I was intrigued by the news report that researchers had calculated the value of pi to 68.2 trillion figures. Pi (defined as the number obtained when the circumference of a circle is divided by the diameter) is a massively important quantity that occurs all over the place but it is hard to imagine what value is gained by achieving such a high level of precision. So my first reaction was, of course, “Why bother?”
This article looks at how much precision is neccssary for any practical application.
Mathematicians have estimated that an approximation of pi to 39 digits is sufficient for most cosmological calculations – accurate enough to calculate the circumference of the observable universe to within the diameter of a single hydrogen atom.
Given that even calculating pi to 1,000 digits is practical overkill, why bother going to 62.8tn decimal places?
De Gier compares the feat to the athletes at the Olympic Games. “World records: they’re not useful by themselves, but they set a benchmark and they teach us about what we can achieve and they motivate others.
“This is a benchmarking exercise for computational hardware and software,” he says.
Harvey agrees: “It’s a computational challenge – it is a really seriously difficult thing to do and it involves lots of mathematics and these days computer science.
“There’s plenty of other interesting constants in mathematics: if you’re into chaos theory there’s Feigenbaum constants, if you’re into analytic number theory there’s Euler’s gamma constant.
“There’s lots of other numbers you could try to calculate: e, the natural logarithm base, you could calculate the square root of 2. Why do you do pi? You do pi because everyone else has been doing pi,” he says. “That’s the particular mountain everyone’s decided to climb.”
I became even more intrigued when I read that it had taken 108 days and nine hours on a supercomputer. Getting time on a supercomputer is not easy and you have to make a strong case to the overseeing committee for why you need it. I doubt that “because we can” or getting into the Guinness Book of Records would cut it. It surely has to be that you are using the pi calculation to test out some new algorithm that has more practical applications. The report says that their algorithm was “almost twice as fast as the record Google set using its cloud in 2019, and 3.5 times as fast as the previous world record in 2020” and the technique could be helpful in “RNA analysis, simulations of fluid dynamics and textual analysis”.
The other interesting question is how anyone would be able to check that they got it right.