Library of Babel

Bidirectional mathematical engine for Borges' Library of Babel. Finds the permanent hexagon address of any text, reads any page at any coordinate, and scores...

A bidirectional mathematical engine for Borges' infinite library.

No database. No storage. No randomness. Same input always produces identical output — across machines, across time.

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What It Does

Forward: Paste any text → get its permanent address (Hexagon, Wall, Shelf, Volume).

Reverse: Give coordinates → get the 3,200-character page that has always lived there.

The Library doesn't generate text. It reveals what was always there.

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Usage

Forward lookup — find where your text lives

from babel_core import format_locate

print(format_locate("call me ishmael"))

Output:

📍 Hexagon 936,177,732,035,491,926 · Wall 3 · Shelf 4 · Volume 21
(Global index: 936177732...)

This text has always existed here. It is not generated — it is found.

Reverse lookup — read a page at any coordinate

from babel_core import format_read_page

print(format_read_page(hexagon=1, wall=1, shelf=1, volume=1))

Output:

📖 Hexagon 1 · Wall 1 · Shelf 1 · Volume 1

sw,quamqysyjnki.eog,u,gl.b.u uuejbadqcfwmbegfeljp.toqwpq... (3200 chars total)

Entropy analysis — how noise-like is a page?

from babel_core import index_to_page, shannon_entropy, space_frequency, classify_page

page = index_to_page(12345)
h = shannon_entropy(page)
sp = space_frequency(page)
tag = classify_page(h, sp)
print(f"H={h:.2f} bits | space={sp:.1f}% | {tag}")

Shannon entropy thresholds (theoretical max for 29-char alphabet: log₂(29) ≈ 4.86 bits):

• 🟢 coherent — H < 3.8 and space > 14% (almost never random — that's the point)
• 🟡 interesting — H 3.8–4.5 or space 6–14%
• 🔴 noise — H > 4.5 or space < 6%

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The Codex

codex.json ships with 7 pre-mapped passages from literature and culture. Zero tokens to browse — it's a static JSON read. The coordinates are permanent and independently verifiable.

from demo import show_codex, add_to_codex

# Display all pre-mapped passages
show_codex()

# Add your own — coordinates computed and persisted immediately
add_to_codex("the medium is the message", "Understanding Media — Marshall McLuhan")

Pre-mapped passages:

• "call me ishmael" — Moby Dick
• "it was a bright cold day in april..." — 1984
• "the library of babel" — Borges
• "in the beginning god created the heavens and the earth" — Genesis 1:1
• "to be or not to be that is the question" — Hamlet
• "it was the best of times it was the worst of times" — A Tale of Two Cities
• "attention is a currency" — High Noon Office

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Three Demo Scripts

Run all four demos at once:

python3 demo.py

Or call individually:

from demo import locate, read_page_demo, entropy_heatmap, show_codex, add_to_codex

# Demo 1: Locate any text
locate("the library of babel")

# Demo 2: Read a page at coordinates
read_page_demo(hexagon=1, wall=1, shelf=1, volume=1)

# Demo 3: Entropy heatmap — 5 random coordinates, ranked by Shannon entropy + space frequency
entropy_heatmap(n=5)

# Demo 4: Codex — browse pre-mapped passages
show_codex()

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The Math

Alphabet: abcdefghijklmnopqrstuvwxyz ,. — 29 characters (Borges' 25-char set extended to full Latin alphabet)

Forward (text → index): Interpret the filtered character sequence as a base-29 integer.

Coordinates:

Volume  = index % 32
Shelf   = (index // 32) % 5
Wall    = (index // 160) % 4
Hexagon = index // 640

Page generation: SHA-256 counter-mode hash expansion. SHA256(gi_bytes || chunk_id) repeated to fill 3,200 bytes, each mapped to the alphabet via byte % 29. Deterministic, chaotic, sub-millisecond.

Note on the LCG approach: A Linear Congruential Generator with a=30, m=29^3200 maps small indices (e.g. 640) to tiny values like 19201, which decode as 3,197 leading 'a' characters when expanded to 3,200 base-29 digits. Hash expansion solves the distribution problem correctly.

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Files

library-of-babel/
  SKILL.md          — This file
  babel_core.py     — Core math engine
  demo.py           — Four runnable demonstrations + codex functions
  codex.json        — Pre-mapped passages (add your own with add_to_codex())
  references/
    spec.md         — Full technical specification

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Setup

No dependencies beyond Python 3 standard library (hashlib, math, collections, json).

cd library-of-babel
python3 demo.py