How many people need to gather together before it becomes more likely than not that at least two of them will share a birthday? The answer might surprise you. It’s just one of the many intriguing facts that I’ve learned at Gresham College.
Gresham was founded in 1597, the brainchild of Thomas Gresham, king of what’s now called the Square Mile. He had also established the Royal Exchange, and decreed that rents paid by merchants there should fund free lectures open to anyone. The arrangement continues to this day. No need to enrol or book: anyone can turn up at any lecture that takes their fancy. So next time you buy a Paul Smith T-shirt or Tiffany ring at the Exchange, congratulate yourself on your contribution to public learning.
The logos of both institutions feature a grasshopper: this was Gresham’s emblem. One of his ancestors was abandoned in the countryside as a newborn baby, and was only discovered when a boy chased a grasshopper into the field. Gresham knew that without that insect he would never have existed.
From the start, lectures were delivered in English as well as Latin (Oxford and Cambridge used only the latter). Gresham also led its more famous cousins in having professors of geometry and astronomy; an early occupant of the second post was Christopher Wren. In 1660 the college gave birth to the Royal Society, which meant that, for a while, the Society’s members were known as ‘Greshamites’. Samuel Pepys attended a 1666 lecture at which one of the first-ever blood transfusions occurred. ‘There was a pretty experiment of the blood of one dog let out, till he died, into the body of another on one side, while all his own run out on the other side,’ he wrote. ‘The first died upon the place, and the other very well, and likely to do well.’
At that time, professors lived in the college (then sited on Bishopsgate). Robert Hooke knocked a hole in his roof so he could stick a telescope through it. There were more shenanigans in the 1890s, when the professor of geometry Karl Pearson illustrated his lectures on the laws of chance by scattering 10,000 pennies across the floor.
By then the college had moved to new premises. They’ve since moved again, to Barnard’s Inn Hall, a 14th-century gem near Chancery Lane. Some of the bigger lectures take place at the Museum of London, while more than 2,000 have been recorded and are available to watch on the college’s website. I love the thought of Thomas Gresham coming back to see his dream of wider learning fulfilled on such a scale.
So how many people do have to gather together for a 51 per cent probability of a shared birthday? It’s just 23. Counter-intuitive, I know, but think of it this way. You’re the first person in the room. The second person to enter has a 1 in 365 chance of sharing your birthday. So does the third person, making it 2 in 365. But there’s also the chance they could share each other’s birthday. Imagine those three possibilities as the three sides of a triangle. When you get to four people there are the four sides of a square, plus the diagonals. Now imagine a 23-sided shape, with every point joined to every other point. The possibilities suddenly seem a lot larger than you assumed…