The Fourth Dimension Simply Explained

Scanned, proofed and corrected from the original hardcover edition for enjoyable reading. (Worth every penny spent!)


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An excerpt from the Introduction:

We observe the forms and positions of objects very largely by sight. Now the organs of sight of a being confined to

some particular space may be supposed suited to the dimensions of his space. The picture formed in the retina of our

eye is two-dimensional, the retina is a surface. A two-dimensional being, unable to perceive anything outside of his

plane would have a one-dimensional retina, or at least his picture of an object in his world would be a mere line,

different pictures being distinguished by the lengths, colors, and shading of these lines. The retina of a four-

dimensional being would be three-dimensional if he is to receive separate impressions from all the rays of light

within a given angle of vision. In fact, the boundary of an opaque object, the part which alone he can see, is

three-dimensional as is always the boundary of objects in space of four dimensions.

It is not easy for us to imagine such pictures, and so we can attempt to get an impression of the shapes of objects

by supposing that a three-dimensional being, a person like ourselves, could pass through a series of parallel three-

spaces (three-dimensional spaces) and in each three-space examine that portion of the object which lies in this

space, that section of the object. This is just as we might suppose a two-dimensional being able to pass through a

series of planes and in each plane to see the section of an object made by that plane. The section which we should

see of a four-dimensional object would be a solid whose surface forms a part of the three-dimensional boundary of the

object. This way of studying four-dimensional objects is discussed quite fully...


There is another somewhat similar way of studying an object that we may find quite useful. We can imagine ourselves

turning from one three-space into another perpendicular three-space. That is, by discarding one of the directions in

our space we can suppose that we take into view the fourth direction, which goes away from our space, and so get its

relation to two of our directions. We shall describe the section of an object made by any three-space as what we can

see in that three-space. We shall do this particularly with reference to the different sections of an object obtained

at any point by taking different perpendicular three-spaces.

One of the first things, for example, that we consider in studying Geometry of Four Dimensions is the line

perpendicular to a three-space; such is the line which goes out from a point in our space in a new fourth direction

perpendicular to all the lines of our space through that point. If we can let go of one of the dimensions of our

space, keeping only that part which lies in a certain plane, and take into view the new fourth dimension, we shall

see a plane and a line going out from it, perpendicular to all the lines of it, something with which we are perfectly

familiar.

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Complete list of contributors:

GRAHAM DENBY FITCH
EDWARD H. CUTLER
CARL A. RICHMOND
CLAUDE BRAGDON
ARTHUR HAAS
LEONARD C. GUNNELL
BURTON HOWARD CAMP
ELIZABETH BROWN DAVIS
G. M. ACKLOM
LOUIS W. WORRELL
ARTHUR R. CRATHORNE
PERCY WILCOX GUMAER
W. S. DAVIDSON
CHARLES JOHNSTON
W. T., HOLLAND
GEORGE GAILEY CHAMBERS
ELMER E. BURNS
A. C. SILVERMAN
WILMOT E. ELLIS