The word dimension has two primary uses in the sciences. The first is geometrical. It assigns some position as a starting point. And then measures the relative position of other objects relative to that starting point.
It measures the relative positions of something relative to that starting point by measuring in three directions: up/down, left/right or back/forward. The details are not all that important. What is essential is that the measurement is performed by a combination of measurements in three different directions. Each of these directions is a separate dimension.
What does this measure? The position of that object relative to the starting point. The concept of dimension is a mathematical abstraction. It uses quantities to represent that relative position.
(That is three-dimensions. You can, of course, perform similar measurements in two dimensions if you wish to ignore the separation between objects in the direction that corresponds to “depth”).
[Editorial: Or, of course, one dimension, if you want to consider things alone a single line.]
Dimension is therefore simply a mathematical abstraction which allows relative positions to be numerically quantified. It is also used for various other geometric purposes. In any case, dimension is a mathematical abstraction used for the purpose of measurement.
The second use of the word dimension is far more mathematically abstract and we will not go into it here. Suffice to say that it too is a mathematical abstraction and does not justify considering space a combination of dimensions.
We may use the concept of dimensions to perform measurements on space but the concept of space is a more fundamental concept than that of “dimension”.
This explanation of “what is space?” is part of one our subscription articles, link provided in the transcript. Check it out for a further explanation of space, time and dimensions.
So, does space have any qualities?
Yes. One can measure the volume or area of space and quantify the extent of that space. One can assign it a finite area or volume.
“Moreover, though separate stretches of what can be termed “space” are measurable (such as the distance between Entity A and Entity B), linear measurements in three dimensions cannot be attributed to the totality of space. As an example, it would be absurd to propose that the entirety of space is twelve billion kilometres long, three billion kilometres wide, and sixteen billion kilometres high”
Here the author is talking about all the relationships we call space considered as a totality. That is, all of “outer space” and all the “space” on Earth.
It is true that this totality of smaller spaces has no measurable qualities. There is no way to quantify the extent of this. This indeed has no qualities. It is simply a totality of all the space between all the things in the universe. There is no way to assign it quantifiable qualities, therefore it has no measurable qualities.
But there isn’t much value in considering space in that sense. There isn’t any value in lumping all these spaces into a larger collection and calling this “space”. The only sense in which the concept “space” has any potentially significant value, is when you consider a given region of space as delimited in some way. And not as some collection of all these spaces.
But even then, the concept of space is not all that important to either philosophy or physics.
But how is that? Does physics not speak of the curvature of space?
It does, but this is not an idea with any merit. Space is an abstraction; it deals with relative positions. And as an abstract relationship, it can no more curve than my relationship with my husband. [Editorial: paraphrasing David Harriman.]
Things curve, but abstractions do not. Trying to explain gravity by the curvature of an abstraction explains nothing. It simply reifies an abstraction. It is a failure to do physics.
The author discusses empty space and correctly dismisses it as invalid for the same reasons we have already discussed. To quote him:
“There is nothing more to be discovered about nothing!”.
We certainly agree with this!
Essay XII: Space as Relationship
“The term ‘space-as-relationship’ is synonymous with ‘distance’ and ‘separation’. In order to have any meaning, it cannot be a metaphysical primary. Rather, it must involve two or more distinct entities, or a single entity capable of motion and having its current position compared with respect to some earlier or later position.”
We have already discussed in what way space is a relationship which describes the distance or separation between entities.
“Thus, the degree to which the boundary of one entity can be separated from that of another can differ in magnitude. This variable separation is the reason for man’s need to use the term “space-as-relationship”
The variable separation is what makes the concept of space useful. And what makes quite a lot of geometry useful. Quite a lot of geometry is applicable to measuring the volume or area of space. And being able to measure the volume or area of space is very useful in many areas of life. This is why space is a very useful concept in general.
But, still, space is not all that useful in physics, which is about the fundamental nature of the universe and not about solving practical problems such as finding out how much land you have so you can find out how many cows to put on it.