Stamp prices and the first maths book

Summary

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More or Less (BBC Radio 4)

Episode: Stamp prices and the first maths book

Date: April 6, 2012
Host: Tim Harford
Guests: Ruth Alexander, Keith Devlin

Episode Overview

This episode of More or Less explores the true cost of posting a letter around the world and uncovers the reality behind claims about UK postal value. It also journeys into mathematical history with a look at the first comprehensive maths textbook in Europe, written by Fibonacci, examining its impact on everyday arithmetic.

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Key Discussion Points & Insights

1. The Real Cost of Postal Stamps in the UK and Beyond

(00:42 - 05:28)

• UK Stamp Prices on the Rise:

  • First class mail price rising by 30%.
  • Second class by almost 40%.
  • Royal Mail claims UK stamp prices remain “amongst the best value in Europe.”

• Scrutiny of Royal Mail’s Claims:

  • Royal Mail states the UK is the cheapest for some letters, under certain conditions (heavy letter, over 50g, second class, and adjusted for purchasing power).
    • [01:20] Ruth Alexander:

      "If you're posting a heavy letter ... and if you adjust the prices to take into account relative purchasing power ... the UK service is the cheapest in Europe."

  • Reality: For a standard first-class letter, the UK is not the cheapest.
    • [02:09] Ruth Alexander:

      "If you post a standard first class letter, the UK is actually in the top 10 of the most expensive countries."

• Ranking UK Postal Costs:

  • 5th most expensive in Europe (standard first class).
  • 7th when adjusted for relative purchasing power.
    • Countries more expensive: Finland, Switzerland, Denmark, Norway, etc.
    • Differences in rankings likely due to calculation methods.

• Global Stamp Price Comparison:

  • [03:18] Tim Harford:

    "Looking at the whole world, which is the most expensive country of all?"

  • Most Expensive:
    • Norway (in absolute prices).
    • Jamaica (when adjusted for purchasing power).
      • [03:42] Ruth Alexander:

        "It costs 120 Jamaican dollars, which... is only US$1.39. But that is still the most expensive postage in the world that we could find."

• Cheapest Places to Send a Letter:

  • Bangladesh (about US$0.05), followed by Thailand, Pakistan, Vietnam, and India.
    • [04:36] Ruth Alexander:

      "Bangladesh, where it costs four taka ... that's about 5 US cents."

• Contextual Challenges:

  • Comparing across nations is tricky due to:
    • Size and geography (e.g., Luxembourg vs. India, Peru’s Andes).
    • Postal service quality, reliability, and efficiency.
      • [05:14] Ruth Alexander:

        "The last time the European Commission checked up on national postal services, they found that Romania and Poland weren't doing very well, whereas Luxembourg and Sweden were the very models of efficiency."

2. History’s First Comprehensive Maths Book: Liber Abaci

(05:28 - 09:04)

• Origins of Modern Arithmetic:

  • Story of Liber Abaci by Leonardo of Pisa (Fibonacci).
  • The book introduced Hindu-Arabic numerals and arithmetic methods to Europe (using digits 0-9).
    • [05:59] Keith Devlin:

      "It really was the first comprehensive, actually the first coverage at all of ... Hindu Arabic arithmetic... all the algorithms, all of the methods we learn at school that had been invented by Indian mathematicians..."

• How Hindu-Arabic Maths Reached Europe:

  • Developed in India, spread through Arabic merchants.
  • Fibonacci encountered these methods in North Africa, recognized their societal potential, and made them accessible to Europeans.

• Why This Was Revolutionary:

  • Replacing Roman numerals (fine for adding/subtracting, useless for multiplication/division).
  • Pre-Fibonacci, calculations done with hands or counting boards—opaque and required specialists.
    • No audit trail or ease of use.
    • [07:13] Keith Devlin:

      "When people did calculations, they did one of two things. Either they counted on their fingers, [or] ... with a board on which lines were ruled, on which you move pebbles around ..."

  • After Liber Abaci, arithmetic became accessible to everyone.
    • [08:15] Keith Devlin:

      "What had once been impossible became completely taken for granted and regarded as just, well, duh, of course we can do arithmetic now."

• The Fibonacci Sequence – Not Fibonacci's Own?

  • Sequence originated in Liber Abaci as a side note/problem, but wasn't Leonardo's focus or invention.
    • [08:22] Keith Devlin:

      "He really had nothing to do with the damn thing... In the 19th century, a French mathematician ... gives it a name, the Fibonacci Sequence. That's the only connection between Leonardo and the Fibonacci sequence, I'm afraid."

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Notable Quotes & Memorable Moments

• "[01:35] Tim Harford:

  'The Royal Mail is basically claiming that posting letters in the UK is cracking value every alternate Tuesday during leap year.'"

• "[02:11] Ruth Alexander:

  'If you post a standard first class letter, the UK is actually in the top 10 of the most expensive countries.'"

• "[03:42] Ruth Alexander:

  'It costs 120 Jamaican dollars, which in fairness is only US$1.39. But that is still the most expensive postage in the world that we could find.'"

