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The Maths of Mozart and Birds
00:09:29
Birds + windows =? The BBC Quiz show The Unbelievable Truth reckons that more than 2...
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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
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hello and welcome to More or Less on the BBC World Service. I'm Tim Harford and spring in my bit of the world has finally sprung. But, oh no, there could be a dark side to this season. There I was in the kitchen with my family, listening to a BBC radio quiz, the Unbelievable Truth. The aim of the game is to deliver a hilarious monologue on a given topic, almost all of which is false, and to smuggle five implausible truths, cunningly concealed amidst the lies. And one of the unbelievable truths which made it past the panelists was in
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America, each day over 2 million birds die crashing into window panes. And at the end of that round, Mark, you've made to smuggle three truths past the rest of the panel. The second truth is that in America, each day over 2 million birds die crashing into window panes.
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But I just found this unbelievable. Charlotte MacDonald, I said, this is one for a statistical sleuth like you.
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Well, the story starts in 1990. That year I was dancing about to this kind of thing.
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Yo, vip, let's kick it. Is this relevant?
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I'm just setting the scene for you. Stop. And out in the us, an ornithologist was writing an article called Collisions between Birds and Windows. He reasoned that there are a lot of buildings in the US and that most buildings have windows. So he looked up the number of buildings in the whole country using U.S. bureau of Census data, and how many were there? About 100 million. He then thought, if we assume that over a year between one and 10 birds will hit windows on every building in the country and die, how many birds would that be?
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So that's multiplication plus assumption. Very neat. And so the fact was born that between 100 million and a billion birds die in the US each year, hitting windows.
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Yes, it features on a bird guide website. And that's where the Unbelievable Truth team found it. They then took the highest number, a billion dead birds, divided it by 365 days and got their figure of more than 2 million a day. But I've spoken to leading bird window collision expert professor Daniel Clem, and he thinks people shouldn't quote this number as if it was some kind of solid fact.
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He's just one expert, and experts do disagree.
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Yes, but Professor Daniel Clem is the ornithologist who came up with the number in the first place.
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I don't believe that anyone should Take those figures as facts. There was some quantitative basis behind it, but it wasn't to the level that one would consider those figures to be facts. It's probably likely, but I don't think any reasonable person should be using those figures as facts until we have more supportive evidence.
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Frankly, I'm shocked. What is the point of having a panel game built on truth and lies if the truths aren't true?
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Yeah, I know. That's what the news is for.
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But the quizmaster, David Mitchell, did have another bird window collision death statistic up his sleeve when one for the UK, he said 100 million birds crash into British windows each year, with a third dying as a result. Is there any more truth in that?
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Possibly. It's a figure from the British Trust for Ornithology, and a few years ago they counted the number of ringed birds found dead from hitting windows and extrapolated up to get a national figure. It's an initial estimate, they say, not robust enough to pass as a hard fact.
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David Mitchell, I trusted you and Charlotte. Thank you. I still trust you. Mozart's final opera, the Magic flute, premiered just 10 weeks before the composer's death and was the biggest popular hit of his life. With its pantomime storyline and catchy tunes, it's said to be one of the most accessible operas for the uninitiated. But there's an awful lot going on beneath the jokes and the musical notes. Oxford professor Marcus De Sotoy recently spoke at London's Royal Opera House about what he finds in the Magic Flute. As a mathematician. Charlotte MacDonald.
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Yes.
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You were in the audience?
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I was.
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Welcome to our mathematical exploration of the Magic Flute and our musical journey through the world of mathematics. Rejoice.
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Behold your tally.
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I think a lot of people have talked about the connection between mathematics and music, and what I wanted to do was to take an opera like the Magic Flute and explore those connections, because I think obviously music is highly emotional, but it's also got a lot of precision and mathematical structure in it. And Mozart loved mathematics. There are lots of examples of him playing with numbers and kind of shapes. The Magic Flute, the last of his operas, is full of kind of numerical and geometric symbolism. So I wanted to sort of take the audience looking through my eyes, or ears, rather what I hear when I hear something like the Magic Flute. It's interesting that Mozart's other operas are very much to do with the human condition. Don Giovanni, Marriage of Figaro. They're very much set in the real world, but the Magic Flute is a much more abstract piece It's a kind of a rather a magical world. And that, I think, gives Mozart the freedom really to play a lot of games. Does anyone know the next number in this sequence? 1. 1, 2, 3, 5, 8, 13, 21. Yes, if you read the DaVinci Code, it's one of the things you have to crack in the DaVinci Code. These are called the Fibonacci numbers because you add the two previous numbers together to get the next one in the sequence. That's the rule. And interestingly, it seems that Mozart, again, is this planned or intuitive? I'm not sure. But the way the Magic Flute is divided up, the first act is divided into eight musical pieces. The second act is divided into 13 musical pieces. Eight plus 13 gives you 21 in total, three Fibonacci numbers. Now, was that just a coincidence? I think not. Mozart had joined the Freemasons seven years earlier. And you can see a lot of kind of Masonic ideas running through this opera. And the masons, of course, have a lot of connections to mathematics through sort of geometry and numbers. The masons, after all, built things, and so mathematics is key to that. So a lot of their rituals have mathematics in it. Now we move through to the importance of the number three. In this opera, we find lots of threes. We've had the three ladies. It's also a very important number for the masons. And Mozart uses this number three to indicate kind of the connections with the masons. One of the rituals that an initiate has to go through is to knock a rhythm on the door of the lodge and it's three notes in a particular rhythm on and done three times. And we hear this triple chord again and again throughout this opera. So here's the triple chord. I think sometimes I've chosen to be a mathematician because when you do mathematics, there's a feeling like you can leave something permanent after your death. Because the power of proof means that something you've proved will be true forever. And I think Mozart's music, perhaps more than anybody's, has that kind of eternal truth about it. It transcends space and time. And he really did achieve life after death through his music.
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Professor Marcus De Sotoy, talking to Charlotte MacDonald about the mathematical properties of Mozart's opera the Magic Flute. If there are any numbers you would like explaining or investigating, you can email us. Our address is more or less@bc.co.uk and you can listen to more editions of this program and sign up for a free download at our website, bbcworldservice.com moreorless
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