And likewise, in the real world (whatever that is) a host of physicists, mathematicians, cosmologists, geometers and other horse-thieves are firmly of the belief that space has shape. They say it can be flat, curved, even foamy!
They may be right, but I just can't get my head around curved space: I can't visualise it. What happens to the matter, the material, the stuff that's occupying that curved space? Does the stuff get curved too? They say that gravity warps space: I can't visualise that either.
But what if matter IS space, and space IS matter? If matter (stuff) and space are the same thing, then we don't have to think about how stuff "fits" into space. And we don't have to think about the shape of the space occupied by the stuff.
There is no space to be occupied. There is no homeless stuff looking to occupy space. There is no occupying going on at all. Because the Stuff is the Space and the Space is the Stuff: curved, flattened, saddle-shaped or hyperbolic.
There is no matter. There is no space. There is no stuff. There is only matterspace, spacematter, stuffspace or spacestuff: It curves. It's flat. It occupies itself, fully and always.
WE ourselves made up the words "space" and "matter" in the first place(?!). WE invented those words so that we can use them to label aspects of Reality corresponding to "spaciness" and "stuffiness".
And when we invented the words, we also created the difference between the things to which the words point.
The difference between space and stuff is artificial, artefactual even, and ought to be treated as such.
The drawing, "Circle Limit IV: Heaven and Hell" (above) by Dutch artist M. C. Escher is said to illustrate the geometry of a certain type of space, called anti-deSitter space after the Dutch mathematician Willem deSitter.
In the drawing, according to the publication Fermilab, "...the curvature of space changes, as one moves outside the circle along its radius. Thus angels and demons, which all would have the same size in Euclidian space, become smaller and smaller in anti-deSitter space."*
Well, Fermilab is entitled to their interpretation. To me the drawing illustrates how space and stuff are really one and the same thing; that devils are no more and no less than the dark space of angels, and angels are no more and no less than the lighter side of devils. And I'm entitled to my interpretation too. And that's the problem.
Words, by their nature, have no absolute meaning but are open to interpretation and elaboration.
No word can stand in fully for the thing it labels. The word is always a sign to the thing, not the thing itself.
No map can ever be identical to the territory it maps. The map is always at a lower resolution, is less detailed, than the territory.
No scientific model or framework can ever be identical to the aspect of reality it models. The model is always at a lower resolution, is less detailed, than reality. If the model fails to correspond accurately to reality, don't blame reality: the inadequacies and deficiencies are with the model and the model-maker.
Well, we've come to the point where your patience has run out and you demand to know just how stuff can be space and space stuff. Presented below (non-MECE**) are a couple of possible explanations, some quite technical.
The problem is that the explanations are expressed in words, and words encourage unproductive argument about meaning, context and category.
To use language is to create and manipulate concepts. And the problem with concepts is they encourage elaboration. And the problem with elaboration is that it leads to more and more elaboration, until we lost sight of the original concept and its implications.
Elaboration leads us away from reality and into the dark forest of human thought. So the two elaborations below are presented not in terms of being true or false, correct or incorrect, but rather to illustrate how difficult it is to approach truth by means of words and thoughts.
- ELABORATION #1:
Space and stuff are different states of the same basic thing, just as steam and ice are different states of water.
In Elaboration #1, spaciness and stuffiness are "mere" epiphenomena -- trivial and insignificant variations of a deeper, underlying element of reality. Of course, to a person dying of thirst, there's a big difference between a block of ice and a glass of water. To the thirsty person, the epiphenomenon is much more than "mere", it's far more critical than the phenomenon itself.
And then there's the matter of energy. Under the conservation laws beloved of physicists, energy cannot be created or destroyed but rather can only be transformed, eg into matter (strictly speaking, mass). And likewise, matter (mass) cannot be created or destroyed but rather can only can be transformed, eg into energy, as we have seen at Hiroshima and elsewhere.(Not to mention the fact that what we call matter is 99.9% empty space, or so they say.)
Space and stuff are related in the same way that matter and energy are related, ie they are forms of each other. In other words: no space, no stuff. Only different aspects of the underlying reality: the Higgs Field!
- ELABORATION #2:
Even the so-called "vacuum" -- space that is supposedly devoid of stuff -- is not empty, dead or sterile but rather the birthing ground of a whole zoo of virtual particles, wavicles, partiwaves that continually wink in and out of existence, delighting in the bafflement they cause. In other words, there is no totally empty space. And that means there is no space at all. Because anything that is not empty, is not space.
And don't think you can use "density" (number of molecules of stuff per standard unit of space) to make a viable distinction between stuff and space. Stuff is space that is more densely packed. And space is stuff that is more loosely packed. There is no infinite density and no zero density***. "Density" is just another word that helps create and validate the artificial distinction between matter and space.
**mutually exclusive and collectively exhaustive (no gaps or overlaps)
***except maybe at the singularities lurking deep within black holes and other paradoxical beasts.