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Math Cloud Google

Google Cloud Calculates Pi To 100 Trillion Digits (engadget.com) 105

Posted by BeauHD from the record-breaking dept.
Google Cloud developer advocate Emma Haruka Iwao and her colleagues say they've calculated Pi to 100 trillion digital decimal places. Engadget reports: Iwao and her team previously set the record in 2019 when they carried out a calculation to an accuracy of 31.4 trillion digits. The benchmark has been broken a few times since then [...]. In a blog post, Iwao wrote that finding as many digits of Pi as possible is a way to measure the progress of compute power. Her job involves showing off what Google Cloud is capable of, so it's not too surprising that Iwao tapped into the power of the platform to perform the calculation.

In 2019, the calculation (which figured out a third as many digits as the most recent attempt) took 121 days. This time around, the calculation ran for 157 days, 23 hours, 31 minutes and 7.651 seconds, meaning the computers were running more than twice as quickly despite Iwao using "the same tools and techniques." Around 82,000 terabytes of data were processed overall. Iwao also notes that reading all 100 trillion digits out loud at a rate of one per second would take more than 3.1 million years. And in case you're wondering, the 100-trillionth decimal place of Pi is 0.
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Google Cloud Calculates Pi To 100 Trillion Digits More

Google Cloud Calculates Pi To 100 Trillion Digits

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  • for randomness :)

    • Around 82,000 terabytes of data were processed overall.

      If only there were a standardized unit that's exactly 1000 times more than "tera".

      Maybe Elon Musk will invent one someday.

    • Re:Great, now test it (Score:4, Interesting)

      by Impy the Impiuos Imp ( 442658 ) on Thursday June 09, 2022 @08:07AM (#62606524) Journal

      In the novel Contact, by Carl Sagan, spoiler
      ===

      Remember in the movie how there were encodings inside encodings inside encodings?Well, trillions of digits out in transcendental numbers like pi, are other encodings, starting with a statistically improbable circle, if the digits are graphed out in an odd base.

      The aliens had discovered this message, but from the creator of the universe, of reality itself.

      The aliens had two great mysteries, that, and the tunnel system. In the novel, they could make the smaller, shorter tunnels, but not the bigger ones, barely mentioned in passing as "this one's much more violent!"

      • Re: (Score:2)

        by nagora ( 177841 )

        That was what I was thinking of.

        Another nice one from SF literature was in one of Saberhagen's Berserker books an alien race demonstrates their level of technology by giving the humans a perfectly circular ring which, when measured, had a circumference exactly three times its diameter (and a perfectly balanced and fair die which always rolled 1).

      • Re: (Score:2)

        by rbrander ( 73222 )

        I really loved that bit. Of course, when I read years later that you can (eventually) find all digits in Pi with just 1-1/3+1/5-1/7+1/9... it hit me that Creator of the Universe guy can also compress a message very, very tightly.

      • Re: (Score:2)

        by neoRUR ( 674398 )

        So you think PI would be different in another created universe?

  • Or is sequence of apparently random digits? Or maybe no one has looked yet...

    • > Or is sequence of apparently random digits? Or maybe no one has looked yet...

      This is what made Contact (Sagan) such a tear-jerking tragedy - when Ellie found a message from God in Pi.

      Thank goodness the movie left that part out.

      • Re: (Score:2)

        by ebcdic ( 39948 )
        It's probably the case that if you go far enough, any message appears in the digits of pi. 100 trillion is 100^7 so if you take adjacent digit pairs as ascii codes you'll find a high proportion of 7-character messages there already.

      • Re: (Score:3)

        by jd ( 1658 )

        Nothing said it was from God. God is introduced only in the film. Sagan was atheist.

        In terms of the conjecture that the universe is mathematical, altering Pi to contain a message is something Sagan could easily have regarded as plausible basic engineering.

      • The real life tragedy about the film "Contact", although Carl Sagan consulted on the movie production, he did not live to see the final cut.

    • Or is sequence of apparently random digits? Or maybe no one has looked yet...

      There's a formula that can calculate any digit independently if you do it in hexadecimal.

      https://en.wikipedia.org/wiki/... [wikipedia.org]

      And if that ain't a message from the cosmic creator then I don't know what is.

      • There's a formula that can calculate any digit independently if you do it in hexadecimal.

