1. It seems silly to me to talk about the space occupied by our bodies as a different category of space than space in general. Other than to indulge a numeology-ish fixation on dividing things into threes, what is the point?

2. The following seems naive:

Furthermore there is yet a another, a third form of space. The space nothing can occupy. The void. The vacuum. If it is occupied it is not a vacuum. It is the true absence of anything material or substantial. — Benj96

See https://en.m.wikipedia.org/wiki/Quantum_vacuum_state.

What evidence is there, that a space as described by you in that quote, exists outside of your imagination?

What evidence is there, that a space as described by you in that quote, exists outside of your imagination — wonderer1

The definition of a vacuum. And the definition of spacetime. And the definition of object permanence and it's implications.

Sure we can talk about space as a singular thing.
But matter has dimensions yes? Width height and length.
And space between matter also has dimensions yes? Distance between objects.

The dimensions of matter are instrinsic to them. The distance between material is extrinsic to it. We wouldn't say what's the distance of an apple. We would say what are it's dimensions.
If there was no need to make distinctions why bother with different vernacular to describe them?

There is space between things. And the space of things. I don't believe that is my imagination at work.

What evidence is there, that a space as described by you in that quote, exists outside of your imagination
— wonderer1

The definition of a vacuum. And the definition of spacetime. And the definition of object permanence and it's implications. — Benj96

Your definition for vacuum is not evidence that there is anything matching that definition.

The dimensions of matter are instrinsic to them. The distance between material is extrinsic to it. We wouldn't say what's the distance of an apple. We would say what are it's dimensions.
If there was no need to make distinctions why bother with different vernacular to describe them? — Benj96

When we are discussing the dimensions of an apple or the distance of an apple from my hand, we are talking about distances in both cases. In the first case, the distance from one side of an apple to the other side of the apple. In the second case, from my hand to the apple.

It looks to me like you are trying to carve nature where there are no joints.

I agree that nature is one unanimous seamless and connected whole. Nothing in pure isolation. And that by us defining things, restricting them to discrete parameters and characteristics we invariably exclude the spectral transient and ultimately flux nature of well, nature.

But breaking down and compartmentalising nature into neat and discrete definitions that are different to one another, we are offered more specificity, insight and knowledge on varying levels of scope.

What I was saying is that the dimensions of our body (a defined space) move through the dimensions of space (the environment). One set of dimensions stays put, the other is in motion within it. So there is some interplay/interaction between these two concepts of dimension and space: in how they interact and relate to one another.

You can't leave your body. So you're stuck in a certain set of spatial dimensions relative to the larger set of spatial dimensions (reality) that we are in motion through. The body is the permanent space of the self and mind. Motion is a temporary space we can and do chnahw through from moment to moment.

Both are space, I agree. But they are regarded differently.

Mathematicians have abstracted the notion of "spaces", introducing "points" in such spaces that can be functions for example. Then there is a question of metrics - how to define and measure "distances". And it's true that various spaces have subspaces - like your walking, talking kind. Objects composed of these kinds of points can be relocated as isomorphisms, etc. One can take a disc in the complex plane and relocate it in the plane, preserving its character. So these subspaces are roughly like what you are describing. Unbeknownst, you are venturing into abstract mathematics.

What evidence is there, that a space as described by you in that quote, exists outside of your imagination? — wonderer1

Good question! All of the examples gave in the OP are not real things, but ideal metaphors of a substance necessary to prevent particular atoms from merging into one big block of matter. Each metaphor is referring back to the intuitive notion of "physical space", postulated by Democritus : that the real world can be boiled-down to rigid material Atoms and fluid metaphysical Void.

"Space" is the water-like void-filling perfect emptiness & ideal nothingness existing as an imaginary fluid substance, which is logically necessary to fill the "space" between atoms : ooops!. That unreal nothingness notion is fundamental to the philosophy of Materialism to this day. Yet ironically, one of the two fundamental essences of Materialism was & is a metaphysical conjecture. Space is by definition, Immaterial. That may be why other early philosophers denied the existence of nothingness, as represented by the symbol "Zero"*1.

