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You'll find this an interesting watch:

Reinventing Entropy Compression is Intelligence Part 1

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

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.

That conclusion is similar to the concept of 'unconditional security' especially WRT one-time pads. The key must be at least as long as the message itself.

Other forms of encryption are based on assumptions and conditions being true (e.g. factoring is a hard problem, etc.) that may or may not be true. We don't know.

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

https://youtu.be/l6DKRf-fAAM

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.

LLM's seem to be the weird interesting outcome of applying lossy (de)compression concepts to text instead of the audio/image/video domains where they have traditionally been used.

If you set temperature to 0.0 you almost have a key-value store, but finding the right key for your value might take some effort.

> you basically need the same amount of data to represent the address of your data as the data itself

Almost like the other Borges work where “the Cartographers Guilds struck a Map of the Empire whose size was that of the Empire”.

How are you generating these lists

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.

This is just WOM with extra steps.

https://en.wikipedia.org/wiki/Write-only_memory_(joke)

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.

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

yes I believe that's the joke

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.

That just means you'll be creating even more valuable metadata to store your files. Win-win.

At least as of 15 years ago when I was in grad school that remained an open conjecture.

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?

I looked into this a bit a while ago, what Sloot did was at least a little 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 :)

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

I have very fond memories of reading that book.

Chaitin's constant does not count? Depends on your definition of constructed, but contrary to "easy" normal numbers such as Champernowne's constant, it's not defined by its sequence of digits.

That’s a lot of negatives!

What do you mean by "non-constructed" here?

You must be fun in RL.

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.")

You will love reading Jorge Borges The Library of Babel.

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

All knowledge already exists. Humans are merely discovering it.

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.

Worse - it's also possible to calculate your time of death! That is: assuming enough compute & knowing how many digits to calculate.

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

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

Perfect crypto!

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

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

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!

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 past and future fake news, and you don’t know which is which.

It isn't actually proven true.

A not so distant calendar also has the day you will pass away.

So does a random number generator

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.

A theory is something you can test, model, write proofs, do calculations, eg quantum field theory, group theory.

Simulation "theory" isnt a theory its a conjecture.

Theres no meat to it.

If we could restore the snapshot from around the year 2000 that'd be great, would like to make some changes.

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

The word 'exist' is doing a lot of work here. Could any computer actually find the value in pi? Each computation takes energy, and there is a finite amount of energy in the universe. Does the value 'exist' in pi if it could never be rendered? How much different is that claim from "our simulated universe is a file on gods computer, located just past the edge of the observable universe or 18 inches away in the 4th dimension"?

A similar thought experiment I've had is with the lottery. With just a few sheets of paper, there exist a sequence of numbers that would completely shut down both major US lotteries - ossibly even get you arrested - if they contained the winning numbers for the next 50, 20, or even 10 consecutive draws. Think about the consequences. You would win, and win again the next draw, and they would be certain you cheated. Then confiscate your pad, and draw again and win a third time. They would have to shut the contest down because this is "mathematically impossible ". But it's not. Just like your thought experiment, it's "just numbers"

> 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.

    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

No it doesn't. Think of the intro of We'll rock you and show me how you perform that on your piano.

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

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.

It almost always will be, except for the extremely rare case of your string being somewhere early in the pi string.

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.

https://math.stackexchange.com/questions/1817064/bbp-formula...