The Birmingham age-herald., 1911-10-15
MATHEMAT|C|ANS IS GHOSTS REALM Have Located It in Fourth
 Dimension GOSSIP OF MYSTIC Shadow With Two Dimensions Sug- gests Theory of Ghost
 Realm in the Fourth
 Dimension

From the Indianapolis Star.
 show me an authentic ghost and will show you where he lives.
 That in substance, Is the challenge or A. certain school of modern mystics, who base their claims to having discovered the dwelling place of spirits on no less rigid science than the science of mathematics.
 As authentic as any of the current ghost stories is one that agitated the It. tie town of Bridgeboro, N J.. few days ago. It seems that a party of people passing a lonely spot in the vicinity of the town along toward midnight saw a dwarf climb out of the Paxton pits For a minute 1t fingered and then, giving piercing screech, vanished into the woods"
 ] s,The old residents say" continued newspaper account, that years ago a re-
 served man, who lived on the outskir's of the village, and whose name never was learned as the family would not mn gle with the villagers, had deformeo son. The man was driving along the coun-
 
 to have overturned and the child fell nlto the pit and broke its neck. The version of the accident was accepted, put Who rumors were afloat at the time Ihose who have seen the spectre describe II as a boy. whose head seems to hang imp | upon his chest" | This is only another one of the millions l and millions of ghost stories that nave | originated and found at least local ac- | ceptance since the birth of time. lhefe | is scarcely a rural district that mas hos l it's barn haunted by the restless ghost or
 some man who hung himself rom u | rafter; or it's lonely old bridge haunted | by the white robbed ghost of a woman Who iumped or fell from it and was droWheo, | or it's dark wooded bend in the roaa where on stormy night, walks 'he | ghost of a wealthy farmer who was way | laid and murdered by highwaymen when | returning home with the proceeds or the | sale of his wheat crop Tn hoiio" pel' strapped around his waist
 l The strangle hold of the ghost s'osY l on the human mind is one of the strang- | est of psychological phenomena. 50 strong is this hold that even the most satrical materialsts have not succeeue'l fin entirely escaping it. A nervous tre'nor Is apt to run through the best of ehein when alone in a forest on dark anu stormy night d huge limb of a tree, emit ting a mournful groan.
 Seeking the Explanation This universal power of ghost lore Eas led serious thinkers in all ages to seek d rational explanation. and has led many of them. as a last resort, to accept ghosts as actual realities Of late years the be- lief in ghosts has been rationally ex- plained at least partially by the VlVia- ness of dreams of dead friends. but ms explanation does not clear up all dltflcui- ties.
 Having accepted ghosts as realities hon est thinkers. until the time of the Leipsic professor, Zollner, few decades aso' were puzzled to find a dwelling place TOT them. once accepted as actualities capa- ble of making themselves visible under certain conditions, it was necessary to explain how they could be in the vicinity of mortals and remain invisible under the other conditions that obtain almost m variably.
 "Whv. they live in the fourth dimen- sion" said Zollner, and his announcement was accepted as a vivid flash of light by thinkers groping in the dark. But what is the fourth dimension? The answer, long known to mathematcldis who invented the theory years before Ioll- ner bounced upon it and appropriated It, is set forth at length in popular essay by Herman Schubert, professor of mathe- matics in the Johanneum, Hamburg, fer many. This essay, with others, has been translated in an easy style by Thomas j.. Mccormack and published under the col lective title of Mathematical Essays and Rrecreation'' by the Open Court com pany of Chicago. Another of the Open Court books in which the theory of the fourth dimension Is discussed in it's rela- tion to geometry is Space and Geome- try" by Carl Mach also translated by Mir Mccormack, but this book is far too technical for the lay reader.
 In his popular essay Prof. Schubert sets forth Zollner's theory and arguments at length. and then very cooly proceeds 10 place bombshell under the whole Zoll- ner structure and blow it sky high. But the structure is such an interesting one, as furnishing habitation for ghosts. that it is worth looking at and admiring he- fore the explosion occurs.
 The idea of the fourth dimension is an easy one to grasp through analogy, but
 it is impossible for any mortal mind to paint actually mental picture Of four dimensional space, just as it is easy to grasp the idea that there never was a beginning to the universe but impossible to explain how that could be.
 The Fourth Dimension
 Here IS lnc lued Ol tue louiti oiiitSiC sion Every object in the world, as we know 1t, has three dimensions-length breadth and thickness. In other words, we live in three dimensional world. Imagine an extension in another direction and you have four-dimensional worl3.
 It is not hard to conceive of world of two dmensions-length and breadth though, of course, nobody can conceive of any life existing in such a world. Geometry constantly makes use of d world of two dimensions, as in the measure ments of squares circles, triangles, etc. The nearest actuaity to a two-dimen- sional world is a shadow. When you walk along in the sun you throw on to the ground thing with length and breadth, but no thickness. Likewise there can be imagined one-dimensonal world, A line with length, but no breadth or thickness.
 Having Investigated the world of one. two and three dimensions, the mathema- ticians conceived a world of four dimen- siops and began examining it's proper ties. Their interesting work in this world of four dimensions is too technical to set forth here, but suffice it to say that it greatly enlarged the horizon of nigner mathematics, and that the work has been carried on so far that the ma thematicans are almost as much at home here as in the worlds of lower dimensions. They have gone So far, indeed as to extend their work into the worlds of five, SIX, seven and higher dimensions
 But it was not the abstruse technicali- Al |. .t.-- I-I --r1