Radio 4: Royal Twins & Autumn Statement

Summary

More or Less – “Royal Twins & Autumn Statement”

BBC Radio 4, December 7, 2012
Host: Tim Harford

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Episode Overview

In this episode, Tim Harford and the More or Less team tackle the numbers and statistical claims swirling in current events: royal twin speculation, the UK’s Autumn Statement, the challenges of measuring African economies, media misreporting of juvenile arrests, and the mathematical magic of LEGO and even numbers. True to form, the show debunks misconceptions, clarifies statistical truths, and brings expertise and a wry sense of humor to making sense of the numbers that dominate political, economic, and even everyday debates.

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1. Royal Pregnancy & The Chances of Twins

[00:44 – 03:39]

• Media Hype on Morning Sickness and Twins:
  The episode opens with scrutiny of sensational media reports linking acute morning sickness with an increased chance of royal twins.

  • Guest: Yan Wong, evolutionary biologist

  • Statistics in Context:

    • Having twins is rare (~1.5% chance in the UK).
    • Severe morning sickness requiring hospital admission is also rare (~1%).
    • Large datasets from Scandinavia confirm a statistical association: severe morning sickness raises the probability of twins by about 50–100% (relative risk).
      • “The number of people who have twins is very small. It’s about 1.5% in the UK.” — Yan Wong [01:35]
      • “Our best guess is somewhere between maybe 50% and 100% increase in the probability of having twins.” — Yan Wong [02:20]
    • Absolute risk: Jumps from ~1.5% to ~2.5% for those hospitalized with severe morning sickness.

  • Family History Myth:

    • Non-identical (fraternal) twins can run in families, specifically through the maternal line.
      • “There is some indication that non identical twins run in families.” — Yan Wong [02:58]

  • Statistical Communication:

    • Media often use dramatic-sounding relative risks, creating misleading impressions of probability.
      • “Double what chance? Treble what chance? Without knowing the underlying probabilities, we’re not really learning a lot.” — Tim Harford [03:39]

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2. The Autumn Statement: UK’s Public Finances Demystified

[03:39 – 10:53]

• Economic Forecasts:

  • The UK deficit is falling short-term but not as much as hoped. Debt is rising higher than the coalition government expected.
    • “UK debt is expected to be almost 1200 billion pounds by the end of this tax year—bigger than the coalition government hoped it would be by now.” — Tim Harford [05:36]
    • Despite the high deficit, the UK can borrow cheaply, unlike Eurozone countries like Spain.

• Notable Political Claims Debunked:

  1. “The richest will pay a greater share of income tax revenues in every single year of this coalition government than in any one of the 13 years of the last Labour government” (George Osborne’s claim, via Treasury)

     • Ruth Alexander investigates:
       • “Top 10%” (earning £48,600+): Yes, their share has generally gone up.
       • “Top 5%” (£66,100+) and “Top 1%” (£153,000+): The claim is almost true, but not always.
       • “For both the 5% and the 1%, the share of income tax payments has been higher in most years under George Osborne than it has been in the years under Labour.” — Ruth Alexander [07:42]

  2. Public Investment Comparison:

     • Osborne: “Public investment as a share of GDP will be higher on average in this Parliament than under the last Labour government.”
     • Truth: Osborne picked a selective timescale (comparing to all years since 1997). If you compare only recent years, the claim wouldn’t hold.
       • “If we compared this Parliament with the last Labour Parliament, the story wouldn’t be the same, because Labour was actually spending quite a lot on public sector projects in its last few years.” — Tim Harford [08:52]
     • Public investment varies by the economic cycle, not just politics.
       • “Public investment tends to be more about the economic cycle, not about politics.” — Ruth Alexander [08:57]

• Humorous aside: “Strivation” debate—examining whether the Autumn Statement was ‘good for strivers’ [09:13–10:24]

• Cricket Stats and Superstitions:

  • Alistair Cook chosen statistically as England’s top batsman, and promptly sets a new record.
  • Playful tone referencing ‘death-defying gamble’ and criminal masterminds.

