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.
Reinventing Entropy Compression is Intelligence Part 1
3blue1brown https://youtu.be/l6DKRf-fAAM?is=ne73FCJ7ErXhzZ-v
(Then it depends on your concern: "Aagh, the aunt fell!" // "Oh yes, that'd be Newton")
This is totally lost on me.
Laws (scientific, philosophical etc.) as compression represent the common side of classes of events - an abstraction of said events, stripping the irrelevant - irrelevant to some perspective, or irrelevant in a potential Procuste's bed. So, laws are compression, but a so extremely lossful compression that the loss can be relevant.
Brutally, "there may be more to the story of the fall of an elderly than just gravitation" - also in the sense that there are details behind the event.
Laws are compression - yes, with caveats.
On a more scientific, epistemological side: Einstein extended Newton covering more exceptions (reducing the abstraction - reducing the loss).
Appears to be lossy then ;)
(Sorry, you have to admit that was too easy to not say)
Back of the envelope calculation for storing valid 4-grams (sequences of four words) is around 10 billion x 14 bits per word = 17 gb for all 10 billion. There are LLMs 100x smaller which can write coherent prose.
GPT-2 for instance achieves roughly 1 bit per byte, so it can be used to compress (english) text 8-fold. Modern models are likely much better.
Almost like the other Borges work where “the Cartographers Guilds struck a Map of the Empire whose size was that of the Empire”.
πfs – A data-free filesystem - https://news.ycombinator.com/item?id=36357466 - June 2023 (107 comments)
πfs – A data-free filesystem - https://news.ycombinator.com/item?id=28699499 - Sept 2021 (30 comments)
PiFS – The Data-Free Filesystem - https://news.ycombinator.com/item?id=26208704 - Feb 2021 (1 comment)
Πfs: Never worry about data again - https://news.ycombinator.com/item?id=21359338 - Oct 2019 (1 comment)
The π Filesystem for FUSE: Store Your Data in π - https://news.ycombinator.com/item?id=19223032 - Feb 2019 (1 comment)
pifs - Avoid disk space usage by saving your files in the digits of Pi - https://news.ycombinator.com/item?id=18687275 - Dec 2018 (1 comment)
πfs – A data-free filesystem - https://news.ycombinator.com/item?id=13869691 - March 2017 (105 comments)
Πfs: Stores your data in π - https://news.ycombinator.com/item?id=10856108 - Jan 2016 (1 comment)
Πfs: Never worry about data again - https://news.ycombinator.com/item?id=10847693 - Jan 2016 (1 comment)
File system that stores location of file in Pi - https://news.ycombinator.com/item?id=8018818 - July 2014 (98 comments)
100% Compression Using Pi - https://news.ycombinator.com/item?id=6698852 - Nov 2013 (32 comments)
(Reposts are fine after a year or so; links to past threads are just to satisfy extra-curious readers)
I think ChrisMarshallNY is right, dang has access to eldritch powers.
I wrote a special native management app, and often use that, to implement dashboard functionality, like the kind of thing that the HN mods do.
Yeah, I could, for example, feed the logs into an LLM, and get fancy reports, but it’s a lot easier to simply hit the charts button in the navbar, and view interactive graphs, customized exactly for my workflow.
It didn't seem very practical.
Spy agencies would not only have to store it all in case it was something valuable, but at some point they may try to crack it because it's indistinguishable from encrypted data and waste resources on it. If enough people did it, total web surveillance could become impractical.
I'll note that any observer already has this problem to the extent that video streams are also encrypted. However most observers presumably recognize the endpoints as well as being able to classify the traffic by means of statistical analysis.
What might be useful would be a tool to generate arbitrary user data of various forms, including HMTL, video, audio, and various message formats. Then it could assemble a convincing traffic stream full of gibberish to exchange with peers at random. You wouldn't even necessarily need all that much of it to overwhelm any would be observers when considered relative to the volume of streaming service traffic that already exists.
This is what stream ciphers are
Find k candidate indices for your data, then locate each of them. If the smallest one is a significantly smaller index space, repeat.
> Now, we all know that it can take a while to find a long sequence of digits in π, so for practical reasons, we should break the files up into smaller chunks that can be more readily found.
> In this implementation, to maximise performance, we consider each individual byte of the file separately, and look it up in π.
But Pi's binary expansion is not very practical for this purpose, since it's 11.0010...
OTOH. e is 10.1011...
Let's stick to fractional digits (the ones right of the binary point) at index 0 we have 1 and at index 1 we have 0.
