[ELI5] What’s the benefit of calculating Pi to now 62.8 trillion digits?


[ELI5] What’s the benefit of calculating Pi to now 62.8 trillion digits?

In: Mathematics

Just the prestige of saying that you did it. You can calculate the circumference of the visible universe to the accuracy of a hydrogen atom with 39 digits of pi.

Part of it, as others said, is simply prestige. Not all mathematics is done to directly solve some “real-world” problem.

It is also a way to test supercomputers.

This is like saying F1 cars could drive upside down in a tunnel.

There is no practical use but it needs to be done just so it can be said it was done. And someone(F1 or the manufacturer) can claim they were at the top of this at some point.

There’s really not a huge benefit to the result of the calculation, but the benefit lies in figuring out how to calculate it. Discovering new computational methods to calculate pi more and more accurately is the benefit to calculating that many digits.

Calculating pi is a well-understood problem that can be used in a couple of basic ways:

* Test (and show off) your fantastic computing system by using the same algorithm others have used to generate more digits within the same amount of time (or the same number of digits in a shorter time, which amounts to the same thing).
* Test/demonstrate a new algorithm, which could have implications for other problems.

Otherwise, actually knowing the value of pi out beyond [39 digits](https://www.sciencefriday.com/segments/how-many-digits-of-pi-do-we-really-need/) is kind of pointless.

We actually don’t fully understand the properties of Pi (or it’s bigger brother Tau). There are open questions about digit distribution that relate to information in Pi (so to speak).

Having more digits let’s us check if our thinking matches observation and look for other patterns.

Also, Pi (Tau/2), like many numbers, is just beautiful. [See here.](https://www.google.com/amp/s/www.washingtonpost.com/news/wonk/wp/2015/03/14/10-stunning-images-show-the-beauty-hidden-in-pi/%3foutputType=amp)

I might be wrong but maybe to test your computer power?

These things are often more about the journey than the destination.

There are very few uses for 62.8 trillion digits of pi. Statistical analysis of the digits might be interesting to a few professionals.

The real interest comes from *being able to*. You don’t want to test your flashy new supercomputer with something new, interesting, unknown, and important. What if it’s wrong? How would you know? No. You test it using something well known, like calculating pi. If you matched the first 30 trillion with the last people to do it, you’re good, but might as well leave it on a while longer to ‘claim the title’. This kind of tit-for-tat, back-and-forth, means knowing more and more digits is a side effect. If knowing digits of pi was super important, Amazon or Google or CERN or several others could blow 62.8 trillion out the water with relative ease. It’s the same with things like the biggest known prime. They have the computing power to ‘win’ easily. But it isn’t important so they don’t.

I don’t actually think there is a tangible benefit to this particular calculation, but I can say, from a computer science background, that having records of very expensive calculations is EXTREMELY useful in order to reduce the overhead for those computations in future. Hash Tables or arrays that hold fixed answers are often MUCH faster to access than manually calculating the answer. So say, maybe 100 years down the road, if we ever need an accurate answer like this, we don’t have to worry about whether it’s “feasible” to calculate it or not, because we have the constant answer. Maybe this particular number isn’t necessary, but the idea that people WANT to calculate large values can have it’s merits in other fields where they need speed or just need the answer because the calculation is beyond reasonable to calculate real time during a specific task.

[Here’s what the authors themselves have to say about that](https://www.fhgr.ch/en/translate-to-englisch-news/newsdetail/die-fh-graubuenden-kennt-pi-am-genauesten-weltrekord/):

> The calculation of the new pi digit world record by the DAViS team at the University of Applied Sciences in Graubünden took 108 days and 9 hours. It is thus almost twice as fast as the record set by Google in its cloud in 2019, and around 3.5 times as fast as the last world record from 2020. The record team from Graubünden is extremely satisfied with how the calculations went. “We wanted to achieve several goals with the record attempt,” says Prof. Dr. Heiko Rölke, head of DAViS. «In the course of preparing and performing the calculations, we were able to build up a lot of know-how and optimize our processes. This is now of particular benefit to our research partners, with whom we jointly carry out computationally intensive projects in data analysis and simulation. ” Thomas Keller, the project manager entrusted with performing the calculations, adds: “The calculation showed us that we are prepared for data and computing power-intensive use in research and development. The calculation also made us aware of weak points in the infrastructure, such as insufficient backup capacities. “

In “Contact”, the Carl Sagan book about first contact with aliens, it was suggested that hidden deep within mathematical constants there are messages or codes from the builders of this universe. So Arroway booked time on the supercomputers to go billions of digits deep into pi and other constants whose names escape me now to find the codes.

Absolutely none. 7 digits will be accurate enough for anything anyone would ever do, and 50 would allow you to compute the radius of the known universe to the width of a proton.

The practical benefits of having more digits of pi are negligible. The real benefit is in testing hardware and algorithms.

The largest possible impact would be if we calculated the next digits and found that they began to repeat. This would fundamentally undermine a fair bit of maths and lead to rapid innovation on topics/theorems that many consider “solved”.

You can find your telephone number and date of birth somewhere in that list of numbers. You can find everyone’s days of birth and telephone number in that list of numbers.

The real question here is who is checking their work?