Shape

174 II Seeing How It Works
This has some history—touching externally and being embedded tangentially
are from Alfred North Whitehead. He uses extensive connection to describe physical
experience in Process and Reality. Intuitively, this relationship is having at least a point
in common. It shows how continuous regions—they’re the earlier events of An Enquiry
Concerning the Principles of Natural Knowledge—interact, and touching for planes, but
also for basic elements of other kinds, is alike in many ways. In fact, the discrepancies
appear to be mostly irrelevant bits of formality. From what I can tell, Whitehead’s
regions and my basic elements are about the same. Notably, every region includes
others—there are no units. And no region includes all of the others—there’s no longest
line, etc.—but any two regions are connected by a third. Disconnected regions don’t
combine to make a region, and it seems that connected regions may or may not do
so. Whitehead gives the following evidentiary series of six diagrams à la Venn
in which regions A and B are connected. In diagrams i, ii, and iii, there’s inclusion
(embedding), in i through iv, overlap, in v and vi, external connection, and in ii and
iii, tangential inclusion. Presumably, the regions in diagram vi don’t form a single continuous
region, while the ones in i through v do. And surely, none of this is a surprise.
Physical experience and visual experience coincide in many ways—surely, the latter is
embedded in the former, and perhaps vice versa to establish identity.
The coincidence between basic elements and Whitehead’s regions is a nice diversion.
And there are other kinds of coincidence that are easy to see, too. Let a basic element
of dimension i coincide with a basic element of dimension i þ 1 if the first one is
also a boundary element of a basic element embedded in the second one. Then points
are coincident with lines