Missouri Valley times. [volume] (Missouri Valley, Iowa) 1874-1931, 1902-03-20
A HARD PROPOSITION
SCIENTIFIC EXPLANATION OF THE
FOURTH DIMENSION.

Though This Measure OF Space
Were the Ability to- Disappear
Through Stone Walls.
Suppose world consisting OF a
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
i terms as above them and below them
and things around them can be push
ed OF pulled about in any direction, but
cannot Be lifted from the plane Peo-
pie and things can pass around each
other, hut cannot step over anything.
These dwellcrs in ''hatland" could con-
strucr n plane geometry which would
be exactly like ours in being based Oh
the aNionls of Euclid. Two parallel
straight lines would never meet, though
continued Indefinitely.
But suppose nat the surface on
which these IS live, instead of be-
| Ing an inflni ly extended plane, is
really the surface CT an immense globe
like the earth on which we live. 1t
peeds no knowledge of geometry, but
only an examination of any globular
object-an apple, for eXample-to show
that il we draw a line as straight as
possible on q sphere and parallel to it
draw a small piece of a second line,
ond continue this in as straight 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 never either perceive or discover.
TO explain hypergeometry proper we
must first set forth what fourth di-
mension of space means and show how
natural the way by which it may be
approached. We continue our analo-
gy from "tiatland." In this supposed
land let us make 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 iniersecting the same
point and perpendicular to both the
other lines. They would at once pro-
nounce this absurd aud impossible 1t
is equally absurd and impossible TO us
1T 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 flat surface, then we can solve the
problem by simply drawing the third
/ line through the paper perpendicular
to it's surface
4 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 "hatland" answered us:
| "The problem is impossible. You cam
not draw amy such line i'll space as we
/ understand it," IL our visitor conceived
OF the fourth dimension, he would re-
ply to us as we replied to the "hat-
land" people: The problem is absurd
and impossible il you confine your line
to space as You understand it, But for
me there is Il fourth dimension in
space. Draw your line through that di-
mension. and the problem will be solv-
ed This is perfectly simple to me; it is
4 impossible to YOU solely because your
conceptions do not admit of more than
three dimensions.
Supposing the inhabitants of flat
land' to be intellectual beings as we
are, it would be interesting to them to
be told what dw'ellers 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 "fatland" inside a circle
drawn OH his plane and ask him to
step outside of it without breaking
through it, He would so 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 it!' hc would exclaim. "I
do not know what that means. can
pass around anything if there is way
open but 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 contine q being able to move
in fourth dimension in the walls Of
dungeon of which the sides, the floor
and the ceiling were all 1mpenetrable
he would step outside Of it without
touching any part of the building just
as easily as we could step over cir
Gle drawn on the plane without touch
ing it, lie would simply disappear
from our view like spirit and perhaps
reappear the next moment outside the
prison. To do this he would have to
make a little excursion in the fourth
Observation-Disclosures Simon Newcomb
i'll Harper's Magazine.
Hia Maiden Name.
1t is said that at certain seasons in