Faced with one cake and eight hungry people, it’s pretty obvious how maths underpins reality. But as mathematics gets further from common sense and into seemingly abstract territory, nature still seems to obey its rules - whether in the orbit of a planet, the number of petals on a flower, or the structure of an atom.
 
But what exactly is the relationship between mathematics and reality? That’s the impossibly difficult question CrowdScience has been set this week by our listener Sergio in Peru. It’s one that’s been pondered by humans for millennia: the Greek philosopher Pythagoras believed “All is number”.
 
Is maths a human construct to help us make sense of reality - a tool, a model, a language? Does maths create its own reality? Or is it reality itself? CrowdScience explores these questions with the help of experts from the fields of philosophy, mathematics and science: Dr Eleanor Knox, Dr Eugenia Cheng, Professor Lucie Green, Alex Bellos and Stefano Centineo.
 
Presenter: Marnie Chesterton
Produced by Cathy Edwards for the BBC World Service (Photo: A young woman with her eyes closed standing in front of chalkboard, working out maths formulas. Credit: Getty Images)

Is maths real?

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Around the world, coastlines are constantly changing due to the power of waves, currents and tides. Coastal areas are also some of the most heavily populated and developed land areas in the world. So it’s not hard to see how the natural process of coastal erosion can cause serious problems for us.    It’s an issue that’s been bothering CrowdScience listener Anne in Miami Beach, Florida. She can see the beach from her window and wonders why after every storm, several trucks arrive to dump more sand on it.   In this first of two programmes, CrowdScience visits Anne’s home in south Florida and finds out how erosion threatens Florida’s famous beaches. She speaks to geoscientist Dr Tiffany Roberts Briggs and hears why it’s such a problem for this tourist-reliant state. Tiffany explains the delicate balance between natural processes and human infrastructure.   Meanwhile, the Caribbean island of Puerto Rico declared a state of emergency in April 2023 due to coastal erosion. Caroline witnesses the impacts of erosion first-hand, as Ruperto Chaparro shows her abandoned houses crumbling into the sea.   But how can we quantify the rate of erosion? Dr Kevian Perez in the Graduate School of Planning at University of Puerto Rico explains the methods they use to monitor Puerto Rico’s coastlines, and how they are evaluating the effectiveness of different mitigation methods.   However, some of the methods used to protect coastal communities from the encroaching sea have done more harm than good. So what are the best ways to tackle this problem? That’s what we’ll be exploring in next week’s programme.   Presenter: Caroline Steel 
Producer: Hannah Fisher 
Editor: Cathy Edwards 
Production Co-ordinator: Liz Tuohy  
Studio Manager: Steve Greenwood and Bob Nettles  Featuring: 
Dr Tiffany Roberts Briggs, Associate Professor at Florida Atlantic University 
Ruperto Chaparro, Director of Sea Grant Programme, University of Puerto Rico 
Anabela Fuentes Garcia, Villa Cristiana community leader 
Dr Kevian Perez, researcher at the Coastal Research and Planning Institute of Puerto Rico at the Graduate School of Planning (Photo: Puerto Rico after Hurricane Maria. Credit: Orlando Sentinel/Getty Images)

Are our coastlines being washed away?

How do we know where a sound is coming from?  Another chance to hear this ear-opening episode, exploring a question from CrowdScience listener Chiletso. One day, he heard his son bounce a ball and instantly knew the direction it was travelling. How?  Anand Jagatia sets out to discover what makes left, right, up and down sound so different.  First, he gets blindfolded, so Alan Archer-Boyd, former auditory scientist and lead engineer at BBC R&D;, can put his sound localisation skills to the test. It turns out that having two ears and pinnae, those flappy bits of cartilage on the side of your head, help a lot.  Professor Eric Knudsen shares how the barn owl’s asymmetrical ears allow it to hunt mice, even in complete darkness.  And Anand uncovers how far he can push his own spatial hearing. Blind activist and researcher Thomas Tajo teaches him how to echolocate like a bat, and Dr Lore Thaler explains what is going on in the brain of experienced echolocators.  This programme was originally broadcast in March 2023.  Presented by Anand Jagatia 
Produced by Florian Bohr for the BBC World Service  Image: Boy with hands at his ears 
Credit: Silke Woweries/Getty Images

How do my ears sense direction?

