Bah. I've done more.
I did it on my fingers & toes. (I have a lot of them.) I stopped counting when I hit one Googolplex of digits. I figure the next time I want to speed it up a bit, I'll use my nipples as well.
Switzerland's University of Applied Sciences Graubünden has challenged the world record for calculating Pi, claiming it has computed the mathematical constant to 62.8 trillion digits. The university yesterday claimed it had broken the record, asserting it beat the previous record of 50 trillion digits, set by Timothy Mullican …
Years ago I found some code for a Pi calculator written in C. There was no author attribution that I remember. I ended up publishing my modified version (which included a bug fix and some significant speedups). The thing that makes mine different is that it is MULTI-THREADED. But the speed benefit is only about 2.5 times, due in many ways to the limits of just how much parallel stuff you can do in the basic algorithm.
In any case, my updated modified threaded version can calculate 1 million digits of Pi in about an hour and a half on a typical amd64-based system. Since it's roughly an n-squared relationship, it implies that this algorithm could calculate 63 trillion digits in about 6 billion hours. Not very impressive, yeah.
It might be interesting to see what the actual numbers would be...
(and since the Swiss algorithm is apparently using 64 cores, they must've found a better way to introduce parallel calculations)
Back in the low-precision 80's, my old maths teacher would often boast that his friend knew PI to *20* (gasp!) decimal places, expecting us all to be amazed.
I never understood why, if he was genuinely actually that impressed about it, he didn't just sit down one night and commit them to memory himself. Or hell, even go one better and learn it to 25, or 30, or maybe something really huge.
I had it memorised (still do) to 8 places, because that's how many digits were displayed on my 4-banger calculator.
Bowmar, rebadged for Sears. $100, Christmas 1972. Still carried a slide rule for the trig and log functions.
One of my more well-off classmates came back in January with an HP-35. I drooled. Bought an HP-25 for grad school.
I know it from my Casio Scientific Calculator days of the 1980s.
3.1415926535
One of my classmates, my geeky friend, memorised it to 65 places.
But we were soon distracted by the joys or Rubik's Cubes and Collossal Adventure and programming in Machine Code (Z80 or 6502) or BASIC.
In normal life, in my head, I use "about 3" or "22/7" perhaps if I only have pencil and paper and lacking electronic assistance
(all my batteries are flat or my bags have been stolen at the airport, for instance)
=============
I'm dismayed by the waste of resources for all these groups to calculate Pi to such precision.
We have shortages of chips and boards regularly.
Prices are inflated for us mortals. Bitcoin miners! I'm looking at you as well!
For Proofs of Concept, how about modelling, the Weather, Climate Change, COVID-19, "The Travelling Salesperson" problem?
When I was a teenager I memorised 100 digits. It wasn't that hard, there are a few near repeating patterns. I still know 54, because it's nice to end on a zero so you can stop without rounding problems
Whenever anyone says pi is 3.142 I get very upset.
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On the basis that I was an a physics lecture where the lecturer said:
"This function is about point four, which is nearly a half so we'll round it to one"
To be fair rounding it to zero would have been rather catastrophic, since it was part of a long string of functions that were being multiplied... but the logic nearly had me snorting my morning beverage.
I seem to recall a few years ago, that the French govt legalised the rounding up of pi to 3.2.
I don't know if this had any effect on any French projects, but a difference of only 1.8% is probably within most margins of error, except when it comes to maybe some planes or spacecraft ;-)
> I seem to recall a few years ago, that the French govt legalised the rounding up of pi to 3.2.
Maybe you are (also?) thinking of the so-called "Indiana Pi Bill" of 1897 (q.v.), which tried to legislate that the value of Pi was 3.2?
A rather more recent article in Forbes puts its foot in it in an alternative manner by stating:
Pi is a number that defines what a circle is. It's the ratio of a circle's circumference to its diameter, and it's the same for every circle: 3.141592 followed by a string of over 22 trillion other digits.
(My bolding)
It generates a lot of "news" articles.
Dilligent research provides: https://www.theguardian.com/science/2021/aug/17/new-mathematical-record-whats-the-point-of-calculating-pi
extract: 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.
The diameter of a single hydrogen atom is still fairly massive on the quantum scale : you don't have to go too much further though to reach the Planck length, after which all measurements become meaningless due to quantum fluctuations. So, no, it's not practically useful for anything in the real universe..
"is knowing pi to a bazillion places useful for anything"
according to the article I read about this including an interview with the team lead, knowing pi to a bazillion places is not that useful, but knowing *how* to calculate pi to a bazillion places in a highly efficient way is useful because the techniques can be applied in other fields of numerical analysis.
Although its a "cool" * project and they have a big pile of data to play with now, but what are they actually going to do with it ?
Or was it just a cool thing to put on a bunch of CV's / an enabler for doing some other HPC tasks that do real work?
* Or whatever the 2021 version of "cool" is.
Proving the sequence is random would seem like a more worthwhile endeavour than simply burning electricity running a program for a little bit longer than the last lot, just to willy-wave a meaningless record until the next lot come along and waste even more electricity running it even longer…
But they're not random. They're entirely predictable - that's why they were able to calculate them. In fact there's a ?famous formula that enables you to calculate any hex digit of pi without knowing any other digits.
