THE MAGIC SQUARE. 



INTRODUCTORY. 



/"^vF ALL the philosophies of modern times there is none that 

 ^-^ has emphasised so much the importance of form and formal 

 thought as the monism of The Monist. An expression of this phi- 

 losophy is found in the following passages : 



4 ' The order that prevails among the facts of reality is due to the laws of form. 

 Upon the order of the world depends its cognisability. 



" . . . . The laws of form are no less eternal than are matter and energy and 

 'Verily I say unto you, till heaven and earth pass, one jot or one tittle shall in no 

 wise pass from the law ! ' 



"The laws of form and their origin have been a puzzle to all philosophers. 

 ' Ay, there's the rub ! ' The difficulties of Hume's problem of causation, of Kant's 

 a priori, of Plato's ideas, of Mill's method of deduction, etc., etc., all arise from a 

 One-sided view of form and the laws of form and formal thought. " 



Considering the stupendous results achieved by engineering 

 and the other applied sciences with the assistance of mathematics, 

 we must confess that the forms of thought are wonderful indeed, 

 and it is not at all astonishing that the primitive thinkers of man- 

 kind when the importance of the laws of formal thought in some 

 way or another first dawned on their minds, attributed magic powers 

 to numbers and geometrical figures. 



We shall devote the following pages to a brief review of 

 magic squares, the consideration of which has led many a man to 

 believe in mysticism. And yet there is no mysticism about them 

 unless we either consider everything mystical, even that twice two 

 is four, or join the sceptic in his exclamation that we can truly not 



