What if, every time you wanted to write down 1,000,000, you had to draw a picture of a god? And what if that number were the biggest you had a symbol for? If you were doing math in ancient Egypt, those were the rules: anything bigger broke math.
As mathematician Richard Elwes shows in Huge Numbers: A Story of Counting Ambitiously, from 4 1/2 to Fish 7 (Basic Books, 2026)this is the strange story of math. Even today, writing down some numbers is beyond us: try it with all the zeroes in a googolplex, or an outrageous alien number like TREE(3). Safer not to try: even harnessing every particle in the universe, you wouldn’t come close. But this book is no mere bestiary of numerical monsters. It shows how, by hunting down and studying ever-bigger numbers, arithmetic has reshaped human thought and made our modern era of science and computation possible.
Where many math books celebrate abstract algebra or ineffable infinities, Huge Numbers is both more practical and far weirder. It reveals a world where most numbers remain out of reach until we discover how to chase them down and tame them, and so remake our world again.

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Most of us today would assume that morality and ethics, being value propositions, are questions for inspired leaders, religious creeds, poets—in other words, for the humanities. But what if I told you that we can construct a system of ethics and morality by studying math—more specifically: the laws of thermodynamics? That’s what Professor Drew M Dalton argues in his latest book. Dalton traces a line of metaphysical inquiry from Kant through Spinoza, Nietzsche, and others up to today to show how we get from E=mc2 to a full-throated call to resist evil and alleviate suffering to our very last breath.

By overturning our assumptions about the nature and value of reality, The Matter of Evil: From Speculative Realism to Ethical Pessimism (Northwestern UP, 2024) presents a provocative new model of ethical responsibility that is both logically justifiable and scientifically sound. Dalton argues for “ethical pessimism,” a position previously marginalized in the West, as a means to cultivate an account of ethical responsibility and political activism that takes seriously the unbecoming of being and the moral horror of existence.

Drew M. Dalton is a professor of English at Indiana University, having received his Ph.D. in Philosophy from the University of Leuven in Belgium. His research focuses on the normative implications of different metaphysical systems and, specifically, he’s interested in how questions of right and wrong, good and evil, beauty and pleasure are framed within aesthetics, literary theory, ethics, and political philosophy. He is the author of Longing for the Other: Levinas and Metaphysical Desire (Duquesne University Press, 2009), The Ethics of Resistance: Tyranny of the Absolute (Bloomsbury, 2018), and The Matter of Evil: From Speculative Realism to Ethical Pessimism (Northwestern University Press, 2023).

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In this episode Pat speaks with Dr Guillermo Badia.

Dr Guillermo Badia is a philosopher working in logic. His research interests are logic in computer science, semiring-based logics and models of computation, and modal, intuitionistic and other non-classical logics.

They discuss logic, murder mysteries, and the counter revolutionary search for truth.

A transcript of this episode will be available on the Concept : Art website here.

Concept : Art is produced on muwinina Country, lutruwita Tasmania. Always was, always will be Aboriginal land.

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Based on decades of research, Beyond the Quantum: A Quest for the Origin and Hidden Meaning of Quantum Mechanics (Oxford UP, 2026) offers a panoramic rethink of quantum physics, with potentially revolutionary implications for cosmology, quantum gravity, and quantum technology.

Properly understood, 'pilot-wave theory' provides a deeper foundation for quantum mechanics, while also going beyond it. First proposed in the 1920s by French aristocrat and physicist Louis de Broglie, and revived in the 1950s by American physicist David Bohm, the theory posits hidden particle motions we cannot currently see or control. The theory is usually regarded as merely an alternative account of the same physics we already know. In fact, pilot-wave theory implies a wealth of new and radical physics beyond the reach of quantum mechanics.

Pilot-wave theory tells us that quantum physics is a special case of something broader and deeper. In more general 'nonequilibrium' conditions, Einstein's relativity and Heisenberg's uncertainty break down. Superluminal signalling becomes possible, and quantum particles can be clearly seen and controlled. This new physics could have left traces in the early universe, and it might be visible today in radiation from exploding primordial black holes. Harnessing this new physics would have transformative technological implications, in particular for communication, cryptography, and computing.

