That’s really an interesting question, yeah.
What do you think?
Well, relativity tries to claim them to be the exact same thing, conflating ontology. From my perspective, there is no existence without affect and thus change. And there can be no affect without distinction and thus distance. But then distance is merely determined by the immediacy of affect.
So I guess that I have to stick with the idea that none can exist without the others and thus none “came first” or “caused” the others.
Did you mean four spatial dimensions? or the “space-time” dimensions?
Either way dimensions are merely mental reference constructs with no physical existence of their own.
It was your wording. So what did you mean by „four dimensional space“?
Oh, that.
No, there are not 4 spatial dimensions in physical reality. In mathematics, you can have any number arbitrarily.
And when I wrote about Riemann’s continuum I meant the spcae-and-time-continuum, thus [i]three dimensions /i and one dimension (time) in one continuum.
To which I responded. So now I don’t really know what you are asking, if anything…? RM:AO uses 3 spatial dimensions and time as either a single or a 3 dimensional concern. Relative time is treated just as any other relative/subjective measurement.
What do you exactly mean by “time as either a single or a 3 dimensional concern”?
Time is the measure of change. In today’s physics, time is given a single dimension with which to measure all change. But note that space is given 3 dimensions in which those changes can occur. The reality is that affects can change at different paces in different directions during the same span of time. As one affect is propagating from right to left, another might be propagating from top to bottom and another forward to back. The speed of their propagation might be different and thus produce a different change-rate in each direction, a different measure of change, “time”, for each direction.
This issue is one of precise accuracy. Three dimensional time provides greater accuracy than 4D relativity, but is very seldom required.
So according to RM:AO you have either a three-dimensional-time or a one-dimensional-time.
Yes, just like you can use spherical coordinates or Cartesian coordinates. It doesn’t change the reality of the situation, merely the manner in which it is being recorded or measured. And you can switch back and forth as long as you don’t get them conflated.
One can switch back and forth between the one- and the three-dimensional-time?
Time is the measure of relative changing.
With respect your changing another person is;
1) changing in the Y direction twice as fast
2) changing in the X direction equally (one)
3) changing in the Z direction not at all
Thus the average changing is equal to your own (zero single dimension time dilation) and thus a single dimension of time would be recorded as showing no difference from you. Using a single dimension for time is a little more primitive.
But in reality, the subject would be altering in a way that would contort its configuration differently than you and the reason for it would be hidden. Using a single dimension for time hides changing variables and promotes mysticism and fantasy physics. It keeps science a little more confused (not that Quantum Phantasy Physics and Relativity were not enough).
Do you geometrically mean this?:
That could be one example. The inner box has X axis motion, but not Z or Y. And even though the whole is not moving relative to the bottom object, the inner box would also have time dilation, perplexing special relativity if they could not see the inner movement.
Space is given 3 dimensions for location.
Motion is given 3 dimensions for direction.
Time can also be given 3 dimensions for vector of relative changing.
This comes into play when trying to justify special relativity with general relativity, motion dilation vs gravitational dilation. Motion time dilation is concerned with one vector of motion and thus only one dimension of relative changing. Gravitation or more properly mass field density (affectance density) affects in all 3 dimensions simultaneously.
Does moving really be a part of geometry?
Could you rephrase that question? 
Translation… Contradiction. If gravity effects all 3 fields than it is a fourth field.
Yes.
The figure in that picture moves, but geometric figures are actually immobile. So, it is a question of definition, of definional logic. If you want to describe a geometrical figure, then you actually do only consider that that figure is static, thus that that figure is immobile.
In this thread we are mainly talking about the philsophical meaning of physics and about physics itself; so moving bodies are one of the main physical premises; but moving bodies are not the main geometrical premises (this does not mean that it is impossible to have also moving bodies as a premise in geometry); so we have to be careful and should not combine physics and mathematics too much. Combining physics and mathematics too much has been being a problem of the physicists for so long - since the 20th century, especially since the second half of the 20th century. Another example is the problem of combining economics and mathematics too much, and this problem has been existing since the second half of the 20th century (we can talk about it in another thread). I do not say that we should not do it, but we should be careful with that. I argue not against the mathematics but against the domination of the megalomania in physicis, economics, and some other scientific disciplines.