Small spending cuts?

Summary

More or Less – “Small Spending Cuts?”
BBC Radio 4, April 1, 2011
Host: Tim Harford

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Episode Overview

In this episode of More or Less, Tim Harford and the team dive into the facts and fallacies surrounding government spending cuts, the true scale of fiscal tightening in the UK, and the ways numbers are used (and misused) in public debate. Alongside analysis of the economic situation, the episode explores the UK’s 2011 census and a fascinating mathematical deep-dive into editing a Beatles classic.

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Main Theme

Are the UK’s government spending cuts really as “savage” as the rhetoric claims, or are they, in fact, “embarrassingly small”? The episode addresses the reality behind the numbers, public interpretation, and political narratives.

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Episode Highlights and Key Segments

I. Opening Banter and Theme Introduction

• [00:14–01:14]
  • Guest appearance by Graeme Seed in a playful exchange about hosting duties, setting the tone for the episode’s focus on numbers in public discourse.

II. How Big Are the Government Spending Cuts?

• [01:19–09:33]

Competing Narratives

• Tim introduces the mainstream claim that cuts are “tough and necessary,” while others call them “savage.”

• Example: Brendan Barber (TUC) protests the “savage cuts.”

  • Quote: “We’re here to send a clear message to the government that we’re strong and that we’re united, that we’ll fight their savage cuts.” – Brendan Barber [02:17]

• Wesley Stevenson surveys the public, eliciting words like “enormous,” “big,” “worrisome,” showing public perception of large-scale cuts.

An Alternate View: Are Cuts “Embarrassingly Small”?

• Fraser Nelson, editor of the Spectator, calls the cuts “embarrassingly small.”

  • Quote: “Total state spending is going down by 0.6% in the coming financial year. Now, that statistic is so small, you can’t really call that a big cut… It is tiny.” – Fraser Nelson [03:37]

• Over the next four years, total cuts are less than 4%, or 0.9% per year.

• The numbers check out with Rowena Crawford from the Institute for Fiscal Studies.

Why the Perception Gap?

• [04:18–06:10]

  • Although total spending falls only marginally, departmental spending (public services) is being cut much more because “annually managed expenditure” (benefits, debt interest, etc.) is rising.

• Insightful Exchange:
  Tim: “So, there are these two big chunks of the government budget… they almost balance each other out. So this is why spending isn’t really being cut by that much.”
  Wesley: [05:00] “That's right... inflation plus unemployment plus debt repayments plus retirement are racking up in that section, and... departmental expenditure limits… are being cut quite radically.”

Inflation Makes It Worse for Departments

• [05:25–06:16]
  • Inflation increases spending on social security and debt payments (inflation-linked), but departmental budgets are set in cash terms and do not adjust, increasing pressure on services.

The Real-World Effects

• [06:16–07:41]

  • Despite the small overall cuts, real reductions impact councils and services—“There are libraries having to be closed, street lights being switched off.” (Fraser Nelson [06:16])

• Quote: “If you ask the average person, how much is he cutting government spending by, they would estimate 10, 15, 20%. Nobody would guess how mild the cuts actually are because the rhetoric has raced away from the economic reality.” – Fraser Nelson [07:57]

How Will the Deficit Actually Fall?

• [07:18–07:57]
  • The deficit reduction relies mostly on increased taxes and expected economic recovery, not deep spending cuts.

Are Politicians Misleading the Public?

• [08:40–09:33]
  • Wesley challenges Nelson on whether omitting detail is misleading. Fraser stands by his decision to focus on total spending for comparability, arguing that the public and press overlook this angle.

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III. Understanding the 2011 Census

• [10:55–14:59]

The Scale and Mechanics of the Census

• Tim interviews Glenn Watson of the Office for National Statistics.

  • Watson describes the logistics and excitement: “We’ve been planning this for the last seven or eight years… millions of forms coming in as we speak.” [11:20]

• 26–27 million questionnaires processed at a Manchester centre “the size of something like five football pitches.” [11:31]

Ambiguities and Criticisms

• Tim raises common user confusions, e.g., the qualifications question and difficulty catering for modern lifestyles (working parents who also care for children).