        The same person found a formula using base 10 this year, so that's more about who was looking than anything else.

      • Re: (Score:2)

        by Viol8 ( 599362 )

        I'm not so sure about the creator part, but it probably says something fundamental about geometry. What that might be is way above my pay grade.

    • Re:Is there any kind of pattern in it? (Score:5, Funny)

      by Immerman ( 2627577 ) on Thursday June 09, 2022 @08:00AM (#62606502)

      Out around the trillionth digit begins the message: "You need a better hobby"

    • Re:Is there any kind of pattern in it? (Score:5, Funny)

      by TheGratefulNet ( 143330 ) on Thursday June 09, 2022 @08:46AM (#62606642)

      I hope they don't get to the end.

      (I'm using the last 4 digits of pi as my luggage code, so I'm hoping it stays secret for a little longer, at least)

      • I heard they actually found the last 4 digits, when they quietly coalesced in the corner, in a container of custard, and then disappeared, forever. So your luggage is probably safe.

    • Or is sequence of apparently random digits?

      AFAWK, pi is an absolutely normal number [wikipedia.org], which means it is a random sequence of digits in any integer base. But there is no proof.

      No rational number is normal.

      There are transcendental numbers that are not normal. For instance, 0.101001000100001000001 ... is transcendental but obviously not normal.

      We don't know if e or sqrt(2) are normal. They are believed to be, but so far, there is no proof.

      Approximately 100% of real numbers are transcendental, non-computable, and absolutely normal. Yet we know of alm

  • Do people also compute ever more accurate approximate ratios? 22/7 was the simple one we used at school IIRC.

    Other than pi*100 trillion / 100 trillion ofc

  • This is 100% useless in itself. Show something interesting, like what's the longest sequence of certain digits, what known physical or mathematical numbers/constants (e.g. e) can be found in the sequence, what's the distribution of digits, etc. etc. etc.

    Otherwise it's just an incredibly huge pile of randomness with zero applicability.

    • Re: (Score:2)

      by gtall ( 79522 )

      So what if it is applicable or not. You should have time-stamped your note: it is not applicable to something NOW, the FUTURE is aways off.

      • Given another team calculated pi to 2 quadrillion decimal places a few years ago, this was a pretty useless endeavour and basically just a waste of Google compute time - even from a computer science perspective, bottlenecks in Google cloud can be found far more efficiently.
      • I mean if you use the first 100 digits of pi you can calculate the volume of the universe down to a fraction of a cm3 (assuming it's a perfect sphere what it really isn't)

    • Re: (Score:2)

      by jd ( 1658 )

      Oh, I dunno. I can see it having quite a lot of uses. For a start, it's not truly random as you can directly calculate any digit without calculating preceding ones. So if it comes up as random in a test, the test isn't as good as you think it is.

      Secondly, it's strange that you CAN calculate any digit directly. Can you do that with e?

      Mathematics isn't about answering the questions you want answered, it's about exploring the consequences of the answers you know about.

    • Google Cloud developer advocate Emma Haruka Iwao

      Her job involves showing off what Google Cloud is capable of

      This is just marketing for Google Cloud.

    • Here's one of those useful patterns [smbc-comics.com].

  • Energy spent? (Score:5, Insightful)

    by dromgodis ( 4533247 ) on Thursday June 09, 2022 @05:45AM (#62606258)

    I wonder how many Wh was burnt on this marketing ploy.

    • > I wonder how many Wh was burnt on this marketing ploy.

      Imagine how little use this is and how the smoothbrains will say it's a better use of energy than finding valid bitcoin blocks.

      • Neither are a good use of energy.

      • Re: (Score:2)

        by tlhIngan ( 30335 )

        Imagine how little use this is and how the smoothbrains will say it's a better use of energy than finding valid bitcoin blocks.

        Technically it is, because it's been calculated and it's done. There is no reason to calculate it again.

        So if you needed that many digits of pi, you can make use of it over and over again without calculating it, amortizing the overall energy spent.

        Whereas bitcoin's purpose is to waste energy. The more you throw at it, the more energy it wastes. After one miner in the entire network

    • Could be worse, it could have been wasted on cryptocurrency. At least someone gets a kick out of this.