So, to encode a stream of bytes so that each bit is encoded as the index of that bit in the e, all you need to do is to xor it with 0xFF
Further reading: https://en.wikipedia.org/wiki/Sloot_Digital_Coding_System
One thing to note is that Sloot consistently refers to his scheme as "encryption" rather than "compression". His encoding scheme originated as a method to encrypt TV repair manuals for his previous project, RepaBase. The idea was that they'd send out a compressed and encrypted database of repair manuals for free, then whenever a technician needed one he would call up RepaBase and pay for the key for that manual. That way, a tech would only need to pay for the manuals he needed instead of for the whole database. The video encoding scheme was basically the same idea except the key was stored on a smart card. Of course the scammy part was misleading investors into believing that all the video data was somehow stored in that decryption key.
But Pi is infinite. And thus this genius contraption will work as long as we have Moore's law on our side :)
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.
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.
It also doesn't contain all past and future knowledge because it also contains all possible falsehoods about the past and future in a way that's indiscernible from the truth.
Encoding information as an offset into a pseudorandom sequence is no more storage efficient than storing the information directly.
Infinities of random sequences exist that can be shown not to contain all data, 0-8 (base 10) is one such random sequence that is trivially proven to never contain 9...
There are no known patterns to pi, but, (I am legitimately curious about this), are there any known sequences e.g. of 1 million 0s and a single other digit within the decimal sequence of pi?
Given how it (pi) looks, I'm of the strong suspicion is that the answer is "no". But of course, proving that requires that some property of the randomness is provable. Which it does feel as if, given there are different infinities, there are also different randomnesses, hence the conjecture is ill-formed and probably incorrect...
(Fun fact: "Chrispratt" is an ancient Californian word that means "Joel McHale didn't want the role.")
https://dn760100.eu.archive.org/0/items/TheLibraryOfBabel/ba...
All knowledge is information. All information is sequences of bits. All sequences of bits are numbers. All numbers already exist.
All files in a computer are sequences of bits. Intellectual work creates files. Intellectual work is number discovery.
Humans are interesting number generators. Humans are anti-random number generators.
Perfect crypto!
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)
> 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.
> Calculate the number of bits to encode that value using log2(938933556), which is ~29.8
Can someone explain these two statements to me?
This is roughly same as saying: "If you rewrite 938933556 as a binary number / usize, it will need 30 bits".
Sanity check: 1101111111|0110111111|0100110100 (| delimits every 10 bigits).
> Since the file is 128 bits long, one would expect this place to be around the 2*128th bit.
This statement is a bit more subtle. As a first ord approximation, we can see pi sort of as a RNG.
If we write pi (ignore the decimal point), as a binary number, we get: 11011001111111011110010101011110001010101111101101110001001100001...
You can... kind of squint and pretend this is a random sequence of 1s and 0s.
Now, if you had a file that is 128 bits (so lots of intermingling 0s and 1s), and each next digit of pi is effectively a coin flip. Pretend 1s are heads, and 0s are tails. You basically have to get the exact 128 consecutive coin flips of the same result as your file to get your file back.
Imagine now, PI not as a number, but a sequence of experiments of flipping the coin 128 times.
- (11011..01000)(10000...00100)....
- ^attempt 1 ^attempt 2
You have to try, on expectation, quite a few times to win this game! Now, you could easily get lucky for sure. But on average, your chance of winning per attempt is roughly 0.5^128! So, how many times do you have to try to win this game? Something like 2^128 times - and you have to consider that each attempt uses 128 bits as well. So more like 2^135. But you don't have to start fresh in each attempt, you can see it as like this: - 11011................00100...
- ( 128 flips )
- ( another 128 )
- ( )
- ... so on and so on
That's where the 2^128 number came from.0x123456789ABCDEF0
use this number as a shorter nibble storage alternative...
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.
jshell> "πfs".toUpperCase()
$1 ==> "ΠFS"
Welcome to Node.js v26.3.0.
Type ".help" for more information.
> "πfs".toUpperCase()
'ΠFS'
Python 3.14.5 (main, May 10 2026, 10:21:34) [Clang 21.0.0 (clang-2100.0.123.102)] on darwin
Type "help", "copyright", "credits" or "license" for more information.
>>> "πfs".upper()
'ΠFS'
echo 'πfs' | awk '{print toupper($0)}'
ΠFSAnd for which the index is easy to compute?
My favourite issue being about GDPR compliance https://github.com/philipl/pifs/issues/56
3._1_415926535897932384626433832795_0_288419716939
> Now, we all know that it can take a while to find a long sequence of digits in π, so for practical reasons, we should break the files up into smaller chunks that can be more readily found.
> In this implementation, to maximise performance, we consider each individual byte of the file separately, and look it up in π.
So not really a compression scheme.
> 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.
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.
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.)
This project makes clear the counter-argument: the input that gets you the file out of π is a badly compressed version of the file.