• "[05:59] Keith Devlin:

  'It really was the first comprehensive, actually the first coverage at all of what we now call Hindu Arabic arithmetic, the kind of arithmetic that we all learn when we're in the elementary school...'"

• "[08:15] Keith Devlin:

  'What had once been impossible became completely taken for granted and regarded as just, well, duh, of course we can do arithmetic now.'"

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Timestamps for Important Segments

• 00:42 – Introduction to post price hikes in the UK and Royal Mail’s claims
• 01:20 – Ruth Alexander explains criteria for UK's "cheapest" status
• 02:09–02:40 – Reality check: UK is expensive for standard letters
• 03:18–03:42 – World comparisons: Norway and Jamaica highlighted
• 04:36–04:49 – Cheapest postal services: Bangladesh, Thailand, Pakistan, Vietnam, India
• 05:28 – Transition to maths history and Fibonacci
• 05:59–08:15 – Keith Devlin on Liber Abaci, Roman numerals, and the arithmetic revolution
• 08:22 – Debunking the link between Fibonacci and the Fibonacci Sequence

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Conclusion

This More or Less episode dissects the real economics behind UK and global postage prices, challenging the Royal Mail's positive spin, and places modern arithmetic in historical context via Fibonacci’s Liber Abaci. With clarity and wit, Tim Harford and his guests reveal not just what the numbers say, but why—and how much—the story behind them matters.

Transcript

[BBC Announcer]

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

[Tim Harford]

this is more Or Less the programme which finds poetry in data. We make an edition of the programme for BBC Radio 4, but this episode was broadcast on the World Service. Hello, and welcome to More or Less on the BBC World Service. We're your weekly guide to the numbers in the news and in life. And hello, and I'm Tim Harford. This week we bring you the story of the very first maths book, the

[Keith Devlin]

beginning of the 13th century. Nobody in Europe had ever seen that kind of thing before.

[Tim Harford]

But first, the price of posting a letter is going up sharply in the UK by 30% for first class mail and almost 40% for second class mail. The Royal Mail says it has to put up the price to protect its future. And it says that UK stamp prices are still amongst the best, best value in Europe. Are they? Right. And what is the cheapest place in the world to post a letter? Or for that matter, the most expensive? Ruth Alexander's been tending to the great

[Ruth Alexander]

more or less spreadsheet and what secrets it holds.

[Keith Devlin]

Tim?

[Tim Harford]

Yes, the Royal Mail has said the UK will remain the cheapest place in Europe to post a letter, or at least a certain type of letter. Ruth?

[Ruth Alexander]

Yes, if you're posting a heavy letter that weighs more than 50 grams, and if you're posting it second class, and if you adjust the prices to take into account relative purchasing power of the different countries, then the UK service is the cheapest in Europe.

[Tim Harford]

So what the Royal Mail is trying to do there is to say everything's expensive in Switzerland. Let's take that into account when we're evaluating whether posting a letter is expensive. And similarly, in Romania, everything's cheap. Is posting a letter also cheap? It all sounds a bit complicated. The Royal Mail is basically claiming that posting letters in the UK is cracking value every alternate Tuesday during leap year. If we skip over these convoluted calculations, what if you post a standard letter? Just one or two sheets of paper. First class? Is the UK still the cheapest place in Europe?

[Ruth Alexander]

No, it isn't.

[Tim Harford]

I knew you'd say that.

[Ruth Alexander]

If you post a standard first class letter, the UK is actually in the top 10 of the most expensive countries.

[Tim Harford]

I see. That's quite a difference. I noticed the Royal Mail hasn't really been trumpeting that fact.

[Ruth Alexander]

No, it hasn't. Our calculations show the UK is the fifth most expensive in Europe with a first class stamp. Soon to cost 60p or almost US$1, it's behind Finland, Switzerland, Denmark and Norway is in first place there. A stamp costs $1.67. If you adjust for the relative purchasing power of the different countries, the UK is in seventh place. And the countries ahead of us are quite different. We're behind Denmark in sixth place, Norway in fifth, then Poland, Latvia, Slovakia, and Bulg is in the top spot for relative expense. When the Royal Mail does these calculations, it places us in ninth position. We haven't been able to establish exactly why our numbers differ, but it's probably because we're using slightly different purchasing power calculations.

[Tim Harford]

Well, any which way you look at it, the UK is still in the top 10 of relative expense. And looking at the whole world, which is the most expensive country of all?

[Ruth Alexander]

Well, we haven't been able to get the data for every single country in the world, but we've had a good go and got the cost of a stamp in 65 countries into the a more or less spreadsheet. And the most expensive of all is Norway, if you're just looking at straight prices. And if you adjust for purchasing power, it's Jamaica.

[Tim Harford]

So posting a letter feels most expensive for people living in Jamaica.

