Compare length-controlled lexical diversity
Separate whole-corpus token/type counts from matched-window vocabulary ratios and inspect length effects.
Goal and how to run
This lesson assumes basic Python knowledge. Read each method and caption before changing parameters. AI exercises are optional; no AI account is needed for the core workflow. Data lives in notebook metadata, so there is no companion data download. Keep the notebook saved in the active working folder.
Your goal is to understand the research question, execute transparent calculations, check the results, and state the limits of the conclusion.
Setup and parameters
from pathlib import Path
import base64, gzip, hashlib, json, platform
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from IPython.display import display, HTML
import re
from collections import Counter
from IPython.display import display as _display
def display(value):
if isinstance(value,pd.DataFrame):
table=value.to_html(max_rows=12,escape=True)
style="<style>.vibeit-readable-table{max-width:100%;overflow-x:auto}.vibeit-readable-table table{width:max-content;max-width:none;border-collapse:collapse}.vibeit-readable-table td,.vibeit-readable-table th{white-space:nowrap!important;word-break:normal!important;overflow-wrap:normal!important}</style>"
return _display(HTML(style+'<div class="vibeit-readable-table">'+table+'</div>'))
return _display(value)
RECIPE_ID='hu02-lexical-diversity'
OUTPUT_DIR=Path.cwd()/"results"/RECIPE_ID
plt.rcParams.update({"figure.dpi":120,"font.size":10,"axes.spines.top":False,"axes.spines.right":False,
"axes.prop_cycle":plt.cycler(color=["#18785f","#416aa6","#bc6541","#9974a5"])})
print("Python:",platform.python_version(),"; NumPy:",np.__version__,"; Pandas:",pd.__version__)
print("Working folder:",Path.cwd())
print("Core data mode: embedded snapshot; no network requests")
Python: 3.13.13 ; NumPy: 2.5.3 ; Pandas: 3.0.6 Working folder: /Users/zhiluo/Developer/vibeit-cookbook/cookbook/downloads Core data mode: embedded snapshot; no network requests
Load the embedded snapshot
def load_snapshot(recipe_id, expected_sha256, snapshot_key):
"""Read embedded data from this notebook, including a renamed copy."""
for path in sorted(Path.cwd().glob("*.ipynb")):
try:
notebook = json.loads(path.read_text(encoding="utf-8"))
metadata = notebook.get("metadata", {}).get("vibeit_cookbook", {})
blob = metadata.get("snapshots", {}).get(snapshot_key)
if metadata.get("recipe_id") != recipe_id or not blob:
continue
if blob.get("sha256") != expected_sha256:
continue
raw = gzip.decompress(base64.b64decode(blob["gzip_base64"], validate=True))
if hashlib.sha256(raw).hexdigest() != expected_sha256:
raise ValueError("Embedded snapshot checksum mismatch: " + snapshot_key)
return json.loads(raw)
except (OSError, json.JSONDecodeError):
continue
raise FileNotFoundError(
"Save/open the complete .ipynb in the active working folder. "
"The embedded snapshot could not be located for " + recipe_id)
SNAPSHOT_HASHES={'novels': 'c03763abb21b2380d2934b088f1c22a6d5a4675b17e23534e3f7343dc90084ec'}
def snapshot(key):
return load_snapshot(RECIPE_ID,SNAPSHOT_HASHES[key],key)
print("Embedded snapshots:",list(SNAPSHOT_HASHES))
Embedded snapshots: ['novels']
Read the method functions
def strip_ebook_wrapper(raw_text):
"""Return the analysis body while the unmodified source/complete license remain in metadata."""
text=raw_text.replace('\r\n','\n').replace('\r','\n')
start=re.search(r'\*\*\* START[^\n]*\*\*\*',text,re.I)
end=re.search(r'\*\*\* END[^\n]*\*\*\*',text,re.I)
if not start or not end or end.start()<=start.end():raise ValueError('Ebook start/end markers not found')
return text[start.end():end.start()]
print("Method ready: strip_ebook_wrapper")
Method ready: strip_ebook_wrapper
def split_novel_chapters(body):
"""Declared two-ebook rule: repeated labels resolve to last heading, excluding their TOCs."""
headings=list(re.finditer(r'(?im)^\s*chapter\s+([ivxlcdm]+|\d+)[.\]]*\s*$',body))
if not headings:raise ValueError('No supported chapter headings')
last={match.group(1).upper():match for match in headings}
chosen=sorted(last.values(),key=lambda match:match.start());chapters=[]
for j,match in enumerate(chosen):
text=body[match.end():chosen[j+1].start() if j+1<len(chosen) else len(body)]
text=re.sub(r'\[Illustration\b[^\]]*\]',' ',text,flags=re.I|re.S)
text=text.replace('_','').replace('’',"'").strip()
if len(text)<300:raise ValueError('Unexpected short chapter after declared TOC rule')
chapters.append(dict(label=match.group(1).upper(),order=j+1,text=text))
return chapters
print("Method ready: split_novel_chapters")
Method ready: split_novel_chapters
def tokenize_words(text):
"""Transparent English-letter tokenizer; punctuation/case decisions are part of the method."""
