Plato’s Heaven: A User’s Guide is based on an in-depth filmed conversation between Howard Burton and James Robert Brown, Emeritus Professor of Philosophy at the University of Toronto. This wide-ranging conversation addresses a central theme in current philosophy: Platonism vs. Naturalism and provides accounts of both approaches to mathematics. The Platonist-Naturalist debate over mathematics is explored in a comprehensive fashion and also sheds light on non-mathematical aspects of a dispute that is central to contemporary philosophy. Thought experiments stand as a fascinating challenge to the necessity of data in the empirical sciences. Are these experiments, conducted uniquely in our imagination, simply rhetorical devices or communication tools or are they an essential part of scientific practice? This book also surveys the current state of this debate and explores new avenues of research into the epistemology of thought experiments.
Howard Burton is the founder of the Ideas Roadshow, Ideas on Film and host of the Ideas Roadshow Podcast. He can be reached at howard@ideasroadshow.com.
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James Robert Brown, “Plato’s Heaven: A User’s Guide” (Open Agenda, 2021)

Interviews with Mathematicians about their New Books
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Natural Sciences

Science & Medicine

Science

The stereotype of the solitary mathematician is widespread, but practicing users and producers of mathematics know well that our work depends heavily on our historical and contemporary fellow travelers. Yet we may not appreciate how our work also extends beyond us into our physical and societal environments.
Kevin Lambert takes what might be a first crack at this perspective in his book Symbols and Things: Material Mathematics in the Eighteenth and Nineteenth Centuries (University of Pittsburgh Press, 2021). An historian of science, Dr. Lambert has shifted in his view of mathematics as a language of science to one as a material practice. Expanding on ideas from historians, archeologists, philosophers, and other scholars of human activity, and through several interweaving vignettes of mathematical work during a technologically dynamic period in British history, he argues that mathematical practice, communication, and even thought occur to a large degree outside the bodies of the persons performing them.
In this interview, we explore Kevin's journal to and through this book project. We discuss how such ideas as Andy Clark's extended mind informed his approach, and we review several of the lively stories—the co-creation of the long-distance mathematical community with the research journal, Peacock's museological argument for the adoption of symbolic algebra, and the foundational entanglement of electromagnetism, quaternions, and the philosophy of space, among others—he drew out of historical and archival sources. (Here i cannot resist mentioning Tait's collection of his intensive correspondence with Hamilton that transformed how quaternions were applied in physics and even conceptualized as mathematical objects.) We close with some thoughts on our own materially extended cognitive work and where Kevin's interests are currently driving him.
Suggested companion works:
• ChatGPT, as a cutting-edge extension of human thought
• work by Courtney Ann Roby, including the forthcoming The Mechanical Tradition of Hero of Alexandria: Strategies of Reading from Antiquity to the Early Modern Period
• Algorithmic Modernity: Mechanizing Thought and Action, 1500-2000, edited by Morgan G. Ames and Massimo Mazzotti
• work by Emily Miller Bonney, for example "A Reconsideration of Depositional Practices in Early Bronze Age Crete"
Kevin Lambert is a historian of science and mathematics in the early modern and modern periods and professor in the liberal studies department at California State University, Fullerton. His recent book Symbols and Things explores mathematics as a way of thinking outside the body and through the material environment. He also recently published a chapter in the volume Algorithmic Modernity that traces the genealogy of algorithmic practices. He is now working on the problem of writing longue durée histories of science. He is close to completing a paper called “Malthus in the Landscape” that investigates the temporalities of global histories. He is also exploring the problem of writing a global history of the early modern sciences without the prism of the so called “Scientific Revolution.” His work can be found on ResearchGate.
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Kevin Lambert, "Symbols and Things: Material Mathematics in the Eighteenth and Nineteenth Centuries" (U Pittsburgh Press, 2021)

What's the best way to determine what most voters want when multiple candidates are running? What's the fairest way to allocate legislative seats to different constituencies? What's the least distorted way to draw voting districts? Not the way we do things now. Democracy is mathematical to its very foundations. Yet most of the methods in use are a historical grab bag of the shortsighted, the cynical, the innumerate, and the outright discriminatory. Making Democracy Count: How Mathematics Improves Voting, Electoral Maps, and Representation (Princeton UP, 2024) sheds new light on our electoral systems, revealing how a deeper understanding of their mathematics is the key to creating civic infrastructure that works for everyone.
In this timely guide, Ismar Volic empowers us to use mathematical thinking as an objective, nonpartisan framework that rises above the noise and rancor of today's divided public square. Examining our representative democracy using powerful clarifying concepts, Volic shows why our current voting system stifles political diversity, why the size of the House of Representatives contributes to its paralysis, why gerrymandering is a sinister instrument that entrenches partisanship and disenfranchisement, why the Electoral College must be rethought, and what can work better and why. Volic also discusses the legal and constitutional practicalities involved and proposes a road map for repairing the mathematical structures that undergird representative government.
Making Democracy Count gives us the concrete knowledge and the confidence to advocate for a more just, equitable, and inclusive democracy.
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Ismar Volić, "Making Democracy Count: How Mathematics Improves Voting, Electoral Maps, and Representation" (Princeton UP, 2024)

