The conclusion being that you basically need the same amount of data to represent the address of your data as the data itself, so it's not really effective at compression, just a fun thought experiment.

The cool part of this in modern times is that LLMs are basically a form of lossy compression that actually achieves the gist of what these tools fail at. Although it is lossy, and requires a massive substrate. This is related to the idea of AI/LLMs being a form of language compression.

πfs – A data-free filesystem - https://smackernews.com/item/36357466 HN - June 2023 (107 comments)

πfs – A data-free filesystem - https://smackernews.com/item/28699499 HN - Sept 2021 (30 comments)

PiFS – The Data-Free Filesystem - https://smackernews.com/item/26208704 HN - Feb 2021 (1 comment)

Πfs: Never worry about data again - https://smackernews.com/item/21359338 HN - Oct 2019 (1 comment)

The π Filesystem for FUSE: Store Your Data in π - https://smackernews.com/item/19223032 HN - Feb 2019 (1 comment)

pifs - Avoid disk space usage by saving your files in the digits of Pi - https://smackernews.com/item/18687275 HN - Dec 2018 (1 comment)

πfs – A data-free filesystem - https://smackernews.com/item/13869691 HN - March 2017 (105 comments)

Πfs: Stores your data in π - https://smackernews.com/item/10856108 HN - Jan 2016 (1 comment)

Πfs: Never worry about data again - https://smackernews.com/item/10847693 HN - Jan 2016 (1 comment)

File system that stores location of file in Pi - https://smackernews.com/item/8018818 HN - July 2014 (98 comments)

100% Compression Using Pi - https://smackernews.com/item/6698852 HN - Nov 2013 (32 comments)

(Reposts are fine after a year or so; links to past threads are just to satisfy extra-curious readers)

Further reading: https://en.wikipedia.org/wiki/Sloot_Digital_Coding_System

One of the properties that π is conjectured to have is that it is normal

conjectured

Glad to see one of my pet points of pedantry come up. No non-constructed irrational number has never been proven to be normal or disjunctive.

Are you sure? It's been a while since you last opened it. Memory is funny like that. The file is fine — maybe take another look with fresh eyes."

from https://github.com/philipl/inferencefs/

Maybe I do not indeed remember properly. Anyway, back to watching "Eternal Sunshine of the Spotless Mind" for the first time, I think.

In this implementation, to maximise performance, we consider each individual byte of the file separately, and look it up in π.

Considering each individual bit separately would be even more performant: you only need the indexes 2 and 33, and there is an efficient mapping of those to the bits in storage.

https://github.com/philipl/pifs/blob/fded8bf7b8f4fc64233e37b...

I’m guessing this is something that could be formally proven?

If our universe is simulated, it must be possible to snapshot the entire state for one iteration (however time now is quantized, open question). "... From here, it is a small leap to see that if π contains all possible files, why are we wasting exabytes of space storing those files, when we could just look them up in π!" (from pifs, above)

This means that not only does a singular snapshot of our universe exists in pi, but every single one does

The information for our entire universe's simulation is stored in pi (and every other number like it)

[1] https://www.youtube.com/watch?v=JcJSW7Rprio

Matches that occur early enough in π to attain significant compression will not be varied. That is, it isn't possible to use π to compress interesting, real-world data because real-word strings are unlikely to arise early.

Meta: every single comment seems to start with some variation of "Reminds me of". Had to get mine in.

Not even sure if there an interesting Collatz-like conjecture here.

0x123456789ABCDEF0

use this number as a shorter nibble storage alternative...

Cache all the last lookups but otherwise just store the index within pi? And for larger files - split them into chunks of whatever size could be handled?

(I mean, I realize this is a joke and can't make sense - but GPUs can be really really fast, and am willing to make a fool of myself by asking.)

And if we had a quantum computer that stores all of pi on one qubit, that could make things even faster ;/

And for which the index is easy to compute?

My favourite issue being about GDPR compliance https://github.com/philipl/pifs/issues/56

So not really a compression scheme.

Why is this thing so slow? It took me five minutes to store a 400 line text file!

Well, this is just an initial prototype, and don't worry, there's always Moore's law!

Seriously? They're only storing individual bytes in pi:

In this implementation, to maximise performance, we consider each individual byte of the file separately, and look it up in π.

So the whole transformation should be trivially reducible to a 256-element lookup table from source byte to location in pi and a similar table used to convert back the other way. Maybe a fancy formula could be used for the (never actually encountered) case in which a byte is encoded by one of the infinite available noncanonical encodings.

3._1_415926535897932384626433832795_0_288419716939

https://ljsimpkin.github.io/pi-compress

It really shows how inefficient such a compression would be. Haha nice idea

Sing, the wrath. Rendering in LaTeX.

[1]: https://smackernews.com/item/48010729 HN

I mean, I get that it's "fun" to store information within the digits of pi. But is this just amusement, or is there a value prop for production use here?

(Speaking as a math major, by the way. I'm sympathetic to the cause.)