return re.findall(r"[a-z]+(?:'[a-z]+)?",text.lower().replace('’',"'"))
print("Method ready: tokenize_words")
Method ready: tokenize_words
Data and model boundary
The snapshot retains complete unmodified source ebooks, including their original licenses. Chapter-based analysis uses 61 Pride and Prejudice chapters and 24 Frankenstein chapters; front matter and Frankenstein framing letters are outside this declared scope. English-letter tokenization is a method choice, not a language-neutral definition. Word frequencies, surface-pattern cooccurrence and SVD axes do not independently establish authorial intent, character relationships or sentiment.
Steps
1. Separate raw TTR from text length
Type-token ratio is distinct normalized types divided by tokens. Whole-book TTR depends strongly on length, so do not rank authors by the two raw numbers. We use the same declared chapter scope.
novels=snapshot("novels");corpus={};chapter_rows=[]
for book in novels["books"]:
chapters=split_novel_chapters(strip_ebook_wrapper(book["raw_text"]))
tokens=tokenize_words(" ".join(chapter["text"] for chapter in chapters))
corpus[book["id"]]={"title":book["title"],"author":book["author"],"chapters":chapters,"tokens":tokens}
for chapter in chapters:chapter_rows.append({"book_id":book["id"],"book":book["title"],"chapter":chapter["order"],"source_label":chapter["label"],"characters":len(chapter["text"]),"tokens":len(tokenize_words(chapter["text"])),"text":chapter["text"]})
chapter_table=pd.DataFrame(chapter_rows)
assert len(corpus[1342]["chapters"])==61 and len(corpus[84]["chapters"])==24
print(novels["source_notice"])
print("Declared chapter counts:",{b:len(corpus[b]["chapters"]) for b in corpus})
display(chapter_table.drop(columns="text").head(8))
summary=pd.DataFrame([{ "book":entry["title"],"tokens":len(entry["tokens"]),"types":len(set(entry["tokens"])),"whole_TTR":len(set(entry["tokens"]))/len(entry["tokens"])} for entry in corpus.values()])
display(summary)
fig,axes=plt.subplots(1,2,figsize=(10,4));axes[0].bar(summary.book,summary.tokens);axes[0].set(ylabel="Processed tokens",title="Unequal corpus lengths")
axes[1].bar(summary.book,summary.whole_TTR);axes[1].set(ylabel="Whole-corpus TTR",title="Length-dependent ratio")
for ax in axes:ax.tick_params(axis="x",rotation=15)
plt.tight_layout();plt.show()
These source ebooks are available free of charge. Complete unmodified source texts and their licenses are included in this snapshot. Project Gutenberg is acknowledged as the transcription source; its name is not used as a course title or endorsement.
Declared chapter counts: {1342: 61, 84: 24}
| book_id | book | chapter | source_label | characters | tokens | |
|---|---|---|---|---|---|---|
| 0 | 1342 | Pride and Prejudice | 1 | I | 4490 | 853 |
| 1 | 1342 | Pride and Prejudice | 2 | II | 4293 | 799 |
| 2 | 1342 | Pride and Prejudice | 3 | III | 9560 | 1704 |
| 3 | 1342 | Pride and Prejudice | 4 | IV | 5931 | 1064 |
| 4 | 1342 | Pride and Prejudice | 5 | V | 5246 | 962 |
| 5 | 1342 | Pride and Prejudice | 6 | VI | 13023 | 2353 |
| 6 | 1342 | Pride and Prejudice | 7 | VII | 11263 | 2000 |
| 7 | 1342 | Pride and Prejudice | 8 | VIII | 10993 | 1936 |
| book | tokens | types | whole_TTR | |
|---|---|---|---|---|
| 0 | Pride and Prejudice | 122185 | 6319 | 0.051717 |
| 1 | Frankenstein | 69610 | 6703 | 0.096294 |
2. Match contiguous sampling-window lengths
For each length, draw 30 seeded contiguous windows from each processed book. Mean and SD describe window variation in this corpus, not independent author experiments. Identical window lengths make the comparison more interpretable.