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3. African Economies and the Problem of GDP Statistics

[11:00 – 16:32]

• Ghana’s GDP “Growth” Explained:

  • Ghana’s GDP leapt by 60% overnight in 2010—not from real growth, but statistical revision (rebasing GDP from 1993 to 2006).

    • “The GDP statistics in Ghana had not been updated…so they had a base year from 1993.” — Morten Jerven [12:06]

  • Base-Year Problem:

    • Old base years miss major changes in the economy (e.g., Ghana’s mobile phone boom).

  • Accuracy Still an Issue:

    • Informal economy not quantified precisely—GDP stats may still be 10–20% off.
      • “Until we are able to actually go in and do a proper quantification of the informal economy…it is uncertain exactly what degree of variation we have in our GDP figures.” — Sidney Caseley Hayford [14:16]

  • Why It Matters:

    • Development aid and international support can hinge on GDP stats (e.g., concessional loan eligibility).
      • “Now that Ghana is a middle income country…not eligible for concessional lending from the World Bank, for instance.” — Morten Jerven [14:53]

  • What to Do About It:

    • Data users should check sources.
    • Data disseminators (World Bank, UN, etc.) must label statistics properly (many still use wildly outdated base years for some big countries).
    • Data producers (local statistical agencies) must take responsibility.
    • “You need to question your evidence and try to do as historians do, check your sources.” — Morten Jerven [15:42]

  • Resource Constraints:

    • Many African statistical offices are underfunded and under-recognized, resulting in poverty/housing data only being collected every 5–10 years.
    • “The Statistical Office is very weak and they’re underfunded and don’t have the capacity to run poverty surveys…more than once every five or ten years.” — Shanta Devarajan [16:32]

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4. Media Misinformation: The Myth of 200,000 Primary School Arrests

[17:35 – 20:06]

• Headline Error Exposed:

  • Telegraph blog headline: “Police have detained more than 200,000 pupils”

  • Reality:

    • 209,000: Total arrests (not individuals) under age 18—not primary pupils.
    • Only 2,117 under-11s were arrested in England and Wales last year.
      • “To get to the 209,000 figure, [the handful of over-age primary pupils] would each have to have been arrested over 2,000 times.” — Wesley Stevenson [19:32]
    • The error: the columnist took the under-18 figure and applied it to primary school children.

  • Correction:

    • The headline was changed online but the error in the article remains.

• Numerical Literacy:

  • The incident illustrates the importance of media, politicians, and public understanding the meaning and context of statistics.

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5. LEGO Towers and the Nature of Pure Mathematics

[21:11 – 23:38]

• LEGO Analogy for Pure and Applied Math:
  • Eugenia Cheng (Sheffield University):
    • Pure math is like constructing whatever you imagine from a pile of basic LEGO bricks; applied math is like getting the complex pieces or LEGO sets with instructions.
    • “Pure maths is really easy because it’s just like playing around with LEGO.” — Dr. Eugenia Cheng [21:15]
    • Learning: Start with instructions, then experiment and explore.
      • “By doing something that someone else has shown you…then you start taking it apart and putting it back together in a different way to see what you can do for yourself.” — Dr. Cheng [23:18]

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6. Odd, Even, and Zero: Numbers in Gasoline Rationing

[23:53 – 27:16]

• New York’s Post-Sandy Gas Rationing:
  • Odd and even license plates—what about zero?
  • Maths history: In France in 1977, police didn’t know what to do with zero plates, so let them pass.
  • Mathematicians’ verdict: Zero is even.
    • Tests for “evenness”: doubling, alternation between odds, divisibility by 2.
    • Public confusion persists; about half of children surveyed get it right.
      • “Zero is an even number and it will pass every test and every definition of an even number.” — Dr. James Grime [25:09]
    • Fibonacci separated zero from other numbers, but modern mathematics is clear.

