248 
Chandler—Transcendental Space. 
the new geometrical views he said: “ Mathematicians dis 
covered direct means for the acquirement of knowledge. But we 
have not long made use of those means. They are shown us by 
the celebrated Bacon. ‘Stop working uselessly trying to draw 
all wisdom out of the reason. Ask Nature. She contains all 
truths, and will answer your questions surely and satisfac¬ 
torily.’ ” It cannot then be out of place in the consideration 
of the views first proposed by Lobachevsky to demur at the 
logical building of a geometry without the rejected axiom, pro¬ 
vided the “space” required for it be “absolute” in the sense of 
free from all conditions of experience. 
In our Euclidian space we can form clear conception of planes, 
and of surfaces of greatly varying curvatures in widely separ¬ 
ated or in intersecting positions. There is a wonderous fascin¬ 
ation in the attempt to extend the analogy, and to think of 
varying forms of three dimensional space scattered through 
space of four dimensions, not necessarily far apart, but, like 
plane surfaces here, very near each other through their whole 
extent, though each of them be boundless. Perhaps we specu¬ 
late on the possible intersections of the different spaces in sur¬ 
faces, as in Euclidian space surfaces intersect in lines. We 
may reach farther, and ask if it may be that the four dimen¬ 
sional space is in turn one of the tenants of space of five dimen¬ 
sions. The grandeur of the thought leads us on, as did an ob¬ 
solete theory that, as satellites revolve around planets, and 
planets around suns, so do these suns around others, themselves 
attendants on still grander centres, until, after long succession 
the universe revolves about the throne of G-od. Of this fantasy 
one of our most noted astronomers has said “The conception is 
so grand that it seems a pity that it is not true. But there is 
no evidence to support it. ” So, recalled from our dream of 
spaces, awaking we seek with earnest desire for evidence, and 
ask whether we must accept the belief that Hyper-Euclidian 
conclusions can have no place in really scientific thought because 
their space is “ transcendent. ” 
Ripon , Wis. 
