Adrian Moore reaches the end of his journey through two and half millennia of philosophical thought about the infinite.

In this final episode, he comes to the conclusion that his voyage through the worlds of philosophy, theology, mathematics and cosmology has in the end led him to ourselves and our place in the universe.

With the help of writers and philosophers as diverse as Rene Descartes, Ludwig Wittgenstein and Iris Murdoch, Adrian returns to the theme of our finite nature and how that is fundamental to our sense of what is infinite. He considers the relation between the infinite and the transcendent and examines where the desire to look for something beyond ourselves belongs in a secular society.

Throughout the series, Adrian and his cast of philosophers have made connections, performed calculations and looked up at the stars in their attempts to clarify what we mean by the infinite. But, his history tells us, it all comes back to us and how we relate to what surpasses our finite nature.

A Juniper production first broadcast on BBC Radio 4 in September 2016.

In his series on thought about infinity through the centuries, Adrian Moore has considered the topic through the lenses of philosophy, theology and mathematics.

Now, in this penultimate episode, the focus is firmly on us.

Adrian ponders our finite nature and confronts the question of whether, if we could, we really would want to live for ever. He brings us the Czech composer Janacek’s opera, with its eponymous heroine Elina Makropulos. Her father, the court physician, has procured an elixir of life for her but, far from making her eternally happy, her long life has become unbearably tedious.

Some philosophers fully sympathise with Elina Makropulos and celebrate our finite nature. Others lament it. But as Adrian discovers, there is consensus on one point – the fact that one day our life will end doesn’t rob it of meaning.

Indeed, it is our very sense of our own finite nature, argues John Cottingham, Professor Emeritus at Reading University, that produces what St Augustine called ‘the restlessness of the human heart’ - our constant desire to reach out for more.

A Juniper production first broadcast on BBC Radio 4 in September 2016.

Does space go on for ever? Are there infinitely many stars?

These are some of the questions Adrian Moore explores in this episode in his series about philosophical thought concerning the infinite.

With the help of the theories of the Ancient Greeks through to those of modern cosmologists, Adrian examines the central question of whether our universe is finite or infinite.

For most of us, looking up at the stars gives us a sense of infinity but, as Adrian discovers, there is a strong body of opinion which suggests that space is finite, albeit unbounded. This is a difficult idea to grasp, but by inviting us to think of ourselves as ants, astrophysics professor Jo Dunkley attempts explain it.

Adrian also tackles the idea of the expanding universe and the logic that leads cosmologists to argue that it all started with a big bang, and may all end with a big crunch.

Finally, we discover from cosmologist John Barrow how the appearance of an infinity in scientists’ calculations sends them straight back to the drawing board. The infinite, which the Ancient Greeks found so troubling, has lost none of its power to disturb.

A Juniper production first broadcast on BBC Radio 4 in September 2016.

Adrian Moore’s series on philosophical thought on infinity finds him mired in a near meltdown in mathematics.

Adrian tells the story of the controversy caused by the work of the German mathematician, Georg Cantor, on the infinite. In a world of paradoxes, we meet the nun who can't decide whether to pray for herself. Her dilemma is beautifully explained by Marcus Giaquinto, Emeritus Professor of Philosophy at UCL, in conversation with Adrian. And we find out how an associated paradox, first posed by one of the giants of 20th century philosophy, Bertrand Russell, devastated the career of another German mathematician and philosopher.

The arguments of the early 20th century no longer plague modern mathematics in the way that they did. As Adrian explains however, by subjecting the infinite to formal scrutiny, mathematicians have ended up confronting puzzles at the very heart of their discipline.

A Juniper production first broadcast on BBC Radio 4 in September 2016.

Adrian Moore continues his exploration of two and a half millennia of philosophical thought on infinity.

Discover the brilliant but tortured German mathematician, Georg Cantor, who devised a way of distinguishing between infinitely big numbers and of performing calculations with them.

His work was revolutionary but, as Adrian discovers, it greatly polarised opinion amongst his late 19th and early 20th century contemporaries - and we hear how Cantor himself suffered a complete breakdown in his mental health.

As Adrian takes us with him deep into the world of infinite set theory, he enlists the help of Mary Leng, Senior Lecturer in Philosophy at York University, and four very familiar twentieth century friends.

A Juniper production first broadcast on BBC Radio 4 in September 2016.

Having looked at the infinite in philosophical and theological terms, it’s time to view it through the lens of mathematics. In the fifth programme in his series, Adrian Moore introduces us to the pivotal role mathematics has played in the quest to understand the infinite.