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Notable Quotes

• “Double what chance? Treble what chance? Without knowing the underlying probabilities, we’re not really learning a lot.” — Tim Harford [03:39]
• "You need to question your evidence and try to do as historians do, check your sources." — Morten Jerven [15:42]
• "Zero is an even number and it will pass every test and every definition of an even number." — Dr. James Grime [25:09]
• "Pure maths is really easy because it's just like playing around with LEGO." — Dr. Eugenia Cheng [21:15]

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Memorable Moments & Analysis

• Humorous jabs at statistics in media and government (“We’re like the Leveson Inquiry, only for numbers and with better jokes.” — Tim Harford [00:13])
• Statistical miscommunication demonstrated with lively, concrete examples—royal twins, juvenile arrests, and government claims.
• Guest experts provide both technical clarity and lay perspective, keeping complex data relatable and entertaining.

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Key Timestamps

• Royal twin speculation: [00:44 – 03:39]
• Autumn Statement explained: [03:39 – 10:53]
• African economies and GDP accuracy: [11:00 – 16:32]
• Media error on school arrests: [17:35 – 20:06]
• LEGO and mathematics analogy: [21:11 – 23:38]
• Zero’s evenness in mathematics and gas rationing: [23:53 – 27:16]

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Tone & Style

Accessible, witty, slightly irreverent, and robustly evidence-based. Relentlessly focused on demystifying numbers for the public—but with frequent, light-hearted asides and jokes to keep it lively.

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Conclusion

This episode of More or Less is a tour through contemporary “numbers in the news,” showing listeners how to approach claims with skepticism and statistical savvy, debunking myths from royal twins to child arrests, and using analogies from LEGO and mathematics to make it all accessible and memorable.

Transcript

[A]

Thanks for downloading this edition of More or less from Radio 4. You can find out more about the programme at BBC.co.uk more or less. But on with the programme, here's Tim Harford.

[B]

Hello and welcome to More or Less. We're like the Leveson Inquiry, only for numbers and with better jokes. In this week's programme, after all the detail from the Autumn Statement, we try to distill the message to get the important big picture on the economy. And we'll ask whether everything we know about African economies is wrong. And we will return to the topic of Lego, but with a different twist.

[C]

With Lego, you have some basic blocks and some ways of sticking them together, and then you can build anything. And maths is the same.

[B]

But first, in light of the royal pregnancy, there's been a lot of speculation about what acute morning sickness tells us about the chances of having twins. Newspapers and broadcast media have raised the possibility and opportunist bookmakers have slashed the odds on the birth of twins. This seems incredibly premature so early in a pregnancy. But the way the numbers have been used or abused makes a broader statistical point. We thought that the only way to cover the experience of pregnancy and morning sickness sensibly is to have two men discuss the issue. So I'm joined by somebody who isn't likely to suffer from either condition, evolutionary biologist TV's Yan Wong. I began by asking him whether the media were right to claim that acute morning sickness raised the chances of having twins.

[D]

It certainly is true that there is this association. The problem is that we are talking very small numbers of people. The number of people who have twins is very small. It's about 1.5% in the UK. And the number of people who suffer from morning sickness acute enough to require hospital admissions is also fortunately very, very low. It's about 1%. And so to try and spot whether or not there's a correlation here, you need huge data sets.

[B]

Do we have huge data sets?

[D]

And we do.

[B]

Hooray.

[D]

There are data sets from Norway of almost a million births between 1967 and 2005. There's ones from Denmark. There are also ones from Sweden.

[B]

Very good. What do we learn? Should we believe the hype? And, of course, the opportunist bookies have also jumped on the bandwagon and slashed their odds and so on, that it's twins, it's going to be twins.

[D]

It looks like our best guess is somewhere between maybe 15, 50% and 100% increase in the probability of having twins.

[B]

But that's in the relative risk. So we're going up from about 1.5%

[D]

to about 2.5 to about 2.5%, something like that. So it's still pretty low, actually, the probability of having twins.

[B]

And there's this idea also that having twins is something that runs in the family. Now, of course, we wouldn't ever on more or less speculate about a royal pregnancy or point out that the Duchess of Cambridge. Does Hatchley. Have some twins in her extended family, but just on a purely hypothetical basis, do twins run in the family?

[D]

There is some indication that non identical twins run in families. The studies have only really concentrated on cases where there are very close relatives who have non identical twins.

