WS MoreOrLess: An apple-a-day

Summary

Podcast Summary: More or Less – "An apple-a-day"

Host: Tim Harford, BBC Radio 4
Episode Air Date: January 20, 2014
Main Guests: Dr. Paul Morantz, Dr. Adam Briggs, Jolyon Jenkins
Episode Theme:
Exploring the evidence behind the claim "an apple a day keeps the doctor away," the nuances of statistical studies in health, and a mathematical card trick illustrating randomness.

---

Episode Overview

This episode opens with headlines inspired by a British Medical Journal (BMJ) article suggesting that eating an apple a day could save as many lives as prescribing statins to everyone over 50. Tim Harford examines the real science behind these claims, discussing the limitations of statistical models compared to clinical trials, and then shifts to a mathematically intriguing card trick that unpacks the concept of randomness in shuffling.

---

Key Discussion Points and Insights

The Apple-a-Day Study: Claims and Critique

[00:18 – 03:27]

• Not a Clinical Trial:
  Tim Harford explains that the BMJ study behind the headlines wasn't a clinical trial but a modeling exercise. Researchers at Oxford used statistical models derived from earlier dietary studies to estimate the potential health benefits if everyone over 50 ate an apple a day.

  "This wasn't an exhaustive clinical trial of munching on apples…They essentially did two thought experiments."
  — Tim Harford [00:37]

• Apples vs. Statins:
  The study estimated that eating an extra apple per day could save 8,500 lives each year in the UK—almost as many as if statins were prescribed to all over-50s.

• Critique from Dr. Paul Morantz:
  Morantz criticizes the methodology, highlighting that statin benefits are based on rigorous randomized controlled trials (RCTs), whereas the apple estimates are extrapolations from less robust nutritional studies.

  "They took data from the statin trials, which were based on randomized controlled trials, and compared it to…apple consumption. But that was…an extrapolation from studies of fruit and vegetable consumption…It's not at the same level of methodological rigor."
  — Paul Morantz [02:01]

• Response from Study Author, Dr. Adam Briggs:
  Briggs acknowledges the limitations: the evidence for apples isn't as strong as for statins, but emphasizes transparency in the assumptions and that simple interventions can yield significant health benefits.

  "Now, it's not as good evidence as statins, but it is the best evidence that is currently available."
  — Adam Briggs [02:34]
  "What we're not saying…is that you should be swapping your statins for apples. Instead, you should be adding in your apple."
  — Adam Briggs [02:54]

Notable Moment

• The light-hearted nature of the study is mentioned, as it appeared in the BMJ's Christmas edition, known for its humor — though Briggs clarifies the potential public health message is serious.

---

The Mathematical Card Trick: How Many Shuffles To Randomize?

[03:27 – 08:58]

• The Trick Setup:
  Tim recounts taking part in a magic card trick orchestrated by BBC journalist Jolyon Jenkins. After mixing and mailing half a deck, Jolyon remotely deduces Tim’s chosen card—demonstrating a principle based on how shuffling affects order.

• Behind the Magic – The Math:
  Jolyon explains the key principle: a riffle shuffle mixes two halves but preserves the internal order of each. By reconstructing the 'chains' or sequences, he identifies the chosen card.

  "If you do a riffle shuffle, the red and the black cards will all be mixed up, but the black cards will still be in their order. They'll still be ace through to king…So you have what you can think of as sort of two interlocking chains of cards, but it is actually possible to reconstitute the chains."
  — Jolyon Jenkins [05:18]

• The Origin of the Trick:
  Invented by Charles Jordan, a Californian chicken farmer, who sold the trick by mail order a century ago.

  "It was invented by a reclusive chicken farmer in California called Charles Jordan 100 years ago, and he sold it by mail order for $2.50…"
  — Jolyon Jenkins [06:49]

• How Random Is a Shuffle?
  Jolyon references mathematician Percy Diaconis’s work on the mathematics of shuffling:

  "If you do six riffle shuffles, you've still got a certain amount of order in the deck, but seven completely destroys the order."
  — Jolyon Jenkins [07:56]

  The transition from order to randomness is like a "cliff edge" after the seventh shuffle.

• Broader Applications:
  The mathematics of mixing (how much you need to stir or mix substances to reach true randomness/homogeneity) has practical implications beyond cards, like in paint and pharmaceutical manufacturing.