Bookshop.org is an online book retailer that donates more than 80% of its profits to independent bookstores. Launched in 2020, Bookshop.org has already raised more than $27,000,000. In this interview, Andy Hunter, founder and CEO discusses his journey to creating one of the most revolutionary new organizations in the book world. Bookshop has found a way to retain the convenience of online book shopping while also supporting independent bookstores that are the backbones of many local communities. 
Andy Hunter is CEO and Founder of Bookshop.org. He also co-created Literary Hub.
Caleb Zakarin is the Assistant Editor of the New Books Network.
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A Better Way to Buy Books

Barbara M. Sattler's book The Concept of Motion in Ancient Greek Thought: Foundations in Logic, Method, and Mathematics (Cambridge UP, 2020) examines the birth of the scientific understanding of motion. It investigates which logical tools and methodological principles had to be in place to give a consistent account of motion, and which mathematical notions were introduced to gain control over conceptual problems of motion. It shows how the idea of motion raised two fundamental problems in the 5th and 4th century BCE: bringing together being and non-being, and bringing together time and space. The first problem leads to the exclusion of motion from the realm of rational investigation in Parmenides, the second to Zeno's paradoxes of motion. Methodological and logical developments reacting to these puzzles are shown to be present implicitly in the atomists, and explicitly in Plato who also employs mathematical structures to make motion intelligible. With Aristotle we finally see the first outline of the fundamental framework with which we conceptualise motion today.
Professor Barbara Sattler is Chair in Ancient and Medieval Philosophy at the Ruhr University Bochum. The main area of her research is metaphysics and natural philosophy in the ancient Greek world.
Morteza Hajizadeh is a Ph.D. graduate in English from the University of Auckland in New Zealand. His research interests are Cultural Studies; Critical Theory; Environmental History; Medieval (Intellectual) History; Gothic Studies; 18th and 19th Century British Literature. YouTube channel.
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Barbara Sattler, "The Concept of Motion in Ancient Greek Thought: Foundations in Logic, Method, and Mathematics" (Cambridge UP, 2020)

A defining feature of nineteenth-century Britain was its fascination with statistics. The processes that made Victorian society, including the growth of population, the development of industry and commerce, and the increasing competence of the state, generated profuse numerical data. 
Victorians and Numbers: Statistics and Society in Nineteenth Century Britain (Oxford UP, 2022) is a study of how such data influenced every aspect of Victorian culture and thought, from the methods of natural science and the struggle against disease, to the development of social administration and the arguments and conflicts between social classes. Numbers were collected in the 1830s by newly-created statistical societies in response to this 'data revolution'. They became a regular aspect of governmental procedure thereafter, and inspired new ways of interrogating both the natural and social worlds. William Farr used them to study cholera; Florence Nightingale deployed them in campaigns for sanitary improvement; Charles Babbage was inspired to design and build his famous calculating engines to process them. The mid-Victorians employed statistics consistently to make the case for liberal reform. In later decades, however, the emergence of the academic discipline of mathematical statistics - statistics as we use them today - became associated with eugenics and a contrary social philosophy. Where earlier statisticians emphasised the unity of mankind, some later practitioners, following Francis Galton, studied variation and difference within and between groups. In chapters on learned societies, government departments, international statistical collaborations, and different Victorian statisticians, Victorians and Numbers traces the impact of numbers on the era and the intriguing relationship of Victorian statistics with 'Big Data' in our own age.
Lawrence Goldman was born in London and educated at Cambridge and Yale. Following a Junior Research Fellowship at Trinity College, Cambridge, he taught British and American History for three decades in Oxford, where he was a fellow of St. Peter's College, and Editor of the Oxford Dictionary of National Biography 2004-2014. Latterly he was Director of the Institute of Historical Research, University of London. His publications include books on Victorian social science and the history of workers' education, and a biography of the historian and political thinker R. H. Tawney. He is now Emeritus Fellow of St. Peter's College, Oxford.
Morteza Hajizadeh is a Ph.D. graduate in English from the University of Auckland in New Zealand. His research interests are Cultural Studies; Critical Theory; Environmental History; Medieval (Intellectual) History; Gothic Studies; 18th and 19th Century British Literature. YouTube channel.
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James Robert Brown, “Plato’s Heaven: A User’s Guide” (Open Agenda, 2021)

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