The Unknowable Adventures of Bobar the Blue Dragon

September 25, 2003
 

Comedian George Carlin once asked, “If there are multiple universes, what do you call the thing they’re all inside of?”  The same question applies to space.  If there are multiple spaces, where do they all exist?  How are they related to each other, spatially?  Assuming, for the sake of argument, that there are multiple spaces, they must be entirely independent of each other.  Furthermore, they can have no spatial relation to each other, for that would imply space between them.  If a spatial relationship exists between the two spaces, it is implied that space exists between them, thus making them not two separate spaces, but rather a single divided space.  It must, therefore, be concluded that if multiple spaces exist, they can have no spatial relation to each other. 

According to Kant, in his Critique of Pure Reason, space is singular.  He says:

[I]f we speak of diverse spaces, we mean thereby only parts of one and the same unique space….  Space is essentially one; the manifold in it, and therefore the general concept of spaces depends solely on [the introduction of] limitations.  (Kant, 69)

 What Kant is saying is that humans can only conceive of one space, and that the idea of multiple spaces is merely the idea of a single divided space.  In other words, if space consists of one cube, and a wall is built through the middle of the cube, the space is still singular, according to Kant. 

            Flatland’s main character, A. Square, lives in a world with only two dimensions, where men are two-dimensional shapes, and women are merely lines, and where the mere mentioning of a third dimension is punishable by death.  Square visits Lineland, a one-dimensional world, in which men are lines and women mere points.  In Lineland, Square tries to illustrate the existence of a second dimension by passing through the line.  The king of Lineland only sees Square as an unmoving point.  Later, Square is visited by a Sphere.  Square first assumes that Sphere is just a circle, because he cannot grasp the concept of the forbidden third dimension.  Sphere tries to illustrate his third dimension by passing through the plane of Flatland, showing Square that his body appears to grow and shrink.  Unable to explain the third dimension, Sphere decides to show him.  Square rises up above Flatland and looks down, seeing all the shapes of the people and the houses, and he finally understands.  Being from a two-dimensional plane, Square is unable to illustrate to his people what the third dimension is, as he is unable to leave Flatland on his own.

            It might seem that the events in Edwin A. Abbott’s Flatland would illustrate the idea of multiple spaces that are spatially unrelated, but this is false.  In order for Square to pass through Lineland and Sphere to pass through Flatland, they must move through space.  Since space is a presupposition for objects to exist, i.e. since objects can only exist in space, it follows that space must exist wherever objects are.  If no space existed around Lineland or Flatland (or Pointland, for that matter), it would be impossible for Square or Sphere to pass through them, since parts of them are moving outside of them.  Supposing no space did exist around Flatland, Sphere would be unable to pass through it.  He would either be cut off or compressed down to two dimensions.  It must, therefore, be concluded that the space depicted in Flatland is singular and divided.

            Conventional wisdom tells us that space is singular.  If another spatially unrelated space were to exist, we would have no way of seeing it.  We would be unable to travel to it.  It would be completely unknown to us.  It might as well not exist, as its existence is inconsequential to us.  The world described by Kant and the universe depicted in Flatland both take the view that space is singular, although neither makes any real argument against any non-spatially related plurality.  They either take the conventional view described above, or the idea never occurred to them.  Either way, they provide no argument.  In Spaces and Times, Anthony Quinton tries to argue against conventional wisdom.

            Quinton argues:

To say a thing is spatial is to say either or both of the following:  (a) that it is extended, that its parts are spatially connected to one another and (b) that it is spatially related, that it is spatially distinct from itself.  It does not follow from either of these or from both of them taken together that it is spatially connected to everything.  It does not follow, then, from the mere conception of a spatial thing that space is a unique individual.  So far, the formal possibility of a plurality of spaces remains open. (Quinton, 66)

My hand, for example, is spatial.  The fingers are an extension of my hand, and they are spatially related to the palm of my hand.  My hand is also spatially related to the keyboard on which I am typing.  It is spatially related to it, frequently coming into contact with it, and it is also spatially distinct from it.  My hand, palm, fingers, and keyboard are spatially related because they all exist in the same space.  According to Quinton, while the relationship between my hand and keyboard may be spatial, the relationship is not necessarily universal.  That is to say that while my hand occupies the same space as the keyboard, it does not necessarily occupy the same space as Bobar the blue dragon from Altoria IV.

            Suppose I had a dream in which I went to Altoria IV and met Bobar the blue dragon.  In the dream, Bobar seems very real.  When he talks to me, his words have meaning.  Everything about Bobar looks and feels genuine.  When I wake up, however, Bobar is gone.  Where did he go?  According to Quinton, it is possible that Bobar never went anywhere.  The space in which Bobar exists is completely separate from the one in which I exist.  While no spatial relationship between the spaces exists, it is possible to traverse from one to the other through an altered state of mind, in this case, dreaming. 

When I dream of tigers, there are generally no tigers anywhere near where I am, my head is not large enough to contain tigers, the possible brain pattern of electrical activity in my brain associated with dreaming of tigers is not identifiable with the tigers I dream of since I know that I have dreamt of tigers but the electrical activity is an unstable compound of hearsay and guesswork.  (Quinton, 69)

            A big problem with Quinton’s dream theory is that it too quick to dismiss the notion that dreams are merely electrical signals in the brain.  Essentially, what he is saying is that since human understanding of the brain is (or was, at the time) so limited, any theories involving brain activity are nonsense. 

            Of all the theories I have studied, Quinton’s seems to be the closest to the truth.  While he does not definitively say that dreams are visions of alternate spaces, he does introduce the possibility.  His dismissal of brain activity is disconcerting, but it is largely inconsequential to his argument, which says only that some dreams may be visions of alternate space.  He leaves the possibility open without making anything definite.  Ultimately, knowledge of other spaces serves no real purpose.  Even if it is possible to acquire such knowledge, our inability to manipulate it makes this entire endeavor pointless.

Bibliography

Abbott, Edwin A..  Flatland: A Romance of Many Dimensions.  Seeley & Co., Ltd., London.  1884

Kant, Immanuel.  A Critique of Pure Reason.

Quinton, Anthony.  Space and Times, from French, Peter.  Philosophers in Wonderland.  Llewellyn Publishers, 1975