• Notable Moment:
  Tim: “You can’t cater for… really obscure niches such as, say, part time working mums.” [14:17] Glenn: “Well, I wouldn’t describe people who are part time working mums as a really obscure niche.” [14:22]

• Watson defends the approach, citing the need for clear, comparable data and the impracticality of capturing every situation.

The Future of the Census

• Discussion of alternative models, like France’s rolling census, and why the UK values a single-day snapshot for resource allocation.

More or Less’s “Alternative Census”

• [15:26–16:48]
  • The show launches its own, less serious survey—ten questions for listeners—to probe aspects of life missed by the official census (e.g., loneliness, perceived quality of life versus parents).

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IV. The Cost of Intervening in Libya

• [16:48–21:48]

Estimating the Expense of Military Action

• Chancellor George Osborne claims Libya costs will be “tens of millions, not hundreds,” but how is that worked out?
• Tim consults Professor Malcolm Chalmers (Royal United Services Institute).

Breakdown of Costs

• Cruise missile: ~£500,000
• Sortie cost: £30,000–£40,000 (but may be lower as these planes would have been used for training anyway)
• Daily cost (benchmark: Kosovo): ~£2 million/day
  • Quote: “We’re talking about of the order of £2 million a day.” – Malcolm Chalmers [18:25]

What if a Plane is Lost?

• Tornados near end of life—would not be replaced. Typhoons are newer:
  • Replacement: £70–100 million
  • Analogy: “Tornado is kind of like a bit of yogurt in the fridge. That’s near its sell by date. We were going to get rid of it anyway, so we might as well eat it.” – Tim Harford [19:13]

Budgeting Between the MOD and Treasury

• For short operations, costs are later settled between departments, with the underlying MOD budget for the coming year not yet settled at the time of broadcast.

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V. Mathematics and Music: The Beatles’ “Strawberry Fields Forever”

• [22:04–27:06]

The Musical Puzzle

• Tim introduces Professor Jason Brown (Dalhousie University), an expert in applying mathematics to music.

• The Beatles' song was made from two takes in different keys (A and B) and tempos. Producer George Martin sped up one take and slowed down the other to splice them together, matching pitch but leaving a tempo mismatch.

Could There Have Been a More Perfect Edit?

• Brown’s research: The logarithmic nature of human pitch and tempo perception means it’s mathematically impossible to match both perfectly unless the takes are slowed down so much that the song would double in length.
  • Quote: “If you did that, then our perception of differences in tempo is such that even the most experienced listener would not notice a change in tempo. But the song would have gone from a four minute song to an eight minute song. And so it really would have seemed like Strawberry Fields Forever.” – Jason Brown [26:23]

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Notable Quotes

• “Total state spending is going down by 0.6% in the coming financial year… It is tiny.” – Fraser Nelson [03:37]
• “So this is why spending isn’t really being cut by that much.” – Wesley Stevenson [05:00]
• “There are libraries having to be closed, street lights being switched off. So there are cuts. But when you add everything up, everything that the government does, we aren’t cutting nearly as quickly as many other countries are.” – Fraser Nelson [06:16]
• “The political rhetoric just races away from the economic reality and we are living in such times.” – Fraser Nelson [07:57]
• “You can’t cater for… really obscure niches such as, say, part time working mums.” – Tim Harford [14:17]
• “Tornado is kind of like a bit of yogurt in the fridge… We were going to get rid of it anyway, so we might as well eat it.” – Tim Harford [19:13]
• “So it really would have seemed like Strawberry Fields Forever.” – Jason Brown [26:23]

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Important Timestamps

• [01:19] Main theme introduction (government spending cuts)
• [02:17] TUC’s Brendan Barber on the “savage cuts”
• [03:37] Fraser Nelson explains the “embarrassingly small” cuts
• [05:00] Spending breakdown: annually managed vs departmental cuts
• [06:16] Real-world impacts and discussion of public services
• [07:57] Political rhetoric vs. economic reality
• [10:55–14:59] In-depth with Glenn Watson, ONS, about the census
• [15:26] The More or Less alternative census
• [16:48–21:48] Libya intervention costs with Prof. Malcolm Chalmers
• [22:04–27:06] Beatles musical math with Prof. Jason Brown

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Conclusion

This edition of More or Less offers a rigorous, witty, and clear-eyed look at the numbers dominating British headlines in early 2011. Listeners walk away with a more nuanced sense of what government spending cuts really mean, how data collection like the census shapes our understanding of society, and the unexpected role of mathematics in the creative choices behind a Beatles masterpiece. As always, the show balances skepticism, clarity, and a healthy respect for what numbers do—and do not—tell us.

