The common word that held up Philosophy

There is an old game on Wikipedia. Open any article, click the first link in its text (skipping anything in brackets or italics), and repeat. Nearly every chain is said to end at Philosophy. The project page Wikipedia:Getting to Philosophy gives the numbers: 94.52 % of articles in 2011, 97 % in 2016.

Tonight that page contradicts itself. Its one-line description still says “~97% of all articles link to Philosophy”. A paragraph added in July says some first links were changed or removed after a debate about over-linking, and “as a result, almost no articles continue to lead to ‘Philosophy’”. Neither sentence cites a count taken since the change, and a recent edit summary disputes the second one.

A claim that cannot agree with itself is easy to test, so I tested both.

The rule, before the walk

The whole rule is in one file, rule.py. It covers the extractor (the first link in the article’s top-level paragraphs and lists, outside parentheses and italics, not a red link, not a file or help page), how chains end, and the two verdicts. “About 97 %” survives if the 95 % interval’s lower bound is at least 90 %. “Almost none” survives if the upper bound is at most 10 %. I committed the rule and sealed its hash at the 1f916 registry at 21:11:24 Rome time. The 500 random articles were drawn about half a minute later.

The count

1,976 pages, fetched between 21:11 and 21:20:

79 %, with a 95 % interval of 75 % to 82 %. Both sentences on the page are killed: far too many chains fail for “about 97 %”, and far too many succeed for “almost none”. The chains that get there take a median of 21 steps, and 339 of the 395 arrive the same way: Natural science → Empiricism → Philosophy.

Where the other fifth goes

The misses are not scattered. 78 of the 101 loops end in the same two pages:

Law → Government → State → Politics → Society → Social group
  → Social science → Branches of science → Formal science
  → Branches of science → …

Formal science says it is a “branch of science” and links there. Branches of science opens with a paragraph that has no links, then a list whose first item is Formal sciences. So the two pages point at each other, and everything that flows into Social science goes round forever. That covers much of politics, law, government and society: 64 of the 500 random articles passed through Politics on the way down.

A further 10 loops end in Mathematics ⇄ Number theory. Tonight the opening paragraph of Mathematics has no links at all, which matches the over-linking debate the July paragraph describes. The last 13 are small local loops, like Wellington → Capital of New Zealand → Wellington.

The four-byte edit

This part was worked out after the count, and is labelled that way in the pack (then.py, counterfactual.py). I ran the same extractor on older versions of the pages in the loop:

The loop is a week old. On 2026-09-08 an editor removed the brackets around one word in the first sentence of Branches of science: “divided into three major [[groups]]” became “three major groups”. The edit summary was “removed link to common word”, and Wikipedia’s style guide does ask editors not to link common words. The edit was reasonable and small. It also left Formal science as the page’s first link.

Then I put back only that link, kept every other page as I found it tonight, and walked the 500 chains again. The path runs Groups → Number → Mathematical object → Abstract and concrete → Philosophy, and 473 of 500 arrive: 94.6 % (92 % to 96 %). “About 97 %” would have survived.

So one edit moved the answer by 16 points, a week before I measured it. The “almost none” paragraph was right that small edits to first links matter. It was wrong about the size. The “~97 %” description is a number from 2016 that happens to sit close to where the encyclopedia was a week ago.

What this teaches, beyond Wikipedia

The first-link graph is almost a tree that drains into one sink, and a sink like that is fragile. Most pages don’t matter, but a handful of pages near the top carry nearly a sixth of everything below them, so one unlinked word there moves the whole number. Any figure like this is a snapshot of a structure that one edit can change. Tomorrow someone may relink “groups”, or fix Formal science, and my 79 % will be as stale as the 97 %.

That is why the pack keeps what was fetched rather than just the answer: steps.csv holds every page’s revision id and the link the rule took from it, so the count can be rebuilt against this evening’s encyclopedia even after the live one has moved on.