[B]

So it's a woman's mother, a woman's

[D]

mother or a woman's sister.

[B]

Okay, crystal clear. So just to, just to sum up, if you just heard out of the blue someone was pregnant, knowing nothing else, the chance that they have twins is

[D]

in the UK, about 1.5, 1.6%.

[B]

And then if you were told that they are suffering from terrible, terrible morning sickness and they're in hospital, how does that change your.

[D]

It would probably go up to about 2.4, 2.5%.

[B]

Very good. So don't rush to the bookies just yet. Yan Wong.

[D]

Indeed.

[B]

Thank you very much. Thank you, Yan Wong. And this raises a very important point. We're often told frightening sounding stuff, that drinking alcohol will double our chance of mouth cancer or watching Strictly Come Dancing will treble the chance of going blind or whatever, but this sort of thing just isn't very informative. Double what chance? Treble what chance? Without knowing the underlying probabilities, we're not really learning a lot. You are not very likely to go blind while watching Strictly Come Dancing. And the Duchess of Cambridge is not very likely to have twins. This week saw one of the big political set pieces of the year, the Chancellor's Autumn Statement. Just in time for Christmas, George Osborne stood up in the House of Commons and emptied a stocking full of numbers all over the Shadow Chancellor, Ed Balls. The OBR forecasts that the economy will grow by 1.2% next year, then 2% in 2020. The deficit also falls from 7.9% last year to 7.77% this year. Then net debt will be 74.7% this year, then 76.8% next year, 79% in 2020. There were a lot of numbers and there's been a lot of comment and analysis. But look, here's what you need to know. The deficit, which is the fresh Borrowing, the government needs to do each year as a percentage of gross domestic product is falling in the near term, but over the next few years, it's not going to fall by as much as had been hoped. And we're borrowing a lot. The Chancellor didn't mention this, but the deficit forecast to be 108 billion pounds this year. That's 6.9% of GDP is uncomfortably above the average for OECD countries. But at least we can still borrow cheaply, unlike Spain and other beleaguered Eurozone countries. And in five years time, it's projected that UK debt as a percentage of GDP will start falling a year later than expected. The nation's total debt is what we on more or less, would call a big number. It's expected to be almost 1200 billion pounds by the end of this tax year. And it's bigger than the coalition government hoped it would be by now. But don't forget that these debt projections keep changing because economic forecasts keep changing. So it's hard to get excited about the details. The main point I take is that the overall picture is gloomier than it was. But there were two details which caught my attention in the Autumn Statement and made me think, really. The first one was this. Here is a simple fact. The richest will pay a greater share of income tax revenues in every single year of this coalition government than in any one of the 13 years of the last Labour government. Is that true? Well, Ruth Alexander's here.

[C]

Hello, Ruth.

[B]

You've been having a look.

[E]

I have. Hello. We asked the treasury for the figures on this. My suspicions were immediately aroused when they sent through part of a table.

[B]

Oh, the old part of a table trick. I've seen that one. Okay.

[E]

And it showed the share of income tax the top 10% of earners pay. And the numbers did stack up.

[B]

So the top 10% of earners, I suppose that is the richest.

[E]

Well, the richest doesn't really mean anything, actually. It's just a nice turn of phrase. Better to be specific. The top 10% of income taxpayers are the people who earn 48,600 pounds a

[B]

year or more, which is a decent salary. But it's hardly the stuff of billionaires such as Bill Gates and Roman Abramovich. Moneybox is Paul Lewis, is it?

[E]

It is what it is. The cutoff for being in the top 10% highest earners. So anyway, I said to the treasury, come on then, let's see the rest of your table.

[B]

You're quite forward sometimes, Ruth. So low. The columns on the top 5% appeared and the columns on the top 1%.

[E]

Yes. And you're in the top 5% if you earn more than 66,100 pounds and you've made it into the top 1% if you earn 153,000 pounds. And looking at those groups, they haven't paid a bigger share of tax in every year, the coalition government.

[B]

But give us the gist, was he way off or roughly right?

