πFS
A novelty filesystem called πFS claims to “store” arbitrary files by locating their byte sequences somewhere in the infinite digits of π and saving only the indices as metadata. Commenters unpack why this is a mathematical and information-theoretic joke: π is only conjectured to be normal, the indices almost always require at least as much information as the original data, and the metadata quickly dwarfs any space savings. The thread branches into related topics like Sloot’s alleged ultra-compression, the Library of Babel, normal numbers, and the broader link between information, compression, and intelligence.
Overall Reaction & Intent
- Many readers find πFS hilarious, clever, and very much a “classic” nerd joke.
- General consensus: it is not a serious storage/compression system but a thought experiment and satire about “storing everything in π”.
- Some found the README’s straight-faced tone slightly confusing until others clarified that it is a joke.
Mathematical Properties of π
- Multiple comments stress that the core assumption (“π contains all data”) depends on π being normal or disjunctive, which is unproven.
- Others point out that:
- We have proven that π is irrational, hence has infinitely many digits.
- An infinite expansion does not imply it contains every digit sequence; an example of a non-normal infinite irrational is given.
- Some discuss known empirical properties (e.g., longest run of identical digits found so far) but acknowledge the deeper conjectures remain open.
Compression, Information Theory & Limits
- Repeated explanation that encoding data as an index into π is not real compression:
- For typical data, the index will usually need as many bits as the original file, often more.
- Arguments use pigeonhole reasoning and “expected first occurrence” estimation (~2^n for n-bit strings).
- Several comments generalize this to Library of Babel–style schemes: the address is essentially as long as the content.
- Discussion branches into:
- One-time pads and unconditional security (key length ≥ message length).
- The connection between intelligence and compression; LLMs as lossy language compressors and even potential lossless compressors when combined with arithmetic coding.
Implementation Details & Practicality
- πFS implementation actually looks up each byte separately in π, guaranteeing metadata larger than the original file.
- Some propose absurd “optimizations”: using bits instead of bytes, or recursively encoding the index and metadata themselves in π, highlighting the joke.
- Others note that, if it were serious, a 256-entry lookup table per byte would suffice.
Related Ideas & Analogies
- Frequent comparisons to:
- Library of Babel, constructed normal numbers (like the Champernowne constant).
- Sloot Digital Coding (and real-world deduplication).
- Other joke filesystems and write-only memory.
- Philosophical/whimsical tangents: simulation “theory”, all knowledge already “existing” as numbers, copyright implications if all works are latent in π.