Drawing intriguing parallels between the present era of quantum physics and past episodes of scientific confusion, this book tells the story of how pilot-wave theory was discovered and abandoned, revived and reconstructed, and how today it can pave the way to a new and radical physics beyond the quantum.

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In the thirteenth-century Mediterranean, commerce transformed as merchants shifted from Roman to Indo-Arabic numerals—an alternative that better facilitated complex calculations. It has long been known that this transition stemmed from Europe’s increasing exchanges with India, Persia, and the Arabic world. Yet much remains to be understood about how Indo-Arabic numerals—and the practical arithmetic they enabled—actually spread across Europe. As Dr. Raffaele Danna shows in The Craft of Indo-Arabic Numerals: How Practical Arithmetic Shaped Commerce and Mathematics in Western Europe, 1200–1600 (Harvard University Press, 2026), it was hundreds of ordinary merchants, schoolmasters, and artisans who nurtured these changes, thereby driving key advances in both commerce and mathematics.

Drawing on an original catalog of more than 1,200 practical arithmetic manuals, Dr. Danna charts the incremental spread of the new figures with unprecedented precision. While Italian merchants were the early adopters, it took nearly three centuries for Indo-Arabic numerals to become established in northern Europe. As Dr. Danna shows, adoption did not follow the routes of maritime trade. Rather, Indo-Arabic numerals moved gradually across the continent through inland networks of practitioners. Everywhere they went, the ten figures enhanced commercial practices and facilitated the emergence of a coherent language of mathematical craft. The growing social circulation of this knowledge, in turn, had a lasting impact on the economic trajectory of Western Europe. By the late sixteenth century, even academics were absorbing lessons from the vernacular tradition—a development that led to the first major breakthroughs in European mathematical theory since antiquity.

Combining economic history with the social history of mathematics, The Craft of Indo-Arabic Numerals illuminates the integral role of practical arithmetic in both intellectual and commercial transformations across Western Europe.

This interview was conducted by Dr. Miranda Melcher whose book focuses on post-conflict military integration, understanding treaty negotiation and implementation in civil war contexts, with qualitative analysis of the Angolan and Mozambican civil wars. You can find Miranda’s interviews on New Books with Miranda Melcher, wherever you get your podcasts.

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A fun, dazzling exploration of the strange numbers that illuminate the ultimate nature of reality.

For particularly brilliant theoretical physicists like James Clerk Maxwell, Paul Dirac, or Albert Einstein, the search for mathematical truths led to strange new understandings of the ultimate nature of reality. But what are these truths? What are the mysterious numbers that explain the universe?
In Fantastic Numbers and Where to Find Them: A Cosmic Quest from Zero to Infinity (FSG,2022), the leading theoretical physicist and YouTube star Antonio Padilla takes us on an irreverent cosmic tour of nine of the most extraordinary numbers in physics, offering a startling picture of how the universe works. These strange numbers include Graham’s number, which is so large that if you thought about it in the wrong way, your head would collapse into a singularity; TREE(3), whose finite nature can never be definitively proved, because to do so would take so much time that the universe would experience a Poincaré Recurrence—resetting to precisely the state it currently holds, down to the arrangement of individual atoms; and 10^{-120}, measuring the desperately unlikely balance of energy needed to allow the universe to exist for more than just a moment, to extend beyond the size of a single atom—in other words, the mystery of our unexpected universe.
Leading us down the rabbit hole to a deeper understanding of reality, Padilla explains how these unusual numbers are the key to understanding such mind-boggling phenomena as black holes, relativity, and the problem of the cosmological constant—that the two best and most rigorously tested ways of understanding the universe contradict one another. Fantastic Numbers and Where to Find Them is a combination of popular and cutting-edge science—and a lively, entertaining, and even funny exploration of the most fundamental truths about the universe.

