What Does ``time'' Mean?

 

This question may seem a little bit curious to some people, especially to scientists studying physical dynamic phenomena. Such problems carry in general an inherent time, just the physical time of nature. Also a video animator usually has this notion of time in his mind when designing a video. This is manifested for example in the unique time slider in many software animation packages.

In these example the term time is always used as the physical time, or at most to some extent modified, which nature gives us. We extend this characterization of time and define: time is an arbitrary but emphasized parameter of the object we study.

As the first consequence of the extended meaning of time let us assume our object depends on a set of parameters. We can emphasize one of those and consider the object as a dynamic process depending on this parameter, now called the time-parameter. During interaction we may choose a different parameter or the other parameters may for instance also depend on the time-parameter.

A second characteristic of our time-parameter is locality. In the extreme for example, every object belonging to a hierarchy may have an own time-parameter. This may seem unnecessary when creating a video which relies on a global time. But when analyzing dynamic processes it is important to see for example the same process running at different speeds or times simultaneously, or fix the time of one of the processes while keeping the others running.

Our definition of a time parameter extends the term time from the physical time to include any real parameters. This arbitrariness for instance allows in multi-parameter systems changing between parameters to analyze different aspects of the problem with the same tools. Surely, the new freedom in the definition of time shall not make things more complicated and possibly only introduce a new parameter. When studying flow problems one would still choose the physical time as time. But even here one might want to see two copies of the flow evolving simultaneously with different times, i.e. speeds.

Summarizing, we use time as follows:

• time is a word for an arbitrary emphasized parameter of a parameter-dependent object
• time is a parameter belonging locally to an animated object.