… Or rather, The Annotated Flatland: A Romance of Many Dimensions, by Edwin A. Abbot, with introduction and notes by Ian Stewart.

Edwin A. Abbott (1838-1926)

He was a brilliant student, winning the highest honors available in the classics, mathematics, and theology. He became a fellow of his college by 23 and a year later took orders as an Anglican priest.  After only a couple of years as a master teacher, he rose to headmaster of a prestigious public school in London at the incredibly young age of 26.

Abbott was a prolific writer of serious books on theology, but his best-known work is this novella called Flatland, published when he was 46, in 1884. A fascinating mathematical construct, Flatland features beings living in a two-dimensional world who encounter a three-dimensional being. Abbott follows their philosophical and mathematical process in trying to make sense of what otherwise would be considered an impossibility in their two-dimensional world.

A Satire

One level of Flatland is a commentary on the hierarchy of Victorian culture, such as the illustration below of two separate doors, one for women and one for men. Women are mere line-segments, whereas men of even the lowest caste are a full shape—a triangle. The “author” of Flatland (the pseudonymous “A Square”) is a gentlemanly square, having received a small inheritance which added to his triangular stature, making him the statelier square.

By Edwin Abbott Abbott (author) – Houghton Library, Public Domain

Climbing the ladder of social influence and recognition, of wealth and power, has strict rules, and not everyone will make it through. Some people—those with irregular sides to begin with—will never be able to climb, nor will their children or children’s children.

Social activism is considered criminally dangerous, and those who show potential beyond their class are either quietly promoted or just as quietly done away with (euthanized, a form of social and family planning that was being popularized in some circles in the late nineteenth century).

Roles within society are rigidly maintained, particularly the dichotomy between men and women, with women always and permanently remaining of an entirely other and second class. Women by their very shape as mere line-segments can never attain anything more than their shape will allow.

By Edwin Abbott Abbott (author) – Houghton Library, Public Domain

A Story of Dimensions

All of Flatland is ruled by circles, a priestly cast of shapes formed by ancient lineages. Their inheritances coming down through countless generations have added so many lines to their forms they have become indistinguishable from the perfection of a circle.

On New Year’s Eve, A Square has a gripping dream in which he encounters beings from a one-dimensional world where the men are lines and the women are mere points of light. These beings are unable to experience the fullness of A Square because he is two-dimensional, and they can only “see” one of his sides at a time. A Square tries mightily to describe the two-dimensional world he comes from to the king of this one-dimensional land (and therefore the wisest and most intelligent of all the line beings), but the Line King simply does not have the capacity to understand what A Square is trying to convey.

But then, A Square is visited by an equally-to-him incomprehensible being—a sphere.

The Sphere reveals itself to A Square as a circle, then as a circle that becomes a point, growing sizes of circles, diminishing sizes of circles, then back to a pinpoint as the Sphere passes its three-dimensional form through A Square’s two-dimensional realm. Talk about a mind-bender! A Square does not have the capacity to perceive all three dimensions of the Sphere, but what he does see is amazing to him.

And then the Sphere brings A Square to Spaceland, a three-dimensional world, that so expands A Square’s vision and understanding, he will never be the same again.

Censure

A critique ensues on the ramifications

  • of intellectual and scientific leaps forward in understanding.
  • on philosophical questions of what creates and maintains society.
  • on what we might today call group-think.
  • of what those with power are willing to do to retain that power.
  • of what happens to innovators and visionaries.

Of particular interest is the censure on “revelations from another world.” Though the top leadership of Flatland secretly know other dimensions exist, they suppress any discussion of it, and stentorian laws are in place to summarily silence any who speak of such things. What this means for A Square becomes painfully poignant as he wrestles with the powerful new concepts he has embraced and the stiff laws and culture of his world.

Spiritual Plane

A bifurcation has happened in Flatland that has split certain elements of society and humanity with something of the same results that perhaps splitting an atom might have. Women and men, for example, are kept carefully apart except under certain highly regulated circumstances. Women are deemed unnaturally dangerous because of the shape of their bodies and must cry out any time they enter a room, or walk about in public lest they be mistaken for a point, or a man is accidentally sliced clean through by one of their lines.

Intellect is split from emotion, so that reason becomes the man’s sole domain, and feeling the woman’s sole domain. Woman are considered, in fact, incapable of reason though they receive educations, and men are considered specially skilled in avoiding emotion and in conversing rationally.

As A Square receives revelation after revelation, he at first thinks he is gaining in reason and becoming even more devoid of emotion, but the Sphere shows A Square how important feeling is, how compassion, for instance, is a God-like quality.

The book itself show how a society’s dogma, based on what is perceived to be truth, can become oppressive. Those in power use dogma to suppress new discovery which undermine their authority and continued claim to power. Knowledge, then, revelation, becomes an enemy to dogma when it questions the “truths” upon which dogma has been founded.

This is edgy stuff!

Those who became believers and spread the Gospel as described in the Greek scriptures met this kind of opposition head on. They were visionaries, religious revolutionaries, worshiping Christ Who is fully God and fully human, a concept no one had ever heard of before, and proclaiming literal resurrection, a feat never before achieved. Their testimony disrupted the dogma of every religion in the known world and suggested a spiritual-physical revelation that is flatly impossible in the world as we know it.

Societal structures were and still are called into question. Those in power then, and today as well, seek to suppress aspects of the Gospel, such as freedom and full equality for all people, men and women of all shapes and sizes.

Some seek to suppress the Gospel entirely.

Others forbid the interpretation of the scriptures in any other than the currently established way.

Even translations of the scriptures come under rigorous demand to conform to certain concepts such as complementarity for some translations, traditional use of male-oriented words over and above gender-neutral language for others, the translation of numbering, of certain adjectives describing categories of people or actions. The list is long

Annotation and Commentary

Ian Stewart enriches the reading of Flatland greatly with his own explanation of Abbott’s various Victorian references, and explication of Abbott’s mathematical allusions. Abbot’s novella is a wonderful read even without these annotations, but with them the reader can enjoy the richness Abbott intended.

As a point of reference, I had all three of our daughters read this book when they were in their variously high school or early college years. They all not only thoroughly understood the story and the meaning, they had enough math knowledge to smile at Abbott’s witticisms.

And that is my personal recommendation as well. This is a great book for youths to really examine their own faith, and to prepare them for how the world really works.


The last page (100) of the first edition | By , Edwin Abbott Abbott, 1838-1926 – Flatland, a Romance of Many Dimensions, 1884. London : Seeley and Co. Made available at flatlandromanceo00abbouoft (online viewer archive.org) converted to PNG and greyscale, B & W points to around 15% and 75%,, Public Domain

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