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Stranger on a Plane: Lessons from Flatland

Walter Myers III

Flatland

In an earlier post, I discussed the diversity of thought within the intelligent design movement with respect to “who” (or what) the designer is. Many, but certainly not all, intelligent design advocates take a theistic position. This view is of course roundly rejected by Darwinian naturalists who believe that natural selection, which consists of blind, undirected processes working on random mutations, is a fully capable substitute for an intelligent designer. Much of their disgust is directed at the suggestion of something that is supernatural, beyond nature, having any role in the evolution either of the universe or of the biological world.

To some this may sound radical, but I think a question that needs to be asked is if the theistic view necessitates that God act in a supernatural sense. As someone who personally accepts the biblical view, I see no reason that must be the case. In fact, I believe the debate of natural versus supernatural, or theist versus atheist, reflects a lack of imagination.

The principle embraced by most naturalists (or more specifically, physicalists) is that the universe is causally closed. Thus, for example, those who take a substance dualist view of the mind and the body could not possibly reconcile an “immaterial” mind with a material body, since immaterial objects (presuming they even exist) are considered causally impotent.

A Scientific Fantasy

In 1884, English clergyman Edwin A. Abbott published a work of science and mathematical fantasy titled Flatland: A Romance of Many Dimensions. Flatland is a narrative tale of a two-dimensional universe on a Euclidean plane, with inhabitants of various planar polygonal shapes (squares, pentagons, hexagons, etc.). The narrator happens to be square in shape, with a wife who is a straight line (as are all women), and children who are all pentagons. Shapes represent the relative status of the denizens of Flatland, where the more sides one has, the greater the scale of “development and nobility.”

The citizens of Flatland have no concept of a solid, since they don’t live in what the narrator calls “Spaceland” (i.e., the three-dimensional world in which we live). They can move freely on their planar surface but have no concept of “rising above” or “sinking below” the surface on which they live. When the narrator, one day, encounters the monarch of “Lineland,” who lives in a one-dimensional space, he finds it impossible to explain to the monarch what a two-dimensional world is like. The narrator enters Lineland and then exits Lineland with only his voice detectable to the monarch. However, the monarch sees this as nothing more than a magic act. He is indignantly convinced that the narrator must be an irrational and audacious man since there could not possibly be any motion other than that along a one-dimensional line. He thus sends the narrator on his way.

Encounter with a Stranger

Subsequently, the narrator of Flatland encounters a “Stranger” from Spaceland, who happens to be a sphere that wants to introduce the mysteries of the three-dimensional world to the people of Flatland. When the stranger crosses his two-dimensional plane, the narrator can see only circles of increasing or decreasing size. Yet when the stranger moves outside his plane, he can only hear the stranger’s voice. While still outside the plane of Flatland, the stranger pokes the narrator from underneath, noting how he can see all of the inner parts of the narrator as well as all the inner parts of Flatland.

Quite different from the narrator’s encounter with the monarch of Lineland, the stranger from Spaceland removes the narrator from the constraints of Flatland and shows him around Flatland from the perspective of the three-dimensional world. Upon seeing the internal workings of his home environment, the narrator asks the stranger if he is a God since only Gods could possibly show him what he has now seen. The stranger replies that he is not. It is the experience of all who live in Spaceland. Indeed, in Spaceland he is no more a God than a common criminal.

Uniting Heaven and Earth

I won’t go further into the story, as the point should be clear. In the same way that the monarch of Lineland thought his world was causally closed, and in the same manner that the narrator of Flatland thought his world was causally closed, why do many of us in three-dimensional space consider our world as causally closed, necessarily? The narrator of Flatland thought the stranger was otherworldly, even a God, and may have continued to think so had the stranger not rebuffed such thoughts after giving him a bird’s eye view of Flatland from the third dimension.

Just as time is another dimension, there is the real possibility that there are further physical dimensions beyond the three (or four, if you include time) that we normally encounter daily. Just as we can look at the plane of a desk, imagining it to be a two-dimensional world where we have the choice to interact with it (for example, placing the pad of our thumb on the desk), or not interact with the desk (taking our thumb away from the desk), we are no more or less material than the two-dimensional world of the desk surface regardless of whether we are in contact with it or not.

If we extrapolate the concepts we have learned from Flatland, we can see that we need not necessarily see dimensions beyond the familiar ones as “supernatural” or “immaterial.” It might be a different dimension of the same or similar substance. Those who can’t grasp it, which would likely be most or all of us, may simply lack the imagination to do so. 

Just as Newton’s Principia united heaven and earth under a new physics with a single consistent set of natural laws, perhaps intelligent design will lead us into an expanded scientific paradigm of laws where we can infer another dimension from its effects in the three-dimensional world. That is the possibility that I gleaned from Flatland.

Image: Cover of Flatland, by Edwin A. Abbott, via Wikimedia Commons.