Gauss famously described mathematics as the queen of the sciences. But how should we think of this discipline? Is it an aloof ruler, mysteriously governing the laws of nature? A vital tool for bettering our lot? Or a story that helps us understand nature?  

Professor Minhyong Kim directs the International Centre for Mathematical Sciences and the Centre for Mathematics for Humanity in Edinburgh. He is an accomplished number theorist — particularly within the field of diophantine equations (the Kim in Chabauty-Kim). And a best-selling author on popular mathematics in Korea. 

A Story For Humanity — Minhyong Kim on Why Maths Will Never End

Why do molecules have a "handedness" when the physics that determines their structure does not?* 

 This is a question emblematic of the philosophy of chemistry; at times, it has been used to argue that chemistry cannot be reduced to physics. However, Vanessa Seifert has a different — yet equally intriguing — answer. This symmetry breaking is closely linked to that contentious area of quantum mechanics: the measurement problem.  

 Vanessa is a Marie Skłodowska-Curie Postdoctoral Fellow based at the University of Athens and a visiting fellow at the University of Bristol. In addition to molecules, we discuss the project of reductionism, laws, and alchemy.  

 I found this to be a wonderful example of the fruitfulness of turning the philosophical gaze to sciences beyond physics.

*(Note, it can't be explained by the chirality of the weak nuclear force)

Links

vanessa-seifert.com [https://www.vanessa-seifert.com/] has links to Vanessa's publications and popular writing  — her articles on philosophy in Chemistry World are a great introduction to a broad range of topics

multiverses.xyz [https://www.multiverses.xyz/] Multiverses home

Molecules & Mirrors —Vanessa Seifert on the Philosophy of Chemistry

Christof Koch is a pioneering neuroscientist and one of the most prominent advocates of a scientific approach to consciousness. He has spent decades working at the intersection of neuroscience, philosophy, and computation.

Christof is one of the foremost proponents of Integrated Information Theory (IIT) — a radical proposal that attempts to explain consciousness in terms of causal structure.  IIT begins not with the brain, but with experience itself. It takes as its starting point what is undeniable: that something is happening right now — that experience exists. It then looks at the features of conscious experience, for example, that is unified yet composed of parts, and contentful. From there, it builds a theory describing which physical systems support conscious states. 

 In this conversation, Christof and I explore what a scientific theory of consciousness might need to achieve, and why behavior alone — even the impressive feats of AI is not enough. Nor indeed is any computational account of consciousness: consciousness is about structure, two structures may lead to the same outcomes, but their form might mean that one is conscious and the other not.   But we also touch on experience beyond theory — Christof’s reflections on psychedelic experiences and the dissolution of the self.

This is a conversation about what it means to be a whole, what makes a system truly unified — and what it might take to understand, and perhaps even expand, the field of consciousness.  Christof’s latest book is Then I Am Myself the World: What Consciousness Is and How to Expand It.

Consciousness is not Computation — Christof Koch

Infinity may seem simple, just the absence of limits. But the closer we examine it, the more it unravels into paradox and mystery. Can some infinities be larger than others? How can an infinite hotel be fully booked yet still have room for more guests?

In this episode of Multiverses, I’m joined by Adrian Moore, professor of philosophy at Oxford, to explore these questions. We dive into Hilbert’s Hotel, Cantor’s revolutionary work on transfinite numbers, and the philosophical and even theological implications of the absolute infinite—the place where maths itself seems to break down.

Along the way, we ask: Is infinity something we can ever truly grasp? Or does it forever retreat beyond our understanding?

If you like these topics, where science, maths give way to the unstable ground of philosophy ... subscribe!

Adrian's academic homepage [https://www.philosophy.ox.ac.uk/people/adrian-moore]

Adrian's book: The Infinite [https://www.amazon.co.uk/Infinite-Problems-Philosophy-W-Moore/dp/0415252857]  

Where Does It End? — Adrian Moore on The Infinite

Mind-wandering is often dismissed as a distraction, an idle drift away from productive thought. But what if this spontaneous movement of the mind is not just a quirk of cognition but a fundamental feature of how we think, create, and find meaning?  