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The Laws of Thought: The Quest for a Mathematical Theory of the Mind (Henry Holt and Co., 2026) is an exploration of the quest to use mathematics to describe the ways we think, from its origins three hundred years ago to the ideas behind modern AI systems and the ways in which they still differ from human minds
Everyone has a basic understanding of how the physical world works. We learn about physics and chemistry in school, letting us explain the world around us in terms of concepts like force, acceleration, and gravity—the Laws of Nature. But we don’t have the same fluency with concepts needed to understand the world inside us—the Laws of Thought. While the story of how mathematics has been used to reveal the mysteries of the universe is familiar, the story of how it has been used to study the mind is not.
There is no one better to tell that story than Tom Griffiths, the head of Princeton’s AI Lab and a renowned expert in the field of cognitive science. In this groundbreaking book, he explains the three major approaches to formalizing thought—rules and symbols, neural networks, and probability and statistics—introducing each idea through the stories of the people behind it. As informed conversations about thought, language, and learning become ever more pressing in the age of AI, The Laws of Thought is an essential read for anyone interested in the future of technology.

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A bold reimagining of life that bridges science, philosophy, cybernetics, and the complexities of biological existence

The Organism Is a Theory: Giuseppe Longo on Biology, Mathematics, and AI (Giuseppe Longo and Adam Nocek, 2026) is an intriguing synthesis of decades of interdisciplinary research by eminent mathematician and biological scientist Giuseppe Longo. A unique collaboration between Longo and philosopher of technology Adam Nocek, the volume confronts foundational issues in the history of mathematics, computer science, physics, and theoretical biology.

Challenging conventional approaches that apply computational and formalist models to the biological world, Longo reveals how the limitations of these models hinder the understanding of organismic complexity, development, and evolution. Through a critique of dominant scientific paradigms, he emphasizes the need for a new biological theory that accounts for the temporal and spatial intricacies of life. Enhanced by Nocek's comprehensive introduction and a fascinating three-part interview with Longo, The Organism Is a Theory offers a bold rethinking of the biosciences, integrating the work of Alan Turing, Bernhard Riemann, Henri Poincaré, Kurt Gödel, and others into Longo's vision of critical biology.

Bridging scientific and philosophical discourses, this book creatively applies insights from mathematics, physics, and computing into the study of the organism to present a new theoretical approach to understanding biological complexity that resists reductive mechanistic and informatic explanations.

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The Necessities Underlying Reality: Connecting Philosophy of Mathematics, Ethics and Probability (Bloomsbury, 2025) is an open access book that covers four decades of work by the leading Australian philosopher, mathematician and historian of ideas, James Franklin.
These interlinking essays are connected by a core theme: the necessary structures in reality that allow certain knowledge of absolute truths. Franklin's Aristotelian realist philosophy of mathematics shows how mathematical truths are directly about physical reality, and at the same time certainly and provably true. Ranging from mathematics to evidence evaluation to ethics, his philosophy of probability sees the relation of evidence to hypothesis, such as in science and law, as purely logical, hence necessary.
Across ethics and the philosophy of religion, the theme of necessity is repeated: basic ethical truths (such as the worth of persons and the wrongness of murder) are shown to have the same certainty as mathematics. Focus on the history of ideas connects the philosophical work in the present with the medieval scholastic tradition, which defended similar necessities but is now neglected.
Here is an up-to-date introduction to Franklin's overall perspective. Recalling Western philosophy to its roots, it reveals the way absolute necessities are discoverable across the abstract fields of mathematics, logical evidence and ethics.

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An award-winning astrophysicist looks at how the understanding of uncertainty and randomness has led to breakthroughs in our knowledge of the cosmos

All of us understand the world around us by constructing models, comparing them to observations, and drawing conclusions. Scientists create, test, and replace these models by applying the twinned concepts of probability and randomness. Exploring how this process has refined our knowledge of quantum mechanics and the birth of the universe,

In The Random Universe: How Models and Probability Help Us Make Sense of the Cosmos (Yale UP, 2025) Andrew H. Jaffe offers a unique synthesis of the philosophy of epistemology, the mathematics of probability, and the science of cosmology.

As Jaffe puts Enlightenment thinkers like David Hume in conversation with contemporary philosophers such as Karl Popper and Imre Lakatos and engages with scientists ranging from Isaac Newton and Galileo to Albert Einstein and Arthur Eddington, he uses Thomas Bayes's seminal studies of statistics and probability to make sense of conflicting currents of thought. This is a deep look into how we have learned to account for uncertainty in our search for knowledge--and a reminder that science is not about facts and data as such but about creating models that correctly account for those facts and data.

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