It may be helpful to illustrate this process by an example. Let us suppose that a man makes an experiment of doing his own portrait from a mirror, which may be plane, concave or convex. If he looks into a plane mirror, he will see his true likeness; even so, if he be a poor designer, he will draw the likeness badly. Let us suppose that the man has beautiful features but because the drawing is very poor, it will not convey the impression that the features of the original were beautiful. If this poor designer were to look into and work from a concave or convex mirror, the drawing of his likeness would have practically no resemblance to his original features. For correct analysis and true definitions of the cardinal classes of life in our world it is necessary to have some just ideas about dimensions or dimensionality. The Britannica gives us some help in this connection. I will explain briefly by an example. Measurable entities of different kinds can not be compared directly. Each one must be measured in terms of a unit of its own kind. A line can have only length and therefore is of one dimension: a surface has length and width and is therefore said to have two dimensions; a volume has length, width and thickness and is, therefore, said to have three dimensions. If we take, for example, a volume—say a cube—we see that the cube has surfaces and lines and points, but a volume is not a surface nor a line nor a point. Just these dimensional differences have an enormous unrealized importance in practical life, as in the case of taking a line of five units of length and building upon it a square, the measure of this square (surface) will not be 5, it will be 25; and the 25 will not be 25 linear units but 25 square or surface units. If upon this square we build a cube, this cube will have neither 5 nor 25 for its measure; it will have 125, and this number will not be so many units of length nor of surface but so many solid or cubic units. It is as plain as a pike staff that, if we confused _dimensions_ when computing lengths and areas and volumes, we would wreck all the architectural and engineering structures of the world, and at the same time show ourselves stupider than block-heads.