rng=np.random.default_rng(42);lengths=[100,500,1000,2000,5000];records=[]
for book_id,entry in corpus.items():
tokens=entry["tokens"]
for length in lengths:
for repeat in range(30):
start=int(rng.integers(0,len(tokens)-length+1));window=tokens[start:start+length]
records.append({"book":entry["title"],"window_tokens":length,"start_token":start,"TTR":len(set(window))/length})
windows=pd.DataFrame(records)
fig,ax=plt.subplots(figsize=(8,5))
for book,part in windows.groupby("book"):
grouped=part.groupby("window_tokens").TTR.agg(["mean","std"]);ax.errorbar(grouped.index,grouped["mean"],yerr=grouped["std"],fmt="o-",label=book)
ax.set(xscale="log",xlabel="Contiguous window tokens",ylabel="TTR; bars = window SD",title="Length-controlled corpus comparison");ax.legend();plt.tight_layout();plt.show()
3. Read normalized frequency-rank curves
Rank words by count and divide by each corpus token total. Log axes expose the descriptive heavy-tailed shape. A curve here does not prove a universal language law or literary quality.
fig,ax=plt.subplots(figsize=(8,5))
for entry in corpus.values():
frequency=np.array(sorted(Counter(entry["tokens"]).values(),reverse=True));ax.loglog(np.arange(1,len(frequency)+1),frequency/len(entry["tokens"]),label=entry["title"])
ax.set(xlabel="Within-corpus frequency rank",ylabel="Relative token frequency",title="Descriptive normalized rank-frequency curves");ax.legend();plt.tight_layout();plt.show()
4. Reconcile windows and export all draws
Each TTR must lie in (0,1], window starts stay within corpus bounds and every book gets equal replication at each length. Save all starts, not only windows supporting a preferred interpretation.
assert windows.TTR.between(0,1,inclusive="right").all()
assert windows.groupby(["book","window_tokens"]).size().eq(30).all()
OUTPUT_DIR.mkdir(parents=True,exist_ok=True);windows.to_csv(OUTPUT_DIR/"all-matched-windows.csv",index=False)
summary.to_csv(OUTPUT_DIR/"length-dependent-corpus-counts.csv",index=False)
print("Matched-window checks passed; exports:",OUTPUT_DIR)
Matched-window checks passed; exports: /Users/zhiluo/Developer/vibeit-cookbook/cookbook/downloads/results/hu02-lexical-diversity
Exercises and reference explanation
- Why not rank authors by whole-book TTR?
- Why keep matched windows and all starts?
Reference explanation. TTR depends on length. Equal windows and recorded starts expose corpus variability without selecting favorable passages or inventing independent author samples.
Keep a copy before changing parameters. Compare old and new figures and record which inputs, calculations and conclusions changed.
Optional AI coding exercises
Prompt 1
Using re/Counter/NumPy/Pandas/Matplotlib, add 3000-token windows with the same replication and recorded seed.
Prompt 2
With the same packages, compare nonoverlapping windows and report their dependence/scope.
Human acceptance. All ratios stay in (0,1], sample lengths and starts are valid and observations are not new books.
Review the edited source, then manually run affected cells and subsequent checks. Ask the assistant to explain the purpose, packages and data provenance of its changes, and reconcile that explanation with actual output.
Optional online extension
RUN_ONLINE_UPDATE=False
if RUN_ONLINE_UPDATE:
import requests
try:
response=requests.get('https://www.gutenberg.org/ebooks/1342',timeout=20)
response.raise_for_status()
print("Source:",response.url)
print(response.text[:700])
except requests.RequestException as error:
print("Online extension unavailable:",type(error).__name__,str(error)[:160])
else:
print("Online extension skipped; embedded core data unchanged")
Online extension skipped; embedded core data unchanged
Sources, snapshots and next steps
Historical novel 1342 — Original novel public domain in USA; complete source ebook and its Project Gutenberg license retained; free distribution and acknowledgment links; retrieved 2026-10-09. SHA-256
3f6bb9d6f78e0293b56acd4714dd68cb7d6d1d293402031ce9d5a216bcaf9d75. Preserve unmodified UTF-8 source including ebook headers and complete license; preprocessing occurs visibly in the notebook.Historical novel 84 — Original novel public domain in USA; complete source ebook and its Project Gutenberg license retained; free distribution and acknowledgment links; retrieved 2026-10-09. SHA-256
7810cd483cffcf2cc8a1d8f0d5807931e69d4f48cd14149b8c76f88af82fead3. Preserve unmodified UTF-8 source including ebook headers and complete license; preprocessing occurs visibly in the notebook.
Next steps. Transfer these methods to your own public or authorized data while retaining input checks, recorded parameters and result validation. Document the new experimental design and method limits; this example does not validate a new experiment. Full data licenses and generation instructions accompany the cookbook.