This chapter is devoted to discussions about the nature of experiments in mathematics during the formative period of experimental mathematics and to a quantitative and qualitative analysis of the journal Experimental Mathematics founded in 1992. Particular attention is paid to interpret the roles of experiment and observation in the mathematical practices surrounding Experimental Mathematics.

This is a transcript of Milne's manuscript notes for a talk which he gave to fellow members of the Cambridge University Natural Science Club in his rooms at Trinity College, Cambridge, on February 6, 1922. The notes are deposited in the Bodleian Library, University of Oxford, Special Collections and Western Manuscripts. The background and essential points of Milne's talk are analysed in the article preceding this one. As far as is known, the text has not hitherto been published. Milne's handwriting (...) is difficult to read, and square brackets [...] denote the addition of a word for clarity of meaning. Meg Weston Smith and Simon Rebsdorf have ventured to fill in some chapter titles just in order to help with the separation of the varying content, hence we have made up all the headlines. All italics correspond to underlined words in the original. The Bergson citations and the Eddington passage at the end of the original text have not been transcribed. (shrink)

In 1876 the Italian physicist and physical chemist Adolfo Bartoli discussed a thought experiment in which he connected the second law of thermodynamics with the hypothetical pressure of radiation. Bartoli's work, published in Italian, exerted some influence on the subsequent development of black-body theory and light pressure research. This influence was mainly due to Boltzmann, who came to the Stefan-Boltzmann radiation law via a reworking of Bartoli's thought experiment. However, contrary to what is usually assumed, Bartoli was himself reluctant to (...) admit the existence of light pressure and soon rejected the hypothesis. Bartoli's work is discussed and related to other work in the areas of radiometer research and thermodynamics. (shrink)

Electricity is hidden within wires and networks only revealing its quantity and flow when metered. The making of its properties into data is therefore particularly important to the relations that are formed around electricity as a produced and managed phenomenon. We propose approaching all metering as a situated activity, a form of quantification work in which data is made and becomes mobile in particular spatial and temporal terms, enabling its entry into data infrastructures and schemes of evaluation and value production. (...) We interrogate the transition from the pre-digital into the making of bigger, more spatiotemporally granular electricity data, through focusing on those actors selling and materialising new metering technologies, data infrastructures and services for larger businesses and public sector organisations in the UK. We examine the claims of truth and visibility that accompany these shifts and their enrolment into management techniques that serve to more precisely apportion responsibility for, and evaluate the status of, particular patterns and instances of electricity use. We argue that whilst through becoming Big Data electricity flow is now able to be known and given identity in significantly new terms, enabling new relations to be formed with the many heterogeneous entities implicated in making and managing energy demand, it is necessary to sustain some ambivalence as to the performative consequences that follow for energy governance. We consider the wider application of our conceptualisation of metering, reflecting on comparisons with the introduction of new metering systems in domestic settings and as part of other infrastructural networks. (shrink)

The story of superheavy elements - those at the very end of the periodic table - is not well known outside the community of heavy-ion physicists and nuclear chemists. But it is a most interesting story which deserves to be known also to historians, philosophers, and sociologists of science and indeed to the general public. This is what the present work aims at. It tells the story or rather parts of the story, of how physicists and chemists created elements heavier (...) than uranium or searched for them in nature. And it does so with an emphasis on the frequent discovery and naming disputes concerning the synthesis of very heavy elements. Moreover, it calls attention to the criteria which scientists have adopted for what it means to have discovered a new element. In this branch of modern science it may be more appropriate to speak of creation instead of discovery. The work will be of interest to scientists as well as to scholars studying modern science from a meta-perspective. (shrink)

While Karl Popper’s philosophy of science has only few followers among modern philosophers, it is easily the view of science with the biggest impact on practicing scientists. According to Peter Medawar, Nobel laureate and eminent physiologist, Popper was the greatest authority ever on the scientific method. He praised the “great strength of Karl Popper’s conception of the scientific process,” a main reason for the praise being “that it is realistic—it gives a pretty fair picture of what goes on in real (...) life laboratories” (Medawar 1990, p. 100). Either explicitly or (more often) implicitly, many scientists subscribe to some version of simplified Popperianism, usually by adopting the demarcation criterion that a .. (shrink)

Summary Cosmology has always been different from other areas of the natural sciences. Although an observationally supported standard model of the universe emerged in the 1960s, more speculative models and conceptions continued to attract attention. During the last decade, ideas of multiple universes (the ‘multiverse’) based on anthropic reasoning have become very popular among cosmologists and theoretical physicists. This had led to a major debate within the scientific community of the epistemic standards of modern cosmology. Is the multiverse a scientific (...) hypothesis, or is it rather a philosophical speculation disguised as science? This paper offers a review of the recent and still ongoing controversy concerning the multiverse, emphasizing its foundational nature and relation to philosophical issues. It also compares the multiverse controversy to some earlier episodes in the history of twentieth-century cosmology when particular theories and approaches came under attack for betraying the ideals of proper science. (shrink)

This book presents the history of how the universe at large became the object of scientific understanding. Starting with the ancient creation myths, it offers an integrated and comprehensive account of cosmology that covers all major events from Aristotle's Earth-centred cosmos to the recent discovery of the accelearting universe.

