and we alone compose symphonies, drive cars, eat spaghetti with a fork and wonder about the origins of the universe.