Transcript

[Tim Harford]

Thank you for downloading the More or Less podcast from the BBC. You can find out more about our programme on our website, BBC.co.uk radio4. But before you do that, here's Tim Har.

[Graeme Seed]

Oh, hello. I'm Graeme Seed, the new presenter of More or Less. You may know me from the Archers, but my real love is mathematics and the numbers that surround us every day. This week we ask, just how big is a hectare? Why do we count sheep rather than, say, cows? Is it possible to cull an exponentially growing population of badgers single handed and, well, solve that age old conundrum? How many men did go to mow the meadow? But first.

[Tim Harford]

Hey, what's going on?

[Graeme Seed]

Tim, I thought you were dead. At the end of the last series, you fell from the roof of White City, falling a total of 20 metres, evidenced by a rather weedy scream timed precisely at two seconds. Which is why I applied for the job of presenter of More or Less.

[Tim Harford]

Well, it was a big fall, but I got better.

[Graeme Seed]

I see. I wish I had.

[Tim Harford]

So does everyone else. Graham. But they can direct their complaints to the Drama Department. This is Current affairs, so if you wouldn't mind.

[Graeme Seed]

Gosh, yes. Sorry.

[Tim Harford]

Thank you. Welcome to More or Less with me, Tim Harford. This week, the Chancellor says that the cost of the intervention in Libya will be tens of millions rather than hundreds of millions of pounds. How does he know? Government spending cuts have been described as everything from savage and ideological to bold and essential. But is it really true they can also be described as embarrassingly small? As completed census forms drop through the letterbox of the Office for National Statistics, we'll be offering our own alternative census and we'll look at the unexpected mathematics of this song.

[Fraser Nelson]

Let me take you down.

[Tim Harford]

But first, the economic story of the year is, of course, government spending cuts. The government say they're tough and a necessary response to the fiscal position they inherited. Others describe them in slightly less heroic terms. Here's Brendan Barber of the tuc.

[Graeme Seed]

We're here to send a clear message to the government that we're strong and that we're united, that we'll fight their savage cuts.

[Tim Harford]

That's what Brendan Barber thinks. Wesley Stevenson's here. Hi, Wes. What do other people think?

[Wesley Stevenson]

Hi, Tim. Yeah, well, rather than assume we know what people think, I decided to venture outside the building and actually find out one word to describe the size of the government spending cut.

[Tim Harford]

Extravagant.

[Wesley Stevenson]

That's my term. Extravagant. You, madam?

[Tim Harford]

Enormous.

Big.

Very big. Ridiculous word. The government spending cuts.

[Glenn Watson]

I think the cuts are far too big.

[Wesley Stevenson]

Worrisome and you, sir, do you have

[Tim Harford]

a word that's necessary?

[Wesley Stevenson]

And what about the size of them? If you were to talk about the size of them, I mean, are they big, are they small? That's difficult to say. Not being an expert in the field,

[Tim Harford]

that's very interesting and not entirely surprising. But of course, where's. Last week the two of us encountered a rather different way of describing these cuts.

[Wesley Stevenson]

Yeah, that's right. From someone who probably is a bit more of an expert in the field, at least embarrassingly small.

[Tim Harford]

Embarrassingly small, yeah. Not quite the phrase most people would use. That's from Fraser Nelson, the editor of the Spectator, who of course has his own particular angle. I talked to him and here's what he said when I asked him to justify himself.