Our guest, Kalina Christoff Hadjiilieva, is a Professor of Psychology at the University of British Columbia where she leads The Cognitive Neuroscience of Thought Laboratory. Her work explores the neural mechanisms behind mind-wandering, uncovering how our brains shift between goal-directed focus and free-flowing exploration.  

Kalina argues that mind-wandering is not a failure of attention but an essential cognitive process—one that fuels creativity, problem-solving, and insight. While some scientists define mind-wandering narrowly as thinking about anything other than the task at hand, she proposes a broader, more dynamic definition: mind-wandering is thought moving freely, unconstrained by immediate demands or rigid patterns.  

Neuroscience has long favored studying controlled, deliberate cognition. The executive brain functions—the ones we can track, measure, and influence—are often given priority. But Kalina points out that the vast majority of brain activity is spontaneous and unexplained. She advocates for a shift in perspective: instead of treating free thought as noise, we should recognize its role in structuring our experiences, shaping our beliefs, and allowing us to make sense of the world. 

 Mind-wandering, Kalina suggests, is not just about distraction—it is about discovery.

37| Mind-Wandering — Kalina Christoff Hadjiilieva on the Science of Spontaneous Thought

Scientific discoveries can often be codified in simple laws, neatly stated in textbooks with directions on applying them. But the enterprise of science is embedded in society. It depends on individuals and economies. It is far from simple to answer the question: How did we get these laws? 

Patricia Fara is an Emeritus Fellow of Clare College, Cambridge. She is a former president of the British Society for the History of Science and has written Science: A Four Thousand Year History,  Newton: The Making of Genius, and numerous other books. 

Patricia discusses the way we often mythologize individual scientists and how the notion of genius has changed over the centuries. She also highlights lesser-known figures, such as Hertha Ayrton, whose contribution should not be measured merely in scientific breakthroughs, but in how they paved the way for further women scientists.

36| History of Science: Mythmaking & Contingency — Patricia Fara

AI can do many things equally well as humans: such as writing plausible prose or answering exam questions. In certain domains, AI goes far beyond human capabilities — playing chess for instance.

We might expect that nothing prevents machines from one day besting humans at every task. Indeed, it is often asserted that, in principle, everything (and more) within the range of human cognition will one day fall within the ken of AI.

But what if there are concepts and ways of thinking that are off-limits to any machine, yet not so for humans? Selmer Bringsjord, Professor in Cognitive Science at RPI joins us this week and argues we need to rethink human thought.

Selmer argues that humans have been able to grasp problems that machines cannot — humans are capable of hypercomputation. Hypercomputation is computation above the Turing limit, as such it can solve problems beyond the power of any machine we can currently conceive.

In particular, Turing computation cannot encompass infinitary logic, yet humans have been able to reason effectively about the infinite. Similarly, Gödel’s theorem points to a class of riddles machines cannot reach, yet human genius has identified.

This is a huge topic, accepting Selmer’s arguments entails accepting that human minds work in a way that evades our understanding — their mechanisms obeying mechanics of which we are wholly ignorant.

Whether or not you agree with Selmer’s conclusions, this is a brilliant exploration of the boundaries of thought.

Links

 * Selmer's Academic Homepage [https://kryten.mm.rpi.edu/selmerbringsjord.html]
 * RPI AI and Reasoning Lab (RAIR) [https://rair.cogsci.rpi.edu/]

35| Hypercomputation: Why Machines May never Think Like Humans — Selmer Bringsjord

There is no consensus on what minds are, but there is plenty of agreement on where they can be found: in humans. Yet human consciousness may account for only a small proportion of the consciousness on our planet.  

