# "Flatland" nitpick: How can A. Square see 3D with a 2D eye? **URL:** \ **Category:** Cafe Society\ **Created:** [September 2, 2009, 3:07pm UTC](https://boards.straightdope.com/t/flatland-nitpick-how-can-a-square-see-3d-with-a-2d-eye/508638 "2009-09-02T15:07:23Z")\ **Posts on this page:** 6\ **Page:** 1
**Author:** ![BrainGlutton](https://avatars.discourse-cdn.com/v4/letter/b/82dd89/32.png) [@BrainGlutton](https://boards.straightdope.com/u/BrainGlutton)\ **Post date:** [September 2, 2009, 3:07pm UTC](https://boards.straightdope.com/t/flatland-nitpick-how-can-a-square-see-3d-with-a-2d-eye/508638/1 "2009-09-02T15:07:23Z")
In Edwin Abbott Abbott’s classic Victorian novel [_Flatland,_](http://en.wikipedia.org/wiki/Flatland) A. Square cannot understand the Sphere’s descriptions of a three-dimensional universe, until the Sphere kind of pops him out of the plane of Flatland into Spaceland. Then, all of a sudden, A. Square can see three-dimensional images just as you and I can – that is, he can see **two** -dimensional images from which 3D space can be inferred, just as you and I can. Previously, in Flatland, he was able to see only one-dimensional images – patterns of line segments – from which 2D space could be inferred. Well and good. But, even when taken out of Flatland, A. Square is still a two-dimensional being **with a two-dimensional eye,** probably resembling a cross-section of a human eye, i.e., it is only a semicircle with an internal semicircular retina, or functional equivalent thereof. It is designed only to perceive patterns of line segments. How can he suddenly see two-dimensional images with such an organ? ---
**Author:** ![Captain\_Amazing](https://avatars.discourse-cdn.com/v4/letter/c/6de8d8/32.png) [@Captain\_Amazing](https://boards.straightdope.com/u/Captain_Amazing)\ **Post date:** [September 2, 2009, 3:33pm UTC](https://boards.straightdope.com/t/flatland-nitpick-how-can-a-square-see-3d-with-a-2d-eye/508638/2 "2009-09-02T15:33:44Z")
"If you’re wondering how he eats and breathes And other science facts, Just repeat to yourself “It’s just a show, I should really just relax” ---
**Author:** ![A\_Man\_A\_Plan\_A\_Canal](https://avatars.discourse-cdn.com/v4/letter/a/839c29/32.png) [@A\_Man\_A\_Plan\_A\_Canal](https://boards.straightdope.com/u/A_Man_A_Plan_A_Canal)\ **Post date:** [September 2, 2009, 5:12pm UTC](https://boards.straightdope.com/t/flatland-nitpick-how-can-a-square-see-3d-with-a-2d-eye/508638/3 "2009-09-02T17:12:24Z")
I forget the deal with Flatland, but humans are able to imagine a three-dimensional world using two-dimensional retinas. How is this possible? Because you have two of them, separated in space, which analyzes the world from slightly different perspectives. The brain does the calculus, and–pow!–you perceive a three dimensional world. Actually, the exact process that occurs in the brain to make this happen is poorly understood. I happen to know about this because I have a disorder that prevents the brain from doing the calculation that is necessary to achieve this effect. I can see just fine out of both eyes, but I don’t have any fusion of the two images which the brain receives, one from each eye. My brain has compensated for this problem by learning to ignore the input from one eye or the other; otherwise, I have diplopia (double vision). In fact, I can “call up” the two images at any time and see two of everything. I’ve been this way since birth, and I don’t really find it a problem at all, but certain situations are very difficult–catching a baseball out of a clear blue sky, for instance. Whenever I go to the eye doctor, I’m quite the hit. Last time they brought some visiting interns in to look me over. AMAPAC ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [September 2, 2009, 5:35pm UTC](https://boards.straightdope.com/t/flatland-nitpick-how-can-a-square-see-3d-with-a-2d-eye/508638/4 "2009-09-02T17:35:13Z")
Actually, the problem is that Square’s eye is only two-dimensional if you count the direction into his body. It’s effectively a _one-dimensional_ eye, used to looking at one-dimensional vistas. By rights, he only ought to be able to see one-dimensional cross-sections through the two-dimensional vistas he’s seeing. It’s as if we took a detector line array and, just because we’re pointing it at a scene, expecting it to act like a CCD camera. An analogy with us would be for a 4-dimensional being to lift us up out of our 3-dimensional space and expect us to see a full 3 dimensions at once, instead of the two-dimensional distas we’re used to looking at. This isn’t an issue of binocular vs. monocular vision – in this analogy we would have to be able to see a full three dimensions, not merely parallax. But, as **Captain Amazing** (quoting MST3K)says, it’s just a show, you should really just relax. If you want more physical rigor in your dimensional fantasies, get a copy of A.K. Dewdney’s **The Planiverse**. > **[The Planiverse](https://en.wikipedia.org/wiki/The_Planiverse)** > > The Planiverse is a novel by A. K. Dewdney, written in 1984. > In the spirit of Edwin Abbott Abbott's Flatland, Dewdney and his computer science students simulate a two-dimensional world with a complex ecosystem. To their surprise, they find their artificial 2D universe has somehow accidentally become a means of communication with an actual 2D world: Arde. They make a sort of "telepathic" contact with "YNDRD", referred to by the students as Yendred, a highly philosophical Ardean, as he begins a jo... > **[Planiverse: Dewdney: 9780671463625: Amazon.com: Books](https://www.amazon.com/Planiverse-Computer-Contact-Two-Dimensional-World/dp/0387989161)** > > Buy Planiverse on Amazon.com ✓ FREE SHIPPING on qualified orders ---
**Author:** ![susan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/susan/32/17537_2.png) [@susan](https://boards.straightdope.com/u/susan)\ **Post date:** [September 2, 2009, 7:44pm UTC](https://boards.straightdope.com/t/flatland-nitpick-how-can-a-square-see-3d-with-a-2d-eye/508638/5 "2009-09-02T19:44:23Z")
Maybe the way Homer did in [“Homer3”](http://en.wikipedia.org/wiki/Treehouse_of_Horror_VI#Homer3). ---
**Author:** ![BigT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bigt/32/12044_2.png) [@BigT](https://boards.straightdope.com/u/BigT)\ **Post date:** [September 3, 2009, 2:24am UTC](https://boards.straightdope.com/t/flatland-nitpick-how-can-a-square-see-3d-with-a-2d-eye/508638/6 "2009-09-03T02:24:48Z")
> [@BrainGlutton](#): > > In Edwin Abbott Abbott’s classic Victorian novel [_Flatland,_](http://en.wikipedia.org/wiki/Flatland) A. Square cannot understand the Sphere’s descriptions of a three-dimensional universe, until the Sphere kind of pops him out of the plane of Flatland into Spaceland. Then, all of a sudden, A. Square can see three-dimensional images just as you and I can – that is, he can see **two** -dimensional images from which 3D space can be inferred, just as you and I can. Previously, in Flatland, he was able to see only one-dimensional images – patterns of line segments – from which 2D space could be inferred. > > Well and good. But, even when taken out of Flatland, A. Square is still a two-dimensional being **with a two-dimensional eye,** probably resembling a cross-section of a human eye, i.e., it is only a semicircle with an internal semicircular retina, or functional equivalent thereof. It is designed only to perceive patterns of line segments. How can he suddenly see two-dimensional images with such an organ? Thus the reason everyone thought he was crazy. I personally say the sphere somehow mind melded with him.