Robin Ince and Brian Cox are joined by Stephen Fry, Simon Singh and Aleks Krotoski to discuss the maths behind 6 degrees of separation and whether there is something special about Kevin Bacon that seems to make him so well connected?
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Episode five of A Further Five Numbers, the BBC radio series presented by Simon Singh.
Curious properties sometimes lurk within seemingly undistinguished numbers. 1729 sparked one of maths most famous anecdotes: a young Indian, Srinivasa Ramanujan, lay dying of TB in a London hospital. G.H. Hardy, the leading mathematician in England, visited him there. "I came over in cab number 1729," Hardy told Ramanujan. "That seems a rather dull number to me."
"Oh, no!" Ramanujan exclaimed. "1729 is the smallest number you can write as the sum of two cubes, in two different ways." Most of us would use a computer to figure out that 1³ + 12³ = 9³ + 10³ = 1729. Ramanujan did it from his sickbed without blinking.
Episode four of A Further Five Numbers, the BBC radio series presented by Simon Singh.
Newton’s equation of gravity included a number G, which indicates the strength of gravitation. It took 100 years before the shy Englishman Henry Cavendish (he left notes for his maids because he was too shy to talk to women) measured G to be 6.67 x 10^-11 Nm²/Kg². It allowed him to weigh the Earth itself. There has been an ever-greater desire to measure this number with accuracy, which even implied an antigravity at times. How did we measure this tiny number and what does it mean for the universe? The Astronomer Royal Martin Rees explains that a large value for G would mean that stars would burn too quickly and a low value would mean that the stars would not form in the first place, so is G perfectly tuned for life? Is God a mathematician?
Episode three of A Further Five Numbers, the BBC radio series presented by Simon Singh.
Six is often treated as 2x3, but has many characteristics of its own. Six is also the "pivot" of its divisors (1+2+3=6=1x2x3) and also the centre of the first five even numbers: 2, 4, 6, 8, 10. Six seems to have a pivoting action both mathematically and socially. How is it that everyone in the world can be linked through just six social ties? As Simon discovers, the concept of “six degrees of separation” emerged from a huge postal experiment conducted by the social psychologist Stanley Milgram in 1967. Milgram asked volunteers to send a package by mail to one of a hundred people chosen at random. But they could only send mail to people they knew on first name terms.
Episode two of A Further Five Numbers, the BBC radio series presented by Simon Singh.
We all remember the story of the Persian who invented chess and who asked to be paid with 1 grain of rice on the first square, 2 on the second, 4 on the third and so on, doubling all the way to the 64th square. He bankrupted the state!
This doubling is a form of exponential growth, which appears in everything from population growth to financial inflation to the inflation theory that supposedly caused the Big Bang.
Episode one of A Further Five Numbers, the BBC radio series presented by Simon Singh.
Literally, the most popular number, as it appears more often than any other number. More specifically, the first digit of all numbers is a 1 about 30% of the time, whereas it is 9 just 4% of time. This was accidentally discovered by the engineer Frank Benford. It works for all numbers – mountain heights, river lengths, populations, etc.
Episode five of Another Five Numbers, the BBC radio series presented by Simon Singh.
In 2000, the UK government received a windfall of around £23 billion from its auction of third generation (3G) mobile phone licences. This astronomical sum wasn’t the result of corporate bidders "losing their heads", but a careful strategy designed to maximise proceeds for the Treasury.
Episode four of Another Five Numbers, the BBC radio series presented by Simon Singh.
Johannes Kepler experimented with different ways of stacking spheres. He concluded that the "face-centred cubic lattice" was best. Using this method, Kepler calculated that the packing efficiency rose to 74%, constituting the highest efficiency you could ever get. But, how to prove it?
Episode three of Another Five Numbers, the BBC radio series presented by Simon Singh.
Think of a number. Any number. Chances are you haven’t plumped for 2 to the power of 13,466,917 -1. To get this, you would need to keep multiplying 2 by itself 13,466,917 times, and then subtract 1 from the result. When written down it’s 4,053,900 digits long and fills 2 telephone directories. So, as you can imagine, it’s not the kind of number you’re likely to stumble over often. Unless you’re Bill Gates checking your bank statement at the end of the month.
Episode two of Another Five Numbers, the BBC radio series presented by Simon Singh.
Picture a gambler. Is it George Clooney, tuxedo ruffled after an all-nighter at a Vegas Black Jack table, or your old Aunt Doris putting down her yearly quid-on-the-nose for the Grand National? Recent research would suggest that it’s neither. Your inveterate gambler is far more likely to be sporting leather patches at their elbows, an unhealthy appetite for corduroy, and a penchant for M-Series rather than Martinis, shaken or stirred. Some mathematicians are putting their mathematical theory where their mouth is and are betting the shirts, stuffed or otherwise, off their backs.
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