The herald-advance. (Milbank, S.D.) 1890-1922, 1902-02-14
HARD PROPOSITION
SCIENTIFIC EXPLANATION OF THE
FOURTH DIMENSION.

To the Lay Mind 1t Would Appear A.
Though This Measure Of Space
Were the Ability to Disappear
Through Stone Walls.
Suppose a world consisting Of a
boundless fiat plane to be inhabited
by reasoning beings who can move
about at pleasure on the plane, but are
not able to turn their heads up or
down or eve to see or think of such
terms as above them and below them,
and things around them can be push
ed Or pulled about in any direction, but
cannOt be lifted from the plane. Peo-
pie and things can pass around each
other, but cannot step Ove anything.
These jewellers in "fatland" could con-
struct a plane geometry which would
be exactly like ours in being based OH
the axioms of Euclid. Two parallel
straight lines would never meet, though
continued indefinitely.
But suppose that the surface on
which these beings live, instead of be-
ing an infinitely extended plane, is
really the surface Of an immense globe
like the earth on which we live. 1t
needs NJ knowledge of geometry, but
only an examination Of any globular
object-an apple, for example-to show
that if we draw a line as straight as
possible on a sphere and parallel to it
draw a small piece of a second line,
and continue this in as straight a line
as we can, the two lines will meet
when we proceed in either direction
One-quarter of the way around the
sphere. For our "fatland' people these
lines would both be perfectly straight
because the only curvature would be
in the direction downward, which they
could lever either perceive or discover.
To explain hypergeometry proper we
must first set forth what a fourth d.
mension of space means and show how
natural the way by which it may be
approached. We continue our analo-
gy from "hatland." In this supposed
land let us make a cross-two straight
lines i~ntersecting at right angles. The
inhabitants of this land understand
the cross perfectly and conceive of it
just as we do. But let us ask them to
draw q third line intersecting the same
point and perpendicular to both the
other lines. They would at once pro-
nounce this absurd and impossible. 1t
is equally absurd and impossible to us
If we require the third line to be
drawn on the paper. But we would re-
ply, IF you allow us to leave the paper
or fat surface. then we can solve the
problem by simply drawing the third
line through the paper perpendicular
to its surface"
Now. to pursue the analogy, suppose
that after we have drawn three mutu-
ally perpendicular lines some being
from another sphere proposes to us the
drawing of a fourth line through the
same point perpendicular to all three
OF the lines already there. We should
answer him in the same way that the
Inhabitants Of "datland" answered us:
THE problem is impossible. You can
not draw any such line in space as we
understand it." If our visitor conceived
of the fourth dimension, he would re-
ply to Us as we replied to the ''fat-
land people: "The problem is absurd
and impossible II you confine your line
to space as you understand It. But for
me there IL a fourth dimension In
space. Draw your line through that di.
mension. and the problem will be SOW
ed. This IL perfectly simple to me: It IL
impossible to you solely because your
conceptions do not admit Of more than
three dimensionA"
6upposing the Inhabitants Of "hat-
land" to be intellectual beings a. we
are. It would be interesting to. them to