3Blue1Brown just released a viduo about this Intelligence-Compression connection.

https://youtu.be/l6DKRf-fAAM

You'll find this an interesting watch:

Reinventing Entropy Compression is Intelligence Part 1

3blue1brown https://youtu.be/l6DKRf-fAAM?is=ne73FCJ7ErXhzZ-v

The level of compression is pretty impressive when you think about it. I wrote a comment a while back which is still true (although bytes should be bits, so in that sense it’s still wrong): https://news.ycombinator.com/item?id=39559969

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.

In some sense, science is the most extreme form of compression - Newtonian mechanics explains an incredible number of phenomena in a few lines of text.

I once interviewed for a company and the interviewer was telling me how he (a vc) funded a project to generate large streams of random numbers; you would select an index at random, share that private key with somebody, and then the subsequent text could be used as a one-time-pad. NSA would be forced to buffer/save the entire stream, which could be generated at GB/sec, if they wanted to decrypt.

It didn't seem very practical.

That seems easy enough to solve. Simply record the index and length in pi of the index and length in pi.

Back in college, I thought I could compress my phone number by telling people its index in pi, but my 7 digit phone number is at an 8 digit index.

I didn’t have the compute to find my 10 digit number with the area code.

TFA addresses this

> 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.

The index of your 20 line file is <20TB number>

yes I believe that's the joke

Point taken about the index potentially being really long. Why would the length be longer than the data? Don’t you need to find the right sequence?

How are you generating these lists

I looked into this a bit a while ago, what Sloot did was at least a bit novel. Basically the way his encoding scheme actually worked was that it would store each line of video into a database, encode each video frame as a series of line lookups, and then store that encoded frame into another database. Then each video is a series of frame lookups. When you hear accounts of him being able to demo smooth playback of 16 videos at once on late 90s hardware, this is how he did it. Because each frame is a series of line lookups, splitting the screen horizontally 16 times and playing 16 videos at once is not any more taxing than playing a single video fullscreen. Similarly, he was able to fast-forward and rewind smoothly because each frame is individually decoded, it's not like traditional video compression where you have to calculate differences from each keyframe. Playing at 2x speed was not any more taxing than 1x speed. Of course he never would have been able to store a video file in 8KB or whatever, but this meant that (for example) if you had a whole season of a TV show in your database, the opening and ending credits would only be stored once.

> The SDCS is only possible if keys are allowed to become infinite, or the data store is allowed to become infinite (...) This would, of course, make the idea useless.

But Pi is infinite. And thus this genius contraption will work as long as we have Moore's law on our side :)

I have very fond memories of reading that book.

Never heard of that one, that's amazing! Love it.

That’s a lot of negatives!

So does every other random infinite sequence of bits. The unintuitive part comes from infinity, not pi.

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.

The worst part is that it contains Star Wars 4-6 from an alternate timeline where Disney did a reboot casting Chris Pratt as Han Solo.

(Fun fact: "Chrispratt" is an ancient Californian word that means "Joel McHale didn't want the role.")

It also contains all past and future fake news, and you don’t know which is which.

You will love reading Jorge Borges The Library of Babel.

https://dn760100.eu.archive.org/0/items/TheLibraryOfBabel/ba...

The person who starts reading ahead into pi will always gets the freshest numbers.

Perfect crypto!

If it makes you feel better, consider that it also contains all plausible and implausible falsehoods about your demise as well.

this statement is equivalent to "pi is a normal number." While most real numbers are normal and pi is suspected to be so, it isn't known.

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

Fear not! It’s probably so deep in pi that you’d pass away listening to someone tell you where!

So does a calendar, if you you buy them enough years in advance.

And also all the days you don’t, so, by itself not very meaningful. Especially since you can’t tell which one is right in advance. In some sense, so does a calendar

It also contains all possible falsehoods and comes with no way to distinguish what's true from what isn't.

It isn't actually proven true.

So does a random number generator

> Since the file is 128 bits long, one would expect this place to be around the 2*128th bit.

> Calculate the number of bits to encode that value using log2(938933556), which is ~29.8

Can someone explain these two statements to me?

Both.

yes, but can you get a tattoo of all tattoos that do not contain themself?

Here is a one page proof that pi is irrational - https://heuklyd.github.io/papers/pdf/Niven-1947.pdf

We definitely know that Pi is irrational, we just don't know if it's normal (i.e. if the PiFS joke even works).

Well, that should get GPT-5.5 extended thinking going for a few weeks.

    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)}'
    ΠFS

Part of the joke is that, in this implementation, the metadata is guaranteed to be larger than the file:

> 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.

Half the time it should be larger, right?

It's a(n IMO weak) argument raised when discussing illegal files/numbers.

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.

I think it's pretty clearly for amusement. And it would kind of spoil the amusement if it were to explicitly mention that it's a joke...

It's a joke.