In the present paper, I go beyond these examples by bringing into play an example that I nd more experimental in nature, namely that of the use of the so-called PSLQ algorithm in researching integer relations between numerical constants. It is the purpose of this paper to combine a historical presentation with a preliminary exploration of some philosophical aspects of the notion of experiment in experimental mathematics. This dual goal will be sought by analysing these aspects as they are presented (...) by some of the protagonists of the eld and discussing them using notions from contemporary philosophy of science. (shrink)

During the last decade new developments in theoretical and speculative cosmology have reopened the old discussion of cosmology's scientific status and the more general question of the demarcation between science and non-science. The multiverse hypothesis, in particular, is central to this discussion and controversial because it seems to disagree with methodological and epistemic standards traditionally accepted in the physical sciences. But what are these standards and how sacrosanct are they? Does anthropic multiverse cosmology rest on evaluation criteria that conflict with (...) and go beyond those ordinarily accepted, so that it constitutes an “epistemic shift” in fundamental physics? The paper offers a brief characterization of the modern multiverse and also refers to a few earlier attempts to introduce epistemic shifts in the science of the universe. It further discusses the several meanings of testability, addresses the question of falsifiability as a sine qua non for a theory being scientific, and briefly compares the situation in cosmology with the one in systematic biology. Multiverse theory is not generally falsifiable, which has led to proposals from some physicists to overrule not only Popperian standards but also other evaluation criteria of a philosophical nature. However, this is hardly possible and nor is it possible to get rid of explicit philosophical considerations in some other aspects of cosmological research, however advanced it becomes. (shrink)

During the last decade new developments in theoretical and speculative cosmology have reopened the old discussion of cosmology’s scientific status and the more general question of the demarcation between science and non-science. The multiverse hypothesis, in particular, is central to this discussion and controversial because it seems to disagree with methodological and epistemic standards traditionally accepted in the physical sciences. But what are these standards and how sacrosanct are they? Does anthropic multiverse cosmology rest on evaluation criteria that conflict with (...) and go beyond those ordinarily accepted, so that it constitutes an “epistemic shift” in fundamental physics? The paper offers a brief characterization of the modern multiverse and also refers to a few earlier attempts to introduce epistemic shifts in the science of the universe. It further discusses the several meanings of testability, addresses the question of falsifiability as a sine qua non for a theory being scientific, and briefly compares the situation in cosmology with the one in systematic biology. Multiverse theory is not generally falsifiable, which has led to proposals from some physicists to overrule not only Popperian standards but also other evaluation criteria of a philosophical nature. However, this is hardly possible and nor is it possible to get rid of explicit philosophical considerations in some other aspects of cosmological research, however advanced it becomes. (shrink)

From a purely formalist viewpoint on the philosophy of mathematics, experiments cannot (and should not) play a role in warranting mathematical statements but must be confined to heuristics. Yet, due to the incorporation of new mathematical methods such as computer-assisted experimentation in mathematical practice, experiments are now conducted and used in a much broader range of epistemic practices such as concept formation, validation, and communication. In this article, we combine corpus studies and qualitative analyses to assess and categorize the epistemic (...) roles experiments are seen—by mathematicians—to have in actual mathematical practice. We do so by text-mining a corpus of reviews from the _Mathematical Reviews_, which include the indicator word “experiment”. Our qualitative, grounded classification of samples from this corpus allows us to explore the various roles played by experiments. We thus identify instances where experiments function as references to established knowledge, as tools for heuristics or exploration, as epistemic warrants, as communication or pedagogy, and instances simply proposing experiments. Focusing on the role of experiments as epistemic warrants, we show through additional sampling that in some fields of mathematics, experiments can warrant theorems as well as methods. We also show that the expressed lack of experiments by reviewers suggests concordant views that experiments could have provided epistemic warrants. Thus, our combination of corpus studies and qualitative analyses has added a typology of roles of experiments in mathematical practice and shown that experiments can and do play roles as epistemic warrants depending on the mathematical field. (shrink)

Classical thermochemistry is inextricably bound up with the problem of chemical affinity. In 1851, when Julius Thomsen began his career in thermochemistry, the concept of chemical affinity had been in the centre of chemical enquiry for more than a century. In spite of many suggestions, preferably to explain affinity in terms of electrical or gravitational forces, almost nothing was known about the cause and nature of affinity. In this state of puzzling uncertainty some chemists felt it more advantageous to establish (...) an adequate experimental measure of affinity, whatever its nature was. One way of providing affinity with a quantitative description was by means of the heats evolved in chemical processes. (shrink)