Space and infinity are some of my favorite ideas, and they seem to naturally go together when we consider the universe. If there were a limit to the universe we could go to the edge and point, asking "how far is that way?" It seems most natural to me to think of space as infinite. And actually it seems to be infinite in opposite infinite ways. There is no end to how small something can shrink. And if I hop towards a limit, there are always infinite sub-steps. So infinity as space seems to be the ground of everything and "what is finite itself" adds form to the chaos. In the end, the world will always seem paradoxical because it has a paradoxically at it's root. What I'd like to know is whether space existing in all possible place is just the mirror image of space being infinitely divisible — Gregory

You seem to think that space is something that is there in the world which one can observe and talk about its properties, as a scientist might talk about star content or plate tectonics. But space has no observable properties, so when you make a move to "divisibility" it is not space, but an abstraction of space you are bringing up, a logically structured method of measurement formally called geometry. Its not space that is divisible at all, and the references to such divisions are really about the mind that adds the, as you say, form to chaos. But then, space isn't chaos either: this would take something observable, that can be out of order in the first place.
No, if you want to get at the heart of space philosophically, you have look to the language that is presupposed in an utterance: before one can even conceive of space in any way at all, there has to be a matrix of language, through which concepts can have any meaning at all. This is not Einstein's space, but what is there prior to Einstein, prior to even the mention of space as a theme of inquiry. Ask: can there be space without the logic to conceive it? Well, the ontology of space is only meaningful if one can posit space securely, and such a positing is essentially a logically structured event, a proposition. No matter how rigorous science gets, it is essentially propositional and therefore presupposes language.
So understanding language is the first order business in the understanding space at the level of basic questions (philosophy).
Or did you think when we observe the world, the world somehow simply intimated itself in the observation, and space presented itself to the brain as if wwe perceiving agencies were some kind of mirror? Look at a physical brain. Does this LOOK like a mirror?
The true beauty of this lies in the radical disillusionment of understanding that we, ourselves, and this world are entirely something Other than what is, well, "out there". And space is, as with all things, pure metaphysics, if there is such a thing (I think there is), at root.

:cool:

It seems most natural to me to think of space as infinite. And actually it seems to be infinite in opposite infinite ways. There is no end to how small something can shrink. And if I hop towards a limit, there are always infinite sub-steps. — Gregory

What you're describing here is a continuum, so I guess that's also your answer.

My take: space is personal. Not just relativistic (fixed by reference frame), but rather each thing that exists has its own personal space. Interactions and correlations are couplings between these spaces that allow us to map one space onto another, approximately at least. These mappings enable a statistical projection of all these things going on in all these spaces onto a single hypothetical space constructed by the mind (or computer). So more like an infinite net, I suppose.

Space is, according to physicists (vide Wikipedia), undefinable; the reason given is that there's nothing more fundamental that can then participate in the definiens.

That space (and time) are metaphysical subjects is common knowledge. What I find interesting though is how space and time feature in everyday, ordinary conversation. The word "game" and the word "space" have Wittgenstein in common, roughly.

Lexicologists have a different opinion no doubt.

My take: space is personal. Not just relativistic (fixed by reference frame), but rather each thing that exists has its own personal space. Interactions and correlations are couplings between these spaces that allow us to map one space onto another, approximately at least. These mappings enable a statistical projection of all these things going on in all these spaces onto a single hypothetical space constructed by the mind (or computer). So more like an infinite net, I suppose. — Kenosha Kid

That's good. Each "thing" has space proper to it. Now how would you relate this to the concepts of chemistry and physics, within which, things move relative to each other? We cannot use an artificial coordinate system representing one "space", because this would be a false representation. Now each thing has its own space, within which it moves and changes, and that space needs to be related to the various "spaces" of every other thing. So we are left with a very complex problem. We need to determine the way that each type of thing moves within its own space, and also we need principles to relate the space of one thing to the space of another thing.

Let's take an object like a chair, or a rock for an example of a "thing". We can say that it has "a space" proper to it. We might define the boundaries of that space with reference to gravity. Now, lets proceed to a molecule, as a "thing" which conventionally is a part of that thing, identified by the example as a chair. The molecule has its own "space" defined by its gravity, and obviously the distinct "spaces" of the molecule and the chair overlap in terms of occupying the same place. What means would you propose for distinguishing the space of the molecule from the space of the chair?

I proposed that the boundaries of a thing's space be determined by a thing's gravity, but what kind of space would be proper to a thing which has no mass? This sort of problem would reveal two distinct types of space, the type of space proper to a massive object, and the type of space proper to something which has no mass. Since the space which is proper to things which have no mass seems to permeate all the spaces of massive things, maybe an understanding of this space could be used to relate all the other spaces of the massive objects to one another. In the case of massive objects, gravity is the defining feature of the space. What features should we look for to define the space of massless objects?

Now how would you relate this to the concepts of chemistry and physics, within which, things move relative to each other? We cannot use an artificial coordinate system representing one "space", because this would be a false representation. Now each thing has its own space, within which it moves and changes, and that space needs to be related to the various "spaces" of every other thing. So we are left with a very complex problem. — Metaphysician Undercover

What you're describing is quantum chemistry :)

Not really, because quantum chemistry is energy based, while my description is mass based. This is a big difference because a molecule is understood to have distinct massive parts, therefore distinct "spaces" by my description. Even an atom is understood to have distinct massive parts. From the energy perspective, the interaction of electrons occurs in one space, rather than a number of different spaces according to distinct massive centers representing distinct spaces.

Particles have distinct spaces in many-body quantum mechanics, and QC approximations like Hartree-Fock.

Although I don't know the history of the word, it seems to me that, before relativity, space was just an expression of common sense and classical non-relativistic physics. Without space there can be no distance. Without distance there can be no velocity. Without velocity there can be no acceleration. Without acceleration there can be no force.

Without distance there can be no volume. Without volume there can be no structure, no chemistry, no form. Can there be mass without volume? Does that mean that without space all there would be is a black hole with the mass of the entire universe.

Space and infinity are some of my favorite ideas, — Gregory

"Space" and "Infinity" are not physical things that can be stretched or compressed or divided. Instead, both are ideas about things (i.e. their relationship). Astronomers are using a metaphor when they talk about the "expansion" of space, or when Einstein presented the notion of "Block Space-Time". For example, in imagination, you can take a knife and carve a chunk of Space into a million pieces, and they will all be the same size as the chunk : infinite or zero. That's because Ideas are Meta-Physical, not Physical ; Ideal not Real ; Relative not Absolute. :smile: