Pine Bluff daily graphic., 1902-04-03
IA HARD PROPOSITION
SCIENTIFIC EXPLANATION OF THE
FOURTH DIMENSION.
To the Lay Mind 1t Would Appear as
Though This Measure of Space
We're the Ability to Disappear
Through Stone Walls.

were the DlSnEReAF
Through Stone Walls.
Suppose Il world consisting of q
boundlcss fat plane to be Inhabited
by reasoning beings who can move
about at pleasure OH the plane, but are
not able to turn their heads up or
down or even TO see or think of such
terms as aboVr them and below Them
and things around them can be push
ed Or pulled about in any direction, but
cannot be lifted fr;3a the plane. Peo
pie and things can raSS around each
other, but cannot step over anything.
These dWcllcrs il "tlatland'' could con,
struct Il plane geometry which would
be exactly like ours in being based on
the aXioms of Euclid. Two parallel
continued inucii2itcly.
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
only an examination Of any globular
object-an apple, for example-to show
that il we draw a line as straight as
possible on sphere and parallel to it
draw small piece Of second line,
nnd continue this in as straight Il line
as we can, the two lines will meet
when we proceed in either direction
l,o
sphere. For our "fatland" people these
lines would both be perfectly straight
because the only curvature would be
i'll the direction downward. which they
could never either perceive or discover.
To explain hypergeometry proper we
must first set fortl, what fourth di-
mension Of space means and show how
natural the way 10y which it may he
approached. We continue our analo-
gy from "hatland." In this supposed
land let us make a croSS-two straight
lines intersecting 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 Il third line intersectin. the same
point and perpendicular to both the
other lines. They would Mt once pro-
Eounce this absurd and impossible. II
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 fiat 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 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 "tlatland' answered us
The problem is impossible. You can
not draw any such limo in space as we
understand it," II our visitor conceived
of the fourth dimension. he would re-
ply to us as We replied to the flat
land" people: The problem is absurd
and impossible il YOU conline your line
TO space as you understand it. But for
me there is Il fourth dimension iu
space. Draw Your line through that di
menSion. and the problem will be solv.
ed. This is perfectly s;piplc to me; it is
impossible to you solely because your