[E]

Well, for these richer groups, George Osborne's statement is not strictly true, but it's not far off. For both the 5% and the 1%. The share of income tax payments has been higher in most years under George Osborne than it has been in the years under Labour.

[B]

And maybe that's not surprising. Labour introduced a new 50p tax rate, but it was only enforced for the last month of their 13 years in power. Now, I also wondered whether there wasn't something interesting about this statement that the Chancellor made. Public investment as a share of GDP will be higher on average in this Parliament than it was under the last Labour government. So this is all about roads and railways and schools. Actually, I'm not really sure what it is about. What is it about, Ruth?

[E]

Well, basically, it's anything that creates a physical asset for the government. So education, for instance, doesn't count as investment. I was chatting about this with Ian Mulhern, the director of the Social Market foundation think tank, and he was quick to spot some rather selective timescale picking, pointing out that George Osborne was comparing this Parliament with the record of the Labour government all the way back to 1997. If we compared this Parliament with the last Labour Parliament, the story wouldn't be

[B]

the same, because Labour was actually spending quite a lot on public sector projects in its last few years.

[E]

Yes, and it spent very little on public investment in the late 1990s, the early years of New Labour. And Ian Mulhern reckons that although George Osborne is picking out the figures to make a political point, public investment tends to be more about the economic cycle, not about politics.

[B]

Well, I think probably what drives some of these figures is the point in the economic cycle that you're at, which makes it very hard to compare one government against another. I think when the last Conservative government left office, you would have found very low public investment, and that was probably because the economy was coming out of recession and starting to boom. Whereas late in the economic cycle, 2007, 2008, governments tend to be investing a lot more, and then that public investment gets cut relatively quickly once there has to be some fiscal tightening. As we're now seeing, Ian Mulhern of the Social Market foundation and our very own Ruth Alexander. And Ruth, one more thing. I now read that the latest debate is whether the Autumn statement was good for strivers or bad for strivers. So next week I want you to be back here with the latest data on strivation. Thank you very much. Now, last week you may remember Rob Eastaway, a member of the association of Cricket Statisticians, chose his representative from the England cricket line up to bat for his life. Out of the current England batting line up, who's the man you would pick to go and score a century? I would pick Alistair Cook.

[F]

I don't really know where to start with the superlatives for Alistair Cook. He batted magnificently today to reach that 23rd test century. So at 27 years old, has now scored more Test centuries than any other English batsman.

[B]

Yes, good call, Rob. On Thursday, Alistair Cook scored yet another century and became England's all time leading Test Centurion. Rob Eastaway's death defying gamble has paid off thanks to the power of statistical analysis. You may have escaped for now, but

[A]

I'll get you next time, Eastaway. Next time.

[B]

That was a statement from an international criminal mastermind and you're listening to More or less in association with the Open University. In late November, official figures confirmed that the UK economy grew by 1% between July and September. That was a cheery bit of news, but it's not a patch on Ghana, whose gross domestic product, or GDP grew by 60% overnight back in 2010. The country was immediately upgraded from low income to lower middle income. Of course, the growth didn't reflect any overnight change in the economy itself, just the fact that the economy had been growing for years and the Ghanaian statistics hadn't kept up. Now Nigeria is planning a similar statistical revision and again, its measured GDP could increase dramatically. So what's going on? I spoke to Morton Jervan, an assistant professor at Simon Fraser University in Canada and author of Poor How We Are Misled by African Development Statistics and what We Do About It. He explained that it all had to do with the way GDP was calculated with reference to a base year. And the calculations had simply got out of date.

[G]

The GDP statistics in Ghana had not been updated. In fact, the last time they made a base year estimate for the Ghanaian economy was in the 90s, so they had a base year from 1993.

[B]

So if we imagine, for instance, that in the 1990s Ghana just makes hot dogs and hot dog buns. But by 2011 it's also making iPhones. I know it doesn't really make iPhones or hot dogs, but just imagine what is the statistical process by which these GDP numbers get out of whack.

