A New Era of Thought

by Charles Howard Hinton

In trying to realize the experience of a plane-being it is best to suppose that its two dimensions are upwards and sideways, i.e., Z and X, because, if there be any matter in the plane-world, it will, like matter in the solid world, exert attractions and repulsions. The matter, like the beings, must be supposed very thin, that is, of so slight thickness that it is quite unnoticed by the being. Now, if there be a very large mass of such matter lying on the table, and a plane-being be free to move about it, he will be attracted to it in every direction. “Towards this huge mass” would be “Down,” and “Away from it” would be “Up,” just as “Towards the earth” is to solid beings “Down,” and “Away from it” is “Up,” at whatever part of the globe they may be. Hence, if we want to realize a plane-being’s feelings, we must keep the sense of up and down. Therefore we must use the Z direction, and it is more convenient to take Z and X than Z and Y.

Any direction lying between these is said to be compounded of the two; for, if we move slantwise for some distance, the point reached might have been also reached by going a certain distance X, and then a certain distance Z, or vice versâ.

Let us suppose the Orange line has moved Z, and traced the Dark-blue square ending in the Reddish line. If we now place a piece of stiff paper against the Dark-blue square, and suppose the plane-beings to move to and fro on that surface of the paper, which touches the square, we shall have means of representing their experience.

To obtain a more consistent view of their existence, let us suppose the piece of paper extended, so that it cuts through our earth and comes out at the antipodes, thus cutting the earth in two. Then suppose all the earth removed away, both hemispheres vanishing, and only a very thin layer of matter left upon the paper on that side which touches the Dark-blue square. This represents what the world would be to a plane-being.

It is of some importance to get the notion of the directions in a plane-world, as great difficulty arises from our notions of up and down. We miss the right analogy if we conceive of a plane-world without the conception of up and down.

A good plan is, to use a slanting surface, a stiff card or book cover, so placed that it slopes upwards to the eye. Then gravity acts as two forces. It acts (1) as a force pressing all particles upon the slanting surface into it, and (2) as a force of gravity along the plane, making particles tend to slip down its incline. We may suppose that in a plane-world there are two such forces, one keeping the beings thereon to the plane, the other acting between bodies in it, and of such a nature that by virtue of it any large mass of plane-matter produces on small particles around it the same effects as the large mass of solid matter called our earth produces on small objects like our bodies situated around it. In both cases the larger draws the smaller to itself, and creates the sensations of up and down.

If we hold the cube so that its Dark-blue side touches a sheet of paper held upwards to the eye, and if we then look straight down along the paper, confining our view to that which is in actual contact with the paper, we see the same view of the cube as a plane-being would get. We see a Light-blue point, a Reddish line, and a Dull-purple point. The plane-being only sees a line, just as we only see a square of the cube.

The line where the paper rests on the table may be taken as representative of the surface of the plane-being’s earth. It would be merely a line to him, but it would have the same property in relation to the plane-world, as a square has in relation to a solid world; in neither case can the notion of what in the latter is termed solidity be quite excluded. If the plane-being broke through the line bounding his earth, he would find more matter beyond it.

Let us now leave out of consideration the question of “up and down” in a plane-world. Let us no longer consider it in the vertical, or ZX, position, but simply take the surface (XY) of the table as that which supports a plane-world. Let us represent its inhabitants by thin pieces of paper, which are free to move over the surface of the table, but cannot rise from it. Also, let the thickness (i.e., height above the surface) of these beings be so small that they cannot discern it. Lastly let us premise there is no attraction in their world, so that they have not any up and down.

Placing Cube 1 in front of us, let us now ask how a plane-being could apprehend such a cube. The Black face he could easily study. He would find it bounded by Gold point, Orange line, Fawn point, Crimson line, and so on. And he would discover it was Black by cutting through any of these lines and entering it. (This operation would be equivalent to the mining of a solid being).