Notable Quote

• "If you're a casino, you need to know about this…three or four riffle shuffles was enough, but it clearly isn't."
  — Jolyon Jenkins [07:56]

---

Timestamps – Important Segments

| Timestamp | Content | |------------|-------------------------------------------------------------| | 00:18 | Introduction to the apple-a-day study | | 02:01 | Critique from Dr. Paul Morantz | | 02:34 | Study author Dr. Adam Briggs responds | | 03:27 | Transition to the card trick story | | 05:18 | Explanation of the shuffle/math principle (Jenkins) | | 06:49 | History and origin of the card trick | | 07:56 | Diaconis’s finding: it takes seven riffle shuffles to randomize | | 08:58 | Jenkins links mixing mathematics to real-world applications |

---

Memorable Quotes

• "They took data from the statin trials, which were based on randomized controlled trials, and compared it to…apple consumption. But that was…an extrapolation…It's not at the same level of methodological rigor."
  — Dr. Paul Morantz [02:01]

• "You could write a more serious, nuanced paper which stresses the fact that actually it could be any extra piece of fruit to do this…What we're not saying…is that you should be swapping your statins for apples."
  — Dr. Adam Briggs [02:54]

• "If you do six riffle shuffles, you've still got a certain amount of order in the deck, but seven completely destroys the order…So it just vanishes the order at 7. It's like a kind of cliff edge."
  — Jolyon Jenkins [07:56]

---

Episode Takeaways

• Statistical Modeling Limitations:
  Media headlines often stretch or oversimplify scientific studies. Statistical models (like the apple-a-day analysis) cannot match the rigor of randomized controlled trials.

• Simple Interventions Matter, But With Nuance:
  While dietary improvements are good, they are not substitutes for medication where indicated.

• Math in Everyday Life:
  Seemingly abstract concepts—like randomness or mixing—have real-world effects, whether shuffling cards, manufacturing paint, or blending medicines.

---

Further Information

Listeners interested in more number crunching or wanting statistical myths debunked can contact the show at [e-mail], or visit bbcworldservice.com/moreorless for more episodes.

---

End of Summary

Transcript

[BBC Announcer]

This is the short edition of More or Less, first broadcast on the BBC World Service.

[BBC Podcast Promoter]

Thank you for downloading from the BBC. For details of our complete range of podcasts and our terms of use, go to bbcworldservice.com podcasts

[Tim Harford]

hello and welcome to More or Less on the BBC World Service. I'm Tim Harford. You may remember this story from December, which made headlines around the world.

[BBC Announcer]

An apple a day keeps thousands of deaths at bay why an apple a day could be as good as a statin for over 50s.

[Tim Harford]

The source of the headlines was a study that featured in the British Medical Journal, or bmj. But contrary to what you might think, this wasn't an exhaustive clinical trial of munching on apples. Instead, a group of researchers at the University of Oxford in the UK used mathematical models based on earlier research about the health benefits of fruit and veg to test the old proverbial an apple a day keeps the doctor away. They essentially did two thought experiments. First, they thought to themselves. Currently, there are 5 million people considered at risk of heart disease who are already prescribed statins by the UK's National Health Service. So what would happen if we prescribed statins to everyone in the UK population over 50? And how many lives might be saved each year by preventing heart disease if we did that? And then the second thought experiment, why not go one step further and see if we could work out how many lives could be saved each year from heart attacks and strokes if everyone in the population over 50 ate an apple. Lo and behold, the researchers found that eating an extra apple a day would indeed save 8,500 lives, almost as many as offering statins to all over 50 year olds. All very nice, but Paul Morantz, a doctor at the Albert Einstein College of Medicine in the United States, had some problems with it. He wrote a blog post about them. Why?

[Paul Morantz]

What they did was, if you'll pardon the pun, compared apples and oranges. They took data from the statin trials, which were based on randomized controlled trials, and compared it to what they actually called apple consumption. But that was already an extrapolation from studies of fruit and vegetable consumption. Even more to the point, no studies of dietary patterns can follow the randomized control trial paradigm. It's not at the same level of methodologic rigor.

[Adam Briggs]

Now, it's not as good evidence as statins, but it is the best evidence that is currently available.

[Tim Harford]

This is Adam Briggs, one of the authors of the study.

[Adam Briggs]

We make very transparent our assumptions and our limitations for this research.

[Tim Harford]

Now, the article featured in the Christmas edition of the bmj, reputed for being more light hearted than usual, and jokes abounded in the piece.

[Adam Briggs]

I don't think we're joking in terms of what the potential benefits can be of preventing disease and ways of doing that. You could write a more serious, nuanced paper which stresses the fact that actually it could be any extra piece of fruit to do this. You could then compare it to other drugs, you compare it to other vegetables, etc. And what we've identified is that simple interventions can lead to really important health benefits. What we're not saying to take it the other way, Tim, is that you should be swapping your statins for apples. Instead, you should be adding in your apple.

