Dimensions, Planes, and Geometry! Oh My!

(disclaimer: This is the rough draft for my honor's essay so I may attempt to wax "collegey" at certain points. Maybe I can fool the professors into thinking I am actually one of "them". :D That would also be why I didn't bring out any spiritual aspects, but there are a few to be had.)


         This Work is Dedicated
By a Humble Native of Flatland
In the Hope that
Even as he was Initiated into the Mysteries
Of THREE Dimensions
Having been previously conversant
With ONLY TWO
So the Citizens of that Celestial Region
May aspire yet higher and higher
To the Secrets of FOUR FIVE OR EVEN SIX Dimensions
Thereby contributing
To the Enlargement of THE IMAGINATION
And the possible Development
Of that most rare and excellent Gift of MODESTY
Among the Superior Races
Of SOLID HUMANITY

There are few books that provide a universal application like Flatlands: A Romance of Many Dimensions. Written by Edward Abbot in 1884, this novel not only acts as an allegory of the social conditions in Victorian England but also gives a principle that can be applied to almost any discipline. Reading this novel gives a glimpse into the idea that assumptions are only as valid as the information that they are formed upon.  

  Flatlands begins with an in depth explanation into the 2-dimensional world where the narrator, A. Square, exists. The denizens of this plane are geometric figures with length and width but without height, and everything appears as a straight flat line to them. They must distinguish themselves and objects through the number of angles that something has, which they ascertain through either feeling the angles or through the “art of seeing”. These arts are important to the Flatlanders because too sharp an angle can kill them.  

   This leads to the explanation of their social system. Male Flatlanders are divided into the four classes which are dictated by the amount and degree of angles a figure has. The most numerous figures are the isosceles triangles that form up the soldier and laborer class. Next highest are the equilateral triangles which represent the middle class and tradesman. The gentleman class is comprised of squares and pentagons. Hexagons form the nobility class. Finally, once a figure has so many angles of small degree that it is nearly indistinguishable from a circle, it joins the ranks of the priestly class, who rule over every aspect of Flatland. This is not an absolute static system. There is a natural law in Flatland that every generation should have one more angle than the previous generation. While this is not always the case, the law does allow a method of social mobility. Although this mobility does not apply to females, they are not figures but appear as straight lines. Because it is a hazard for a figure to be of irregular size and shape, any person that has a misshapen angle is put into a penal institution, and it can impede the aforementioned natural law.

  At this juncture, the author explains more about the circles and the events surrounding their dominion. The higher up a figure went in the social ladder the faster that figure’s successive generation would gain angles, but this advantage has a parallel handicap. The more angles a figure has the less fertile it is, and the harder it is to create non-irregular offspring. This fact makes the ruling circles, which we are told have monopolized power based on “perfect configuration of angles”, conservative in the extreme. They fear revolts and the disappearance of their mandate, and this is the context for the main part of the novel.

  Part two of this novel is about the enlightening adventure of the narrator. He is living through the passing of a new millennium in Flatland, and he has a vision that takes him to a realm of 1-dimension, length. Called Lineland, the Square observes, through interaction with the king of Lineland, that the inhabitants of this plane are completely unaware of other dimensions, and they are unwilling to even consider the possibility. A. Square tries many ways to convince the king of a second dimension but ultimately fails, is shouted down by the inhabitants, and wakes to his own home.

  Further on during that night, the square meets a sphere which is likewise visiting him as he visited Lineland. Just as A. Square attempted to enlighten the King about a second dimension, the sphere tries to explain a third dimension. This is ultimately just as fruitless, and the sphere is forced to pull the square out of his 2-D existence into a 3-D plane called Spaceland.

  In this plane, our narrator is shown the “wonders” of Spaceland. He also observes Flatland in its 2-D state from a 3-D perspective. This has the effect of creating an insatiable curiosity on the part of A. Square. He pushes his guide for a 4^th and 5^th dimension, exasperating the sphere to the point where he returns him to Flatland. This does not last long as our narrator is again given a vision by the sphere to another new plane, the plane of 0-D. This plane is contained within one point and one Solipsistic inhabitant. This inhabitant can conceive no other being, existence, change, or movement. In fact, the very intervention of the Square is taken by the Point as a manifestation of his own mind.  

  At this point, one should begin to grasp the universal application of this novel. In any profession, relationship, or science that humanity has, there are assumptions and biases that have developed about the way things are done. These provide foundational tradition on the methods employed in those areas. But, it is important, imperative, to realize that these assumptions are based upon the observable knowledge present, and thus that premise is limited to that same observable knowledge. One can draw a parallel in this respect to these assumptions and the dimensional planes of this novel. Each indigenous life form of the respective lands drew their view from the knowledge that was available to them at that point, and the incorporation of these “extra dimensions” was incomprehensible to them until the proper observation of it was able to be found. If this idea is applied to historical examples, there are numerous references to be drawn.

  The development of science is just one such reference. Until the Copernican Revolution, it was widely considered that the universe was arrayed in a geocentric model. This was postulated with the observable data at hand, thus it was valid but still wrong. The discovery of the heliocentric universe was one instance where the “plane” of astronomy was lifted upwards to a better understanding. Antonie van Leeuwenhoek opened a similar transition when he unveiled the cellular construction and biology. This opened the door to a whole new understanding of biology.

  Science is not the only area where this thought can be applied. Business and economics also reflect this pattern. The understanding of the way money and production flow has moved from different “dimensions” of understanding across history. While there are many different views on this subject, that doesn’t invalidate the idea the perspective on the subject has changed considerably.

 In addition, it is worth noting that when this understanding is reached it doesn’t mean that all previous information is thrown away. Many times the facts we know are part of the larger truth.

  This is relevant, not only to the study of historical transitions, but also to modern individuals’ lives. If one analyzes the assumptions he holds, there is every chance that he may realize his own limitations. Through this realization, one can to look beyond this limitation for a solution to his own limited observable data.

  Flatlands can teach SUNY Fredonia students this universal principle of challenging assumptions to find the truth. It could be promoted through the series of special objectives for students in individual departments to find new ways of looking at problems and developing abilities. To motivate students for reading the book and achieving this goal, each department would provide a challenge for their majors. The winner would be the student(s) who were able to create the most creative solution to the problem. Winners would have this count towards their cumulative GPA, and would be given an award.

   While many books attempt to inspire the reader towards creativity, I haven’t read one that could do it better than Flatlands. This novel, while entertaining, shows a greater moral of expanding one’s understanding towards truth.