Euclidean Distance Viewed Through Systemic Functional Linguistics

Penrose (2004: 384):

In Euclidean geometry, whether 1-dimensional or 3-dimensional, there is a notion of distance. In the 3-dimensional spatial case, this is to be ordinary Euclidean distance (measured in metres, or feet, say); in the 1-dimensional case, this distance is the ordinary time interval (measured, say, in seconds).

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From the perspective of Systemic Functional Linguistic Theory, distance is the extent, the interval, between locations in space or time. Because time is the dimension of the unfolding of processes, time is measured by the interval between locations in the unfolding of a (relatively) constant cyclical process, such as the ticking of a clock, the rotation of the Earth on its axis, or the revolution of the Earth around the Sun. It is important to distinguish the dimension, time, from the process which provides the unit (interval) of measurement, the ticking of a clock.