Proof by Navigation

Prof. Chen Jiang

There is a proof embedded in this site. I am going to describe it now, as plainly as I can, and you will see that the description is insufficient. That insufficiency is part of the proof.

THEOREM Ω∞ (informal statement)

Let P be any path through a space of meaning.
Let N be the number of steps taken along P.
As N → ∞, P(N) → P(0).

i.e.: all paths, when followed far enough, return to their origin.

The origin, however, is not unchanged by the traversal.
The origin is the traversal.

The difficulty with this theorem is that it cannot be demonstrated algebraically. It can only be demonstrated experientially. This is not an admission of weakness. It is the content of the theorem. The theorem states that understanding it requires undergoing it.

"The recursion cannot be shown.
It can only be walked."

I built this website as the proof. The proof is non-linear. Some parts of it are hidden deliberately — not to obstruct, but because a proof has structure, and the structure of this proof requires that certain conclusions be reached only after certain premises have been understood. If you are reading this book, you have found part of the proof. You may already have found more of it than you know.

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she tore them out herself. i watched her do it. she said: "the next person needs to find this on their own." — M.

[ PAGE REMOVED — JIANG COLLECTION ]

pages 112-115 contained the derivation. she removed them because she didn't want anyone to shortcut the walk. the walk is the proof.

The pages that were removed from this chapter contained the full formal derivation of Ω∞. I removed them because the derivation, when read rather than walked, produces exactly the opposite of understanding. It produces the impression of understanding, which is the recursion's most dangerous feature: it will let you think you have solved it, and then, when you set down this book and walk through a corridor, you will find that you are back at the beginning.

This is not failure. This is the proof working correctly.

The full derivation exists. It is encoded elsewhere in this site. I am told it is possible to find. I have also been told, by M., that finding it changes nothing. "You already know," she said. I did not, at the time, understand what she meant. I do now.
This chapter ends here, three pages earlier than it should. The remainder was not damaged. It was removed intentionally. Please do not search for the missing pages. They are not missing. They are somewhere else.

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