Explorations of multidimensional space and time with linear and angular motion.
Time in the Bible is duration, not what is called thermodynamic time or the arrow of time. There is no inevitability about time in the Bible, unlike the increasing entropy of thermodynamic time. In the Bible time has a beginning and an ending. Time is an era, an age, a period of time. It is […]
I have written several times about differences between ancient and modern ways of thinking, for example, this post on Biblical geocentrism. Another way to look at this is whether time or space are primary. What does this mean? We are most familiar with the primacy of space. Things exist within space as mere objects, and
Space and time are complementary aspects of movement. Although space has been associated with stasis and time with change, they both entail movement. Space is the distance side of movement and time is the duration side. There are two ways of looking at movement: one is from the perspective on or within the moving object
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
Is a light-year a unit of length or of time? It’s a unit of length but it depends on a unit of time, the year. What about a meter? “The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second.” So the
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.
In a previous post on Different directions for different vectors I gave this example, for which I’m switching North and East: Suppose someone drives 30 miles North in 50 minutes, then turns East and drives 40 miles in 50 minutes. Overall, they have driven 70 miles in 100 minutes but as the crow flies they
The symmetry of space and time is based on the existence of a constant of proportionality that converts space into time and time into space. This number is a fixed speed for travel under free-flow conditions for the mode of travel. Such a constant makes it arbitrary whether one answers “how long” with a length
The post Lorentz for space and time derived the standard (spatial) Lorentz transformation and also the temporal Lorentz transformation. It is surprising in this age of relativity how the standard Lorentz transformation is dependent on absolute time. While time is relativized in the sense of Lorentz and Einstein, it remains absolute in the sense of
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
