Ruyer gives an explanation of “existing in a dimension” in his 1952 book Neo-finalisme that has since been given in other popular accounts of physics (Ruyer says that the explanation was popular even in his day). The explanation turns on considering what it would take to hide something from a being existing in one dimension, two dimensions, etc. For a being living in a two dimensional world (a “flatland”) we could hide a treasure simply by putting it inside a circular vault – though someone living in three dimensions outside of this could “magically” rifle the vault without even having to open the door. Those of us in the third dimension could, that is, pick out the treasure without even having to touch the walls of the vault, and just as easily make it reappear “from nowhere”. The residents of this flatland are not completely unaware of this sort of magical power, however – for they could see themselves as having a similar transcendence to those living in “line-land”. In line-land, the residents hide their treasures by putting them on the other side of points; though the residents of flatland could rifle this vault without even having to touch the point-wall, and could put the treasure back again “from nowhere”.
Ruyer draws a gorgeous conclusion from this: to be in a dimension means to have all the objects of a lower dimension “layed-out in from of oneself” in plain view. Said another way, it is existence in ones own dimension that allows for hiddenness, while at the same time making all in the lower dimensions unhidden. For us, three dimensional things are “solids”, just as two dimensional things are solids for those in flatland, and points are solids for those in line-land. This “solidity” consists in rendering things opaque to sensation. Solidity is whatever makes things invisible, untouchable, or somehow resistant to sense. More importantly, this “solidity” enters into language as “the real” or “the substantial”, and it is incoherent or “against common experience” that being would be anything other than the “solid”.
But not quite. The analogy shows us an aspect of the non-categorical concept of being that we already possess. We can make higher dimensions thinkable and therefore such transcendence of a given dimensionality must enter into the possibilities of being at least in the intentional order. No given dimensionality can be essential to our notion of being. There is no value of N-dimensions that can serve as the limit of the one who understands being. This understanding is distinguished at its root from the understanding that is systematized from sense observation, i.e. science. To the extent that we are three dimensional, our physics will always be three-dimensional, or take this as a fundamental principle; for these three dimensions will be “space” in the same way that a 37-dimensional being would have a 37 dimensional physics which would take “space” as obviously 37-dimensional. “Three dimensions” would be nothing but a “mathematical abstraction” whose “real existence” would be an insurmountable problem in the philosophy of mathematics (no doubt there would be “Platonists” who argued that three dimensional beings “really exist”). For such a physics in higher dimensions, nothing in our “space” would be hidden or inaccessible – he could touch our spleen without having to go through our skin, and see any food in our stomach without having to look through anything (this would, in fact, require only a 4 dimensional existence, but we exaggerate for the sake of the ontological point). Taken in this way, physics is essentially dimensionally bound discourse, that is, a discourse that takes some given dimensionality as the standard of “the real” or even of “being”. One can define his terms as he chooses (though even here there are limits) but this cannot do away with the trans-categorical notion of being, truth, good, unity or otherness that cannot be restricted to taking some given dimensionality as a principle for the real.