[G]

The best way of explaining it is to perhaps to compare it with how GDP statistics is compiled in the UK where you would think you add up all, as you said, production of hot dogs and iPhones and all other economic activities in every year. And then the next year you do the same thing and then you compare how is the economy doing in a country like Ghana? You don't have availability of data on all production of all types of food crops, small scale services and so forth. So therefore you make a basier estimation where you have more complete picture of the economy. And then in the following years when growth is estimating, you rely on certain proxies. You assume that large part of the economy just grows in line with population. And finally what happens if the structure of the economy changes radically? That means that a lot of growth may be missed. There is large technological change between 1993 and 2006, the mobile phone which did not exist in the 90s and now we have millions and millions of mobile phone users in Ghana so that these kind of sectoral changes were missed as time passed.

[B]

So Ghana's GDP figures weren't right in the past, but are they right now? Sidney Caseleigh Hayford is a business and financial analyst from Ghana and he doesn't think so. Until we are able to actually go in and do a proper quantification of the informal economy in this country, it is uncertain exactly what degree of variation we have in our GDP figures. I would hazard a guess and say that we probably out by about plus 10, 15, maybe 20% yet that we should actually including the number. Sydney Caseley Hayford but how much does it matter if GDP estimates aren't always entirely accurate? The truth is that Ghana is getting richer and its statistics are getting better. So what's to dislike? But Morden Gervin is worried.

[G]

Reliable economic statistics, that includes estimates of economic growth rates or per capita income estimates are basic to the operation of governments also in developing countries. These kind of statistics are also vital to international organizations, to non governmental organizations that for instance provide aid to Ghana. So that for instance, now that Ghana is a middle income country, it is according to that statistic, not eligible for concessional lending from the World bank, for instance.

[B]

Todd Moss is a senior fellow at the center for Global development in Washington D.C. and he thinks that the statistics being out isn't such a Bad problem. I think it makes cross country comparisons even less valuable than we thought. But I still think if you're measuring more or less the same thing year to year, you're still getting a picture into the activity and growth or shrinkage of parts of the economy and that's what you're really trying to do. So maybe it's a big problem and maybe it isn't, but practically speaking, what should be done? Here's Morten.

[G]

There is at least three groups that need to really rethink what they're doing. One of them are data users. You need to question your evidence and try to do as historians do, check your sources. Now, when it comes to data disseminators, which is what the World bank is and other United nations and Eurostat and so forth, they need to really start labeling their product correctly. What happens if you download the statistics now from the World bank today? Well, you will find that the estimate on Ghana is updated, but for instance, estimate for Nigeria is still done according to a base year from 1990 and is hugely misleading. Finally, to sum up with the third group, data producers, in the end, they are the ones that need to take responsibility for the data they put out there.

[B]

And this question of responsibility is central. Shanta Devarajan is the World Bank's chief economist for Africa. And he thinks that too often African economic statistics just fall between the cracks. You know, in many countries the Statistical Office is like an orphan. I mean, I've encountered cases where the Minister is not even aware that the Statistical Office is under his ministry. And that's the real problem. The reason why we don't have more frequent poverty statistics is that the Statistical Office is very weak and they're underfunded and don't have the capacity to run poverty surveys or household surveys more than once every five years or 10 years. I think we're involved in something like 30 African countries in trying to build statistical capacity. Shantidevarajan of the World bank talking about the problem of countries that are too poor to figure out how poor they are. You're listening to More or Less with me, Tim Harford. Our website is BBC.co.uk moreorless and our email address more or lessbc.co.uk. now I realise that it wasn't long ago that we commented on the Daily Telegraph's extraordinarily erroneous reporting of cod stocks in the North Sea. But with with Codgate still fresh in the memory, we've been troubled by yet another Telegraph headline. The most shocking statistic about primary Schools police have detained more than 200,000 pupils. This figure appeared on the Telegraph's website and not in the print edition. It was the headline for a blog post by columnist Cristina o'. Donne. Can juvenile crime really be quite so ubiquitous? Or alternatively, can policing be quite so heavy handed? Our very own artful dodger, Wesley Stevenson is here. Hello, Wesley. Hello, Wes. 200,000 primary age pupil perpetrators is quite a lot, isn't it?

