THE FOURTH DIMENSION. 



105 



that we cannot explain a trick easily and naturally does not irrevo- 

 cably prove that it is accomplished by other means than those 

 which the world of matter presents. 



Still better known than this last performance is Slade's experi- 

 ments with knots. To explain this in connection with the fourth 

 dimension, we must resort again to the plane and the flat worm in- 

 habiting it. To two parallel lines in a plane let the two ends of a 

 third line, which has a double point, that is, intersects itself once, 

 be attached. Our flat worm would not be able to untie the loop 

 formed by the doubled third line, which we will call a string, be- 

 cause it cannot execute motions in three dimensions. If, therefore, 

 a two dimensional prestidigitateur should appear and accomplish 

 the trick of untying this loop without removing the two ends of the 

 string from the parallel lines, he will have accomplished for our flat 

 worm a supersensuous experiment. A human being engaged in the 

 service of the prestidigitateur could execute for him the experiment 

 by simply lifting the string a little out of the plane, pulling it taut, 

 and placing it back again. This suggests the following analogous 

 experiment for three-dimensional beings. The two ends of a string 

 in which a common knot has been made are sealed to the opposite 

 walls of a room. The problem is to untie this knot without break- 

 ing the seals at the two ends of the string. Everybody knows that 

 this problem is not soluble, but it may be calculated mathemati- 

 cally that the knot in the string can be untied as easily by motions 

 in a fourth dimension of space as in the experiment above described 

 the knot in the two-dimensional string was untied by a three-dimen- 

 sional motion. Now as Slade untied the knot before ZGllner's eyes 

 without apparently making any use of the ends fastened in the 

 walls, Zollner was still more firmly confirmed in the view that Slade 

 had power over spirits who performed the experiments for him. 



Still more far-reaching is the theory of Carl du Prel concerning 

 the relations of the material and the four-dimensional world. (Com- 

 pare his numerous essays in the spiritualistic magazine Sphinx.} 

 Just as the shadows of three-dimensional objects cast on a wall are 

 controlled in their movements by the things whose projections they 

 are, in the same way it is claimed does there exist back of every- 



