Even more pi in the sky: Calculating 100T digits of pi on Google Cloud

Reading that, it's hard not to see the parallels to Darren Aronofsky's movie Pi. Building a supercomputer in an apartment to find patterns in Pi that have some higher meaning, the computer constantly breaking, etc.

Dammit I was going to post this, but you beat me to it!

But the base 10 formula needs Bernoulli numbers, which themselves are defined recursively, meaning the required iterations are just hidden and not removed.

Fun fact: Mahler famously showed that if p/q is a rational number then |\pi - p/q| > 1/q^42. So we can't have a string of 4242T zeros after first 101T digits :-) The exponent 42 has since been improved by a series of works to 7.1032 - https://arxiv.org/abs/1912.06345

I seem to remember reading a sci-fi story quite a long time ago where the characters discover a message embedded in pi but only after many digits were calculated.

I think the implication was something about simulations or maybe instructions on how to build a device. Can't quite remember the details.

It is almost certain that pi does contain sequences of zeroes of arbitrary length, but that following those zeroes are other numbers.

But more weirdly, it's possible to find any string of digits within the digits of pi. So there are going to be quite a few zeros in there, followed by ever more non-zeros.

Transcendental numbers are truly awesome.

And how much a computer that could have done the computation all by itself would have cost (by putting enough storage in a single chassis without needing a SAN).

I would imagine doing something like storing 12 decimal digits every 5 bytes (exploiting 10^12 <≈ 2^40) would be simple enough, great for random access, and good enough at compressing (within 10% of theoretical optimal treating pi as a random sequence of digits) that it's not worth spending a lot of time trying to improve upon that.

Of course, under a different set of constraints, one may find something better.

It should be noted that y-cruncher, that closed-source program, is responsible for every pi computation record since 2010 (back then the record was 2.7T digits). Traditionally these records were held by supercomputers, but it seems that pi computation is no longer a good way to benchmark or stress-test them [1], leaving only interested individuals in the scene.

If pi computation were useful by its own, or there were a lot of people working towards records, we can expect multiple competitive pi computation programs where some of them are hopefully F/OSS. (The algorithm itself is not exactly secret anyway and big ideas are already in public, what makes y-cruncher special is its meticulous optimization.) But I don't see anything like that. There seem no actual demands for pi computation software, not just F/OSS.

[1] http://numberworld.org/y-cruncher/faq.html#why_desktops

I found it pretty amazing the codebase that cracked 100T digits (and the previous records too) were started as a guys high school project.

Yet, it's supposed to happen at the 10^20-th digit in base 11. Mere 10^14 digits aren't enough.

They ran this in us-central1-c (Iowa) [0] which as of 2020 was 93% renewable [1].

The energy crisis mainly affects oil and coal prices in the US so I don't believe Google's renewable-powered computations should have any effect.

If they'd run it in Germany where people are being asked to conserve electricity, things might be different.

[0]: https://github.com/GoogleCloudPlatform/pi-delivery/blob/main...

[1]: https://cloud.google.com/sustainability/region-carbon

The main node has 64 physical cores and 1TB of RAM, and the 24 storage nodes have 8 cores and 16 GB of RAM (192 cores and 384GB of RAM total).

So we are using 256 cores and 1.5 TB of RAM, so probably about 7.5 kW or so. Over 5 months, the compute would have used 27 MWh, so about the energy content of ~750 gallons of gas.

The storage will obviously use more energy (I don't know if they are using spinning disks or SSDs), but I think ~50-100 MWh for the entire computation is a reasonable estimate.

I'm hoping for something closer to the ending of Carl Sagan's novel, "Contact". It only mentioned pi on half a page, but it sticks with you.

I won't spoil it, but that book beautifully walked a skeptical / existential / transcendental line and makes you feel a special warmth despite being so immeasurably small.

The book was much better than the (quite adequate) film.

Sagan was an extraordinary communicator.

How would you know it's an infinite series if you're only computing a finite number of digits?

(Also Pi is irrational, so this won't happen.)

When I am king I will make it illegal to loudly worry about environmental impact (or anything else) without providing an order of magnitude estimate for the size of the problem. You don't even have to be right, just take five seconds to conjure a vaguely plausible number.

Honestly probably less than all the showers you took in the same amount of time.