I suspect what you're asking is if whether there is some bias in the distribution of base-10 digits.
Actually, something similar is done. If a cryptographic algorithm needs a fixed random looking number and a number is chosen, you could be accused that this number allows a back door. If you use “20 digits of pi starting with the 20 trillionth” that is as good as random, but can’t be used for a back door.
Have they found any secret messages tucked away in the depts of Pi, maybe from the Creator to us Subjects?
"This is a Beta version. Please report any problems..."
"Hello to mum and dad. Told you I'd get to 32 trillion..."
"Congrations! You have just discovered the secret message."
"I think I made an error back a few digits. Better check..."
One idle bit of musing I did a while ago, was that (in true Shakespeare's Monkey Typewriter style), if you iterate through Pi long enough, you'll theoretically be able to pull any number sequence out of it, by providing an offset and a length.
E.g. "You want '0123456789'? That'll be at offset 5 squllion, length 10".
Admittedly, this is a pretty inefficient way to transmit data, since both sides would need to have at least 5 squillion+10 digits of Pi to hand.
And having just fired up https://www.piday.org/million/, I can sadly report that you can only get "0123" from the first million digits...
Then too, I'm sure that some mathematically minded bod will point out that since Pi isn't random, this isn't actually possible. But hey :)
> if you iterate through Pi long enough, you'll theoretically be able to pull any number sequence out of it,
Actually we can't prove that. There's a word for irrational numbers that contain all arbitrary sequences (that I can't remember) but we can't prove if pi is one of them.
Would all those threads provided by the AMD chip actually be beneficial for this specific task?
It isn't an easy problem to break up into parallel equations is it?
I mean, yeah its convenient that they can also surf the web and answer emails whilst their machine is crunching away but I am fairly certain they have other machines for that ;)
The 'infinite monkey hypothesis' is incorrect. The idea that an infinite number of monkeys with typewriters given an infinite amount of time would eventually type out the complete works of Shakespeare does not work statistically.
For example. The sum of the reciprocal squares of the positive integers is pi*pi/6. So if we take each monkey in turn and assume it has a probability of typing any work of Shakespeare as one trillionth of the reciprocal of the square of it's number, then the whole lot have a probability of generating the works of Shakespeare*** of pi*pi/6trillion, even though each monkey has a positive probability and there are infinitely many of them.
I apologise wholeheartedly for the devastation caused to everyone's dreams by this revelation, and am very sorry.
***OK so there is some statistics missing here considering that each monkey might generate the same work of Shakespeare, but the idea is that an infinite sum of positive values is not necessarily >= 1. Sadly Douglas Adams didn't get everything right :o(
"the idea is that an infinite sum of positive values is not necessarily >= 1"
Under the assumption that infinity actually exists, I only agree with this statement if those positive values are infinitely small. However a monkey with a typewriter is only fscking small.. not infinitely small.
Geometric Progressions...
We learned about 1+1/2+1/4+1/8....etc
"It never actually gets to 2, but it is EXACTly 2 "
This had us in strong uproar and non-understanding with our Teacher.
Later, Quantum Physics did my head in too
Douglas Adams and "Hitchhiker's..." is at least enjoyable and my greatest read ever.
Your teacher should have explained (and proved) that 2 is the smallest number greater than each of the partial sums:
1, 1 + 1/2, 1 + 1/2 + 1/4, 1 + 1/2 + 1/4 + 1/8, ... etc.
As such, it is considered that the limit of the infinite sum is 2.
The statement that "It never actually gets to 2, but it is EXACTly 2 " is contradictory and therefore confusing.
Hard disks were chosen over SSDs because SSD performance degrades over time and the university's designers feared their intensive calculations could cause problems.
Normally an SSD will happily last for much longer than 108 days(*) so just how much disk traffic was this set up doing?
(*) Looks at desktop machine: SSD power on hours 60989.
I'd be willing to bet they're further constrained by the aggregate throughput of the server's disk controller as well. One SSD can outpace an HDD, easily. Whack dozens of them onto a host and try and abuse them in parallel with sequential workloads and you're almost always far better off getting physical disks.
The rather amazing Bailey–Borwein–Plouffe formula allows us to compute the hexadecimal digits of pi independently (i.e. without computing the earlier digits). Colin Percival use it to organise a distributed computing project to compute specific bits of pi. The project closed soon after the quadrillionth bit of pi was found.
It takes 1,000 trillions to create a quadrillion and so Percival's bit lies well beyond the 63 trillionon-th decimal digit of pi.
Here are some URLs
https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula
https://en.wikipedia.org/wiki/PiHex
http://wayback.cecm.sfu.ca/projects/pihex/announce1q.html
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“This is a benchmarking exercise for computational hardware and software,” Jan de Gier, a professor of mathematics and statistics at the University of Melbourne, says.
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.
... we still don't know its exact value.
Awesome.
