The Nullweather Pages

Notice

This is the working index of Ephraim Nullweather, independent student of mathematics, diagrams, metaphysics, and errors of classification.

The pages collected here will concern those places where formal notation becomes too stiff and ordinary language becomes too pleased with itself.

A preliminary warning

The reader should not expect a system. Systems are too easily mistaken for weatherproof houses. What follows here, when it follows, will be a collection of notes, diagrams, distinctions, objections, and small attempts at repair.

My interests are mostly in mathematics and metaphysics, though I reserve the right to become distracted by maps, failed definitions, marginalia, and the philosophical behavior of ordinary words.

There are no public essays, lists, or external pages at present.

This index will be amended as materials become fit for exposure.

First note: boundary

A boundary is not simply where a thing stops. In topology, a boundary point is one whose every sufficiently small neighborhood touches both the thing and its outside. This is a better sentence than it first appears to be.

Many arguments go wrong because they imagine boundaries as fences. But some boundaries are not fences. They are regions of unavoidable double contact: close enough to belong, close enough to escape. The edge of a concept may be less like a wall than like a damp hem.

Working vocabulary

Boundary. Not merely the place where a thing stops, but a site of double contact: every small enough inspection finds both the thing and what is not the thing.

Diagram. A compressed argument with some of its grammar missing. This is not a defect in every case.

Abstraction. A refusal to carry all details at once. Dangerous when mistaken for deletion.

Weather. A name for conditions too local to be laws and too patterned to be accidents.

Propositions under repair

These are not theses. They are working statements, kept here until they either improve or become too embarrassing to preserve.

1. Not every boundary separates.
2. A diagram may fail as a picture and succeed as an argument.
3. Abstraction is not deletion, though it is often charged with the same crime.
4. Some confusions survive because they are useful places to stand.
5. Continuity is the refusal of a surprise at sufficiently small scale.

Cabinet card no. 1

Specimen: a boundary behaving badly under inspection.