Fergus County argus. [volume] (Lewistown, Mont.) 1886-1946, 1902-04-02
A HARD PROPOSITION
SCIENTIFIC EXPLANATION OF THE
FOURTH DIMENSION.
To the Lay Mind II Would Appear ns
Though This Measure of Space
Were the Ability TO Disappear
Through stone walls.

~ inc buy Alhhu ~ ThPFtaA n
Though This Measure OF Space
Were the Ability TO Disnppear
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 even TO see or think OF such
terms as above them and below them,
and things around them can he 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 "latland" could con
struct a 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 m immense globe
like the earth on which we live. II
needs no knowledge of geometry, but
only an examination Of any globular
object-an apple, for example-to show
that IL we draw q line as straight as
possible on a sphere and parallel to 1t
draw q 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 'latland" 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 d.
mension of space means and show how
natural the way by which 1t may be
approached. We continue u analo-
gy from "fatland." In this supposed
land let US make q cross-tw0 straight
lines intersecting at right angles. The
inhabitants of this land understand
the cross perfectly and conceive Of 1t
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
IL 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 a 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 "natland" answered us,
"The problem is impossible. You can
not draw any such line in space as we
understand It," II our visitor conceived
Of the fourth dimension, lie would re.
ply 10 us as we replied TO the fiat
land" people: 1.-THE problem is absurd
and impossible If you conline your line
TO space as you understand it. But fol
me there is a fourth dimension "
space. Draw your line through that di
mension, and the problem will be solv
cd. This is perfectly simple TO me; it Il
impossible 10 you solely because you
conceptions do not admit of more thar
three dimensions"
/, Supposing the Inhabitants OF "1at
/, land" TO be intellectual beings as W
) are, it would be interesting 10 them L
be told what dwellers of space in three
dimensions could do. Let us pursue TIN
analogy by showing what dwollers il
> four dimensions might do. Place (;
dwcller of 'latland' inside n circl,
t drawn on his plane and ask him {,
step outside of 1t without breakin,
: through 1t. He would 20 all around
and, finding every inch of 1t closed, h,
. would say 1t was impossible from tn
very nature of the conditions. But,
we would reply, 'that is because o
your limited conceptions. We can stel
, over It,"
"Step over it" he would exclaim. %
do not know what that means. I cal
pass around anything If there is a way
4 open. but cannot imagine what yol
mean By stepping Owe it."
!, But we should simply step over thu
line and rcappear on the other side
r So If we conilne n being able to move
G in n fourth dimension in the walls Of
r dungeon Of which the sides, the foo,
and the ceiling were all impenetrabl,
z he would step outside of it withou
touching any part OF the building jus
r as easily as w could step over a cir
b Gle drawn on the plane without touch
Ing 1t. He would simply disappea
from our view like n spirit and perhap
reappear the next moment outside tn
prison. To do this he would have I
make n little excursion in the fourtl
Observation-Disclosures Simon NewcomI
In Harper's Magazine.