VIII. DIMENSIONS, SHAPES, AND INTERSUBJECTIVITY
We live in a three-dimensional world. Too quick. We conceive of our world as three-dimensional, but it doesn’t follow that it is. Though it may be – we’ll have to see – that for all intents and purposes the three-dimensionality of our world is as we conceive it to be. Can we imagine a four-dimensional world? We cannot, because we have no idea what that would look like. But can we imagine a two-dimensional world? We can, because we do. The Simpsons live in such a world, and they seem to do just fine.
But maybe that’s only because they imagine they’re living in a three-dimensional world. And if so, maybe that’s what we do too. That is, we’re not actually stepping out of our house. We’re not appearing in front of the door. We’re now just finding ourselves juxtaposed over what was the door. But if so, then once again we are living in a three-dimensional world for all intents and purposes. How so? Because it’s for all intents and purposes that we’ve set ourselves to task constructing a fundamental ontology.
Let this be granted. But need it also be granted that these dimensions intersect at right angles? It does not. So why do we conceive of them that way? I think it’s because right-angle intersections give us eight specifiable coordinates of space with consistent volumes. That is, we start stacking our volume-consistent atomic cubes along these right-angled intersections such that we can say that the atomic cube specified by these eight coordinates is identical in volume to the atomic cube specified by any other eight coordinates. And why do we want to do that? Because we want to be able to say that this set of occupied spaces – this Great Dane, for example – is bigger than that set of occupied spaces – that Chihuahua, for instance.
It’s true that the diagonal of our atomic cube will be the square root of 3 times its side. So is the atomic dimension the side or the diagonal? Since we can derive either from the other, it doesn’t matter. But if we don’t like there being these two (albeit interdefinable) measures, we could replace our atomic cubes with atomic spheres. But then we’d be saddled with unoccupiable spandrels. And the idea of unoccupiable space just downright terrifies me!
Too quick. Since the locations of the centre of a sphere is specifiable, likewise is the location of a spandrel. So now we have two kinds of atomic occupiable spaces: the spheres and the spandrels. Have we violated Occam’s razor? Not if for some reason we think it important that every edge of an atomic space be equidistant to every other edge of it. But hang on. Every edge of a spandrel will not be equidistant to every other edge of it. Dammit! Even in fundamental ontology, there are no free lunches.
Notwithstanding these Occamite worries, why do we seem to prefer spheres over cubes? Could it be because of gravity? That somewhere in the back of our reptile brain we pick up on the symmetry of the force of gravity, which, unlike the asymmetry of it on the surface of the planet, produces a sphere rather than a plane? Yes, we see it in heavenly bodies, but would our reptile brains have attributed it to gravity? Probably not. So what would explain this predilection?
I’m probably out to lunch on this, but I think it might have something to do with the shape of our hands, for which holding a sphere is much more comfortable (and so natural) than holding a cube. So we like spheres, and we project that affection into our ontology.
As I say, this is probably just a just-so story, and I certainly won’t go to the wall for it. All I will say is that if a world of cubes resonates less than a world of spheres, there’s got to be some explanation for that asymmetry of resonance, an explanation I’ll just have to leave to my obvious betters.
Whether we’re talking cubes or spheres, our three dimensions will intersect at every set of coordinates. So to specify locations we need to settle on what we’ll regard as an origin. As a first pass – and for many intents and purposes this remains the default – the origin of my world is wherever I am. But for most intents and purposes this won’t do. Why not? For two reasons. First, because I move, and I don’t want to have to reconfigure my entire world every time I do. And second, because I need to triangulate with others on the objects in our environment. So we tend to settle on a common fixed origin, like Greenwich meets the equator, or the cenotaph in the city’s Central Park. Or we might index the origin. The restaurant is a block north and two blocks east of my house. But if I want you to meet me there, I privilege what you take to be your origin and tell you it’s two blocks south and a block west from yours.
This ability to put ourselves in the other’s shoes, or more generally see the world from her perspective, has obvious ethical implications. But we’ll leave that for another day. Here it should suffice to note that origins are moveable and indexed to the purposes of the moment. When we want to index it to a wide range of potential purposes, we create maps. We create maps to share. But we also create maps for ourselves. And what I want to turn to now is what that map has to look like. By which I don’t mean what, for any one of us, it does look like. Rather, for any one of us, what it would look like if we were bereft of any interests or cognitive limitations peculiar to us. In other words, the map of all possible maps.
Categories: pure philosophy
Paulosophical Vimplications 
Leave a comment