[Tim Harford]

Adam Briggs. Now, a magician recently sent me a pack of cards through the post. Look at the cards to make sure they're not in any particular order, he said. And then cut them. And then cut them again, he said. And then take the deck, split it into two and riffle shuffle the two halves together. I then had to divide the deck into two stacks again, take a card from the middle of one of the stacks, look at it, remember it, and then put that card back in the middle of the other stack. And then the magician said, take either of the two stacks, either the one with the chosen card or the one without it, and give that stack a good shuffle and then send it back to me. And then the magician said, I will endeavour to surprise you. So I decided I would keep half of the deck, which had my chosen card in it, and I sent the other half by courier to the magician. And that magician's name was Jolyon Jenkins. He's a fellow journalist at the BBC. And here he was the next day, having received half the pack of cards, surprising me from a radio studio 100 miles away.

[Jolyon Jenkins]

I detected that it was a low card and I think it was a black card. And I think by the power of the mind alone, I'm putting myself on the line here. I think it was the three of clubs. Well, that's the card you're holding up.

[Tim Harford]

He has, in fact, got it right. Wow. Well, after I'd picked myself up off the floor, I asked Jolyan how he'd done it. Jolyan, I'm quite impressed. I have no idea how you did it. You did give us the deck of cards in advance, but it looked random to me, so. So how did you do it?

[Jolyon Jenkins]

Well, as you say, the cards weren't in any particular order, but I did know the order which they were in. So that was the first thing. So you cut the deck to start with, but that doesn't change the order. And then you did a riffle shuffle. And the riffle shuffle is interesting because it destroys one aspect of the card's order, but it preserves another aspect. So if you imagine that you have half a deck of cards, say all the clubs which are black, and you have them in order, ace through to king, and then on top of that, you have all the hearts which are red, and you have them also ace through to king, so you've got all black, followed by all red. Now, if you do a riffle shuffle, the red and the black cards will all be mixed up, but the black cards will still be in their order. They'll still be ace through to king.

[Tim Harford]

Yeah.

[Jolyon Jenkins]

And the red cards will still be ace through to king. So you have what you can think of as sort of two interlocking chains of cards, but it is actually possible to reconstitute the chains. Now, what you did, when you took a card out of one half of the deck and put it in the other half, it meant that one of the chains was broken up and then you shuffled the deck again. But that didn't matter because the card was still in the wrong half of the deck. You could have shuffled that as much as you wanted. So when I got the cards back, I had to sort of reconstruct the chain and see which card was either missing from a chain or in the wrong place.

[Tim Harford]

Now, this trick was originally a mail order trick. We did it at a mail order. Am I right? It was originally performed by mail.

[Jolyon Jenkins]

Well, yes, it's a funny story. It was invented by a reclusive chicken farmer in California called Charles Jordan 100 years ago, and he sold it by mail order for $2.50, which was a lot of money in those days. And you paid 50 cents up front for him to do the trick, and then if he wanted to know how it was done, you paid him the extra $2.

[Tim Harford]

And this, presumably, was a money spinner. Did he invent other tricks?

[Jolyon Jenkins]

Yes. And? Well, he played around with this principle, and he came up with a version which involved three riffle shuffles. Now, if you do that, then it works about 85% of the time, which isn't really enough. Certainly I wasn't going to take that chance. But what was clever was that he found out how to maximize the chances of it working. And it's only very recently that someone has shown through simulating it on a computer, that the method he came up with is actually the way, which maximizes the chance of it getting right. So then the question then sort of arises, so how many riffle shuffles do you actually need to do to make a deck completely random?

[Tim Harford]

So this is where the maths comes in, right?

[Jolyon Jenkins]

Yes. And, well, you've had this guest on your program before, Percy Diaconis, professor of maths and a colleague, they looked at it and they found that if you do six riffle shuffles, you've still got a certain amount of order in the deck, but seven completely destroys the order. So if you're a casino, you need to know about this, because people used to assume that three or four riffle shuffles was enough, but it clearly isn't. But what's interesting in a way is that it's not a linear process. So there's still quite a lot of order in 5 and then still some in 6, but really none in 7. So it just vanishes the order at 7. It's like a kind of cliff edge. And if you think of other areas of life that could actually be important, I mean, if you're a paint manufacturer, you need to know how much to mix your paint to be sure that it's absolutely mixed. And it may be that you need to do it a fairly precise amount and the same, if you're making drugs, you don't want kind of clumps of the agent in with the filler. So this actually has real world applications.

[Tim Harford]

Jolly and Jenkins, mathematical Magician. If there are any numbers you'd like us to check or to explain, do please email us at more or lessbc.co.uk and you can download the program and many others for free at our website, bbcworldservice.com More or less

[BBC Podcast Promoter]

there are dozens of different podcasts now available from the BBC, including news, documentaries, science, business, arts and sport. For details of them all, go to bbcworldservice.com podcasts.