Flatlanders and the Proofs for the Existence of God

I read this a while ago and knew that I had to share it with the world. It comes from a summary of Edwin Abbot’s 1884 Flatland by Michael Shermer where he tells the story of how a square, living in ‘Flatland’ – a 2-dimensional world – meets a circle who has some very strange ideas.

The circle tells him that there are actually other dimensions… another reality where shapes have 3 dimensions rather than 2. This makes no sense to the square… and eventually the circle (Sphere) unceremoniously grabs the square and pulls him into his own 3-dimensional world. Where the square is now a cube.

The cube then asks if there is another dimension… a place where everything has 4-dimensions rather than three. This reasoning is met with indignation by the Sphere. How ridiculous is a world where there are 4 dimensions?

Shermer continues, taking the story to its conclusion with the proofs for the existence of God:

“Like the Cube’s impudent challenge to use the Sphere’s own analogies to argue for yet a higher dimension [4-dimensions], the proofs of God can themselves be used to consider the possibility of another being still higher, ad infinitum. Like the two dimensional Flatlanders who could not grasp the nature of three-dimensionality despite ironclad logic and reasoning, God’s existence or nonexistence cannot possibly be understood in human terms. What cannot be understood, cannot be proved. What is unprovable is insoluble.”

Shermer, Michael. 1999. How we Believe: The Search for God in an Age of Science. New York: W.H. Freeman, p. 15


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About Chris

Scholar of religion/nonreligion... PhD Student (Lancaster University), blogger, singer, actor, thinker... Northern Irish living in Scotland. Co-founder of The Religious Studies Project. Director at the NSRN. Baritone masquerading as a tenor. Vegetarian for no particular reason.

7 responses to “Flatlanders and the Proofs for the Existence of God”

  1. Will Bartlett says :

    I like this as a story, but the analogy is slightly uncomfortable, in that the square has the circle-who-in-his-own-world-is-a-sphere to tell him that there are these other possibilities; there is no pretence at logic or proof, merely a statement of experience. This statement of experience would only exist in the 3 dimensional world if there was a shape from the four dimensional one masquerading as 3D in the sphere’s world, which is not a given. I feel like I am nit-picking but at the same time it should matter that if you accept that the only evidence of one world in the other is statements of experience rather than logical proofs, it doesn’t matter that the existence of the other world renders irrelevant the logic-based-on-observable-rules of the first; the only reason to suspect the existence of a 5th dimension, a level above that of the original messenger, would be if you were told that such a thing existed by a being claiming to have experienced it. There are no “same proofs, same logic”, so there is no real need to accept the ad infinitum problem. I… am not sure my thought was really communicated (or if it is valid anyway) but your post was interesting.

  2. religionandmore says :

    I totally get what you’re saying Will and it definitely makes sense. I suppose if the square had reasoned to a possible third dimension before meeting the sphere it might be a bit different. I think the point is that reasoning to something doesn’t mean that it exists. Sure the sphere showed the square the third dimension… but eventually this may not be possible if we keep progressing forward. I think the point is that just because our brains, which are constrained by their three-dimensionality, cannot comprehend something, doesn’t mean that it’s not the case.

    In Shermer’s context, he is using it to show that those who posit the existence of a God, or eternity, or whatever and cannot prove this, cannot stop the positing from going innumerable stages further than the other realities they posit. But maybe it doesn’t work so well for this purpose :) Thanks for your comments… are you back in Edinburgh soon? Hope so mate.

  3. moshesharon says :

    Everything within the universe is in a state of perpetual motion passing from one moment to the next. Every thought is related to what happened before, what’s going on now or what will be in the future. As time passes, the current moment ceases to exist and a new instant comes into being. The future becomes the present and the present becomes the past. Such is the essence of change and the nature of time. This thought, however, begs the question, “If physical being is in a perpetual state of motion and change, what is the constant?” If nothing remains the same then by what cause do the processes of life perpetually repeat themselves exactly the same way with the celestial bodies moving repetitively through space-time in perfect order. The inescapable conclusion, therefore, is that there is a universal constant; a standard by which all things follow a particular order without deviation as if following a prime directive. http://moshesharon.wordpress.com

  4. religionandmore says :

    With my layman’s knowledge of science, I would respond by saying:
    – Is not energy constant? Or mass?
    – And that the processes of life DO NOT perpetually repeat themselves exactly the same way, and neither do the celestial bodies move repetitively through space-time in perfect order. Things may seem constant and eternal in our limited temporal view, but…
    – I am not denying that there is a universal constant… or an answer to Douglas Adams’ question of ‘life, the universe and everything’, but it would be arrogant of us to presume that a) there was one b) we could understand it. This doesn’t mean that trying to find it isn’t a worthwhile cause.
    – But whilst I may not agree… thanks for participating in the dialogue :)


  5. moshesharon says :

    The reproductive process is the very thing that is repetitive. Each species has to follow the same pattern to reproduce. Even when adaptations or mutations occur, the next generation has to repeat the same process to reproduce.

    As far as mass or energy being constant, the Lorentz contraction theory would cast some doubt on that, I would think.

    As for the celestial bodies, I am no astrologer, so I look at the stars from a layman’s perspective. The sun hasn’t missed rising in the East and setting in the West as far back as I can remember. However, I can’t disagree that in an ever expanding universe the planets could be revolving randomly around their respective suns, and the galaxies certainly have enough space to avoid being in a bumper car situation, but it all does seem rather miraculous in any event given our comparative insignificance.

  6. Ellie D. says :

    My high school Physics teacher once paraphrased this summary from Michael Shermer to the class! This was back in 2004! Anyhoo, happy to find this here :) And this reminds me very much of colors and how our eyes cannot perceive all colors but we know that different animals have different rods and cones and whatnot. Probably not a fool-proof thought but just wanted to share!

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