104 THK FOURTH DIMENSION. 



dimension, we must first conceive of two-dimensional reasoning be- 

 ings, or, let us say, two-dimensional worms, living and moving in a 

 plane. For a creature of this kind it will be self-evident that there 

 are no other paths between two points of its plane than such as lie 

 within the plane. It must, accordingly, be beyond the range of 

 conception of this worm, how any two-dimensional object which lies 

 within a circle in its space can be brought to any other position in 

 its space outside the circle without the object passing through the 

 barriers formed by the circle's circumference. But if this worm 

 could procure the services of a three-dimensional being, the trans- 

 portation of the object from a position within the circle to any posi- 

 tion outside it could be effected by the three-dimensional being sim- 

 ply taking the object out 0/"the plane and placing it at the desired 

 point. This object, therefore, would, in an inexplicable manner, 

 suddenly disappear before the eyes of the worms who were assem- 

 bled as spectators, and after the lapse of an interval of time would 

 again appear outside the circle without having passed at any point 

 through the circle's circumference. If now we add another dimen- 

 sion, we shall derive from this trick, which is wholly removed from 

 the sense-perception of the flattened worms, the following experi- 

 ment, which is wholly beyond the perception of us human beings. 

 Inside a glass sphere, which is closed all around, a grain of corn is 

 placed ; the problem is to transport the corn to some place outside 

 the sphere without passing through the glass surface. Now we 

 should be able to perform this trick if some four-dimensional being 

 would render us the same aid that we before rendered the two- 

 dimensional worm. For the four-dimensional being could take the 

 grain of corn into his four-dimensional space and then replace it in 

 our space in the desired spot outside of the glass sphere. Slade 

 performed this trick before Zflllner. Its mere performance sufficed 

 to convince this latter investigator that Slade had here made use of 

 a four-dimensional agent, who, in respect of power of motion, con- 

 trolled his four-dimensional space as we do our three-dimensional 

 space. It never occurred to Zollner that this experiment was the 

 cleverly executed trick of a prestidigitateur, or, as it would at once 

 occur to us, that the whole thing was a sensory illusion. The fact 



