More or Less: Behind the Stats
More or Less makes sense of the numbers that surround us and that rule our world. With wit, freshness and simplicity Tim Harford shows the genuine significance of statistics, productivity, performance indicators, measurements and quantification of every kind. We all use numbers in so many ways to argue about, understand, help make sense of the world around us. More or Less hopes to make that task easier, more entertaining, more surprising. This half-hour programme is broadcast at 1330 on Friday afternoons and repeated at 2000 on Sundays on Radio 4.
In this one-off documentary, David Malone looks at four brilliant mathematicians - Georg Cantor, Ludwig Boltzmann, Kurt G?del and Alan Turing - whose genius has profoundly affected us, but which tragically drove them insane and eventually led to them all committing suicide.
The film also talks to the latest in the line of thinkers who have continued to pursue the question of whether there are things that mathematics and the human mind cannot know. They include Greg Chaitin, mathematician at the IBM TJ Watson Research Center, New York, and Roger Penrose.
Dangerous Knowledge tackles some of the profound questions about the true nature of reality that mathematical thinkers are still trying to answer today.
Part 1: God’s messenger
The film begins with Georg Cantor, the great mathematician whose work proved to be the foundation for much of the 20th-century mathematics. He believed he was God’s messenger and was eventually driven insane trying to prove his theories of infinity.
Ludwig Boltzmann’s struggle to prove the existence of atoms and probability eventually drove him to suicide.
Part 2: The Enigma
Kurt Gödel, the introverted confidant of Einstein, proved that there would always be problems which were outside human logic. His life ended in a sanatorium where he starved himself to death.
Finally, Alan Turing, the great Bletchley Park code breaker, father of computer science and homosexual, died trying to prove that some things are fundamentally unprovable.
This is the extraordinary story of a beautiful mathematical formula that changed the world, the financial markets, and indeed capitalism itself. It could do the unthinkable - it took the risk out of playing the money-markets. To its inventors it brought the Nobel Prize for economics. To those who used it, it brought great wealth. But this glittering tale would end in tragedy.
The Black Scholes formula was invented 25 years ago, by three young mathematicians. They had been trying to solve a problem that had plagued economists for centuries - how to counter the randomness of market forces and the irrationality of human behaviour that made the markets dangerously turbulent. Whilst pondering this dilemma, they made a remarkable discovery.
The search for a way to price option contracts began in earnest when the thesis of an unknown student named Louis Bachelier was unearthed in the 1950s. Working at the beginning of this century, Bachelier had set out to do something no-one had ever done before - using a series of equations he created the first complete mathematical model of the markets. He had realised that stock prices moved at random and that it was impossible to make exact predictions about them, but Bachelier said he had also found a solution - through the pricing of a financial contract called an option.
The risk in the stock market is that if you buy a stock today the price can drop in the future and you could lose money but if you pay for an option contract this gives you the right to wait and buy the stock if it reaches some agreed price in the future, but there’s no obligation. If the stock fails to reach that price you can opt out and you would lose only the cost of the option. In theory options are a perfect way to get rid of risk, but there was a problem. How much would someone pay for such absolute peace of mind?
Bachelier believed that if someone could discover a formula that would allow option contracts to be widely used, they would be able to tame the markets completely, but he died before he could find it. By the end of the 60s, academics were no nearer to pricing options than they’d ever been. But all this was about to change when Myron Scholes and his colleague Fischer Black set out to tackle the problem of options…
At its simplest level, the Black Scholes formula could be used to hedge against losing any bet, by working out how to place another bet in the opposite direction. That way, you couldn’t lose. The formula had the almost magical ability to allow you to make a fortune with the minimum of risk. But there was one problem. In the time it took to make the calculation, the fast moving markets had moved on and the calculation would effectively be out-of-date.
However, unbeknown to them, the problem had already been solved by a financial genius called Bob Merton. Using an idea taken from rocket science, the value of an option could now be constantly recalculated and the risk eliminated continually.
Myron Scholes and Bob Merton joined forces with the greatest dealers on Wall Street, and started a legendary company - Long Term Capital Management (LTCM). Relying on mathematics, the company traded and borrowed on a scale never seen before. But the mathematical model was based on normal market behaviour and unforeseen events were about to send the markets wild. The calculations in LTCM’s models became hopelessly out of kilter, and when the company collapsed last year, it nearly brought down the entire global economy.
Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before
(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)