[Fraser Nelson]

Quite simply, total state spending is going down by 0.6% in the coming financial year. Now, that statistic is so small, you can't really call that a big cut. Bald, brash. It is tiny. It's about as small as George Osborne dares.

[Tim Harford]

Fair enough. And actually, that's not just for this year. Fraser Nelson also told me the same thing's basically true for the next four years. If you add up all the cuts for the next four years, they are less than 4% in total, about 0.9% on average per year, which really doesn't sound much.

[Wesley Stevenson]

The first time I heard this, I thought there might be something wrong here, because it seems so hard to believe, really. But we checked it out with Rowena Crawford from the Institute for Fiscal Studies.

[Tim Harford]

Fraser Nelser's numbers are basically correct in that the government is only cutting total spending over the next four years very slightly. However, some areas of public spending are actually increasing over the next four years, and that means that spending on departments is going to see much more rapid cuts than total spending as a whole.

Ok, so there are these two big chunks of the government budget here. It's split between annually managed expenditure, which is benefits, interest payments on the national debt, and departmental expenditure limits, which are, I guess, what most people would think of as public services. So we're talking about defence, education, policing, schools and hospitals, all that kind of thing. And they're about the same size?

[Wesley Stevenson]

Yes, that's right. They're about half and half. On the one side, you've got the annually managed expenditure, and this is actually growing fairly quickly. Inflation plus unemployment plus debt repayments plus retirement are racking up in that section, and on the other side, the other half you've got the departmental expenditure limits, and that's actually being cut quite radically, and in the end they almost balance each other out. So this is why spending isn't really being cut by that much.

[Tim Harford]

And you mentioned inflation. Now, when I first heard Fraser Nelson's claim, I assumed that he hadn't adjusted for inflation. He was talking about sort of cuts in cash terms, not cuts in real terms. But no, he has. He's adjusted for inflation. All of the stuff that we've talked about are real terms cut. And when we spoke to Rowena Crawford, she pointed out that actually, inflation makes this lopsided squeeze on departmental expenditure even worse.

So higher than forecast. Inflation will tend to increase spending on areas that are inflation linked, particularly Social Security spending and also debt interest payments. However, because of the way departmental spending is planned in the uk, spending for departments is set in cash terms in the spending review and they won't be changed in future. Even if inflation were to rise now,

nobody is actually claiming that public services are going to sail through this untouched. Even Fraser Nelson doesn't say that.

[Fraser Nelson]

Yes, they are being cut. And you can go down a level if you want and say that if you strip out health, they're being cut even more because the health budget's actually going up. You can strip out capital and current expenditure and say that the current cuts are even worse than the capital ones. There are so many ways to peel this onion and different politicians do it in different ways to suit them. The figure I used was for total spending, because that's nice and simple and it's internationally comparable. There is no doubt that there are real cuts going out there. Any council right now is going through immense pain. There are libraries having to be closed, street lights being switched off. So there are cuts. But when you add everything up, everything that the government does, we aren't cutting nearly as quickly as many other countries are.

[Tim Harford]

This is actually really quite depressing. In a sort of fantasy economy. What you'd really want to see is public services to be massively well funded and at the same time, somehow, magically, government spending to be as small as possible, because that keeps taxes low and keeps the deficit low, but you pay off the debt, that kind of thing,

[Wesley Stevenson]

because what we've actually got is completely the opposite of that. Public services are being squeezed. But George Osborne hasn't really managed to make that much of a dent in. In public spending as a whole. So you may ask, how is it, if public spending isn't dropping, that we're going to cut the deficit? Well, the only reason the deficit is going to fall is because actually taxes are going up and the economy is expected to recover.

[Tim Harford]

Well, I suppose the government would say the other reason the deficit is shrinking is because they've managed to keep a lid on spending. You know, they're not letting it get out of control. It is interesting, though, and Fraser Nelson made this point. The political dialogue is. Is very much on both sides about how big these cuts are.

