iSoul In the beginning is reality

Time and linear motion

This post follows the previous one on circular motion.

A timeline shows a linear representation of time (click to enlarge):

A calendar can be linear, too:

Linear calendars and clocks could be thought of as representing a kind of distance. It’s as if a clock were fastened to a wheel moving along a line. The result could be a digital clock that’s like an odometer of a vehicle moving at constant speed.


Let such a linear clock be the reference motion for a body in linear motion. The rate of motion would be the ratio of the distance covered by the body and the distance covered by the linear clock, which would be a dimensionless ratio.

The result of using a linear clock is similar to multiplying by the speed of light to convert elapsed time into a distance: ct. But a linear clock provides measurements whereas dimensional conversion is an abstraction that depends on instantaneous quantities.

What does this say about defining space and time? It could be that time means whatever is used for the reference motion, whether that is in units of distance or duration. Or it could be that time is duration, whether that is duration of the reference motion or the target motion. There are two kinds of time, reference time, which flows on indefinitely, and duration time, which depends on a particular motion.

The duration concept of time could be called durachrony (from dura(tion), Latin durare, harden + chrony, Latinized Greek khronos, time). The continuous flow concept of time could be called hydrochrony (from Greek hydro, fluid + Latinized Greek khronos, time). Note that the former term is about hard, solid time and the latter term is about soft, fluid time.

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