I Multiple dimensions of time are easier to see if we look at transportation. Consider the time table of a railway or subway system. Directions are typically shown by the station at the end of each line. The time table lists arrivals and departures – events in space and time. A railway station some distance […]
I’ve written about terminology and used new terms before, for example, Movement and dimensions. I want to take another look at coining new terms needed for studying movement and the symmetry of space and time. In what follows, the terms pace, lenticity and relentation have new senses. Consider these parallel terms, defined with respect to
There are three main arguments for duration to have three dimensions: (1) The speed of light is a conversion factor between length space (distance) and duration (distime). Transportation conversion factors include the maximum, minimum, or typical speeds associated with different travel modes. Since length space is three dimensional, its conversion into duration space is also
If there exists a constant, characteristic speed, then one may speak of the characteristic conversion of space and time. For example, the speed of light in a vacuum is a defined constant in the SI system of units. So in physical science and its applications one may speak of the characteristic conversion of space into
A circle or sphere are omnidirectional in two or three dimensions, respectively. This is equivalent to isotropy, uniformity in all directions. A straight line is unidirectional but multiple straight lines may require multiple dimensions. This is equivalent to rectilinear homogeneity. Pure space or average space is homogeneous and isotropic. Then space may be modeled by
There are many examples of two-dimensional time maps in transportation, although the authors do not acknowledge the multiple dimensions of time in their maps. Let’s start with a map of New York travel times on commuter rail which shows the travel time in minutes from Manhattan to commuter rail stations during the evening rush period.
It is not unusual to seek the route in space that minimizes travel time, for example, a drive from point A to point B may go out of the way to include a high-speed facility that reduces travel time even if it increases distance traveled. But what about routes in time? Does it ever make
Travel, that is, the movement of something, includes transporting and signalling. To transport means to take something (e.g., people or goods) from one place to another by means of a vehicle or the like (e.g., a car). To signal means to transmit information or instructions from one place to another through a medium or the
Consider again the now-classic scenario in which observer K is at rest and observer K′ is moving in the positive direction of the x axis with constant velocity, v. This time there is a characteristic constant speed, c. The basic problem is that if they both observe a point event E, how should one convert
Consider the now-classic scenario in which observer K is at rest and observer K′ is moving in the positive direction of the x axis with constant velocity v. The basic problem is that if they both observe a point event E, how should one convert the coordinates of E from one reference frame to the
