There is a long history of conundrums that the concept of space generates and magicians very skillfully use the illusions of space to effectively fool us about objects. Infinitely divisible and filled with nothing, the characteristics of space are a recipe for illusion and paradoxes even though empty space is what we discover most of the universe to be. We never seem to doubt the existence of the singular nothing that is an empty void space, which is an absence of sensation, even though we might doubt the existence of an object that we actually do sense. Space, after all, is everywhere the same nothing and has an intuitive and innate feeling of nothing about it in spite of our natural anxiety about the void of empty space.
Likewise there are many empty moments of continuous time that we call inaction between the occasional actions of our lives, but we keep the action of continuous time connected between moments that we sense of objects. That is, we do not imagine a timeless eternity of inaction between the actions of our lives.
We often define things by stating what they are like, and continuous space is very much like continuous time. In other words, time and space are in some sense just different representations of the same metric of action. We can only define an axiom in terms of other axioms and so if both space and time are like each other, space and time are just different versions of the same axiom of time delay.
Discrete matter and time delay predict object action in time and the prediction of a Cartesian location or motion or force field results in continuous space and motion emerging from discrete matter, time, and action. In order to understand reality, we must first understand the axioms that define that reality and although the dark void of empty space is a very intuitive and innate concept, we only know if it is an axiom by describing what space is like. It would appear that instead of space being uniquely axiomatic, space and motion both emerge from the actions of objects in time. Space and motion allow us to keep track of separate Cartesian objects with our minds. While space and motion helps us keep track of objects and predict action, space does not exist independent of or orthogonal to discrete time delay.
There is the obvious something that separates objects from each other and therefore objects seem to need the continuum of empty space to move around just like objects need continuous time to prevent everything from happening at once. Given the axiom of action, which is the product of matter and time, where once again action as an axiom is defined by the product of two other axioms, time and matter. We can also define action as the product of matter and displacement, which further suggests that time and space are simply complementary metrics for action.
Since they are complementary, we define space just like we define time; with an action like a footstep or a meter and an accumulation of those moments as action. Although we think of distance in space as a length, the metric of that length is also a part of distance. A separation, then, has both an integration of matter as action and the moment of that action, such as a footstep or a meter.
The discrete time delays that we sense from objects imply that there is a continuous time space and since we move both forward and backward in space, we should also move forward and backward in time. In fact, we only predict objects into a future space based on our memory of them in the space of our past. We have a fading memory or knowledge of the past locations and motions of objects that permits us to predict their futures and so memory is an accumulation of past actions as experience. While we sense past locations and motions for objects, those sensations are simply a memory while the projections of objects' locations and motions in the future are only about the possibilities for our future and not necessarily about which future will occur.
Continuous space and time emerge from action as discrete time delays of objects and it is possible to project continuous time from motion in space and vice versa. The way that objects move is by changing their inertial mass over time and that change in inertial mass tells us about their motion and the way the the universe matter changes around an object tells us about an objects relations with other objects. The electromagnetic or gravitational fields that affect an object are equivalent to changes in decay or shrinkage of the universe and it is the shrinking universe that is the source of all force and motion.