Melvyn Bragg and guests discuss the mathematical structures that lie within the heart of music. The seventeenth century philosopher Gottfried Leibniz wrote: ‘Music is the pleasure the human mind experiences from counting without being aware that it is counting’. Mathematical structures have always provided the bare bones around which musicians compose music and have been vital to the very practical considerations of performance such as fingering and tempo. But there is a more complex area in the relationship between maths and music which is to do with the physics of sound: how pitch is determined by force or weight; how the complex arrangement of notes in relation to each other produces a scale; and how frequency determines the harmonics of sound. How were mathematical formulations used to create early music? Why do we in the West hear twelve notes in the octave when the Chinese hear fifty-three? What is the mathematical sequence that produces the so-called ‘golden section’? And why was there a resurgence of the use of mathematics in composition in the twentieth century? With Marcus du Sautoy, Professor of Mathematics at the University of Oxford; Robin Wilson, Professor of Pure Mathematics at the Open University; Ruth Tatlow, Lecturer in Music Theory at the University of Stockholm.
Tagged with “mathematics” (45)
New findings are fueling an old suspicion that fundamental particles and forces spring from strange eight-part numbers called “octonions.”
On this week’s show, we’re exploring infinity and beyond with artist and writer James Bridle and mathematician Marcus du Sautoy.
Through his visual art and writings on technology and culture, James Bridle has been at the forefront of our understanding of tech for the last decade – and from his perspective, the view of our future is both exciting and gloomy. He sat down with the Guardian’s technology reporter Alex Hern to talk about his book, New Dark Age.
Limits are grist to the mill for Marcus du Sautoy, professor of public understanding of science at Oxford University. His mission is to explore – and if possible, explain – the unknown, so following hot on the heels of his bestselling book What We Cannot Know, is How to Count to Infinity. Meeting with Richard Lea at the Hay festival, Du Sautoy explained how a German mathematician first proved the existence of infinity in 1874, and what the concept means for our understanding of the universe.
Lord Byron’s only legitimate child is championed by Konnie Huq.
From Banking, to air traffic control systems and to controlling the United States defence department there’s a computer language called ‘Ada’ - it’s named after Ada Lovelace - a 19th century mathematician and daughter of Lord Byron. Ada Lovelace is this week’s Great Life. She’s been called many things - but perhaps most poetically by Charles Babbage whom she worked with on a steam-driven calculating machine called the Difference Engine an ‘enchantress of numbers’, as her similarly mathematical mother had been called by Lord Byron a "princess of parallelograms". Augusta ‘Ada’ Byron was born in 1815 but her parents marriage was short and unhappy; they separated when Ada was one month old and she never saw her father , he died when was eight years old. Her mother, Annabella concerned Ada might inherit Byron’s "poetic tendencies" had her schooled her in maths and science to try to combat any madness inherited from her father. She’s championed by TV presenter and writer -Konnie Huq, most well known for presenting the BBC’s children’s programme - ‘Blue Peter’ and together with expert- Suw Charman- Anderson, a Social technologist, they lift the lid on the life of this mathematician, now regarded as the first computer programmer with presenter Matthew Parris.
Geeks versus government – the story of public key cryptography.
Take a very large prime number – one that is not divisible by anything other than itself. Then take another. Multiply them together. That is simple enough, and it gives you a very, very large “semi-prime” number. That is a number that is divisible only by two prime numbers. Now challenge someone else to take that semi-prime number, and figure out which two prime numbers were multiplied together to produce it. That, it turns out, is exceptionally hard. Some mathematics are a lot easier to perform in one direction than another. Public key cryptography works by exploiting this difference. And without it we would not have the internet as we know it. Tim Harford tells the story of public key cryptography – and the battle between the geeks who developed it, and the government which tried to control it.
Melvyn Bragg and his guests discuss Euler’s number, also known as e. First discovered in the seventeenth century by the Swiss mathematician Jacob Bernoulli when he was studying compound interest, e is now recognised as one of the most important and interesting numbers in mathematics. Roughly equal to 2.718, e is useful in studying many everyday situations, from personal savings to epidemics. It also features in Euler’s Identity, sometimes described as the most beautiful equation ever written.
Colva Roney-Dougal Reader in Pure Mathematics at the University of St Andrews
June Barrow-Green Senior Lecturer in the History of Maths at the Open University
Vicky Neale Whitehead Lecturer at the Mathematical Institute and Balliol College at the University of Oxford
Melvyn Bragg and his guests discuss Fermat’s Last Theorem. In 1637 the French mathematician Pierre de Fermat scribbled a note in the margin of one of his books. He claimed to have proved a remarkable property of numbers, but gave no clue as to how he’d gone about it. "I have found a wonderful demonstration of this proposition," he wrote, "which this margin is too narrow to contain". Fermat’s theorem became one of the most iconic problems in mathematics and for centuries mathematicians struggled in vain to work out what his proof had been. In the 19th century the French Academy of Sciences twice offered prize money and a gold medal to the person who could discover Fermat’s proof; but it was not until 1995 that the puzzle was finally solved by the British mathematician Andrew Wiles.
Marcus du Sautoy Professor of Mathematics & Simonyi Professor for the Public Understanding of Science at the University of Oxford
Vicky Neale Fellow and Director of Studies in Mathematics at Murray Edwards College at the University of Cambridge
Samir Siksek Professor at the Mathematics Institute at the University of Warwick.
Melvyn Bragg and guests discuss the problem of P versus NP, which has a bearing on online security. There is a $1,000,000 prize on offer from the Clay Mathematical Institute for the first person to come up with a complete solution. At its heart is the question "are there problems for which the answers can be checked by computers, but not found in a reasonable time?" If the answer to that is yes, then P does not equal NP. However, if all answers can be found easily as well as checked, if only we knew how, then P equals NP. The area has intrigued mathematicians and computer scientists since Alan Turing, in 1936, found that it’s impossible to decide in general whether an algorithm will run forever on some problems. Resting on P versus NP is the security of all online transactions which are currently encrypted: if it transpires that P=NP, if answers could be found as easily as checked, computers could crack passwords in moments.
Interview with Alex Bellos, author of the book Grapes of Math: How Life Reflects Number and Numbers Reflect Life.
On "Word of Mouth" program on New Hampshire Public Radio
Brian Cox and Robin Ince are joined by comedian Dave Gorman, and maths author Alex Bellos, and number theorist Vicky Neale to discuss the joy of numbers and why we are all closet mathematicians at heart.
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