Our guest, Kristin Andrews, is a Professor of Animal Minds at the University of York, Ontario, Canada. She is a philosopher working in close contact with biologists and cognitive scientists and has spent time living in the jungle to observe research on orangutans.  

Kristin notes that comparative psychology has historically resisted attributing such things as intentions, learning, consciousness, and minds to animals. Yet she argues that this is misguided in the light of the evidence, that often the best way to make sense of the complexity of animal behavior is to invoke minds and intentional concepts.  

Recently Kristin has proposed that the default assumption — the null hypothesis — should be that animals have minds. Currently, biologists examine markers of consciousness on a species-by-species basis, for example looking for the presence of pain receptor skills, and preferential tradeoffs in behavior. But everywhere we have looked, even in tiny nematode worms, we find multiple markers present. Kristin reasons that switching the focus from asking "where are the minds?" to "what sort of minds are there?" would prove more fruitful.  

The question of consciousness and AI is at the forefront of popular discourse, but to make progress on a scientific theory of mind we should draw on the richer data of the natural world.  

 * Kristin's website [https://www.kristinandrews.org/] has links to her books and papers. 
 * As an introduction to her thinking How To Study Animal Minds [https://www.goodreads.com/en/book/show/51763564-how-to-study-animal-minds] is a gem of a book.

34| Animal Minds — Kristin Andrews on why assuming consciousness would aid science

Things happen. Or they don’t. How then should we make sense of claims that something might happen?

If all these claims do is express doubt, then the puzzle can be easily resolved. But if the claims capture some objective feature of the world, what is it?

Our guest is Alastair Wilson, a professor of philosophy at the University of Leeds. He takes chance seriously, in particular, he is a realist about our modal claims (claims like “either candidate could win” or “if Szilard hadn’t got Spanish flu, the atom bomb would not have been invented”) may be true or false, not just opinions or expressions of ignorance.

Alastair does this by connecting our modal talk to Everettian quantum mechanics. He argues that modal claims are assertions about the many worlds within the universal wavefunction. If in all worlds where Szilard did not succumb to Spanish flu, the atom bomb was never invented, then this claim would be true.

It is a bold and fascinating way of bringing physics and metaphysics together. What can happen, what is possible, what could have been? These become questions for natural science.

 * Alastair's website [https://alastairwilson.org/]
 * Nature of Contingency: Quantum Physics as Modal Realism [https://www.amazon.co.uk/Nature-Conti...]

33| Taking Chance Seriously — Alastair Wilson on Quantum Modal Realism

The launch of ChatGPT was a "Sputnik moment". In making tangible decades of progress it shot AI to the fore of public consciousness. This attention is accelerating AI development as dollars are poured into scaling models. 

 What is the next stage in this journey? And where is the destination?   

My guest this week, Nell Watson, offers a broad perspective on the possible trajectories. She sits in several IEEE groups looking at AI Ethics, safety & transparency, has founded AI companies, and is a consultant to Apple on philosophical matters.  Nell makes a compelling case that we can expect to see agentic AI being soon adopted widely. We might even see whole AI corporations. In the context of these possible developments, she reasons that concerns of AI  ethics and safety — so often siloed within different communities — should be understood as continuous.  

 Along the way we talk about the perils of hamburgers and the good things that could come from networking our minds.  

Links

 * Nell's book: Taming The Machine: Ethically Harness The Power Of AI  [https://www.amazon.co.uk/Taming-Machine-Ethically-Harness-Power/dp/1398614327]
 * Multiverses home [http://multiverses.xyz]

AI Moonshot — Nell Watson on the Near & Not So Near Future of Intelligence

Coffee table conversations with people thinking about foundational issues.  Multiverses explores the limits of knowledge and technology.  Does quantum mechanics tell us that our world is one of many?  Will AI make us intellectually lazy, or expand our cognitive range? Is time a thing in itself or a measure of change? Join James Robinson as he tries to find out.

James Robinson

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