He begins by enlisting the help of very modern technology and considering the real question put by an 11 year old boy - what is zero divided by zero?

That’s the trigger for Adrian’s investigation of the calculus – the tool we use to reckon with very small quantities. It plays a huge part in many aspects of modern-day design, medicine and statistical work, but what is less well-known is the seventeenth century row between two eminent scientists as to who actually invented it. Adrian meets science writer, Brian Clegg, to find out about the race to claim credit.

It didn’t just cause a storm at its inception - we hear about the disagreements that dogged the calculus’s early days, with the church too getting involved in the disputes about the infinitely small.

But as Adrian discovers, the quest to understand the infinite has left us with a branch of mathematics of unparalleled importance.

A Juniper production first broadcast on BBC Radio 4 in September 2016.

Adrian Moore brings us to the verge of the modern world and the way we think now. He leaves the arguments of the medieval church and renaissance thinkers behind and steps into the world of enlightenment philosophy, as heralded by Rene Descartes.

Adrian tells us that Descartes was a typical enlightenment philosopher, seeking to establish what understanding we can have of the infinite using our own finite intellectual resources. How can we have any sense of infinity, if we have no direct experience of it?

Adrian describes Descartes’ attempts to establish a secure foundation for his beliefs, beginning with his questioning of his own existence and then of the existence of God.

We also meet the British empiricists who took issue with Descartes, and finally Immanuel Kant, who believed that each human being is of infinite worth.

The soundtrack is Beethoven’s eighth string quartet, which is said to have been inspired by Kant’s vision of our place as human beings in the universe.

A Juniper production first broadcast on BBC Radio 4 in September 2016.

Adrian Moore reaches the third stage of his journey through thought about infinity, describing how the church attempted to stamp its authority on the debate and how that led to some explosive disagreements amongst medieval thinkers.

With the help of Cecilia Trifogli, Lecturer in Medieval Philosophy at Oxford University, Adrian finds out about the life of St Thomas Aquinas. Aquinas defied his mother to become a Dominican friar – she had hoped for a career in the more prestigious Benedictine order for him – and, more importantly, he attempted to engineer a reconciliation between the theories of Aristotle on the infinite and the doctrines of the Catholic church.

He was successful up to a point and, once the church had embraced Aristotle’s teachings as the new orthodoxy, philosophers stepped out of line at their peril. The famous dissenter and innovator, Galilei Galileo, did just that. He dared to add his contradictory views to the debate and introduced a series of paradoxes which foreshadowed much later thinking on infinity.

Adrian presents us with a vivid picture of the clash between theology and Greek philosophy, and a sense of the ongoing struggle of both to understand the infinite.

A Juniper production first broadcast on BBC Radio 4 in September 2016.

In the second part of his journey through two and half millennia of philosophical thought, Adrian Moore introduces us to the Greek philosopher, Aristotle, who attempted a reconciliation between the idea of things going on for ever and ever and the Greeks’ abhorrence of the very notion.

We hear how he came up with the idea of two different types of infinite - the potential and the actual - and how it was the potential infinite that he presented as the acceptable face of infinity.

With the help of Ursula Coope, Professor of Ancient Philosophy at Oxford University, Adrian explains the idea of infinite divisibility and re-visits the paradoxes of Zeno which suggest that motion isn’t possible. He carries out his own experiment to see whether using Aristotle’s theory of the infinite he can disprove Zeno’s conclusions and actually get himself home.

And he reveals how Aristotle’s theory of the infinite held sway for thousands of years, despite the challenges to it.

A Juniper production first broadcast on BBC Radio 4 in September 2016.

Adrian Moore starts his journey through philosophical thought on infinity over the last two and a half thousand years.

In the first episode, he finds out why the idea made the Greeks so uncomfortable and introduces us to some of the first great thinkers on infinity.

We meet Pythagoras and his followers who divided the world into two fundamental cosmic principles. On one side was everything they thought of as limited or finite, and therefore good, and on the other everything they considered unlimited or infinite, and therefore bad.

The Pythagoreans thought they could explain the world around them in terms of the numbers - 1, 2, 3, 4, etc - which we use to count finite collections of things, and they were utterly dismayed when they discovered that not every calculation produced the neat answer they expected. According to legend, one of their number was shipwrecked at sea for revealing this discovery to their enemies!

And we meet Zeno of Elea who, after wrestling with the notion of infinity, came to the conclusion that movement itself was impossible.

A Juniper production first broadcast on BBC Radio 4 in September 2016.