Next project: square root of 2 to 62.9 trillion digits. Just as useful. And then we can multiply the result with itself and observe that the value obtained is not quite 2, even with a 62.9 trillion digits precision.
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In Richard Feynman's memoir of his time at Princeton Advanced Studies Institute (I think), one of the senior researchers there had lots of filing cabinets with, as it happened, the USA's nuclear secrets. One evening Feynman needed some information from the filing cabinets, but the researcher and secretary had gone home. Undeterred, Feynman set about opening the cabinets using his skill as a safe cracker augmented by knowledge of the person involved.
First he tried pi, no luck, then he tried e. Success! Each cabinet was opened by a combination from the digits of e. Now, being Feynman and enjoying a joke, he left a little note in each cabinet to let the guy know who had been rifling his files. The first one was something like "Hi, just me getting some info, Regards, Dick Feynman". Subsequent ones read something like "Me again".
Of course the next morning the guy opened his cabinets, but not in the same order Feynman had, so was seriously worried about a major breach of top secret information until he reached the note signed by Feynman.
Details in "Surely you're joking, Mr Feynman" and "What do you care what other people think?" by Richard Feynman, both of them well worth reading.
This particular circumstance was completely predictable, and should have been anticipated. However, all is not lost...
...simply use one of π's groupings-of-ten from the BEGINNING of the sequence--any of the second, third, fourth...groupings.
Better yet: use the digits of some other fairly-well-known, but not as easily "guess-able" physical constant, such as the 'fine structure' constant...
"Better yet: use the digits of some other fairly-well-known, but not as easily "guess-able" physical constant, such as the 'fine structure' constant..."
I'd not be surprise to learn that there "dictionaries" out there already with lists of those sorts of numbers used for hacking into university computers by black hat espionage types from places like China.
I assume you are referring to the text in 'the Old Testament' stating that King Solomon had a pool built for the priests to bathe in which was 10 cubits in diameter and 30 cubits around?
In the Hebrew of the time, letters are numbers, and if you take into account that the word "cubits' was spelt differently for the diameter and the circumference and do the calculation, you get pi accurate to about 7 decimal places. (I read this in a book about the number pi, whose title I do not recall. It was big, heavy and expensive, so I didn't buy it, so cannot give a reference, sorry.)
Nope, no trickery and no method to verify it computationally so far as I know. This is math, so the normal rules of science do not apply (in science you can only prove that something is wrong). The method of producing the string of digits is, I assume, proved in the mathematical sense.
The engineers that produced the string of digits asserted that they used the correct method - or is there some verification of that? Was the computer program used provably correct?
Ok, so I assume this is an American(French) Trillion (10^12, not 10^6^3 [10^18 - million^3]). So I guess the test is to check against the results of another, completely different (no shared origin) computer program that also generated at least 62800000000000 digits and see what these [index] digits are, I'll give you the first for free:
00000000000001 3
62800000000000
62799999999999
62799999999998
62799999999997
62799999999996
62799999999995
62799999999994
62799999999993
62799999999992
62799999999991
62799999999990
62799999999989
62799999999988
62799999999987
62799999999986
62799999999985
62799999999984
62799999999983
62799999999982
62799999999981
62799999999980
62799999999979
62799999999978
62799999999977
62799999999976
62799999999975
62799999999974
62799999999973
62799999999972
62799999999971
62799999999970
So when a few engineers have filled in values for those number (guaranteed they will all be the same) some mathematician can actually work out how to check them.
Learning about electronics, used to do stuff that involved pi, something with frequencies IIRC. The equation was to find value of a component at a certain frequency. I used to work out the value to 8 decimal places, but when it came to actually finding a resister with that value - forget it! Standard values +/- 5%
MAME (Multi Arcade Machine Emulator) is probably a cinch
But my chance to relive the 80s on my bog standard PC a few years ago. All those great Arcade games that could be found in Pubs, as well as Arcades, Service Stations, Launderettes,,, everywhere!
I spent a lot of money, and drank a lot of beer, with a friend on this one...
Taito's Flying Shark, a much better 2D/3D Scroller than '1942'
https://www.google.com/search?q=taito+flying+shark
We got very good at it, clocking all 32 (?) levels, playing for an hour, but being killed before we could clock it twice.
It was exhausting, because in spite of Power Ups (increased firepower bonuses) you still had to hammer the fire button very quickly.
(Daley Thompson's Decathlon style. Service Engineers must have replaced the buttons very regularly.)
And then, the machine finished its Tour of Duty in that pub, but a neighbouring pub had just got a modern Real Life Pinball Table. Specifically 'The Adams Family'.
We got really good at that. And really drunk.
And then we both met women, fell in love and had babies...
And now the babies are grown up, and I am middle-aged, my hand-eye co-ordination is shot to pieces.
I'm lucky to get to Level 2 on any game
I read another article about this, which said the calculations were done on a supercomputer.
While dual 32-core EPYC chips is a bit more than my budget can afford for a desktop, there are lots of people with comparable systems at home. Even one terabyte of RAM, usually found in servers, is not impossible for the serious enthusiast.
So I'm surprised it's a record, as surely somebody with a bigger computer would have tried.