[Ruth Alexander]

Yes, it costs $120. $120, 120 Jamaican dollars, which in fairness is only US$1 39. But that is still the most expensive postage in the world that we could find. On the other hand, for send a letter not just within Jamaica, but to most of the Caribbean, to Central South America and North America, two continents, that's not bad value. Then maybe the next most expensive place we've found is Peru. There it costs three soles to put a stamp on a letter. And to put that into context, here's a BBC journalist who lives there, Mattia Kabica.

[Mattia Kabica]

With three soles, an average Peruvian in a poor neighborhood could buy a whole meal, talking about soup and chicken and rice. Or you can travel in the Peruvian capital, Lima, across the city three times on a bus.

[Tim Harford]

If I wanted to get the best value for money from a postal service, where should I be posting my letter?

[Ruth Alexander]

Bangladesh, where it costs four taka to send a letter, that's about 5 US cents. And Bangladesh is followed closely by Thailand, Pakistan, Vietnam and India is also relative value for money.

[Tim Harford]

Now this whole thing has me thinking, I guess posting a letter in somewhere small like Luxembourg, it's very different from posting a letter in India, where you're going to reach a billion people, or in Jamaica, where you can reach two continents, or In Peru, where you have to get over the Andes or the Amazon. I mean, we're really not comparing like with like here. And I suppose also the quality, the reliability of the service has got to

[Ruth Alexander]

count for something and that's hard to survey internationally. The last time the European Commission checked up on national postal services, they found that Romania and Poland weren't doing very well, whereas Luxembourg and Sweden were the

[Tim Harford]

very models of efficiency, just like you. Thank you, Ruth. Now, the numbers we used to do basic sums weren't always at our fingertips. I've been finding out how numbers became established in the ancient Arab world and then how they journeyed on to Europe in what was basically the first maths textbook ever written. Its author was Leonardo of Pisa, better known as Fibonacci. Keith Devlin of Stanford University in California has been finding out about this book which was titled rather beautifully, Liba Abachi.

[Keith Devlin]

It really was the first comprehensive, actually the first coverage at all of what we now call Hindu Arabic arithmetic, the kind of arithmetic that we all learn when we're in the elementary school, counting with the 10 digits from 0 through 9, all the algorithms, all of the methods we learn at school that had been invented by Indian mathematicians in about the first six or seven centuries of the current era. Then the Arabic speaking traders in Muslim world who were trading between North Africa and Europe and the Orient, they discovered these methods and they started using them in their trade. And then some of their scholars started developing them. And one of the offshoots was what we now call algebra. And so for several hundred years, it was those traders that were sort of developing it and using it. And it was in North Africa when Leonardo, who was a teenager, who'd gone over to join his father, who was a customs official in Buja, Leonardo sees these traders in the coffee shops using this incredible method. And he recognizes that once this can change the world. If I can package this and make it accessible to ordinary people, then anyone can do their own arithmetic.

[Tim Harford]

And the key thing here is, I mean, it's not to modernize, it's not anything very remarkable. It's not a sort of a particular trick, it's just leaving Roman numerals behind.

[Keith Devlin]

Roman numerals are fine for adding and subtracting, but that's not very useful when you're working out volumes of things that you want to buy. And so you need multiplication and division and Roman numerals are hopeless for that. So when people did calculations, they did one of two things. Either they counted on their fingers, the other way they used to calculate was with a board on which lines were ruled, on which you move pebbles around, then you record the answers in Roman numerals. So, first of all, you couldn't do your own calculations. You had to have someone who'd spent many years becoming efficient at using one of these two physical calculating methods. Another drawback was there's no audit trail. If you carry out a long calculation and then one of the two parties disputes the answer, you can't just go back over the working like we would today. The workings disappeared. The measure of the size of the revolution that followed Leonardo's publication of Liber Baci is precisely that what had once been impossible became completely taken for granted and regarded as just, well, duh, of course we can do arithmetic now.

[Tim Harford]

You said Leonardo of Pisa is more commonly known as Fibonacci. I think people will be surprised you haven't mentioned the Fibonacci sequence.

[Keith Devlin]

Yeah, the one person who wouldn't be surprised would have been Leonardo himself. He really had nothing to do with the damn thing. Every now and then he would throw in a whimsical problem just to sort of lighten the load. And one of the whimsical problems was a problem about a fictitious rabbit population. And you have to figure out how many rabbits there are in this population after they've been breeding for a year. That problem wasn't original to him then. In the 19th century, a French mathematician who's looking through Leonardo's work sees this sequence in Liber Verbacci, knows that this sequence has interesting properties to do with the way flowers and plants grow and that kind of thing, and he gives it a name, the Fibonacci Sequence. That's the only connection between Leonardo and the Fibonacci sequence, I'm afraid.

[Tim Harford]

Keith Devlin, author of the man of Numbers if you have a numerical or statistical query, please email more or lessbc.co.uk and you can download our podcast via our website, bbcworldservice.com more or less. Until next week, goodbye. More or Less was presented by me, Tim Harford, the Financial Times undercover economist. The producer was Ruth Alexander and the editor, Richard Varden.

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