πFS

Original Article ↗ Hacker News Discussion ↗

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.