Einstein put a damper on the ancient notion of nothingness by combining the human definition of linear physical extension --- as a means to measure a hypothetical box to contain matter --- with the measurement of cyclic change by combining both into a third empty container for stuff, that he called "space-time". He then added insult to injury by postulating another imaginary container in the form of an unchanging four-dimensional box : Block Time. Yet, in his metaphors, he often resorted to physical notions, such as "warped space". No wonder Benj commented that "space is a strange concept ". :smile:


*1. Zero: The Biography of a Dangerous Idea
https://www.amazon.com/Zero-Biography-Dangerous-Charles-Seife-ebook/dp/B000QUEHLM/ref=sr_1_2?crid=2VZN0THCBZ7NV&keywords=zero&qid=1686607308&s=books&sprefix=zero%2Cstripbooks%2C107&sr=1-2

It looks to me like you are trying to carve nature where there are no joints. — wonderer1

The boundary between an organism and its environment is surely salient though, and an organism works hard to preserve that boundary.

A house, by comparison, does not work to ensure its inside remains separated from its outside.

Not quite. There is also a form of space no one else can entirely occupy. That is the space we carry with us our entire life. Intractable and inescapable. The space of the self. Wherever one goes, there their body is. The space ones body always occupies by virtue of being material, physical, substantial. — Benj96

You stand here and I'll stand there. Now our bodies are occupying the opposite "form of space" we each were in a moment ago. However, we must exclude the fact that the Earth has moved and so have the spaces we each occupied a moment ago. So we haven't really swapped the same spaces we each occupied a moment ago.

Furthermore there is yet a another, a third form of space. The space nothing can occupy. The void. The vacuum. If it is occupied it is not a vacuum. It is the true absence of anything material or substantial. — Benj96

What space is it not possible for anything to occupy? And why is it impossible for anything to occupy it? Perhaps a black hole? But a black hole - just like any other object - moves through space too, thus freeing up that space for other objects to occupy.

Do you mean at a given moment in time?

Generally speaking 'space' is used in two senses; geometric space and ontological space. In physics there are two geometric spaces, the quantum spacetime of energy and the ordinary spacetime of material objects. Since these two geometries are different the universe consists of two spacetimes, two universes. Particles live in quantum spacetime and large objects live in physical spacetime. This is why location is so ambiguous in physics; where is a particle? It is nowhere if by 'where' we mean a location in 4D spacetime. It is elsewhere, in quantum spacetime.
In an ontological sense both spacetimes are 'here' in ontological space but being distinct geometries they are distinct universes.
The geometry of a space is determined by the objects that inhabit that space. Two different geometries can exist in the same ontological space.

In an ontological sense both spacetimes are 'here' in ontological space but being distinct geometries they are distinct universes. — EnPassant

Well, they certainly have a variety of metrics which supposedly reduce to one another as scales change. I wasn't even aware there were quantum spacetimes. Thanks.

When we ask 'where' a particle is we must specify which spacetime we are talking about, quantum or physical spacetime. Since particles don't exist in physical spacetime and we can't map quantum spacetime, we don't know where the particle is.
We can only detect trace effects* that the particle leaves on physical spacetime.
This is why Bohr said it is meaningless to ask where a particle was prior to detection because it has no location in 4D spacetime. 'Detection' is when a particle leaves a trace effect in physical spacetime.

*eg a spot on a photographic plate.

Two different geometries can exist in the same ontological space. — EnPassant

But not at the same time and in the same respect. Physical universes are purely formal mathematical entities. Change the math and you change the world.

Ontological universes can similarly be many if we allow our implicit ontological presumptions not to be necessary. For example, psychological and social universes are also possible and can be shown to be more real than any philosophical ontological universe.