Today there are over eight billion people on Earth. That’s an awe-inspiring figure… but how does it compare to the vast numbers who came before us? Listener Alpha wants to know how many people have ever existed, so CrowdScience sets out to do a historical headcount. The Population Reference Bureau in the USA estimated this number back in the 90s, and have been updating their calculations ever since. Demographer Toshiko Kaneda explains how their model works, the assumptions it makes – and the huge uncertainties around the number it comes out with. We first need a date for when ‘humans’ first began, so Caroline travels to the Natural History Museum in London to meet human evolution expert Chris Stringer, and marvel at his collection of replica fossil skulls. Chris demonstrates how to distinguish our species, Homo sapiens, from other species like Neanderthals. When did these species first appear - and which of them count as human? And once you know where to start the clock, how do you estimate the numbers of people alive at different points in history? For a population demographer like Walter Scheidel, it helps that some ancient civilisations kept detailed censuses, a few of which have survived to the present day. Caroline and Walter pour over one of these census fragments, and learn how to combine them with other archaeological clues to get some very rough numbers. And finally: what does the future of our population look like? Poonam Muttreja from the Population Foundation of India discusses developments in the world’s most populous country, as well as the big demographic trends ahead for humanity.  Presenter: Caroline Steel 
Producer: Phil Sansom 
Additional Recording: Umaru Fofana 
Editor: Cathy Edwards 
Production Co-ordinator: Connor Morgans 
Studio Manager: Sue Maillot  Featuring:
Toshiko Kaneda, Technical Director of Demographic Research, Population Reference Bureau
Chris Stringer, Research Leader in Human Evolution, Natural History Museum London 
Walter Scheidel, Professor of Classics and History, Stanford University 
Poonam Muttreja, Executive Director, Population Foundation of India

How many people have ever existed?

We spend a lot of our time thinking about climate change, but listener Paul has a question that isn’t usually part of the conversation. He wants to know whether a hotter atmosphere will affect how often volcanoes erupt, or make them more explosive when they do. CrowdScience travels to New Zealand to search for answers, exploring volcanic craters and discovering traditional Maori knowledge about volcanoes. Contributors: 
Geoff Kilgour, Volcanologist, Geological and Nuclear Sciences Taupo, New Zealand
Heather Handley, Volcanologist, University of Twente, The Netherlands 
Pouroto Ngaropo, Historian and Matauranga Māori expert, Rotorua, New Zealand  Presenter: Caroline Steel
Producer: Emily Bird 
Editor: Cathy Edwards
Production Co-Ordinator: Connor Morgans
Sound Engineer: Steve Greenwood (Photo: Icelandic volcano. Credit: KRISTINN MAGNUSSON/Getty Images)

Could climate change lead to more volcanic eruptions?

Many of us have habits that calm us down in times of stress. Things we find deeply comforting, like sucking our thumb or biting our nails. We might not even be aware we’re doing them, but they play a fundamental role in helping us regulate our emotions.   Our question this week comes from CrowdScience listener and nail-biter, Ash. He wants to know where these habits come from. And since his pet dog is also a nail-biter: do we share these traits with other animals?  Recently, a video of a mouse cleaning up a man’s shed took the internet by storm. Was this a house-proud mouse, or was it the animal's way of making sense of a frenetic environment? An emerging field of scientists focusing on animal behaviour and emotions help us shed some light on such questions.   Along the way we meet a dog training specialist, learn what a sniffari is, go for playtime with a thumb-sucking otter, and visit an OCD clinic. We’ll also be getting tips on how to give your pets the best home environment, and meet an animal enrichment officer in South Africa, who knows how to spot the signs of an unhelpful habit developing.  Contributors: 
Karolina Westlund, Ethologist, Stockholm University and ILLIS 
Ben Terry, CBT Therapist, Priory Hospital North London 
Karin Pienaar, Animal Behaviourist, COAPE International 
Candice Ward, Animal Behaviourist, Johannesburg Zoo Jaak Panksepp clip: The science of emotions: Jaak Panksepp at TEDxRainier  Producer: Robbie Wojciechowski
Presenter: Alex Lathbridge
Editor: Cathy Edwards
Production co-ordinator: Connor Morgans
Additional recording by Elna Schutz (Photo: Portrait of border collie puppy biting a curtain. Credit: Rawlstock/Getty Images)

Is maths real?

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