Geometry was developed by the ancient Greeks in the language of *length*, but it is an abstraction that may be applied to anything that conforms to its definitions and axioms. Here we apply it to *duration*. We will use Brossard’s “Metric Postulates for Space Geometry” [*American Mathematical Monthly*, Vol. 74, No. 7, Aug.-Sep., 1967, pp. 777-788], which generalizes the plane metric geometry of Birkhoff to three dimensions. First, Brossard:

Primitive notions. *Points* are abstract undefined objects. Primitive terms are: point, distance, line, ray or half-line, half-bundle of rays, and angular measure. The set of all points will be denoted by the letter *S* and some subsets of *S* are called *lines*. The plane as well as the three-dimensional space shall not be taken as primitive terms but will be constructed.

Axioms on points, lines, and distance. The axioms on the points and on the lines are:

E_{1}. *There exist at least two points in S.*

E_{2}. *A line contains at least two points.*

E_{3}. *Through two distinct points there is one and only one line.*

E_{4}. *There exist points not all on the same line.*

A set of points is said to be *collinear* if this set is a subset of a line. Two sets are *collinear* if the union of these sets is collinear. The axioms on distance are:

D_{1}. *If A and B are points, then d(AB) is a nonnegative real number.
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D_{2}. *For points A and B, d(AB) = 0 if and only if A = B.*

D_{3}. *If A and B are points, then d(AB) = d(BA).*