[Fraser Nelson]

You do get these occasions in politics where the political rhetoric just races away from the economic reality and we are living in such times. It suits the Conservatives to say we are cutting. We're being very bold and brash. It suits Labour to say you guys are being cruel and radical and far too ambitious in these cuts. In fact, George Osborne is taking all of the political pain for not very much economic progress. This is the worst of all possible worlds, I think, because if you ask the average person, how much is he cutting government spending by, they would estimate 10, 15, 20%. Nobody would guess how mild the cuts actually are because the rhetoric has raced away from the economic reality.

[Wesley Stevenson]

This is the problem I've got here. If we go back to Fraser's original blog post, isn't he just being a bit naughty by not giving the full picture? Because he could have made it clear that while public spending was almost flat dropping a little bit, departmental spending is still falling and we're still going to have big cuts in public services.

[Tim Harford]

I did put that to Fraser, and to be honest, his conscience is clear. He's standing his ground.

[Fraser Nelson]

We described it as total state spending. I think that is one of the most simplest phrases in the English language. I mean, at the end of the day, are we getting more or less government spending? If you want to answer that question straight, you don't give all these little sub definitions. Now. On our website, we do break things down in several ways pretty much every day of the week. But total spending, while it's the simplest category, is the one which people are spending absolutely no attention on. So we flagged up attention to that because we thought the rest of Fleet street had its attention somewhere else.

[Tim Harford]

Fraser Nelson of the Spectator, and previously Rowena Crawford of the Institute for Physical Studies, and of course, our own Wesley Stevenson. Thank you, Wes. You're listening to More or Less, in association with the Open University, and I'm Tim Harford. While we were off air, Japan was struck by a devastating earthquake and a tsunami that caused over 11,000 confirmed deaths, with another 16,000 people still missing. It also badly damaged the Fukushima nuclear power station. And ever since, the airwaves have been full of the story of the fight to get the reactors under control and of alarming sounding releases of radiation. Several listeners have written in to ask us to explain how radiation numbers are calculated, what counts as a radiation risk and how safe nuclear power is. These are very good questions, but they're also questions that have been exhaustively covered by Radio 4 while we were off air. So we're going to point you to an online essay by David Spiegelhalter, friend of More or Less and Winton professor for the Public Understanding of Risk at Cambridge University. David Spiegelhalter makes the point that in the worst releases of radiation, such as at Chernobyl and in the aftermath of the bombs dropped on Hiroshima and Nagasaki, the number of people killed by this radiation exposure has not been in the tens of thousands as sometimes assumed, but at worst in the hundreds and perhaps much less than that. We've posted a link to Professor Spiegelhalter's essay On our website, BBC.co.uk,

[Glenn Watson]

thanks for

[Tim Harford]

your questions and comments. Do please keep them coming in To More or lessbc.co.uk or via the More or Less website. Now. This week was also the week in which, for the first time in 10 years, the entire population of the UK was instructed to fill in a census form. I spoke to Glenn Watson, who's in charge of the census, at the Office for National Statistics. I suggested that for the census team, this must be a pretty big moment.

[Glenn Watson]

This is really exciting. We've been planning this for the last seven or eight years and, yes, Sunday night was census night and there are millions and millions of forms coming and winging their way back to us as we speak.

[Tim Harford]

What happens next?

[Glenn Watson]

Well, all the questionnaires are heading to our processing centre in Manchester. It's the size of something like five football pitches. And that's where all of the 26, 27 million questionnaires will be received and will be scanned and the initial processing will take place. Our final results will be be published in the middle of 2012.

[Tim Harford]

Well, congratulations. We're fans of numbers, so obviously we wish you well. I have to strike a slightly sour note at this point. You've had, as you say, seven or eight years to think about this. It did seem to me, reading through the census, that still some of the questions were a bit ambiguous. Let me give you an example and you can tell me if I'm just being silly. Question 25 is about qualifications and it says, which of these qualifications do you have? For all qualifications you hold, select the appropriate options, click or tick all that apply but then some of the boxes seem to be mutually exclusive. So you're given the option of if you've got one to four GCSEs or if you've got five or more GCSEs. You know, I have got one to four GCSEs and also I have more than five GCSes. So what should we have done and is there anything you could have done to make it clearer?