  • Quick googling gave me a formula to exchange digits to bytes. 100 trillion digits should be around 41.5 TB.

  • Why waste half a year of Google Cloud compute power to perform an almost entirely useless calculation? Does calculating n digits of pi get slower as you approach the nth digit? If you need a benchmark result couldn't you just write a routine to arrive at the digits per calculation hour to a certain degree of accuracy instead?

    Imagine how much energy/pollution/heat went into this.

    • Re: (Score:2)

      by gtall ( 79522 )

      It might be useless to you, but if you are doing research on the contents of pi, then it is very useful. And those contents might only be applicable in the future, which apparently you cannot see.

      • Re: (Score:2)

        by Zak3056 ( 69287 )

        It might be useless to you, but if you are doing research on the contents of pi, then it is very useful. And those contents might only be applicable in the future, which apparently you cannot see.

        There is a claim above that a team calculated Pi to 2 quadrillion decimal places several years ago, so if what you care about is the contents there's no benefit to this at all unless the purpose of the exercise is to check the original result (in which case, you would probably not be touting the fact that you did something that's already been done 20x more precisely in the past).

        • That calculation was of the 2 quadrillionth digit only (it may have been binary rather than decimal, I don't recall right now) - and not every digit up to that point.

      • Comment removed based on user account deletion

        • Re: (Score:1)

          by DeQueue ( 112880 )

          >Plus how else would we know that the last 99 trillion digits are all '9'?

          There are, in fact, six nines in a row starting at the 762nd decimal place. Nobel laureate Richard Feynman supposedly was aware of this sequence and supposedly wanted to recite pi to this point, up to the six nines,[1] so that he could then say "and so on" implying that the nines continued ad infinitum. Douglas Hofstadter apparently had the same idea for the same joke.

          https://en.wikipedia.org/wiki/Six_nines_in_pi

          [1] Edit: Arrrrg

    • Completely agree. A waste of energy; not only in the physical sense but also the intellectual sense.

  • How did they verify it? (Score:3, Interesting)

    by damn_registrars ( 1103043 ) <damn.registrars@gmail.com> on Thursday June 09, 2022 @06:08AM (#62606288) Homepage Journal
    They came up with an answer 100 trillion digits long, but how did they verify that the answer was a correct - or better - approximation than earlier approximations of pi? Otherwise once you get past a trillion (likely even far fewer) digits you could likely just let your cat walk across the num pad for a day or so to churn out random digits and it would be hard to prove the difference.

    • Re:How did they verify it? (Score:5, Interesting)

      by jd ( 1658 ) <imipakNO@SPAMyahoo.com> on Thursday June 09, 2022 @08:03AM (#62606508) Homepage Journal

      You can calculate any digit directly without calculating intermediate digits, so you can check their calculation by picking N digits at random, directly calculating them and seeing if you get the same answers. You don't need all 100 trillion, the odds of getting 100 digits correctly placed should be good enough as validation.

      • You can but there's still computational complexity involved in getting to that digit. The beauty is that it's in linear time, so you'll get there faster than any other algorithm but it will still take you a long time to calculate the 100 trillionth digit.

    • They calculate it twice, using two different formulae, and compare the results.

    • They came up with an answer 100 trillion digits long, but how did they verify that the answer was a correct - or better - approximation than earlier approximations of pi?

      It was better and more correct on the basis of the approximation being longer and to more decimal places. This isn't guesswork or trial and error. There are well understood methods for iteratively calculating pi to any arbitrary precision you like, all you need to do is throw computing power at it.

      There are also multiple ways to compute pi each with different computational complexities so you can just verify the results against each other.

      Unless they have 66MHz Pentiums in their cloud pool there's no reason

  • Well, as an exercise in "yes we can do it", it's nice, but not ultimately useful given that you only need the first 38 decimal places or so.

    • Re: (Score:2)

      by jd ( 1658 )

      You only need that much for what?

      Let's say spacetime is curved and not flat, just curved very very gently. So gently that the curvature is less than 0.04 degrees in a span halfway across the visible universe.

      What is the minimum number of digits of Pi you would need in order to represent the complete universe (type 1 multiverse if you're fussy) and thus model the physics of it?

      Let's say superstrings and membranes exist. How many digits of Pi would you need to model the physics of these things correctly?