Space refers to the 3-dimensional geometric structure of measurable volume, regardless of whether it contains matter as such. I take up space (volume), I move through space and I leave space to be filled as I do so, but I don’t find it necessary to isolate these three ‘forms’ as if they have no axiomatic relation to each other, only separate relations to my perceptive self (I).

When I was pregnant, the volume within my ‘body’ taken up by a child was always their body. My body incorporated space for theirs to grow, but there’s a difference here between ‘body’ and ‘space’ that seems to be missing. Body refers to a perceived object within this 3D relational structure we call space.

Likewise with sex - my partner does not share occupancy. We do not take up the same space - rather, my body makes space for theirs.

Spacetime refers to the 4-dimensional geometric structure of perceivable change. To call this a geometric ‘space’ is a misnomer, and to refer to quantum and material ‘spacetimes’ as distinct ‘spaces’ just goes to show how much we rely on concretising concepts to describe our understanding of reality. Spacetime refers to a geometric structure, and ‘space’ refers to a limited aspect of that. Quantum spacetime is not ‘elsewhere’ - like ordinary spacetime, it’s merely imperceptible to us within a single observation event - in the same way that the earth’s rotation is unobservable from one physical location.

As I understand it, Einstein’s ‘block time’ refers to the four-dimensional structure of a single temporal aspect within the 5-dimensional ‘block universe’ - which is a geometric structure of meaningful potentiality. This, too, is not a ‘space’ in the sense of taking up volume ‘elsewhere’. It’s the same space, perceived differently. Space exists within spacetime, which exists within potentiality - not as entities, but as geometric relational structures.

So the space of the self, and general space are superimposed but are not equal. And that shows how truly complex the dimensions, definitions and meanings of space are. And how they relate to the things that occupy them, or don't. — Benj96

What you refer to as ‘the space of the self’ is constructed similar to ‘block time’: meaningful potentiality within a single temporal aspect. It’s a spatial perception of self as defined in one moment, relatively inaccurate in the next. Space is the geometric relational structure within which this ‘space of the self’ is mapped according to affected perception/potentiality, rather than observation.

Physical space is an emergent property of matter. It is a physical object just like a table or a chair. Physical spacetime has an extra dimension, time. If the physical matter in the universe evaporates back to pure energy, physical spacetime disappears and we are left with the spacetime of energy. We would no longer have a 4D space. We would have something more exotic. Scientists speculate that quantum spacetime has 11 dimensions.

Physical space is an emergent property of matter. It is a physical object just like a table or a chair. Physical spacetime has an extra dimension, time. If the physical matter in the universe evaporates back to pure energy, physical spacetime disappears and we are left with the spacetime of energy. We would no longer have a 4D space. We would have something more exotic. Scientists speculate that quantum spacetime has 11 dimensions. — EnPassant

Sure. Physical space is a ‘material object’ like a table or a chair in that it is measurable in three dimensions - but only in relation to other material objects. Physical spacetime is an ‘energy event’ in that it is calculable/perceivable in four dimensions, but only in relation to other energy events. This doesn’t preclude my suggestion that space refers to the geometric structure of three dimensions. The question may be whether time is a physical dimension, or whether the notion of physicality is dependent on consciousness as an ‘observer event’ in a system of ongoing relation with ‘matter’…

Scientists’ speculation of up to 11 dimensions is quantifiable, sure, but that doesn’t render it more likely - just more mathematical, thus attracting more time, effort and attention from theoretical physicists. Yet it relies on no physicality. That’s a big ‘IF’.

A six-dimensional structure of reality has symmetry: three dimensions of ‘matter’, and three of ‘energy’. It doesn’t rely on any hypothetical absence of physicality, but rather recognises the perceived duality of matter/energy, with consciousness as a two-way conversion system.

It seems to me that (ontological) space has the potential for any number of dimensions. Physical matter can manifest 4 dimensions. I suspect that dimensions are an emergent property of matter. 4 dimensions is the limit that matter can manifest. If matter evaporates back into energy the 4 dimensional spacetime would evaporate and we would be in a quantum universe of X dimensions.

See my last answer.