[Glenn Watson]

Well, the instructions on the question are quite clear, actually. They say tick every box that applies if you have any of the qualifications listed. So in your case, you could tick the 1 to 4 GCSEs and you could tick the 5 plus GCSEs and that would be okay. Had you just ticked the five pluses there, that would be okay for us as well. And let me explain why.

[Tim Harford]

Okay. In fact, I did only tick the 5 plus.

[Glenn Watson]

So what's most important to users of census statistics on this particular question is what the highest level of qualifications that people have. And so during all of our testing and all of our research, we found that the best way of capturing that information was actually doing it as we've done it, because some people find it a bit difficult to understand what the highest level of qualification is with you got old and new systems alongside each other.

[Tim Harford]

Let me put another question to you. And again, clearly this isn't a hanging offence, but you've had a long time to think about this. My wife was complaining that she had done some work in the week before the census. Not very much actually, because she spends a lot of time looking after the children who are preschool age. So she ticked the box to say she'd done some work and then was then very cross that she was told to skip over the question. That would have let her register the fact that she was looking after the children. So she felt she wanted to tick both boxes and in fact, she may even have ticked both boxes as an act of petty rebellion. Would it have been so hard to adjust the census in a way that could incorporate people who juggle multiple responsibilities and many people who do well, I

[Glenn Watson]

mean, you can appreciate just how many possible permutations and combinations there are. We can't cater for absolutely every possible circumstance and everything that people would want to do.

[Tim Harford]

You can't cater for sort of really obscure niches such as, say, part time working mums.

[Glenn Watson]

Well, I wouldn't describe people who are part time working mums as a really obscure niche. Of course, what they do is very, very important. But we've designed the census Questionnaire to meet the majority of. I think that's exactly what it does.

[Tim Harford]

There are question marks over the future of the census. Maybe this will be the last census. Some countries do it differently. We have this grand project where every 10 years we take a snapshot of the nation. In France, they have what they call a rolling census. Over the course of several years, they will eventually get round to sampling everyone in the population, but they have a rolling subsample. Is that something that might appeal to the Office for National Statistics, that kind of model?

[Glenn Watson]

I am aware of the French model. It's quite interesting. And I think what would probably happen if we tried to do something similar here, I think we'd find that people found it to be inappropriate to be basing that on up to date information for part of the country, but information that was one or two or three or four or five years out of date for other parts of the country. I think consistency and having the information counting at the same point in time for every part of the country is a really, really important principle for the fair allocation of scarce public resources.

[Tim Harford]

Glenn Watson from the Office for National Statistics, he made it sound pretty complicated, but is it? We've decided to put together our own alternative census. The official census will tell us how many we are, where we live, with whom, and more good, hard facts. But we wondered, could we yield some surprising data by asking less obvious questions? Are we, for example, a selfish lot? Are we lonely? Do we think we have a better or worse quality of life than our parents had when they were our age? There are no such questions in the 2011 census. That's why we've created our own. While the ONS had 10 years and 482 million pounds to throw at their census, we had a few days and no money to throw at ours. So we're not sampling the nation, but the audience of more or less and our little known junior partner, the Today programme. Naturally, it will be a non representative sample rather than a full population survey, but we hope we'll learn something from it. Peter Lin, a professor of survey methodology at the Institute for Social and Economic Research at Essex University, has been helping us design the questions. So please pop to the Today programme website BBC.co.uk today and fill in our 10 question survey. It's open now and for the next two weeks. Now, Libya seems to be in a full fledged civil war and the UK is part of an international coalition intervening in the conflict with airstrikes and a no fly zone. Last week, the Chancellor George Osborne took on the question of what all this might cost. The House will understand that it is too early to give a robust estimate of the costs of the operations in Libya. But what I can say is that the cost should be modest compared to some other operations like Afghanistan. And the Ministry of Defence's initial view is that these will be in the order of the tens of millions, not the hundreds of millions of pounds. I can tell the House today that whatever they turn out to be, the additional costs of operations in Libya will be fully met from the reserve. One of the problems, of course, is that nobody knows how long this is going to last. And then there are the indirect costs. Even setting aside the potential loss of life, this conflict is doing funny things to the price of oil, for example, but concentrating on what we know for sure, there are still puzzles. For instance, when we shoot a missile at a Libyan radar station, how much does that cost? The Ministry of Defence, Bearing in mind that we already bought the missile and we might not buy a replacement, I asked Professor Malcolm Chalmers of the Royal United Services Institute to help us figure it all out.