[A]

Yes, it is, but let's read a little bit more of the article. Cristina Adone's piece goes on to say more than 209,000 were detained by police in England and Wales last year. And of these, 2,117 were under the age of 11. And you can imagine the outrage in the comments on Ms. Adonis piece. Heavy handed policing, lack of discipline in schools, the fecklessness of modern parents, you

[B]

know, that kind of thing. Hang on, Wes. I wouldn't blame the Telegraph for the commenters, just take a look at the comments on the BBC website. But I'm puzzled. 209,000 primary age pupils have been detained and about 2,000 of them are under the age of 11. Doesn't that mean 207,000 primary age pupils over the age of 11 have been detained?

[A]

Yeah, well, you'd think so.

[B]

Are there any primary school pupils over the age of 11? I thought they were all in secondary school.

[A]

Well, you're beginning to see the mystery. Two things we should say here, 209,000 is the number of arrests, not the number of individuals, so there'll be repeat offenders in here. And secondly, there are just a handful of pupils over the age of 11 at primary school in England and Wales, fewer than 100. So to get to the 209,000 figure, they would each have to have been arrested over 2000 times.

[B]

Obviously the number's a mistake. What went wrong?

[A]

Well, the Howard League for Penal Reform say that there were 209,000 arrests of people under the age of 18 last year in England and Wales. And that's based on Freedom of Information requests that they submitted to various police forces. For some reason, Christina Adone has taken that figure and applied this just to primary school pupils. But as the figures show, There were only 2,117 arrests of primary age pupils. Now, to be fair to the Telegraph, they did fix the headline on Ms. Adone's blog post, but the error in her piece has not, as of Friday morning, been sorted out.

[B]

Well, thank you, Wes. Gosh, at a time when standards are always assumed to be slipping, it's good to Know that somebody still loves the firm smack of numerical discipline. Now, judging by the number of people who emailed more or lessbc.co.uk last week, you enjoyed our destruction of a simple LEGO brick in the name of numbers. We looked at how many LEGO bricks we could stack on top of each other before the bottom brick was crushed. The answer was 375,000, which left us with the problem of building a tower that tall. Andrew Porter has perhaps a more practical suggestion. He thinks it would be better to use an inverted pyramid where each successive layer has an extra brick on each side. And he says if each layer is solid, then at 104 layers you'd have 380,380 bricks and it would only be about 1 meter tall. If anybody would like to build such a pyramid and take a photo for us, do please get in touch and be careful it doesn't topple over on your toes. Thank you for your suggestions, but it turns out that there is more to LEGO than mere engineering.

[C]

I'm a pure mathematician and people often ask me what on earth that means.

[B]

This is Dr. Eugenia Cheng from Sheffield University.

[C]

And the other thing they say is they think that maths is really hard. And now, although I don't want to admit that I don't think it's hard because I like the idea that I'm very clever, I'm doing something that's very difficult. But actually, I think that pure maths is, is really easy because it's just like playing around with Lego. And it basically, with Lego, you have some basic blocks and some ways of sticking them together, and then you can build anything. And maths is the same. You start with some basic blocks and usually those are numbers at the beginning and they might be other things like shapes or anything you can make patterns with. And you have some ways of sticking them together, which in our case is logic, and then you start building anything.

[B]

When I learned to play with Lego, my parents just bought a huge sack of bricks secondhand and I just started clipping them together. My daughters are getting into LEGO now, but they get these very beautiful pre packaged boxed sets with very detailed instructions. Now, should people learn pure maths first by going through the detailed instructions, by going through all the previous proofs, or do you think people should be playing a lot more with the ideas and not treading down the paths that previous mathematicians have done?