      More

  • I'm curious (Score:3)

    by argStyopa ( 232550 ) on Thursday June 09, 2022 @06:23AM (#62606316) Journal

    What is a "digital" decimal place and how does it differ from say, a normal decimal place except perhaps in pretentiousness?

    • Re: (Score:2)

      by GoTeam ( 5042081 )

      What is a "digital" decimal place and how does it differ from say, a normal decimal place except perhaps in pretentiousness?

      A decimal place that doesn't appreciate the audio quality of analog? That, or it listened to Bad Religion and got inspired!

  • Google supercomputing peepee wants to assert dominance. It's not about how long it is, it's how you use it. So, are we going to gain any insights from this? Any plans on that front? Otherwise it might as well be a number in a trump card game.
  • Google has announced Pi is being sunset. (It will be replaced by a chat app.)
  • ...how come no one has asked they yet?
  • What was the bill you received for ~158 days of CPU time on Google Cloud? MrPCsGhost
  • What's the meaningful use of such accuracy of Pi? Just trying to understand the carbon footprint of half a year calculation that doesn't give much except bragging rights.

    • What's the meaningful use of such accuracy of Pi? [...] doesn't give much except bragging rights.

      The blog post provides an answer and you were completely right:

      You may not need to calculate trillions of decimals of pi, but this massive calculation demonstrates how Google Cloud’s flexible infrastructure lets teams around the world push the boundaries of scientific experimentation. It's also an example of the reliability of our products ...

  • How big would a circle have to be for this to have a 1% error in a circumference calculation? Would you have to run all the digits to get an accurate answer?

  • Yes, why climb Mount Everest, YOLO etc. Google demonstrates that massive resources can be brought to bear on math problems. Yay! For the rest of us:

    For you .NET folks, System.Math.PI.
    For you Java folks, java.lang.Math.PI
    For you Python folks, math.pi

  • The Chudnovsky Brothers [wikipedia.org] set pi-calculating records on a supercomputer they built in their NYC apartment in the 1980s. I first learned of this in a marvelous 1992 New Yorker article (linked in the Wiki page).
  • What google seems to do: give you a mess of machines to compute your nicely-threaded project. What you won't so-far give you: a machine capable of solving a one badass single-threaded problem, requiring a large amount of memory. I watched their solution come down like a cheap airplane.

    You can probably remove two mealy legal words in the title ; P
  • Woa, what an achievement!
    Soon enough we'll be able to calculate Pi to 200 trillion digits, that means we will be able to ... need help finishing this sentence.

  • And in case you're wondering, the 100-trillionth decimal place of Pi is 0.

    In case anyone else was wondering, the googolth digit is 4 and the (googol+1)st digit is 2.

    Go ahead. Prove me wrong; I'll wait.

  • ...at the 420,254,652,124th digit.

  • And the result has the same usefulness to humankind as the google result.

  • Caterpillar announced that its latest excavator had dug and filled the same hole 20,000 times, for a new record.

  • What's the 100 trillion +1 place? Is it zero also?
    Have we found the end of pi?

  • I calculated a million digits of Pi on my first home computer. The computation was written in Ocaml, which has the advantage of having a nice bignum library, and functional programming is cool for maths stuff. I used a variant of Machin's method, which is pretty old stuff, and rather slow. it basically speeds up computing pi using arctangents. The power series for atan(x) converges very slower. The more digits you add, the slower it gets. Improved arctangent methods, like the one I used, give you linear rat

  • I am a student in the math faculty, and I am interested in anything related to apps and extensions for calculating facilities. I had some complicated academic issues, searching for Google Clouds to figure out my exercises. However, I found https://edubirdie.com/do-my-math-homework [edubirdie.com] to solve my faculty problems. I had to do my math homework, and their doers helped me and provided work for a deserved A grade. Therefore, it is a perfect option for everyone who needs help and has issues with some math exercises.
  • There are many benefits of using printable number kindergarten worksheets [brighterly.com] for preschool children. These worksheets are great for practice, math centers, and home use. The worksheets range from 11 to 20. Kids can practice their counting skills by coloring the pictures according to the color key or by making posters displaying their number skills. These worksheets are also great for practicing handwriting and number formation skills. They are ideal for parents and educators who want to introduce numbers to t

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