[Malcolm Chalmers]

Well, a cruise missile will cost something of the order of half a million pounds, perhaps a little bit more the cost of a sortie. Well, it could be 30 or 40,000 pounds, but here I think it's more difficult because some of those aircraft would have been used for training purposes in any case. So the additional cost of using it on an operation instead might be less than that. That's something which will be negotiated by the treasury and the Ministry of Def later on, but as a broad brush estimate, looking at what previous conflicts like Kosovo cost, I think we're talking about of the order of £2 million a day.

[Tim Harford]

Two million a day. And of course, that assumes that we don't get any planes shot down. I mean, if we were to lose a fighter plane, let's say the pilot ejects and he's okay, we get him out, but we lose a plane. How much is that?

[Malcolm Chalmers]

Well, this will depend on whether we need to replace the plane. Some of the aircraft involved in strike operations or tornadoes are pretty near the end of their life. So we would not replace those aircraft. So the treasury would probably say, well, tough, you're not going to get any money for that. The Typhoon aircraft, on the other hand, the ones policing the no fly zone, are relatively new. So there, I think you might be talking about £70 million for the aircraft alone. And then there'll be the question of the munitions and, and other equipment on which would add some significant figures. So something of the order of 70 to 100 million.

[Tim Harford]

70 to 100 for a typhoon. But Tornado is kind of like a bit of yogurt in the fridge. That's near its sell by date. We were going to get rid of it anyway, so we might as well eat it.

[Malcolm Chalmers]

Well, Tornado is still very usable, as we can see in Libya, but we have plans to replace them with other aircraft in due course. So really, there would be no argument for getting additional funding if we lost a Tornado.

[Tim Harford]

Now, I'm just quickly doing the maths, because I'm that kind of guy. You said a rule of thumb, based on past experience, £2 million a day. George Osborne says tens of millions of pounds, not hundreds of millions of pounds. Presumably, then, the working assumption of the MOD is that this is going to last a month or two and no longer.

[Malcolm Chalmers]

I think that would be the working assumption. I think it will not be tens of millions if this operation goes on for a year. For example, if you're talking about a very long operation, and the no Fly zone in Iraq, of course, lasted for many years. So I think George Osborne is assuming that this operation will be over in a month or two.

[Tim Harford]

What confuses me is some of this is part of the mod's problem and some of this is part of the Treasury's problem. And how is that figured out?

[Malcolm Chalmers]

Well, what happens in a relatively short operation, as we hope this one will be, is that after the operation, essentially, the MOD and Treasury accountants get together and negotiate how much extra money the mod will get on its budget to pay for this operation. Some parts of it are very clear, but some of them aren't because they involve assumptions about what the MOD would have done if the operation had not taken place.

[Tim Harford]

And what is the MoD's budget next year?

[Malcolm Chalmers]

We're right at the end of this financial year, at the end of March, for Nick's financial year, there is no agreed breakdown of how the MOD will spend its budget allocation for Nick's financial year year. And that means working out what the baseline for calculating operational costs is very difficult because certainly one of the areas in which people were talking about quite significant cuts to balance the books for next year was further cuts in RAF training, which, of course will reduce the baseline for calculating operational costs. So that's really quite significant. And it may be that people will be looking for creative ways of using this operation to effectively plug gaps that would otherwise have been created.

[Tim Harford]

So you say the budget for next financial year hasn't been ironed out yet. Forgive the really silly question, but when does the next financial year start, Is it the same as the tax year? Because if it's the same as the tax year, it starts on Wednesday.

[Malcolm Chalmers]

It's quite soon indeed. The next government financial year starts exactly the same as everybody else's.

