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The Cone

Imagine that we could take a line as we take a spurtle (in Scotland, this is about ten or eleven inches of half-inch-diameter, wooden rod, usually with the effigy of a thistle carved at one end, traditionally for stirring porridge)—and use it to "stir space".

If we were to stir in such a way that a fixed point on the line would trace out a circle, then the line would sweep out a surface that is a right circular cone.

This cone has a vertex, equivalent to the place at which we grasp the spurtle. The line pivots in/on it.

I stress that this point does
not divide the line (two would, but there is only one), so the vertex does not divide the cone.  In the literature, one often sees it written that a cone consists of two parts, called "nappes", that meet in the vertex.  This is mistaken.  A cone must cut the plane at infinity as it passes through it.  Just how that cut looks is a matter of great interest, and some controversy!
a cone encloses However, the cone does divide the volume of space into two, as the animation alongside fairly fancifully tries to convey--no passage is available to either a blue or a red 'mote' from one "solid sector" to another that does not encounter the cone's surface.

The cone can be considered to "enclose" one of these two portions of volume, either at will.  In fact, it encloses both portions at once, but we are probably accustomed to regarding the "smaller" as the enclosed.  But in the general way of cones, "inside" and "outside" are not defined.  Only enclosure is.

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