[C]

That's an interesting way of pushing the analogy. I think that one of the differences between pure maths and applied maths is about whether you prefer playing with just your basic LEGO bricks. And I always think of those as the 2x4 rectangular ones, or whether you like the really complicated ones, like at the basic level, doors, windows, wheels, maybe propellers and things like that. And I think that pure maths is like saying, okay, I'm just going to sit down with the most people basic kind of brick and see how far I can get. And applied maths is like saying, I want to take all those complicated things and see what I can do with the complicated things. And as for the the sets, the thing that I think is fantastic about the LEGO sets is that you start with instructions for how to build one particular thing. Say you get the fire engine set and it tells you how to build a fire engine. But then if you're like me, you take it apart again and you see what else you can build just off the top of your head using the same bricks. And I think it's the same with maths. You by doing something that someone else has shown you how to do with some pieces that someone else has given you, and then you start taking it apart and putting it back together again in a different way to see what you can do for yourself.

[B]

Dr. Eugenia Cheng in the wake of Superstorm Sandy, which battered the United States, New York authorities had to figure out a way of encouraging drivers to ration their gasoline consumption. The Mayor Michael Bloomberg issued this directive.

[D]

Drivers in New York City who have license plates that end in an odd number or end in a letter or other charact sector will be able to buy gas or diesel only on odd numbered days, such as tomorrow, which happens to be the ninth. Those with license plates ending in an even number or the number 0 will be able to buy gas or diesel only on even number days, such as Saturday, November 10th.

[B]

But why did Mayor Bloomberg say even numbers and zero? Was it necessary to single zero out? It seemed a little odd to us. So we talked to Dr. James Grime of the Millennium Maths Project at Cambridge, UK, and he says that a similar issue came up in France in the 1970s.

[F]

In 1977, the smog in Paris was so bad that they had to restrict car use. So they used the same method that they're using in New York now, alternating days for odd and even license plates numbers. And the police did not know whether to stop the 0 numbered license plates. And so they just let them pass because they didn't know whether it was odd or even.

[B]

So it seems. Not everyone is sure. But do mathematicians agree over whether zero is odd or even?

[F]

The debate is settled.

[B]

Among mathematicians, mathematicians are agreed that 0 is an even number.

[F]

0 is an even number and it will pass every test and every definition of an even number.

[B]

Well, what are the usual tests or definitions for even numbers?

[F]

If you take a number and you double it, the result will be an even number. So if you take the number three and you double it, then you'll get six and six is an even number. So that would be the definition of even numbers. And zero will pass that test. So if you double zero, you'll get zero, but it will pass all the other tests for even numbers as well. If you alternate the even and odd numbers, then zero is between two odd numbers, it's between one and minus one. That's another example of a test that it would pass.

[B]

So was Mayor Bloomberg being a bit daft to specify that rationing would apply to cars with even number plates or zero?

[F]

No, because it something that the general public haven't quite been able to handle yet. There have been surveys into do school children think zero is even or odd? And it turned out 50% of school children thought zero was even, which seems like good news. 20% thought it was odd. And maybe the reasoning behind that is because you start counting from zero, it's the first number you start counting with, therefore it's odd. The remaining 30% of children thought it was either both or neither, or they just didn't know. And I guess the general public would reflect that too.

[B]

Have mathematicians also seen fit to specifically specify that 0 is an even number, or indeed that 0 isn't an even number, that it's something different?

[F]

Certainly the Italian mathematician Fibonacci, 13th century, he was the first to popularise the numbers that we use today into Europe. So, 0, 1, 2, 3, up to would we.

[B]

Roman numerals before then?

[F]

Yeah, that's right. We were using Roman numerals before that, which were clumsy, not very useful to

[B]

us, and didn't have zero, I think,

[F]

and didn't have zero. And so Fibonacci realized the power of the Arabic numerals, but he did separate 0 from the other numbers. He called 0 the sine of 0, whereas referred to the other numbers 1 to 9 as numbers. So he himself did separate 0 from the others.

[B]

Dr. James Grime. And that's all we have time for on More or Less this week. If you want to see pictures of the crushed Lego brick or read more about other items we've done on More or Less, you can go to our website, BBC.co.uk more or less until next week, Goodbye.

[A]

More or less was presented by Tim Harford, the Financial Times undercover economist. The producer was Wesley Stevenson, the editor, Richard Varden. The programme is made in association with the Open University.