Butler citizen. [volume] (Butler, Pa.) 1877-1922, 1902-03-06
A HARD PROPOSITION
SCIENTIFIC EXPLANATION or THE
FOURTH DIMENSION.

To the Lay Mind 1t Would Appear as
Though This Measure of Space
Were the Ability to Disappear
Through Stone Walls.
Suppose q world consisting of a
boundless fat 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 even 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 over anything.
These dwellers in ''flatland" could con-
struct plane geometry which would
be exactly like ours in being based on
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 no 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 q second line,
and continue this in as straight line
"a fv-n rrfl
when we proceed in either direction
one-quarter of the way around the
sphere. For our "flatland" people these
lines would both be perfectly straight
because the only curvature would be
in the direction downward, which they.
could never either perceive or discover.
To explain hypergeometry proper we
must first set forth what a fourth di-
mension of space means and show how
natural the way by which it may be
approached. We continue our analo-
gy from "f1atland." 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 a third line intersecting the same
tpoint 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
l.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 n 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 "fiatland" 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 fiat
land" people: "The problem is absurd
and impossible If you confine your line
to space as you understand it But for
me there is a fourth dimension in
space. Draw your line through that di-
mension, and the problem will be solv-
ed. This is perfectly simple to me; 1t is
impossible to you solely because your
conceptions do not admit of more than
! three dimensions"
Supposing the Inhabitants Of "fat-
land" to be intellectual beings as we
are, it would be interesting to them to
be told what dwellers of space in three
dimensions could do. Let us pursue the
analogy by showing what dwellers in
four dimensions might do. Place a
dweller of "flatland" inside q circle
drawn on his plane and ask him to
step outside Of it without breaking
through it He would go all around,
and, finding every inch of it closed, he
would say it was impossible from the
very nature of the conditions. "But, !"
we would reply, ''that is because of
| your limited conceptions. We can step
| over it"
"Step over itp' he would exclaim. 81
do not know what that means. / can
pass around anything If there is way
open. hut cannot imagine what you
mean by stepping over it."
But we should simply step over the
line and reappear on the other side.
So If we confine being able to move
in a fourth dimension in-the walls of q
dungeon of which the sides, the floor
and the ceiling were all impenetrable
he would step outside Of it without
touching any part of the building just
as easily as we could step over a cir
Gle drawn on the plane without touch
ing it He would simply disappear
| from our view like a spirit and perhaps
reappear the next moment outside the
prison. To do this he would have to
make a little excursion in the fourth
dimension.-Professor Simon Newcomb
in Harper's Magazine.