[Tim Harford]

Malcolm Chalmers of the Royal United Services Institute. Some time ago we talked to a Canadian professor of mathematics and who spends his time using maths to solve musical puzzles. Well, now he's solved a new one. Hannah Barnes, the newest member of the more or less team, has been talking to him about his work.

[Jason Brown]

My name is Jason Brown. I'm a professor of mathematics at Dalhousie University in Halifax, Canada. My research involves applying mathematics to music, and in particular the music of the Beatles. So I was looking at the song Strawberry Fields Forever, and there's a wonderful story that goes behind the song. John Lennon wrote the song in 66 and the Beatles recorded it and they got down a version which was take seven in the key of A at a slow tempo.

[Tim Harford]

Strawberry Fields Forever take seven remix from four track, take six.

[Jason Brown]

Then they let it rest for a while and John Lennon wasn't happy with, with that take. And so they came back and they did another version which turned out to be in the key of B at a faster tempo, which was more to John's liking.

[Wesley Stevenson]

Let me take you down Cause I'm going to Strawberry Fields.

[Jason Brown]

The problem was that John, when listening to it, decided that he liked the first half of take 7 in the key of A and the second half of take 26 in the key of B. And so he went to George Martin and he said, george, what I'd like to do is to have you edit the two pieces together. And George said to him, john, John, John. He must have said, you can't do that. They're in different keys and at different tempos and you can't match them. And then John said to George Martin, well, that's not my problem, that's your problem. So at that point, George Martin had to decide how he was going to proceed. So he decided to speed up the take that was in the key of a, take 7, and slow down the other take, take 26, which was in the key of B until they matched pitch and they matched pitch at B flat. That was his choice. He made a cut around the 1 minute mark and edited them together. And most people would be hard pressed to even sense that there was an edit at that point.

[Tim Harford]

So what's the lyric at that point, that one minute mark?

[Jason Brown]

It's, let me take you down. You can slow down and speed up tapes to change the pitch, and you can also slow them down to change the tempo. But both are proportional to the speed change. So if you want to change the pitch, it's unlikely you're going to be able to change the tempo to the same degree. So he had a choice, George Martin did. He could either match the pitch for the two takes or he could match the tempo. And we're much more discriminating about pitch. We hate things that are out of tune. So he decided to match the pitch exactly and let the tempos vary as they had to. When he decided to match the pitches, in the end, what happens is there's about a 12 beat difference between the two takes when they're spliced together. And for a lot of people, they don't notice the change in tempo. But One Beatle, Paul McCartney, has an impeccable sense of rhythm. And he said he didn't really notice the edit, but he always felt that the second half of the song was a bit manic, was too fast.

[Tim Harford]

Turning to the maths behind this, how complicated was it? How did you go about it?

[Jason Brown]

Well, the math is actually not too complicated. Once we figured out that the way we listen to and discriminate pitch and tempo are really very similar, it's on what's called a logarithmic scale, we quickly found out that changing the pitches to match would leave us with the same percentage difference in the tempos, and that would mean that we couldn't match Paul's sensibilities in terms of tempo. And the mathematical question I wanted to answer was, could there have been a different way to edit the two takes together in such a way as to satisfy Paul?

[Tim Harford]

And is there?

[Jason Brown]

Well, surprisingly, the answer is no. There is, though, one solution, and that was to slow them down both takes quite a bit, almost an octave. And if you did that, then our perception of differences in tempo is such that even the most experienced listener would not notice a change in tempo. But the song Strawberry Fields Forever would have gone from a four minute song to an eight minute song. And so it really would have seemed like Strawberry Fields Forever.

[Tim Harford]

Jason Brown of Dalhousie University. That's all we have time for this week, but we'll be back next week. Until then, there's always our website, BBC.co.uk more or less, for David Spiegelhalter's essay, photos of our guest presenter Graham Seed, our podcast, our archive, our own little census and much more. And you can email us with your questions and comments at more or lessbc.co.uk. please do. And until next week, goodbye.

More or Less is presented by Tim Harford, the Financial Times undercover economist, with a little help from Graham Seed. The More or Less team is Richard Varden, Richard Knight, Wesley Stevenson and me, Hannah Barnes. More or Less is made in association with the Open.