More or Less: Behind the Stats - US National Debt: is $32 trillion a big number?

?This episode was updated on 26th June to remove an error in how we quantified 32 trillion dollars? The level of US government debt has just surpassed 32 trillion dollars. Negotiations over raising the borrowing limit once again went down to the wire a few weeks ago. But how concerned should we all be about how much the US government borrows? We investigate with the help of Kent Smetters, professor at the Wharton School of the University of Pennsylvania and Betsey Stevenson, Professor of Economics and Public Policy at the University of Michigan.

More or Less: Behind the Stats - Mortgages, birth rates and does space contribute 18% to UK GDP?

Mortgage rates have risen to 6%. But are things as bad as when rates were much higher in the 1970s and 80s? We look at just how much pain today's rises mean. Also will there be just 6 grandchildren for every 100 South Koreans today? And we look into a claim that the space industry supports 18% of the UK's economy.

Presenter: Tim Harford Series Producer: Jon Bithrey Reporters: Beth Ashmead Latham, Nathan Gower, Charlotte McDonald Sound Engineer: James Beard Production Co-ordinator: Brenda Brown

Start the Week - Sums, stories and musical scores

Kirsty Wark celebrates the artistry of numbers with three mathematicians Eugenia Cheng, Sarah Hart and Emily Howard.

Eugenia Cheng asks Is Maths Real? in her new book, which offers a new way to look at the subject by focusing on the questions, rather than the answers. She explores how asking the simplest of questions – ‘why does 1 + 1 = 2?’ – can get to the very heart of the search for mathematical truth.

Sarah Hart wants to break down the perceived barriers between mathematics and the creative arts. In Once Upon a Prime: The Wondrous Connections Between Mathematics and Literature she reveals the geometry lurking in Moby-Dick, George Eliot’s obsession with statistics, and Jurassic Park’s fractal patterns.

Emily Howard has a dual passion for maths and music. In her compositions she plays with mathematical shapes and processes. Her new record Torus, released on NMC Recordings in April, brings together works including sphere and Compass.

Producer: Katy Hickman

More or Less: Behind the Stats - Electric vehicles, 600 million bottles and does oral sex cause cancer?

There's been a lot of coverage about the risks electric cars may pose to infrastructure like bridges and car parks. We look at how much heavier EVs are. Plus we look at a new study that suggests a link between breastfeeding and improved grades at GCSE level. Also is throat cancer now primarily caused by a sexually transmitted disease - and are 600 million bottles going to litter Scotland because of disagreements with the UK government over the new Deposit Return Scheme?

Start the Week - Hacking and cybercrime

Just how safe is the online world? Yale Professor of Law and Philosophy Scott Shapiro delves into cybersecurity in his book, Fancy Bear Goes Phishing. The book’s title derives from the exploits of ‘Fancy Bear’, an elite unit of the Russian military intelligence that hacked the US Democratic National Committee in 2016. From a bored graduate student who accidentally crashed the nascent internet, to cyber criminals and bot farms, Shapiro looks at the dark history of the information age.

Dr Alice Hutchings first began researching cybercrime in the late 1990s, while working in industry, and is now Director of the Cambridge Cybercrime Centre. She argues that the romanticised image of the underground hacker as an anti-authoritarian ‘lone wolf’ who possesses technological wizardry is outdated. Hacking has become industrialised with criminals able to buy ‘off-the-shelf’ tools to infect computers.

While hackers constantly look to exploit vulnerabilities within the technology, one of the major weak points are users themselves. Jenny Radcliffe’s job is to expose the flaws and weaknesses in security operations. In People Hacker she explains how she uses a blend of psychology, stagecraft and charm to gain access to computer systems, and reveals how people can boost their security and make her job more difficult.

Producer: Katy Hickman

More or Less: Behind the Stats - Counting Hunger in India

How prevalent is hunger and malnutrition in India? With Indian data journalist Rukmini S, we interrogate recent claims that hunger has worsened dramatically in recent years, and explore how malnutrition affects child mortality in the world?s most populous country.

Presenter: Tim Harford Producer: Nathan Gower Editor: Richard Vadon Programme Coordinator: Brenda Brown Sound Engineer: Neil Churchill

More or Less: Behind the Stats - Lib Dem ambulance claims, affordable rent and goat meat

The Liberal Democrats say 120 people a day in England died last year whilst waiting for an ambulance. We investigate whether the claim stands up to scrutiny. Also Rishi Sunak's pandemic-era scheme Eat Out To Help Out is back in the spotlight. How much did it really contribute to a second wave of infections? We look at a claim that no single woman in England on an average salary can afford to rent a home of her own. And Jonathan Agnew said on Test Match Special that goat is the most eaten meat in the world. Is he right?

Presenter: Tim Harford Series Producer: Jon Bithrey Reporters: Jo Casserly, Nathan Gower Editor: Richard Vadon Sound Engineer: James Beard Production Co-ordinator: Brenda Brown

(Woman looking for a flat to rent. Credit: Oscar Wong/Getty images)

Start the Week - Allergies and the Microbiome

Billions of people worldwide suffer from some kind of allergy and this is the focus of Theresa MacPhail’s book, Allergic. As a medical anthropologist and allergy sufferer herself she looks back at the history of diagnosis and treatment and investigates the worrying increase in numbers. It's thought by 2030 half the population will be sufferers.

James Kinross is a colorectal surgeon and suggests that some of the answer as to why there’s been a rise in allergies lies in the imbalance of our microbiome - our inner ecosystem of viruses, bacteria and other microbes. In his book, Dark Matter, he argues that the microbiome is under threat from our modern lifestyles, the food we consume, and the air we breathe.

Fermented foods are now thought to be integral to a healthy gut because they provide a vast amount of natural probiotics which can boost immunity and soothe the digestive tract. Johnny Drain is a materials scientist and a chef who believes in the benefits of fermentation, and has looked worldwide for innovations in techniques and flavours.

Producer: Natalia Fernandez

More or Less: Behind the Stats - A short history of data

We live in a world where data is everywhere ? informing if not governing our lives. But this wealth of data didn?t just turn up overnight. Tim Harford talks to academics Chris Wiggins and Matthew Jones, whose new book How Data Happened aims to explain how the world we know today has been shaped by not just technological developments but battles around how emerging sources of data should be utilised.