“From dreams I proceed to facts”


Reading Flatland changed my life

The novella was published in 1884 by Edwin A. Abbott–an English schoolmaster. The novella is narrated by a square living in a two-dimensional world. One night, he is visited by a Sphere, or, rather, from his point of view, a Circle of varying diameter.

The Sphere has come to explain to him that there is a dimension he knows nothing about—a dimension along a hereto unknown direction “Upwards, not Northwards.”  To help the Square understand, the Sphere first teaches him by analogy. The two figures descend into Lineland and observe a one-dimensional world.

Although the Square can see similarities, the analogy is not sufficient for him to make the conceptual leap to three dimensions.  He doesn’t achieve full understanding until the Sphere plucks him from his world and raises him on high.  Once he has transcended his world, the Square sees farther than the Sphere; he begs to be shown the fourth dimension, but the Sphere refuses to believe in any dimension larger than the ones he has experienced.

This Sphere has came in search of a disciple willing to preach the Gospel of Three Dimensions to the inhabitants of Flatland, but, after his departure, the Square is unable to convince his fellow inhabitants of Flatland since he is unable to provide the practical demonstration that the Sphere vouchsafed to him.

Abbott expects more of us than of the Square or the Sphere.  Like the Sphere, we have never seen the fourth dimension, but we are expected to understand it by allegory.  What is more, we are expected to succeed where the Square failed.  We must be able to communicate this new knowledge to others who also have also never had direct experience of the phenomena under consideration.

The above paragraph perfectly describes my difficulties in convincing others to share my beliefs about the wonders of topology or the objective existence of morals.  It wasn’t until long after I read Flatland that I began to worry about what kind of epistemology could support my beliefs about the world, but Flatland and the many mathematical books and classes that followed it were my real introduction into metaphysics. Without perfect knowledge or direct experience of a hypercube, I nonetheless had away describe it and to formulate hypotheses about its properties.

Even with only imperfect access to morality, we can find a way to talk about moral laws in much the same way we speak of topological laws.  In a special series, I’ll be posting everyday about what I believe those laws are and how we ought to examine them.  In tomorrow’s post, I’ll begin with negation, discussing how we rule out possible moralities and why this is of critical importance.

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  • http://samjackson.org Sam Jackson

    I saw "objective existence of morals" and ran away. I see how you would experience difficulty convincing others… and would just like to point out that same is itself highly hilarious.Epistemology and metaphysics tend to provoke allergic responses for me in large doses.As long as you don't begin like Ayn Rand (step 1: state axioms, do not allow them to be questioned or discussed) I'll hear you out :)

  • http://www.blogger.com/profile/03615608336736450543 Hendy

    This will be fun! I've started Flatland at least twice but never finished it! It's on my bookshelf right now :) This could be a good prompting!

  • http://www.blogger.com/profile/16496144988509668275 Leah

    It's fantastic, Hendy. You should definitely read Sphereland afterwards (written by a different author many years later). It makes a lot of ideas about an expanding universe much easier to grasp.Flatterland, yet another sequel from yet another author, is also good, but much harder going. I didn't manage to finish it on the first go-round, since its discussion of quantum theory went over my head. I quite enjoyed it a few years later, though.

  • http://www.blogger.com/profile/07095873709252976052 Dominick Lawton

    The initial axiom here is that morals follow the same sorts of rules, or at least that the rules of morals fit together the same way and can be discussed the same way, as metaphysics. What's your argument for that?

  • http://www.noforbiddenquestions.com NFQ

    Oh, I came here to recommend Flatterland, but I'm glad to see you've already read it. :) Nice post.One of my favorite parts about Flatland was the social commentary. (And there's such a lot of it!) Maybe that's just because the geometry parts were not new to me when I read it.

  • http://www.blogger.com/profile/16496144988509668275 Leah

    Dom, I’d say primarily that metaphysics and mathematics gave me a better way to talk about morality, as a system I don’t understand in full but about which can still make conjectures and statements. I don’t think morality is necessarily a system of axioms and rules of deduction (and I promise I’ll talk more about what do think morality is soon.

  • http://www.blogger.com/profile/10019240793982424774 Christian H

    I'm just being picky here, but you say, "but we are expected to understand it by allegory," when you mean, "by analogy."